UPA Manual of Tournament Formats

The UPA Manual of Tournament Formats

Version 2.1 - March 26, 1993

Submitted by Eric Simon

Copyright (c) The Ultimate Players Association, 1994

Accepted by the UPA as the Official Tournament Format Document for all UPA Series Tournaments at the Annual Meeting, January, 1993.

Please direct comments on this document to Eric Simon (70540.1522@compuserve.com).


Table of Contents

  • 1. Introduction
  • 2. Basic Theories of Tournament Scheduling
  • 3. Three Teams
  • 4. Four Teams
  • 5. Five Teams
  • 6. Six Teams
  • 7. Seven Teams
  • 8. Eight Teams
  • 9. Nine Teams
  • 10. Ten Teams
  • 11. Eleven Teams
  • 12. Twelve Teams
  • 13. Thirteen Teams
  • 14. Fourteen Teams
  • 15. Fifteen Teams
  • 16. Sixteen Teams
  • 17. Seventeen Teams
  • 18. Eighteen Teams
  • 19. Nineteen Teams
  • 20. Twenty Teams

  • All of the above (approx. 150kb)
  • Detailed Contents

  • 1. Introduction
  • 2. Basic Theories of Tournament Scheduling
  • 2.1. Seeding
  • 2.2. How to Seed
  • 2.3. A One-Day or Two-Day Format?
  • 2.4. How to read these schedules
  • 2.5. Tie breakers for round-robins
  • 2.6. Tie Breakers for double elimination tournaments
  • 3. Three Teams
  • Table 3.1. Three-Team Round-robin
  • 3.1 The Three team tie-breaker problem
  • 4. Four Teams
  • Table 4.1. Pre-set four-team round-robin
  • 4.2. The flexible four-team round-robin
  • Table 4.2.1. Flexible four-team round-robin; 1 and 4 play first
  • Table 4.2.2. Flexible four-team round-robin; 1 and 3 play first
  • Table 4.3. Four-team single elimination
  • Table 4.4. Modified four-team double elimination
  • 5. Five Teams
  • 5.1. One team advances
  • 5.1.1. Seven game option
  • 5.1.2. Six game option
  • 5.2. Two teams advance
  • 5.3. Three teams advance
  • 5.4. Four teams advance
  • 5.5. Five teams advance
  • 5.5.1. Seven game option one
  • 5.5.2. Seven game option two
  • 5.5.3. Eight game option
  • 5.6. One day format
  • Table 5.1.1. Five-team round-robin
  • Table 5.1.2. Five-team round-robin split into two parts
  • 6. Six Teams
  • 6.1. One team advances
  • 6.1.1. Seven round option
  • 6.1.2. Eight round option
  • 6.2. Two teams advance
  • 6.3. Three teams advance
  • 6.4. Four teams advance
  • 6.4.1. Option one
  • 6.4.2. Option two
  • 6.5. Five or Six teams advance
  • Table 6.1. Six-team round-robin.
  • Table 6.2. Six team single elimination.
  • Table 6.3. Six team modified elimination.
  • Table 6.4. Six team modified elimination, seeding from two pools.
  • Table 6.5. Six team modified bracket - only two qualify.
  • 7. Seven Teams
  • 8. Eight Teams
  • 8.1. Seeding into two pools of four
  • 8.2. Four Fields:
  • 8.3. Three or Four Fields; more than four teams advancing
  • 8.4. Four fields, four or more advancing, round-robin
  • Table 8.1.1. Eight-team double elimination format
  • Table 8.1.2. Eight-team modified elimination format
  • Table 8.2. Two pools of four on three fields
  • Table 8.3. Eight team round-robin
  • 8.5 Two-Division Modified Single Elimination
  • 9. Nine Teams
  • 9.1. One team advances
  • 9.2. Two teams advance
  • 9.2.1. Option One - Six Teams Advance to Second Day
  • 9.2.2. Option Two - Double Elimination on the Second Day
  • 9.3. Three teams advance
  • 9.4. Four through nine teams advance
  • 9.4.1. Option One - Nine Team Round-Robin
  • 9.4.2. Option Two - Double Elimination on the Second Day
  • 9.5. Starting with two unequal pools of four and five
  • 9.6. Discussion of a Nine Team Round-Robin
  • Table 9.1.1. Nine team round-robin grid
  • Table 9.1.2. Nine team round-robin, general
  • Table 9.1.3. Nine team round-robin over two days
  • 10. Ten Teams
  • 10.1. One team advances
  • 10.2. Two teams advance
  • 10.2.1. Option One - Six Teams Advance to Second Day
  • 10.2.2. Option Two - Double Elimination on the Second Day
  • 10.3. Three teams advance
  • 10.4. Four teams advance
  • 10.4.1. Option One - Double Elimination on the Second Day
  • 10.4.2. Option Two - Six Teams Advance to Modified Round-Robin
  • 10.5. Five or six teams advance
  • 10.5.1. Option One - Modified Elimination on the Second Day
  • 10.5.2. Option Two - Double Elimination on the Second Day
  • 10.6. Six through eight teams advance
  • 10.7. Seeding for pools of five
  • Table 10.1. Ten team round-robin grid
  • Table 10.2. Ten-team modified elimination
  • 11. Eleven Teams
  • 11.1. One team advances
  • 11.2. Two teams advance
  • 11.2.1. Option One - Six Teams Advance to Second Day
  • 11.3. Three teams advance
  • 11.3.1. Option One - Six Teams Advance to Modified Elimination
  • 11.3.2. Option Two - Six Teams Advance Modified Round-Robin
  • 11.4. Four teams advance
  • 11.4.1. Option One - Double Elimination on the Second Day
  • 11.4.2. Option Two - Six Teams Advance Modified Round-Robin
  • 11.5. Five or more teams advance
  • 11.5.1. Option One - Modified Elimination on the Second Day
  • 11.5.2. Option Two - Double Elimination on the Second Day
  • 11.6. Six through eight teams advance
  • 11.7. Seeding for two unequal pools of five and six
  • 11.8. Sample Schedule
  • Table 11.1. Eleven team round-robin grid
  • 12. Twelve Teams
  • 12.1. One team advances
  • 12.2. Two teams advance
  • 12.3. Three teams advance
  • 12.3.1. Option One - Six Teams Advance to Modified Elimination
  • 12.3.2. Option Two - Six Teams Advance to Modified Round-Robin
  • 12.4. Four teams advance
  • 12.4.1. Option One - Six Teams Advance to Modified Elimination
  • 12.4.2. Option Two - Six Teams Advance to Modified Round-Robin
  • 12.5. Five or six teams advance
  • 12.5.1. Option One - Modified Elimination on the Second Day
  • 12.5.2. Option Two - Double Elimination on the Second Day
  • 12.6. Six through eight teams advance
  • 12.7. Seeding for two pools of six
  • 12.8. Sample Schedule
  • Table 12.1. Twelve team round-robin grid
  • 13. Thirteen Teams
  • 13.1. The first day of play
  • 13.1.1. Overview
  • 13.1.2. Seeding
  • 13.1.3. Schedule
  • 13.2. One team advances
  • 13.3. Two teams advance
  • 13.4. Three through seven teams advance
  • 13.5. Eight or more teams advance
  • Table 13.1. Thirteen team round-robin grid:
  • Table 13.2. Seeding an 8-team bracket from three pools
  • 14. Fourteen Teams
  • 14.1. The first day of play
  • 14.1.1. Overview
  • 14.1.2. Seeding
  • 14.1.3. Schedule
  • Table 14.1. Fourteen team round-robin grid:
  • 15. Fifteen Teams
  • 16. Sixteen Teams
  • 16.1. One team advances, or other Non-UPA Tournaments
  • 16.2. Two teams advance (UPA Standard Double Elimination Format)
  • 16.3. Five thru Eight Teams Advance
  • Table 16.1. Sixteen team round-robin grid
  • 17. Seventeen Teams
  • 18. Eighteen Teams
  • Table 18.1. Eighteen team round-robin grid
  • 19. Nineteen Teams
  • 20. Twenty Teams
  • Table 20.1. Twenty team round-robin grid

  • 1. Introduction

    It is said that when you get right down to it, there are only two essential ingredients to a tournament: fields and a schedule. Once the games finally begin, tournaments pretty much run themselves if the schedule (which should include field numbers and a field map) is self explanatory.

    Unfortunately, scheduling is not so easy for UPA tournaments. Sure, for most other tournaments, when you limit the number of teams to four, or eight, or sixteen, scheduling is fairly easy. But at sectionals (or even regionals in those situations where there are not sixteen teams), where every eligible team is guaranteed a spot things aren't so easy. Try devising a schedule for a thirteen team tournament while keeping everyone happy.

    The fact is that most UPA Tournaments do more than pick a single winner. This makes scheduling infinitely more difficult than non-UPA tournaments. Ordinarily, it doesn't matter if you come in third or fourth at a tournament, but if the top three teams qualify to the next level, the schedule must be scrupulously fair to teams that have a shot at the third place spot.

    Not all UPA Sectional Tournaments have been run well in the past. Not everyone who is a sectional coordinator has run a tournament before. And those that have, have probably only been concerned about a format that picks a winner. Many sectional coordinators are also competing on one of the teams in the tournament, which leaves him or her open to charges of bias, both in terms of format and seeding. Some sectional tournaments have been utter disasters because something very unexpected happened, and all of a sudden some people realize that the format wasn't even-handed. At that point, the tournament director is faced with sticking with an unfair format because that's what the captains agreed to, or unfairly changing the format after play has started. Neither situation is acceptable.

    This manual attempts to alleviate these problems. We have tried to be fair to all teams involved, analyzing different situations and unlikely scenarios. We hope that this manual makes running a tournament easier for you. No one can claim that the format of a tournament is biased when it's an official "UPA Sanctioned Format."


    2. Basic Theories of Tournament Scheduling

    There are a couple of basic rules that should be applied to tournament scheduling, each of which is elaborated below. They are:
    1.
    Every team must get an equal chance and there should be as much independence from seeding as possible.

    That is, all teams should have a fair shot at winning the tournament (and/or qualifying to the next level). No team should have to do something different in the schedule from the other teams because of how they are seeded. Now it may be that some pools are of different size than other pools (there just isn't any number that divides into thirteen!), but in this case an entire pool is playing more games than other pools. No team in the larger pool is doing anything different than any other team in that pool.

    There have been some awfully "funky" formats for sectional tournaments before. I can recall one in which the top seeded team completely bypassed the first day of the tourney, and were automatically placed in a "winners" pool of the next day (i.e., different "divisions.") Such tournaments have their place, and may even be desirable in certain circumstances, but not for UPA Series events (unless teams have a choice of the division in which they would like to be placed).

    2.
    Each team should get a good number of games.

    Teams that travel from far away should be able to go home after a tournament feeling like they played their fair share of games, no matter where they finished. This means that teams should be eliminated from the tournament as late as possible, and that if they are eliminated early, there are 'Division II' options available to them. On the other hand,

    3.
    Teams should not have to play more than four games per day.

    Four games per day, games to 15, is about the most any team should be asked to play. (Limited exceptions for five games to 13). People who are into triathlons and marathons can go compete in those other competitions. Furthermore, these games should be scheduled in two-hour time blocks (with a cap of "plus two" after 1 hour and 40 minutes). Time caps are needed, not only for scheduling purposes, but so that a team does not have to play more than eight hours of Ultimate in a day. In those games where the wind is strong, both teams have good defenses, or neither team has a good offense, games to 15 can drag out for a long time. A succession of long, killer games often results in unwarranted injuries.

    There are exceptions to this rule, but they should be limited to Regional and post-Regional play. For example:

    • In the standard Regional format (16-team, double elimination), teams that advance through the losers bracket can play up to four games in a day, where some of the games are to 17.
    • In the 1989 Easterns there were 21 teams, three pools of five and one pool of six. The pool of six played five games, although the games were to 13.
    Again, these exceptions were Regionals or Easterns, where, presumably, the teams are stronger than they are at Sectionals.

    Another set of exceptions come into play when a tournament is faced with an undesirable number of teams. For example, thirteen teams is just a difficult number to work with. Many of these situations are dealt with by eliminating the number of teams to eight teams after the first day, and then a double elimination format the second day. The double elimination format, however, results in five games, and so games can be no longer than to the score of thirteen.

    4.
    The order of the games should be fair.

    Should this be in here? What is fair? Can anybody help out at all here?

    2.1. Seeding

    "Seeding" a tournament is a way of ranking the teams and, assuming there is pool play, distributing the teams into the pools in such a way as to be fair to the teams involved, and to avoid matching up the best teams in the early rounds. For example, suppose, at your sectional, you were trying to choose the top three teams to qualify for regionals. The last situation you want is where a team gets beaten by the number one and number two teams and never has a chance to compete against the number three team. Suppose you had ten teams divided into two pools of five. You would try your best not to put the two best teams in the same pool. If this is difficult to determine (and it sometimes is in those sections where teams don't play each other often), you would try to make sure that when pool play is done, the top three teams in each pool have not yet been eliminated.

    Ideally, it shouldn't matter where or how teams are seeded. Indeed, when the entire tournament is in one round-robin pool, it doesn't matter how the teams are seeded. Attempts have been made, in every format in this manual, to minimize the effect of seeding. A team might get eliminated earlier or later because of where they were seeded, but whether or not the team qualifies for the next level tournament should not depend on seeding.

    2.2. How to seed

    Ranking the teams is your business. It is useful to get as much information as possible beforehand; i.e., which teams have beaten other teams, etc. As general rules, one should take into account the entire season, giving more weight to games and tournaments that were played more recently. (In college situations, the "Top 20" rankings service can be used as a guide; the rankings should not necessarily be controlling).

    Anybody want to elaborate on 'general principles' of seeding here?

    2.3. A One-Day or Two-Day Format?

    For Regional Championships:
    Even though there may be as few as four teams, two days of play are expected for teams that will be competing for spots at nationals. There should be no exceptions (except in the case where there are three teams or less competing).
    For Sectional Championships:
    Sectionals should be a two-day tournament. If there are 7 or more teams competing, then there are no exceptions to this rule (except as noted in the format descriptions). If there are 6 or less teams, there are limited circumstances where a oneday format is acceptable. Whether or not there are two days of play depends on the characteristics of the section. Where most, sometimes all, of the teams advance, and none of the teams are traveling far, a one-day tournament might be acceptable. The sectional coordinator should ask the teams in the section if they prefer a one- or two-day tournament. Note: a greater weight should be given to the preferences of the teams that are travelling far, and, secondarily, to the weaker teams. If the weaker teams want to play more games, the better teams should accommodate them. This is even more important if the weaker teams face elimination at sectionals. The UPA should afford them the opportunity to play more games before their season ends.
    The round-robin schedules should be modified:
    The round-robin schedules were computer-generated. Such things like equity regarding which fields are played on have not been taken into account. Neither has the order of the games. So, for example, if you are trying to choose one winner from the tournament, you will want to schedule the top two seeds to play each other the last round. Suppose, however, you had ten teams in two pools of five, and you were going to choose the top two teams from each pool to go into the semifinals. In that case, you would schedule seeds 2 and 3 to play each other the last round. That is the game that will mean the most, not 1 v 2 if both teams have already essentially qualified.

    2.4. How to read these schedules

    Below is a sample six-team round-robin schedule. First look at the schedule "matrix." The team numbers go down the side, the round numbers go across the top. So, for example, in this matrix, team number 3 plays team number 6 in the first found.
              Six Teams
    
                1  2  3  4  5
                -  -  -  -  -
            1 - 5  4  3  2  6
            2 - 4  3  6  1  5
            3 - 6  2  1  5  4
            4 - 2  1  5  6  3
            5 - 1  6  4  3  2
            6 - 3  5  2  4  1
    
    In the schedule below, each row is a round, and each column can be a field. So, in the first round, 1 plays 5 on field one, etc.
            1 v 5   2 v 4   3 v 6
            1 v 4   2 v 3   5 v 6
            1 v 3   2 v 6   4 v 5
            1 v 2   3 v 5   4 v 6
            1 v 6   2 v 5   3 v 4
    

    2.5. Tie breakers for round-robins

    The worst part of a round-robin is the possibility of a three-way tie between teams that have all beaten each other. (E.g., A beats B, B beats C, and C beats A). One unlucky team will have to finish 3rd when they only lost one game. This is the very reason why the UPA tries to avoid pool play when the third place team can get eliminated. So, for example, in a tournament that is organized into 4 pools of 5, where the top 2 teams advance, a team can lose one game, to the best team, and be denied the chance to finish in the top eight.

    Nevertheless, while the UPA tries to minimize such situations, they all can't be avoided. The following are the UPA Standard set of round-robin tie breaker rules.

    Rule 1. A given tie-breaker rule applies equally to all the teams that are tied.
    For an example of this application, see Example 3.1.

    Rule 1a. If, after the application of a given rule, all of the teams are still tied, go to the next rule. For an example of this application, see Example 3.3.

    Rule 1b. If not all teams, but one or more subgroups of the teams are tied, separate these teams into groups and go back to rule 2 with each of the groups individually. For an example of this application, see Example 3.2.

    Rule 2. Won-loss records, counting only games between the teams that are tied.
    Example 2.1. A and B are tied for third place at 4-2, and during the tournament, A has beaten B. Then, A gets third place and B gets fourth place. When only two teams are involved, this rule is commonly called "head-to-head."

    Example 2.2. A, B, and C, are tied for first place; they are all 3-2 after the six team round-robin. A has beaten both B and C, while B has beaten C. The records among the three teams only are: A is 2-0, B is 1-1, and C is 0-2. A finishes first, B finishes second, and C finishes third.

    Example 2.3. A, B, and C are in a three-way tie. A has beaten B, B has beaten C, C has beaten A. The relevant records for all three teams are 1-1. This tie-breaker won't work, and you must go on to tie-breaker #3.

    Rule 3. Point differentials, counting only games between the teams that are tied.
    Example 3.1. A, B, C are in a three-way tie for first place. A has beaten B 15-10, B has beaten C 15-12, and C has beaten A, 15-13. A's point differential, then, is +5 and -2, which equals +3. B's is -2 and C's is -1. A finishes first, C finishes second, and B finishes third. Note that the three point differentials, in this case, +3,-2,-1, must always add up to zero. Note also that we do not use the point differential to choose the winner and then go "head to head" to choose the other two. This would be a violation of Rule #1, which say that we must apply a tie-breaker rule equally to all the teams that are tied.

    Example 3.2. A, B, C are in a three-way tie for first place. A has beaten B 15-11, B has beaten C 15-12, and C has beaten A, 15-13. A's point differential, then, is +4 and -2, which equals +2. B's is -1 and C's is -1. A takes first place. B and C are still tied. When, after the application of a rule, there are still teams that are tied, we go back to rule 2. Since B beat C, B takes 2nd place, and C takes 3rd. At this point we do not go onto rule 4.

    Example 3.3. A, B, C are in a three-way tie for first place. A has beaten B 15-13, B has beaten C 16-14, and C has beaten A, 15-13. A's point differential, then, is +2 and -2, which equals +0. B's is 0 and C's is 0. This tie-breaker can not be applied, go on to tie-breaker rule 4, unless there are only three teams in the pool to begin with, in which case you should have played an extra point. See the discussion on three-team pools in Section 3.1.

    Rule 4. Point differentials, counting games against all common opponents.
    Example 4.1. As in example 3, above, A, B, C are in a three-way tie for first place in a four team pool. A has beaten B 15-13, B has beaten C 16-14, and C has beaten A, 15-13. All three point differentials are 0. Suppose all of them have played D; A beat D 15-9, B beat D 15-7, and C beat D 15-12. B takes first place (because their point differential against the common opponent, D, was +8), A takes second (by beating D by six goals), and C takes third (beating D by three goals).

    Rule 4a. Multiple games against common opponents are averaged.

    Example 4.2. Assume all of example 1, but that, for some reason, B beat D twice, 15-7 and 15-12. Take the average of the scores and only count it once, thus, we would calculate the point differential as though B beat D once, by a score of 15-9.5. Then A takes first (point differential of +6), B takes second (we count, as a point differential, the score of 15-9.5, which is 5.5), and C takes third (beating D by three goals).

    Rule 5. Point differentials, counting games against all common opponents, excluding each team's best and worst differentials.
    This is about the same as Rule 4, except that the best and worst scores are eliminated. This eliminates "blowouts" with which the teams in question might have been involved.

    Rule 6. Points scored, counting only games among the teams that are tied.
    Note to UPA officials: I thought long and hard about whether we should count most points scored, or least points allowed. There is really no good reason why one should count more than the other. The reason why I chose points scored, is that it, at least, provides an incentive for the game to start on time, and to minimize all the things that delay games (extra long time outs, excessive foul calling, procrastinating at the beginning of games and at the beginning of the second half, stalling in the hope that the game is capped, stalling because the team is tired, etc.).

    Rule 7. Points scored, counting games against all common opponents.

    Rule 8. Points scored, counting games against all common opponents, excluding each team's best and worst scores.

    Rule 9. Sum of the square roots of the absolute values of the point differentials, counting games against all common opponents.
    This has the effect of minimizing the effect of blowouts without totally excluding them from consideration. Thus, as described in the example below, a team that wins its games by the scores of 15-8 and 15-10 will have a better differential that a team that wins 15-12 and 15-4. (One might assume that at a certain point, the losing team in the 15-4 game gave up since points became somewhat irrelevant to them.) It also has the added benefit of making it almost mathematically impossible to still be tied after this rule, unless all the scores of the teams involved are identical.

    Strictly speaking, mathematically, the computation regarding losses should be subtracted. Here's an example:

            A beats W 15-12         B beats W 15-8
            A beats X 15-4          B beats X 15-8
            A lost to Y 15-8        B lost to Y 15-12
            A lost to Z 15-8        B lost to Z 15-4
    
    Suppose, further, that these were the only games involving common opponents of A and B, and that all the tie-breakers are the same through the first eight rules. Then, applying this rule, A's differentials are 3, 11, -7 and -7. The tie-breakers, then, are
            A's tie breakers = sqrt(3) + sqrt(11) - sqrt(7) - sqrt(7)
            B's tie breakers = sqrt(7) + sqrt(7) - sqrt(11) - sqrt(3)
    
    A's tie breakers are approximately -0.2 while B's tie breakers are approximately +0.2.

    Rule 10. Flip a disc.
    As a last resort, discs should be flipped. Two discs should be flipped with one team calling "odd" or "even."

    2.6. Tie Breakers for double elimination tournaments

    A double-elimination tournament can leave an ambiguity for third place under certain conditions. This is patently unfair for those regions that are picking three teams fron Regionals to qualify for Nationals. The following are the rules to break that tie, or order of precedence:
    Rule 1. Won-loss records, counting only games between the teams that are tied.
    Example 1. A and B are tied for third place at 4-2, and during the tournament, A has beaten B. Then, A gets third place and B gets fourth place. When only two teams are involved, this rule is commonly called "head-to-head."

    Rule 2. Number of wins against the top two teams.
    Example 2. C and D have finished 3rd and 4th respectively, but both teams have lost only to the top two teams, A and B. During the tournament, however, C actually played B twice, once winning, and once losing. D played B once. Both teams lost one game to A. C, by having one win against B finishes ahead of D, who has no wins against B.

    Rule 3. The point differentials of the losses of common opponents (use the average if a team has lost twice to the same team).
    Example 3.1. C and D come in third and fourth, respectively, in their double-elimination, but each team lost only to A and B, and they have not played each other. If neither team has any wins against A and B, use the point differentials of C's and D's games against A and B only. C lost to A 19-13 and to B, 19-11. D lost games to A 19-9, and to B 19-18. C's loss differential is -14, D's is -11. D takes third place.

    Example 3.2. The same as above except that D's two losses were to B, 19-9 and 17-14, and D never played A. Averaging the scores would give a score of 18-11.5, or a point differential of 6.5. C's point differential is -6, and so C takes third place.

    Example 3.3. The same as above except that D's two losses were to B and to E. The loss to B was 19-9, the loss to E was 17-14.

    Should it be relevant if C has played E ? I don't know the answer, and so I am not finishing this example.

    Rule 4. Point differentials of all common opponents.
    This really can't be done until the issues in Example 3.3 are decided.

    3. Three Teams

    There is not a lot you can do with a three team tournament, although you only need one field. The following is a round-robin tournament for three teams.

    Table 3.1 - Three-Team Round-robin

                1  2  3
                -  -  -        1 v 3
            1 - 3  B  2        2 v 3
            2 - B  3  1        1 v 2
            3 - 1  2  B
    

    3.1. The Three team tie-breaker problem

    When all three teams in a pool finish with 1-1 records, apply the standard tie-breakers, but you should add the following rule to the tournament: If each team has a point differential of zero after the last game, one additional point should be played.

    There are problems with this, and in any tournament where a three-team pool exists, this tie-breaker must be discussed before play starts.

    Example 1.
    A beats B 15-12. B beats C 15-12. Now A and C play, and the three-way point differential tie would exist if C beats A by three. Not only is there a three way tie, but if all three scores are identical, none off the other tie-breakers will work. If this is the case, simply add the rule that if the game ends with C beating A by an identical score as the other two, then the game is extended for one more point. The point differential tie will then be broken. What follows, if you continue the example, is that the team that scores the extra point takes first, the team that gave it up takes third, and the team that has the bye must take second place.
    Remember, this provision only goes into effect if all three scores are identical; if merely all three point differentials are indentical, that is not enough to trigger this provision (see next example).

    The problem with this, of course, is that where a team finishes, in part, is due to the round in which that team has a bye. The team with the third round bye takes second place, while the other two teams battle for first and third. On the other hand, if you don't make a provision such as this, none of the other tie-breakers work. This is why this tie-breaker must be discussed and agreed to be all captains before play starts.

    Example 2.
    A beats B 15-12. B beats C 14-11. C beats A 15-12. All three point differentials are zero, but not all the scores are indentical. The tie can be broken, however, with tie-breaker rule #6, which is "points scored, counting only games among the teams that are tied." A has scored 27 points, B and C have each scored 26 points. A takes first place, and you attempt to break B and C's tie by going back at the first rule. On head-to-head (rule #2), B beat C, and so B takes second and C takes third.

    4. Four Teams

    For Regional Championships:
    Even though there are only four teams, two days of play are expected for teams that will be competing for spots at nationals.
    One team advances:
    Use 4.1 on the first day, and 4.3 the second day.
    Two or three teams advance:
    Use 4.1 on the first day, and 4.4 the second day, the modified double-elimination. This is a very exciting format because, on the second day, there is a game for first place (in the second round), and, in the third round, there is only one game: the match for second place.
    For Sectional Championships:
    Whether or not there are two days of play depends on the characteristics of the section. See the discussion of "A One-Day or Two-Day Format".
    One day format:
    one team advances: Use 4.2.1.
    two teams advance: Use 4.2.2.
    three teams advance: Use 4.2.1.
    four teams advance: Use 4.2.1.
    Two day format:
    one team advances: Use 4.1 on the first day, and 4.3 the second day.
    two teams advance: Use 4.1 on the first day, and 4.4 the second day.
    three teams advance: Use 4.1 on the first day, and 4.4 the second day.
    four teams advance: Use 4.1 on the first day, and 4.4 the second day.

    Table 4.1 - Pre-set four-team round-robin

                1  2  3
                -  -  -
            1 - 3  2  4        1 v  3   2 v  4
            2 - 4  1  3        1 v  2   3 v  4
            3 - 1  4  2        1 v  4   2 v  3
            4 - 2  3  1
    
    If the top two teams are advancing you probably want to have the 2-3 game last, since that is the most important game. If you are trying to choose a winner, or the top team out of the four-team pool, the 1-2 game should be scheduled last.

    4.2. The flexible four-team round-robin

    Who plays who in the first round should be dependant upon whether 2nd place "matters" or not. For example, if, say, all you are choosing is a winner, or, all four teams are advancing and all you are accomplishing with the round-robin is seeding for the four teams, you might schedule 1-4 and 2-3 for the first round. However, suppose the top two teams advance. In that case 2-3 is a very important game, and it would be better not to schedule it for the first round. A first round of 1-3 and 2-4 would be preferable. If, say, second place is crucial for some reason or another, you would want to play 1-3 and 2-4 the first round, and have the two winners each play each other the seond round. In that way, one of the third round games may be "the game" for second place.

    Table 4.2.1. Flexible four-team round-robin; 1 and 4 play first

    First round:
    1-4 and 2-3.
    Second round:
    winners play losers. In other words, the winner of each game plays the loser of the other game. This will increase the chances pof two undefeated teams playing each other in the third round.
    Third round:
    the remaining game of the round-robin.

    Table 4.2.2. Flexible four-team round-robin; 1 and 3 play first

    First round:
    1-3 and 2-4.
    Second round:
    winners play losers. In other words, the winner of each game plays the loser of the other game. This will increase the chances of two undefeated teams playing each other in the third round.
    Third round:
    the remaining game of the round-robin.

    Table 4.3. Four-team single elimination

    This should never be used alone. A team should never be eliminated from a tournament after losing only one game. On the other hand, this is a fairly typical format for use in the second half of a tournament.
            1 -----
                A  -----_
            4 -----     _
                     C  _ -----
            2 -----     _ first place
                B  -----
            3 -----
    

    Table 4.4. Modified four-team double elimination

    This format is very exciting if second place matters. Alone, it doesn't offer much. A team that loses two games is finished. But it has its place if used as the second day of a tournament where you have eliminated down to four teams the day earlier.
            1 -----                          LA -----
                A  -----_                         D  -----_
            4 -----     _                    LB -----  E  _ ------
                     C  _ -----                           _ second place
            2 -----     _ first place             LC -----
                B  -----
            3 -----                          loser of game E is third place
    

    5. Five Teams

    A five-team tournament requires two fields and five rounds. Only under the most extreme circumstances should there be only one day of play, and that, only at Sectionals. Under the one-day scenario, the round-robin alone is four games for each team (in five rounds), and to do any more would be violating the 4-game limitation rule.

    For some of the formats, where there are lots of games, you might consider making the round-robin games to 13.

    For Regional Championships:
    Even though there are only five teams, two days of play are expected for teams that will be competing for spots at nationals. You must use one of the two-day options.
    For Sectional Championships:
    As mentioned above, a one-day tournament is only permitted under extreme circumstances and only at Sectionals. (See the discussion on "A One-Day or Two-Day Format". Use the two-day options.

    5.1. One team advances

    5.1.1. Seven game option:
    Use Table 5.1.1 (round-robin) on the first day. The top four teams qualify and use Table 4.2.1, the flexible four-team round-robin. Four of the five teams get to play seven games, and the last round almost always is a "finals," i.e., the game for first place. The only down side to this format is the potential problem of deciding first place on point differentials in a three-way tie.
    5.1.2. Six game option:
    Use Table 5.1.1 (round-robin) on the first day. The top four teams qualify and use 4.3, a single elimination on the second day. In this option three of five teams get only 5 games or less. No team enjoys sticking around overnight only to get eliminated the first round on the second day. This format could be made a bit less objectionable if the last round of the round-robin was on the second day, although a problem may arise because the team with the bye might have an unfair advantage. On the other hand, this option avoids the potential problem of deciding first place on point differentials in a three-way tie.

    5.2. Two teams advance

    Use Table 5.1.1 (round-robin) on the first day. The top four teams qualify and use Table 4.4, the modified double-elimination. This is a very exciting format because, on the second day, there is a game for first place (in the second round), and, in the third round, there is only one game: the match for second place. This format requires eight rounds, five for the round-robin and three for the modified double-elimination. The most games a team will play is seven.

    5.3. Three teams advance

    Use Table 5.1.1 (round-robin) on the first day. The top four teams qualify and use Table 4.2.1, the flexible four-team round-robin. Four of the five teams get to play seven games, and the last round almost always is a "finals," i.e., the game for first place. Additionally, the other game in the last round is usually to decide third and fourth place. This makes for a very exciting second day. This format requires eight rounds, five for the round-robin and three for the flexible four-team round-robin. All the teams involved in the second day will play seven games.

    5.4. Four teams advance

    Not written yet.

    5.5. Five teams advance

    5.5.1. Seven game option one:
    Use Table 5.1.1 (round-robin) on the first day. The fifth place team takes fifth place. The other four teams and use Table 4.2.1, the flexible four-team round-robin. Four of the five teams get to play seven games, and the last round almost always is a "finals," i.e., the game for first place. The potential problem of deciding places on point differentials is not very relevant since all five teams qualify anyway.
    5.5.2. Seven game option two:
    Use Table 5.1.1 (round-robin) on the first day. The first place team takes first place. The other four teams and use Table 4.2.1, the flexible four-team round-robin. Four of the five teams get to play seven games. The potential problem of deciding places on point differentials is not very relevant since all five teams qualify anyway. This option may only be used if all the teams agree on it at the captains meeting. This format is probably preferable where there is one team that is clearly much stonger than the rest, and none of the other teams would want to play that team twice in the same weekend.
    5.5.3. Eight game option:
    Use Table 5.1.1 (round-robin) for both days. This gives every team eight games. The only problem is that this format requires five rounds each day, and teams that travel far may not want to stick around that long on the second day. At least a majority of the teams must agree to this format at least 24 hours in advance, or all five teams must agree to this format at the captains meeting before you can use this format.

    5.6. One day format

    Use Table 5.1.1. Only under the most extreme circumstances should there be only one day of play, and that, only at Sectionals. Under the one-day scenario, the round-robin alone is four games for each team (in five rounds), and to do any more would be violating the 4-game limitation rule.

    Table 5.1.1. Five-team round-robin

    The following is a straight five-team round-robin, which takes five rounds. Should circumstances require, you can split the round-robin over two days and six rounds. Each team will get exactly one bye and two games each day. This is much preferable to simply taking this schedule and playing three rounds one day and two rounds the other. The split schedule appears in Table 5.1.2.

    For some of the formats, where there are lots of games, you might consider making the round-robin games to 13.

                 1  2  3  4  5
                 -  -  -  -  -
            1 _  4  2  5  3  B        1 v 5   2 v 4
            2 _  3  1  4  B  5        1 v 3   4 v 5
            3 _  2  5  B  1  4        2 v 5   3 v 4
            4 _  1  B  2  5  3        1 v 4   2 v 3
            5 _  B  3  1  4  2        1 v 2   3 v 5
    

    Table 5.1.2. Five-team round-robin split into two parts

    This is a five-team round-robin that is split into two parts. If, for some reason, you wanted to have the round-robin over two days, this schedule provides each team with an equal number of byes and games each day. This schedule might be used if, for instance, you had a huge three-day tournament with limited field space. However, unless the games are pretty long, teams will probably not like travelling far and only playing two games in a day. The UPA used this format for its Nationals, some years back, when there were ten Open Division teams and five Women's Division teams, most recently in 1985. The round-robin took the first two days, and semis and finals were played on the third day. Round-robin games for the Open Division in 1985 were to 19.
            first part:           second part:
             1 v 5   2 v 4         1 v 4   2 v 3
             2 v 5   3 v 4         1 v 2   3 v 5
             1 v 3                 4 v 5
    

    6. Six Teams

    A six team tournament is still small enough to handle a round-robin. The problems with setting a six-team tourney up as two pools of three are (1) not enough games; and, (2) too much can depend on seeding. Actually, the worst problem is the possibility of a three-way tie. There are no tie-breakers that work for a three-way tie in a three-team pool (but see "The three-team tie-breakers problem").

    A round-robin of six teams must be spread out over two days. Play four rounds the first day, and the fifth game as the first round on the second day. Because no team has a bye during the round-robin, no team has an unfair advantage for the games that follow the round-robin. For some of the formats, where there are lots of games, you might consider making the round-robin games to 13.

    Commonly, tournament schedulers like to pit the top two seeds against each other during the last round of a round-robin. This is not a good idea, however, when the round-robin is spread over two days because then the top two seeds might be playing each other twice on the second day. Make sure that these two teams play each other on the first day.

    For Regional Championships:
    Even though there are only five teams, two days of play are expected for teams that will be competing for spots at nationals. You must use one of the two-day options.
    For Sectional Championships:
    As mentioned above, a one-day tournament is only permitted under extreme circumstances and only at Sectionals. (See the discussion on "A One-Day or Two-Day Format".) Use the two-day options.

    6.1. One Team Advances

    6.1.1. Seven round option
    Use Table 6.1 (round-robin) split over the two days. The top four teams qualify and use 4.3, a single elimination when the round-robin is finished. The teams that make it to the finals will be playing seven games over the weekend.

    Be sensitive to the fact that some teams might be sticking around overnight only to play in a single round-robin game when they have already been eliminated on the first day. Such a team may not show up, and this creates all sorts of problems. One way to avoid this is to have a leisurly start on the first day and only play three round. Then, the second day involves two games of round-robin, and two rounds to finish the four-team single elimination. Another possibility, is to use the option below.

    6.1.2. Eight round option
    Use Table 6.1.1 (round-robin) over the first two days, playing four of the rounds on the first day. After the round-robin is completed, use Table 6.2 (6-team single elimination) for the last three rounds. Although this format takes eight rounds, most teams will play only six or seven games.

    There are two advantages to this format. First, a team can only get eliminated by losing a game (i.e., there is no possiblity of a team going home an account of a point-differential). Second, a team can lose all four games on the first day and still have an incentive to show up the second day, because, theoretically, they can still win the tournament.

    6.2. Two Teams Advance

    Use Table 6.1.1 (round-robin) over the first two days, playing four of the rounds on the first day. After the round-robin is completed, use Table 6.2 (6-team single elimination) for the last three rounds. Although this format takes eight rounds, most teams will play only six or seven games.

    6.3. Three Teams Advance

    Use Table 6.1.1 (round-robin) over the first two days, playing four of the rounds on the first day. After the round-robin is completed, use Table 6.3 (6-team modified elimination) for the last three rounds.

    6.4. Four Teams Advance

    Use Table 6.1.1 (round-robin) over the first two days, playing four of the rounds on the first day. After the round-robin is completed, you have a bunch of options:
    6.4.1. Option one
    The top two teams play each other for first and second place. The bottom four teams play a modified double elimination, Table 4.4. This can be pretty exciting, because the last game of the entire tournament is for the last and final spot. (Of course, when you look at Table 4.4, the teams that come in first and second are actually coming in third and fourth here, since the top two teams have already been separated out and are playing each other for first and second place).
    6.4.2. Option two
    Use Table 6.3 (6 team modified elimination).

    6.5. Five Or Six Teams Advance

    Use Table 6.1.1 (round-robin) over the first two days, playing four of the rounds on the first day. After the round-robin is completed, use Table 6.3 (6 team modified elimination).

    Table 6.1. Six-Team Round-Robin

    The following is a straight six-team round-robin, which takes five rounds. Should circumstances require, you can split the round-robin over two days. As mentioned in the introduction to this section, when the round-robin is split over two days, and it is to be followed by some sort of elimination, do not schedule the top two seeds to play against each other. If you do, it is likely that they will be playing against each other twice in one day.

    For some of the formats, where there are lots of games, you might consider making the round-robin games to 13.

                1  2  3  4  5
                -  -  -  -  -
            1 - 5  4  3  2  6        1 v 5   2 v 4   3 v 6
            2 - 4  3  6  1  5        1 v 2   3 v 5   4 v 6
            3 - 6  2  1  5  4        1 v 6   2 v 5   3 v 4
            4 - 2  1  5  6  3        1 v 3   2 v 6   4 v 5
            5 - 1  6  4  3  2        1 v 4   2 v 3   5 v 6
            6 - 3  5  2  4  1
    

    Table 6.2. Six Team Single Elimination

                    1 -----
                        C  -
            4 -----        -----_
                A  --------     _
            5 -----          E  _ ___________
                    2 -----     _ first place
                        D  -    _
            3 -----        -----
                B  --------
            6 -----
    

    Table 6.3. Six Team Modified Elimination

                    1 -----
                        C  -
            4 -----        -----_
                A  --------     _
            5 -----          E  _ _____
                    2 -----     _
                        D  -    _         winner E: first place
            3 -----        -----          loser E:  second place
                B  --------               winner F: third place
            6 -----                       loser F:  fourth place
                        LC -----          winner G: fifth place
                             F  -----
                        LD -----
    
                   LA -----
                        G  -----
                   LB -----
    

    Table 6.4. Six Team Modified Elimination, Seeding From Two Pools

                   A1 -----
                        C  -
           A3 -----        -----_
                A  --------     _
           B2 -----          E  _ _____
                   B1 -----     _
                        D  -    _         winner E: first place
           B3 -----        -----          loser E: second place
                B  --------               winner F: third place
           A2 -----                       loser F: fourth place
                        LC -----          winner G: fifth place
                             F  -----
                        LD -----
    
                   LA -----
                        G  -----
                   LB -----
    

    Table 6.5. Six Team Modified Bracket - Only Two Qualify.

    Note that this format is not to be used in situations where more than two teams qualify for the next level.
                 A1 -----
                      C   -----------
                 B1 ----- first place
    
            A2 -----
                 A  -----_
            B3 -----     _
                      D  _-----_
            A3 -----     _     _
                 B  -----      _
            B2 -----           _ ------------
                               _ second place
                               _
                       LC -----
    

    7. Seven Teams

    Unfortunately, there's nothing very good you can do with seven teams. Below is what a round-robin might look like. You may want to switch the order of the games depending upon your needs.
                1  2  3  4  5  6  7
                -  -  -  -  -  -  -
            1 - 6  2  5  B  4  7  3        1 v 5   2 v 4   6 v 7
            2 - 5  1  4  7  3  6  B        2 v 7   3 v 6   4 v 5
            3 - 4  7  B  6  2  5  1        1 v 4   2 v 3   5 v 7
            4 - 3  6  2  5  1  B  7        1 v 7   2 v 6   3 v 5
            5 - 2  B  1  4  7  3  6        1 v 3   4 v 7   5 v 6
            6 - 1  4  7  3  B  2  5        1 v 6   2 v 5   3 v 4
            7 - B  3  6  2  5  1  4        1 v 2   3 v 7   4 v 6
    

    8. Eight Teams

    Eight teams is a wonderful number to have. Besides the standard UPA options, there are other possibilities that can be used for non-UPA sanctioned play. They are listed at the end of this section. Not yet.
    For Regional Championships:
    Two days of play are expected for teams that will be competing for spots at nationals. You must use one of the two-day options.
    For Sectional Championships:
    As mentioned above, a one-day tournament is only permitted under extreme circumstances and only at Sectionals. (See the discussion on "A One-Day or Two-Day Format".) The fair one-day format, and thus the only exception to this rule, is when only one team advances. Care must be taken, however, so that no team plays more than four games in one day.

    8.1. Seeding Into Two Pools Of Four

    The pools should be set up so that pool A has seeds 1, 4, 5, and 8. Pool B should have seeds 2, 3, 6, and 7.

    8.2. Four Fields

    There are two pools of four, and each pool plays a round-robin. This takes up three rounds. This is followed by an eight-team double elimination format (see Table 8.1.1). The first round of the double elimination starts on the fourth round of the first day. In the table, A1 refers to the first place finisher of pool A, etc.

    Note, if more than four teams are advancing, the format described in 8.3 can be used.

    Note: what's the point of double elimination if only one team is advancing?

    8.3. Three or Four Fields; more than four teams advancing

    This is a format that gives each team lots of games. It is an unaccaptable format, however, if less than four teams are advancing.

    On the first day, play a round-robin. On the second day, split the teams as following: the top two teams in each pool move to pool A, the other two teams in each pool move to pool B. Then, the teams each new pool can play a round-robin. The teams from pool A finish in 1st through 4th. The teams from pool B finish in 5th through 8th.

    The format can be done with only three fields, because, fortunately, two pools of four can be played on three fields, in four rounds. (See Table 8.2).

    Note that on the second day's play, each team will play one other team that they have already played the day before. If there is extreme weather (e.g., very hot, cold and rainy, etc.) or if many of the teams are new or low on numbers, you can eliminate the repeat game. In other words, pool A plays a round-robin on the second day, but instead of playing a repeat game, count the game from the day before. So, in effect, in each pool on the second day, two teams will be starting with a 1-0 record, and two teams with an 0-1 record, and will have to play two games to complete the round-robin. This format, then, gives each team three games the first day and two games the second day. This format was used in the Spring 1989 M.A. Regionals, where (a) some of the teams were new; (b) it was a very hot weekend; and, (c) all eight teams qualified for Easterns.

    The schedule for the second day's pool play should be tailored to the strength of the teams. See the discussion of the "flexible" four team round-robin (4.2). You can also play, instead of the second day's round-robin, a modified four-team elimination on the second day (see Table 4.4).

    The reason why this format is unacceptable for qualifying four or less teams is that it is possible to finish fifth while losing only one game. If, in one of the pools, there is a three way tie for first, one of those teams will be relegated to the losers pool and can finish no higher than fifth despite losing only one game. This less of a problem if five or more teams are qualifying.

    8.4. Four Fields, Four Or More Advancing, Round-Robin

    The only two problems with round-robins are: (a) the three-way tie situation; and (b) not all the teams may be able to stand up to the rigors of seven games in one weekend. In other formats where there may be seven games, if a team can't hack it and forfeits, then that team simply doesn't go on. But in a round-robin, suppose a team is 2-4 going into the seventh round and drops out? What are you supposed to do with the teams that already lost to the dropping team? Suppose they drop out in the middle, creating an unfair "bye" situation?

    If you're certain that teams will not drop out, and if you are qualifying more than four teams, a round-robin will guarantee the most possible games for everyone.

    A round-robin of eight teams takes seven rounds. If the first four rounds are the first day, and the last three on the second day, there is time for a finals pitting the top two teams, if everyone is up for it.

    Table 8.1.1. Eight-Team Double Elimination Format

        Saturday  Sunday . . .
        last      Round 1   Round 2
        round
    
        A1 -----
             A  ---------_
        B4 -----         _                           1st place - winner of I
                     E   __________                  2nd place - winner of N
        B2 -----         _         _                 3rd place - loser of N
             B  ---------          _                 4th place - loser of M
        A3 -----                   _                 5th place - winner of Q
                               I   _ ___________     6th place - loser of Q
        A2 -----                   _ first place     7th place - winner of P
             C  ---------_         _                 8th place - loser of P
        B3 -----         _         _
                     F   __________
        B1 -----         _
             D  ---------
        A4 -----
                  Round 1   Round 2    Round 3  Round 4
              LA --------
                     G   ----------
              LB --------     J    -----------_
                       LF ---------           _
    
              LC --------                M    ---------
                     H   ----------           -        _
              LD --------     K    -----------     N   _ ____________
                       LE ---------                    _ second place
                                             LI -------
    
                       LG ---------
                              P    -----------
                       LH ---------
    
                                LJ ----------
                                        Q    ---------
                                LK ----------
    

    Table 8.1.2. Eight-Team Modified Elimination Format

    NOTE: This format is not UPA approved for when more than one team advances. In such cases, the format in Table 8.1.1 should be used (or some variation).
        Sunday . . .
        Round 1   Round 2
        round
    
        A1 -----
             A  ---------_
        B4 -----         _
                    E    ___________
        B2 -----         _          _
             B  ---------_          _
        A3 -----                    _
                               I    _ ___________
        A2 -----                    _  1st place
             C  ---------           _
        B3 -----         _          _                1st place - winner of I
                    F    ___________                 2nd place - loser of I
        B1 -----         _                           3rd place - winner of K
             D  ---------                            4th place - loser of K
        A4 -----                                     5th place - winner of J
                                                     6th place - loser of J
             LA ---------                            7th place - winner of M
                    G    -----------_                8th place - loser of M
             LB ---------      J    _ __________
             LC ---------           _  5th place
                    H    -----------
             LD ---------
    
                      LE -----------
                               K     ----------
                      LF ----------- 3rd place
    
                      LG -----------
                               M     ---------
                      LH ----------- 7th place
    

    Table 8.2. Two Pools Of Four On Three Fields

            A1-A3  A2-A4  B1-B4
            A1-A4  B1-B3  B2-B4
            A2-A3  B1-B2  B3-B4
            A1-A2  A3-A4  B2-B3
    

    Table 8.3. Eight Team Round-Robin

                1  2  3  4  5  6  7
                -  -  -  -  -  -  -
            1 - 7  2  5  3  6  8  4        1 v 2   3 v 8   4 v 7   5 v 6
            2 - 6  1  4  7  8  5  3        1 v 5   2 v 4   3 v 6   7 v 8
            3 - 5  8  6  1  4  7  2        1 v 3   2 v 7   4 v 5   6 v 8
            4 - 8  7  2  5  3  6  1        1 v 6   2 v 8   3 v 4   5 v 7
            5 - 3  6  1  4  7  2  8        1 v 8   2 v 5   3 v 7   4 v 6
            6 - 2  5  3  8  1  4  7        1 v 4   2 v 3   5 v 8   6 v 7
            7 - 1  4  8  2  5  3  6        1 v 7   2 v 6   3 v 5   4 v 8
            8 - 4  3  7  6  2  1  5
    

    8.5. Two-Division Modified Single Elimination

    (Note - this is not to be used for UPA qualifying tournaments; however it is an excellent format for other tournaments where the object is to pick a single winner, while giving all teams as many games as possible).
    DIVISION I
    Round #1   Rnd 2      Rnd 3                             Rnd 3
    
    A1 -----                                           LE -----------
         A  ---------_                                          K    ---------
    D2 -----         _                                 LF ----------- 3rd place
                   E _----------_
    B2 -----         _          _                      LG -----------
         B  ---------           _                               M    ---------
    C1 -----                    _                      LH ----------- 7th place
                              I _____________
    A2 -----                    _  1st place
         C  ---------_          _
    D1 -----         _          _
                   F _----------
    B1 -----         _
         D  ---------
    C2 -----
    
           LA---------
                   G  ----------_
           LB---------        J _____________
           LC---------          _  5th place
                   H  ----------
           LD---------
    
    ----------------------------------------------------------------------
    DIVISION II
    Round #1   Rnd 2      Rnd 3                             Rnd 3
    
    A3 -----                                           LE -----------
         A  ---------_                                          K    ---------
    D4 -----         _                                 LF ----------- 3rd place
                   E _----------_
    B4 -----         _          _                      LG -----------
         B  ---------           _                               M    ---------
    C3 -----                    _                      LH ----------- 7th place
                              I _____________
    A4 -----                    _  1st place
         C  ---------_          _
    D3 -----         _          _
                   F _----------
    B3 -----         _
         D  ---------
    C4 -----
    
           LA---------
                   G  ----------_
           LB---------        J _____________
           LC---------          _  5th place
                   H  ----------
           LD---------
    
    Recommendation:  All games to 15, except Division I games E, F, and I,
    which are to 17, and I to 19 by mutual agreement.  For the sixteen game
    schedule, all games to 17, and Division I finals to 19 by mutual agreement.
    

    9. Nine Teams

    Nine teams is a lousy number to have. For initial play you must either make two unequal pools of 4 and 5, or play a nine-team round-robin over two days. Actually, this latter alternative, commonly overlooked, is a pretty good format. It's a great way to get lots of games for everyone, if each team is willing to make the committment, ahead of time, to finish the schedule. If you have time for five rounds each day, you can schedule each team for four games and one bye. See the schedule, Table 9.1.3.

    Note, the round-robin is not an acceptable format if less than three teams are qualifying, because of the three-way tie for first place possibility. See Section 9.6 for more details about this option.

    Three pools of three is never acceptable. Simply too much depends upon seeding in such a format.

    9.1. One Team Advances

    Start with two unequal pools of four and five (see Section 9.5).

    On the second day, the top four teams in each pool play an eight-team single elimination. (Note, the brackets and the initial pairings for the single elimination is the same as the upper half of the 8-team double elimination format, see Table 8.1.1).

    Note, it is not acceptable to take only the top two teams from each pool and have semi's and finals, because of the possibility of a three-way tie for first in one of the pools.

    9.2. Two Teams Advance

    9.2.1. Option One - Six Teams Advance to Second Day:
    Start with two unequal pools of four and five (see Section 9.5).

    On the second day, the top team in each pool play each other. The winner takes first place. The loser still has another game to play. The second and third teams in each pool play a four-team loser's bracket; i.e., a semis and a final. This takes two rounds. The winner of this bracket, then, plays the loser of the game for first place. The winner of this game takes second place. The brackets for this second day are shown in Table 6.5.

    9.2.2. Option Two - Double Elimination on the Second Day:
    Note, because of the number of games involved, you must get approval from a majority of the teams playing before you can use this format.

    Start with two unequal pools of four and five (see Section 9.5).

    On the second day, the top four teams in each pool play an eight-team double elimination. (See Table 8.1.1).

    This involves an awful lot of games for some of the teams. It is possible that one or two teams will play five games the second day. Note, too, that one of the pools will have played four games on the first day. (In women's play, the first round of the double elimination could be an abbreviated game to 11, (since no one gets eliminated after only one game). Otherwise, all of the games should be to 13 (except for the winner's bracket final, which is to 15).

    9.3. Three Teams Advance

    Start with two unequal pools of four and five (see Section 9.5).

    On the second day, the top three teams in each pools play a six-team modified double elimination (see Table 6.4).

    9.4. Four Through Nine Teams Advance

    9.4.1. Option One - Nine Team Round-Robin:
    This is a great format if you have the time for five rounds per day. (And, if you are in daylight savings time, this should be no problem). Each team plays four games per day, with one bye per day. See Table 9.1.3; also see Section 9.6 for a more detailed discussion of the round-robin.

    9.4.2. Option Two - Double Elimination on the Second Day:
    Start with two unequal pools of four and five (see Section 9.5).

    On the second day, the top four teams in each pool play an eight-team double elimination. (See Table 8.1.1).

    This involves an awful lot of games for some of the teams. It is possible that one or two teams will play five games the second day. Note, too, that one of the pools will have played four games on the first day. (In women's play, the first round of the double elimination could be an abbreviated game to 11, (since no one gets eliminated after only one game). Otherwise, all of the games should be to 13 (except for the winner's bracket final, which is to 15).

    To ease things, you might consider eliminating the very last round of the double elimination. The last round is for second and third place, which may not be very relevant if four or more teams are qualifying anyway. If this game is not played, use the tie-breakers for double elimination (Section 2.6). In the Mid-Atlantic, a format similar to this was used, and this game was optional. I.e., the team that wanted to play was given second place; if both wanted to, they played; if neither wanted too, or it was too late, we used the tie-breakers.

    9.5. Starting With Two Unequal Pools Of Four And Five

    The pools should be seeded as follows:
                    Pool A:                 Pool B:
                    Seed #1                 Seed #2
                    Seed #4                 Seed #3
                    Seed #5                 Seed #6
                    Seed #8                 Seed #7
                    Seed #9
    

    Certainly it is unfair that all the teams in Pool A have to play one more game than those in Pool B, but there is no alternative, other than to have a round-robin of nine teams, or to have three pools of three. A mitigating factor, however, is that the two weakest teams are in Pool A. Furthermore it is acceptable to play to Pool A games to two fewer points than Pool B games (i.e., play Pool A games to 13 and Pool B to 15, or, for women, 11 and 13).

    Another potential problem is that Pool B's games require only three rounds, and Pool A's games require five. One can, however, stretch Pool B's games over four rounds, using a schedule like the following:

                     A1-A5  A2-A4  B1-B3  B2-B4
                     A1-A3  A4-A5  B1-B4
                     A2-A5  A3-A4  B2-B3
                     A1-A4  A2-A3  B1-B2* B3-B4*
                     A1-A2  A3-A5
            * this game could be given some extra rest time before the round.
    

    9.6. Discussion Of A Nine Team Round-Robin

    The worst problemn that can happen in any round-robin is when one of the teams drops out before the tournament is over. The best course of action, of course, is to do all that can be done to insure that it doesn't happen. (I.e., make sure the teams know well ahead of time about the format, and discourage teams from showing up without a commitment that they will finish the tournament).

    When a team does drop out, the only fair course of action is to not count any game in which the offending team has played. This will surely elate those teams which now get to remove a loss from their record (and frustrate those teams which must remove a win from their record), but the alternative, giving a win-by-forfeit to any team that has not played the team that has dropped out, is worse. This is unfair to any team which has lost to the offending team. And for teams getting a win-by-forfeit, what should the score be? Suppose a team getting a win is involved in a tie-breaker situation and the score of the win-by-forfeit comes into consideration?

    Lastly, it should be restated that it is official UPA Policy that if a team does not finish the tournament (i.e., drops out and loses by forfieting), they can not qualify for the next event. So, for example, if a team at sectionals is 5-1, then drops out, thinking that they will finish at 5-3 and qualify for regionals, forget it. None of their games count. They aren't even 0-8, they are 0-0, and it's almost as if they didn't even show up to the tournament. (Their appearance will count, however, for the purposes of dues, memberships, and "years of qualification," etc.).

    Table 9.1.1. Nine Team Round-Robin Grid

                1  2  3  4  5  6  7  8  9
                -  -  -  -  -  -  -  -  -
            1 - 8  3  7  2  6  B  5  9  4
            2 - 7  B  6  1  5  9  4  8  3
            3 - 6  1  5  9  4  8  B  7  2
            4 - 5  9  B  8  3  7  2  6  1
            5 - 4  8  3  7  2  6  1  B  9
            6 - 3  7  2  B  1  5  9  4  8
            7 - 2  6  1  5  9  4  8  3  B
            8 - 1  5  9  4  B  3  7  2  6
            9 - B  4  8  3  7  2  6  1  5
    

    Table 9.1.2. Nine Team Round-Robin, General

            1 v 3   4 v 9   5 v 8   6 v 7  bye: 2
            1 v 7   2 v 6   3 v 5   8 v 9  bye: 4
            1 v 6   2 v 5   3 v 4   7 v 9  bye: 8
            2 v 9   3 v 8   4 v 7   5 v 6  bye: 1
            1 v 2   3 v 9   4 v 8   5 v 7  bye: 6
            1 v 5   2 v 4   6 v 9   7 v 8  bye: 3
            1 v 9   2 v 8   3 v 7   4 v 6  bye: 5
            1 v 4   2 v 3   5 v 9   6 v 8  bye: 7
            1 v 8   2 v 7   3 v 6   4 v 5  bye: 9
    

    Table 9.1.3. Nine Team Round-Robin Over Two Days

    In this format, there are five rounds each day, and each team has four games each day. Most teams have a bye in the middle round (good for grabbing some lunch). Additionally, five teams have a bye during the presumably good 1 vs. 2 game, and they can watch the game.
            First Day
             1 v 5   2 v 4   6 v 9   7 v 8  bye: 3
             1 v 9   2 v 8   3 v 7   4 v 6  bye: 5
             3 v 9   5 v 7                  bye: 1, 2, 4, 6, 8
             1 v 4   2 v 3   5 v 9   6 v 8  bye: 7
             1 v 8   2 v 7   3 v 6   4 v 5  bye: 9
    
            Second Day
             1 v 3   4 v 9   5 v 8   6 v 7  bye: 2
             1 v 7   2 v 6   3 v 5   8 v 9  bye: 4
             1 v 2   4 v 8                  bye: 3, 5, 6, 7, 9
             1 v 6   2 v 5   3 v 4   7 v 9  bye: 8
             2 v 9   3 v 8   4 v 7   5 v 6  bye: 1
    

    10. Ten Teams

    10.1. One Team Advances

    Start with two pools of five (see Section 10.7).

    On the second day, the top four teams in each pool play an eight-team single elimination. (Note, the brackets and the initial pairings for the single elimination is the same as the upper half of the 8-team double elimination format, see Table 8.1.1).

    Note, it is not acceptable to take only the top two teams from each pool and have semi's and finals, because of the possibility of a three-way tie for first in one of the pools.

    10.2. Two Teams Advance

    10.2.1. Option One - Six Teams Advance to Second Day
    Start with two pools of five (see Section 10.7).

    On the second day, the top team in each pool play each other. The winner takes first place. The loser still has another game to play. The second and third teams in each pool play a four-team loser's bracket; i.e., a semis and a final. This takes two rounds. The winner of this bracket, then, plays the loser of the game for first place. The winner of this game takes second place. The brackets for this second day are shown in Table 6.5).

    10.2.2. Option Two - Double Elimination on the Second Day:
    Note, because of the number of games involved, you must get approval from a majority of the teams playing before you can use this format.

    Start with two pools of five (see Section 10.7).

    On the second day, the top four teams in each pool play an eight-team double elimination. (See Table 8.1.1).

    This involves an awful lot of games for some of the teams. It is possible that one or two teams will play five games the second day. Note, too, that one of the pools will have played four games on the first day. (In women's play, the first round of the double elimination could be an abbreviated game to 11, (since no one gets eliminated after only one game). Otherwise, all of the games should be to 13 (except for the winner's bracket final, which is to 15).

    10.3. Three Teams Advance

    Start with two pools of five (see Section 10.7).

    On the second day, the top three teams in each pools play a six-team modified double elimination (see Table 6.4).

    10.4. Four Teams Advance

    10.4.1. Option One - Double Elimination on the Second Day:
    Start with two pools of five (see Section 10.7).

    On the second day, the top four teams in each pool play an eight-team double elimination. (See Table 8.1.1).

    This involves an awful lot of games for some of the teams. It is possible that one or two teams will play five games the second day. Note, too, that everyone will have played four games on the first day. In women's play, the first round of the double elimination could be an abbreviated game to 11, (since no one gets eliminated after only one game). Otherwise, all of the games should be to 13 (except for the winner's bracket final, which is to 15).

    To ease things, you should consider eliminating the very last round of the double elimination. The last round is for second and third place, which may not be very relevant if four or more teams are qualifying anyway. If this game is not played, use the tie-breakers for double elimination (Section 2.6). In the Mid-Atlantic, a format similar to this was used, and this game was optional. (i.e., The team that wanted to play was given third place; if both wanted to, they played; if neither wanted too, or it was too late, we used the tie-breakers.)

    10.4.2. Option Two - Six Teams Advance to Modified Round-Robin
    This is a good option, because the six teams that advance all get to play three games when the round-robin is finished. Furthermore, the four teams that do not advance, can play a some sort of schedule among themselves.

    Start with two pools of five (see Section 10.7).

    When the round-robin is finished, the top three teams in each pool each play the three teams from the other pool. When this is done, each of the six teams will have played each of the other teams, and it is as if a round-robin has just been played. In other words, count the records of the teams from the first round-robin.

    Some people are resistant to this idea because there is no "finals." But that problem can be avoided by scheduling the two top teams for the last round. As a matter of fact, the last round is pretty exciting for all of those concerned; furthermore, it is quite likely that the third and fourth best teams get to play each other for third place, and the fifth and sixth best teams play each other for fifth place, all in the last round.

    Here is a complete example. Suppose that when the round-robin is over, the teams' records are as follows:

                            Pool X          Pool Y
                            A 4-0           P 4-0
                            B 3-1           Q 3-1
                            C 2-2           R 2-2
                            D 1-3           S 1-3
                            E 0-4           T 0-4
    
    Further, suppose that each team beat all the teams below it. Then, the second day's schedule would be:
                            Round 1:  A vs R   P vs B   Q vs C
                            Round 2:  A vs Q   B vs R   P vs C
                            Round 3:  A vs P   B vs Q   C vs R
    
    The key is that A and P start off this round-robin with a 2-0 record (i.e., A's previous round-robin games against B and C "carry over" into this round-robin). Teams B and Q are 1-1, etc.

    To make the schedule more generalized, you would write it up as:

                            Round 1:  X1-Y3    X2-Y1    X3-Y2
                            Round 2:  X1-Y2    X2-Y3    X3-Y1
                            Round 3:  X1-Y1    X2-Y2    X3-Y3
    

    10.5. Five Or Six Teams Advance

    10.5.1. Option One - Modified Elimination on the Second Day:
    Start with two pools of five (see Section 10.7).

    When the round-robin is finished, the top four teams in each pool play an eight-team modified elimination, (see Table 8.1.2).

    10.5.2. Option Two - Double Elimination on the Second Day:
    Start with two pools of five (see Section 10.7).

    When the round-robin is finished, the top four teams in each pool play an eight-team double elimination, (see Table 8.1.1). that you might consider that the last round of the elimination not be played. This option is described more fully in Section 10.4.1.

    10.6. Six Through Eight Teams Advance

    Start with two pools of five (see Section 10.7).

    When the round-robin is finished, all ten teams enter the ten-team modified elimination format (see Table 10.2).

    The ten-team modified elimination is a good example of a format designed to minimize the effects of seeding. For example, a team that finishes second in their pool can still finish in seventh place. Similarly, a team that finishes fifth in their pool, can still finish as high as sixth place. In other words, if, mistakenly, most of the good teams were in one pool, this elimination bracket ought to take care of it.

    10.7. Seeding For Pools Of Five

    The pools should be seeded as follows:
                    Pool A:                 Pool B:
                    Seed #1                 Seed #2
                    Seed #4                 Seed #3
                    Seed #5                 Seed #6
                    Seed #8                 Seed #7
                    Seed #9                 Seed #10
    
    The round-robin for each pool will take five rounds (four games and a bye). A schedule for a five-team round-robin may be found in Table 5.1.1).

    Table 10.1. Ten Team Round-Robin Grid

                  1  2  3  4  5  6  7  8  9
                  -  -  -  -  -  -  -  -  -
             1 -  9  2  5  8 10  4  7  3  6
             2 -  8  1  4  7  3  6  9 10  5
             3 -  7 10  6  9  2  5  8  1  4
             4 -  6  9  2  5  8  1 10  7  3
             5 - 10  8  1  4  7  3  6  9  2
             6 -  4  7  3 10  9  2  5  8  1
             7 -  3  6  9  2  5  8  1  4 10
             8 -  2  5 10  1  4  7  3  6  9
             9 -  1  4  7  3  6 10  2  5  8
            10 -  5  3  8  6  1  9  4  2  7
    
            1 v  2   3 v 10   4 v  9   5 v  8   6 v  7
            1 v  5   2 v  4   3 v  6   7 v  9   8 v 10
            1 v  8   2 v  7   3 v  9   4 v  5   6 v 10
            1 v 10   2 v  3   4 v  8   5 v  7   6 v  9
            1 v  4   2 v  6   3 v  5   7 v  8   9 v 10
            1 v  7   2 v  9   3 v  8   4 v 10   5 v  6
            1 v  3   2 v 10   4 v  7   5 v  9   6 v  8
            1 v  6   2 v  5   3 v  4   7 v 10   8 v  9
            1 v  9   2 v  8   3 v  7   4 v  6   5 v 10
    

    Table 10.2. Ten-Team Modified Elimination

              A1  -----
                     E  -----          1st place
              B1  -----
    
                     LE -----_
       A2   -----             _
               A  -----    J   _______  winner J: 2d place
       B3   -----      _      _         loser  J: 3d place
                     F  -----
       A3   -----      _
               B  -----
       B2   -----
                     LF -----_
                           K  _ ______  winner K: 4th place
               LA -----      _          loser  K: 5th place
                     G  -----_
               LB -----
    
                     LG -----_
       A4   -----            _
               C  -----    M _ _______  winner M: 6th place
       B5   -----      -     _          loser  M: 7th place
                     H  -----
       A5   -----      _
               D  -----
       B4   -----
                     LH -----_
                           N  ________  winner N: 8th place
               LC -----      _          loser  N: 9th place
                     I  -----
               LD -----
    

    11. Eleven Teams

    11.1. One Team Advances

    Start with two unequal pools of five and six (see Section 11.7).

    On the second day, the top four teams in each pool play an eight-team single elimination. (Note, the brackets and the initial pairings for the single elimination is the same as the upper half of the 8-team double elimination format, see Table 8.1.1).

    Note, it is not acceptable to take only the top two teams from each pool and have semi's and finals, because of the possibility of a three-way tie for first in one of the pools.

    11.2. Two Teams Advance

    11.2.1. Option One - Six Teams Advance to Second Day
    Start with two unequal pools of five and six (see Section 11.7).

    When the round-robin is finished, the top team in each pool play each other. The winner takes first place. The loser still has another game to play. The second and third teams in each pool play a four-team loser's bracket; i.e., a semis and a final. This takes two rounds. The winner of this bracket, then, plays the loser of the game for first place. The winner of this game takes second place. The brackets for this second day are shown in Table 6.5.

    11.3. Three Teams Advance

    11.3.1. Option One - Six Teams Advance to Modified Elimination
    Start with two unequal pools of five and six (see Section 11.7).

    When the round-robin is finished, the top three teams in each pools play a six-team modified double elimination (see Table 6.4).

    11.3.2. Option Two - Six Teams Advance Modified Round-Robin
    This is a good option, because the six teams that advance all get to play three games when the round-robin is finished. Furthermore, the five teams that do not advance, can play a similar schedule among themselves.

    Start with two unequal pools of five and six (see Section 11.7).

    When the round-robin is finished, the top three teams in each pool each play the three teams from the other pool. When this is done, each of the six teams will have played each of the other teams, and it is as if a round-robin has just been played. In other words, count the records of the teams from the first round-robin.

    Some people are resistant to this idea because there is no "finals." But that problem can be avoided by scheduling the two top teams for the last round. As a matter of fact, the last round is pretty exciting for all of those concerned; furthermore, it is quite likely that the third and fourth best teams get to play each other for third place, and the fifth and sixth best teams play each other for fifth place, all in the last round.

    A complete example exists at Section 11.8.

    11.4. Four Teams Advance

    11.4.1. Option One - Double Elimination on the Second Day
    Start with two unequal pools of five and six (see Section 11.7).

    When the round-robin is finished, the top four teams in each pool play an eight-team double elimination, (see Table 8.1.1), except that the last round of the elimination should not be played.

    This involves an awful lot of games for some of the teams. It is possible that one or two teams will play five games the second day. Note, too, that one of the pools will have played five games on the first day. (In women's play, the first round of the double elimination could be an abbreviated game to 11, (since no one gets eliminated after only one game). Otherwise, all of the games should be to 13 (except for the winner's bracket final, which is to 15).

    To ease things the very last round of the double elimination should not be played. The last round is for second and third place, which may not be very relevant if four or more teams are qualifying anyway. If this game is not played, use the tie-breakers for double elimination (Section 2.6). In the Mid-Atlantic, a format similar to this was used, and this game was optional. I.e., the team that wanted to play was given third place; if both wanted to, they played; if neither wanted too, or it was too late, we used the tie-breakers.

    11.4.2. Option Two - Six Teams Advance Modified Round-Robin
    This is a good option, because the six teams that advance each get to play three games when the round-robin is finished. Furthermore, the five teams that do not advance, can play a similar schedule among themselves.

    A complete example exists at Section 11.8.

    11.5. Five Or More Teams Advance

    11.5.1. Option One - Modified Elimination on the Second Day:
    Start with two unequal pools of five and six (see Section 11.7).

    When the round-robin is finished, the top four teams in each pool play an eight-team modified elimination, (see Table 8.1.2).

    11.5.2. Option Two - Double Elimination on the Second Day:
    Start with two unequal pools of five and six (see Section 11.7).

    When the round-robin is finished, the top four teams in each pool play an eight-team double elimination, (see Table 8.1.1), except that the last round of the elimination should not be played. This option is described more fully in section Section 11.4.1.

    11.6. Six Through Eight Teams Advance

    Start with two unequal pools of five and six (see Section 11.7).

    When the round-robin is finished, the top five teams in each pool enter the ten-team modified elimination format (see Table 10.2).

    The ten-team modified elimination is a good example of a format designed to minimize the effects of seeding. For example, a team that finishes second in their pool can still finish in seventh place. Similarly, a team that finishes fifth in their pool, can still finish as high as sixth place. In other words, if, mistakenly, most of the good teams were in one pool, this elimination bracket ought to take care of it.

    11.7. Seeding For Two Unequal Pools Of Five And Six

    The pools should be seeded as follows:
                    Pool A:                 Pool B:
                    Seed #1                 Seed #2
                    Seed #4                 Seed #3
                    Seed #5                 Seed #6
                    Seed #8                 Seed #7
                    Seed #9                 Seed #10
                                            Seed #11
    
    The round-robin for each pool will take five rounds (even though the teams in pool A only get four games). A schedule for a five-team round-robin may be found in Table 5.1.1; a schedule for a six-team round-robin is in Table 6.1.

    11.8. Sample Schedule

    The following sample schedule is one you might use where the round-robin goes into the first round of the second day. Then, if you use, for example, a modified six-team modified double elimination (see Table 6.4), which takes three rounds, the entire tournament fits neatly into a four-rounds-per-day schedule.
            Start   Cap
            10:00 11:40     A1-A4   A3-A5    B1-B5   B2-B4   B3-B6
            12:00  1:40     A1-A5   A2-A3    B1-B4   B2-B3   B5-B6
             2:00  3:40     A2-A5   A3-A4    B1-B6   B2-B5   B3-B4
             4:00  5:40     A1-A2   A4-A5    B1-B2   B3-B5   B4-B6
              (Sunday)
             9:00 10:40     A1-A3   A2-A4    B1-B3   B2-B6   B4-B5
    
    The order of the games in this format was given a lot of thought. Here are some of the factors:

    Table 11.1. Eleven team round-robin grid

           1  2  3  4  5  6  7  8  9 10 11
           -  -  -  -  -  -  -  -  - -- --
      1 - 10  2  5  8 11  3  6  9  B  4  7
      2 -  9  1  4  7 10  B  5  8 11  3  6
      3 -  8 11  B  6  9  1  4  7 10  2  5
      4 -  7 10  2  5  8 11  3  6  9  1  B
      5 -  6  9  1  4  7 10  2  B  8 11  3
      6 -  5  8 11  3  B  9  1  4  7 10  2
      7 -  4  B 10  2  5  8 11  3  6  9  1
      8 -  3  6  9  1  4  7 10  2  5  B 11
      9 -  2  5  8 11  3  6  B  1  4  7 10
     10 -  1  4  7  B  2  5  8 11  3  6  9
     11 -  B  3  6  9  1  4  7 10  2  5  8
    
     1 v  2   3 v 11   4 v 10   5 v  9   6 v  8
     1 v  5   2 v  4   6 v 11   7 v 10   8 v  9
     1 v  8   2 v  7   3 v  6   4 v  5   9 v 11
     1 v 11   2 v 10   3 v  9   4 v  8   5 v  7
     1 v  3   4 v 11   5 v 10   6 v  9   7 v  8
     1 v  6   2 v  5   3 v  4   7 v 11   8 v 10
     1 v  9   2 v  8   3 v  7   4 v  6  10 v 11
     2 v 11   3 v 10   4 v  9   5 v  8   6 v  7
     1 v  4   2 v  3   5 v 11   6 v 10   7 v  9
     1 v  7   2 v  6   3 v  5   8 v 11   9 v 10
     1 v 10   2 v  9   3 v  8   4 v  7   5 v  6
    

    12. Twelve Teams

    A twelve team tournament is not all that much easier to run than an eleven team tournament. Pools of three, as discussed in the section on nine-team tournament, are never acceptable for UPA play. There are not enough games, and far too much depends on seeding. Additionally, the possibility of a three-way tie exists. There are no tie-breakers that work for a three-way tie in a three-team pool (but see Section 3.1).

    Three pools of four can be difficult because whenever there is a round-robin pool, you must allow for the possibility of a three-way tie for first. The only way to allow for that is to take the top three from each pool, and then to have them play-off. But here, taking the top three would leave you with nine teams. Generally speaking, three pools of four is not the way to go, except for certain situations, detailed below.

    The preferred method, therefore, for all variations of a twelve team tournament is to start off with two pools of six.

    A round-robin of six teams must be spread out over two days. Play four rounds the first day, and the fifth game as the first round on the second day. Because no team has a bye during the round-robin, no team has an unfair advantage for the games that follow the round-robin. For some of the formats, where there are lots of games, you might consider making the round-robin games to 13.

    Commonly, tournament schedulers like to pit the top two seeds against each other during the last round of a round-robin. This is not a good idea, however, when the round-robin is spread over two days because then the top two seeds might be playing each other twice on the second day. Make sure that these two teams play each other on the first day.

    12.1. One Team Advances

    Start with two pools of six (see Section 12.7).

    When the round-robin is finished, the top four teams in each pool play an eight-team single elimination. (Note, the brackets and the initial pairings for the single elimination is the same as the upper half of the 8-team double elimination format, see Table 8.1.1).

    Note, it is not acceptable to take only the top two teams from each pool and have semi's and finals, because of the possibility of a three-way tie for first in one of the pools.

    12.2. Two Teams Advance

    In this format, six teams advance to the modified elimination.

    Start with two pools of six (see Section 12.7).

    When the round-robin is finished, the top team in each pool play each other. The winner takes first place. The loser still has another game to play. The second and third teams in each pool play a four-team loser's bracket; i.e., a semis and a final. This takes two rounds. The winner of this bracket, then, plays the loser of the game for first place. The winner of this game takes second place. The brackets for this second day are shown in Table 6.5.

    12.3. Three Teams Advance

    12.3.1. Option One - Six Teams Advance to Modified Elimination:
    Start with two pools of six (see Section 12.7).

    When the round-robin is finished, the top three teams in each pools play a six-team modified double elimination (see Table 6.4).

    12.3.2. Option Two - Six Teams Advance to Modified Round-Robin:
    This is a good option, because the six teams that advance all get to play three games when the round-robin is finished. Furthermore, the six teams that do not advance, can play a similar schedule among themselves.

    Start with two pools of six (see Section 12.7).

    When the round-robin is finished, the top three teams in each pool each play the three teams from the other pool. When this is done, each of the six teams will have played each of the other teams, and it is as if a round-robin has just been played. In other words, count the records of the teams from the first round-robin.

    Some people are resistant to this idea because there is no "finals." But that problem can be avoided by scheduling the two top teams for the last round. As a matter of fact, the last round is pretty exciting for all of those concerned; as a matter of fact, it is quite likely that the third and fourth best teams get to play each other for third place, and the fifth and sixth best teams gplay each other for fifth place, all in the last round.

    A complete example exists at Section 12.8.

    12.4. Four Teams Advance

    12.4.1. Option One - Six Teams Advance to Modified Elimination:
    Start with two pools of six (see Section 12.7).

    When the round-robin is finished, the top three teams in each pools play a six-team modified double elimination (see Table 6.4).

    12.4.2. Option Two - Six Teams Advance to Modified Round-Robin
    This is a good option, because the six teams that advance all get to play three games when the round-robin is finished. Furthermore, the six teams that do not advance can play a similar schedule among themselves.

    A complete example exists at Section 12.8.

    12.5. Five Or Six Teams Advance

    12.5.1. Option One - Modified Elimination on the Second Day:
    Start with two pools of six (see Section 12.7).

    When the round-robin is finished, the top four teams in each pool play an eight-team modified elimination, (see Table 8.1.2).

    12.5.2. Option Two - Double Elimination on the Second Day:
    Start with two pools of six (see Section 12.7).

    When the round-robin is finished, the top four teams in each pool play an eight-team double elimination, (see Table 8.1.1), except that the last round of the elimination should not be played. This option is described more fully in Section 10.4.1.

    12.6. Six Through Eight Teams Advance

    Start with two pools of six (see Section 12.7).

    When the round-robin is finished, the top five teams in each pool enter the ten-team modified elimination format (see Table 10.2).

    The ten-team modified elimination is a good example of a format designed to minimize the effects of seeding. For example, a team that finishes second in their pool can still finish in seventh place. Similarly, a team that finishes fifth in their pool, can still finish as high as sixth place. In other words, if, mistakenly, most of the good teams were in one pool, this elimination bracket ought to take care of it.

    12.7. Seeding For Two Pools Of Six

    The pools should be seeded as follows:
                    Pool A:                 Pool B:
                    Seed #1                 Seed #2
                    Seed #4                 Seed #3
                    Seed #5                 Seed #6
                    Seed #8                 Seed #7
                    Seed #9                 Seed #10
                    Seed #12                Seed #11
    
    The round-robin for each pool will take five rounds. A schedule for a six-team round-robin may be found in Table 6.1.

    12.8. Sample Schedule

    The following sample schedule is one you might you where the round-robin goes into the first round of the second day. Then, if you use, for example, a modified six-team modified double elimination (see Table 6.4), which takes three rounds, the entire tournament fits neatly into a four-rounds-per-day schedule.
            Start   Cap
            10:00 11:40     A1-A5   A2-A4   A3-A6  (pool B is the same)
            12:00  1:40     A1-A4   A2-A3   A5-A6
             2:00  3:40     A1-A6   A2-A5   A3-A4
             4:00  5:40     A1-A2   A3-A5   A4-A6
              (Sunday)
             9:00 10:40     A1-A3   A2-A6   A4-A5
    
    The order of the games in this format was given a lot of thought. Here are some of the factors:

    Table 12.1. Twelve Team Round-Robin Grid:

           1  2  3  4  5  6  7  8  9 10 11
           -  -  -  -  -  -  -  -  - -- --
      1 - 11  4  9  2  7  5 10  3  8 12  6
      2 - 10  3  8  1  6 11  4  9 12  7  5
      3 -  9  2  7  5 10 12  8  1  6 11  4
      4 -  8  1  6 11 12  9  2  7  5 10  3
      5 -  7 12 10  3  8  1  6 11  4  9  2
      6 - 12 11  4  9  2  7  5 10  3  8  1
      7 -  5 10  3  8  1  6 11  4  9  2 12
      8 -  4  9  2  7  5 10  3 12  1  6 11
      9 -  3  8  1  6 11  4 12  2  7  5 10
     10 -  2  7  5 12  3  8  1  6 11  4  9
     11 -  1  6 12  4  9  2  7  5 10  3  8
     12 -  6  5 11 10  4  3  9  8  2  1  7
    
     1 v  4   2 v  3   5 v 12   6 v 11   7 v 10   8 v  9
     1 v  9   2 v  8   3 v  7   4 v  6   5 v 10  11 v 12
     1 v  2   3 v  5   4 v 11   6 v  9   7 v  8  10 v 12
     1 v  7   2 v  6   3 v 10   4 v 12   5 v  8   9 v 11
     1 v  5   2 v 11   3 v 12   4 v  9   6 v  7   8 v 10
     1 v 10   2 v  4   3 v  8   5 v  6   7 v 11   9 v 12
     1 v  3   2 v  9   4 v  7   5 v 11   6 v 10   8 v 12
     1 v  8   2 v 12   3 v  6   4 v  5   7 v  9  10 v 11
     1 v 12   2 v  7   3 v 11   4 v 10   5 v  9   6 v  8
     1 v  6   2 v  5   3 v  4   7 v 12   8 v 11   9 v 10
     1 v 11   2 v 10   3 v  9   4 v  8   5 v  7   6 v 12
    

    13. Thirteen Teams

    Thirteen teams, believe it or not, is not such a bad number to have, if you are picking less than eight teams. If you are picking eight or more teams, see Section 13.5.

    13.1. The First Day Of Play

    13.1.1. Overview:
    In all of the formats described below, the first days' play is as follows:

    Start off with three pools: one of five teams, the other two of four teams each. Round-robin within each pool. Eight teams qualify for the next day's elimination. Those eight teams are: 3 from pool A, 2 each from pools B and C, and the winner of a play-off game between the 3rd place finisher of B and C.

    13.1.2. Seeding:
    The initial seeds should be as follows:
                    Pool A          Pool B          Pool C
                    Seed #1         Seed #2         Seed #3
                    Seed #6         Seed #5         Seed #4
                    Seed #7         Seed #8         Seed #9
                    Seed #12        Seed #11        Seed #10
                    Seed #13
    
    13.1.3. Schedule:
    The following is a good schedule to use:

    Assume that pool A has five teams, and pools B and C have four teams each.

                    Fields:  1      2      3      4      5
                    9:00   B1-B3  B2-B4  C1-C4  A1-A4  A3-A5
                    10:45  B1-B2  C1-C3  C2-C4  A1-A3  A2-A5
                    12:30  B3-B4  C1-C2  C3-C4  A4-A5  A2-A3
                    2:15   B1-B4  B2-B3  C2-C3  A1-A5  A2-A4
                    4:45                 3B-3C* A1-A2  A3-A4
    
    (* this game is the one between the third place finishers of pools B and C)
    
    Note that the round-robin for the two pools of four (B and C) are played over four rounds on three fields. They could be played on three rounds on four fields, but there are two disadvantages of that method. First, it takes up an extra field. Second, most of the teams would be done after the third round while pool A still has two more rounds to go. The schedule above uses less fields and keeps more players around.

    13.2. One Team Advances

    When only one team advances, there is no need for you to schedule all five rounds of the round-robin on the first day. You can make the games longer, and play the last round as the first round on the second day. This is because the single elimination that is to follow only takes three rounds.

    The eight teams simply enter the single elimination bracket. (See the initial bracket set-up, Table 13.2.)

    13.3. Two Teams Advance

    When two teams advance, the eight teams must play a double elimination for the second day. The only problem is that the double elimination takes five rounds. Games must start on time. Caps must be enforced strictly. The first round games might be shortened a bit, since no one can get eliminated after losing the first game. The Mid-Atlantic Women used this format for their Regionals in the fall of 1989, and it worked out well. On the second day, games were to 13, except the last round was to 15. Rounds were scheduled for 9, 10:45, 12:30, 2:30, and 4:30. Even though time caps were strictly applied, one of the rounds slipped a bit because the game didn't finish till about a half-hour past the cap. Additionally, we were lucky that we still had daylight savings time, and that it was still light enough to play until about 6:45. Another option to be considered is to have the first round games to 11 points. This should present no problem because no teams are eliminated during that round.

    For the initial bracket set-up, see Table 13.2. For the rest of the double elimination, see Table 8.1.1.

    13.4. Three Through Seven Teams Advance

    When more than two teams advance, the eight teams can play a double elimination for the second day by eliminating the last round.

    For the initial bracket set-up, see Table 13.2. For the rest of the double elimination, see Table 8.1.1. This option is described more fully in Section 13.3.

    13.5. Eight Or More Teams Advance

    Last minute suggestions: take the top team from each pool. They are the top three, and they can play their own round-robin to determine first through third.

    Next, determine the next eight teams: the three second and third place teams, the fourth place team from pool A, and one other team. I don't know how to get this other team. Perhaps the last place team with the smallest losing differential between themselves and the second-to-last place team. Or, how about the two teams with the smallest losing differentials play off? The best scenario, of course, is if during the course of the first day, one of the teams decides that they don't want to go on to the next tournament. Whatever is decided, however, make sure all the captains agree on it.

    Then, these eight teams go into the double elimination, see Table 8.1.1. Of course, the teams will not be playing for 1st through 8th, like in the table. Take the top five teams from the bracket (1st through 5th in the table), and they are 4th through 8th in this format.

    Good luck!

    Table 13.1. Thirteen Team Round-Robin Grid:

           1  2  3  4  5  6  7  8  9 10 11 12 13
           -  -  -  -  -  -  -  -  - -- -- -- --
      1 - 12  2  5  8 11  B  4  7 10 13  3  6  9
      2 - 11  1  4  7 10 13  3  6  9 12  B  5  8
      3 - 10 13  B  6  9 12  2  5  8 11  1  4  7
      4 -  9 12  2  5  8 11  1  B  7 10 13  3  6
      5 -  8 11  1  4  7 10 13  3  6  9 12  2  B
      6 -  7 10 13  3  B  9 12  2  5  8 11  1  4
      7 -  6  9 12  2  5  8 11  1  4  B 10 13  3
      8 -  5  B 11  1  4  7 10 13  3  6  9 12  2
      9 -  4  7 10 13  3  6  B 12  2  5  8 11  1
     10 -  3  6  9 12  2  5  8 11  1  4  7  B 13
     11 -  2  5  8  B  1  4  7 10 13  3  6  9 12
     12 -  1  4  7 10 13  3  6  9  B  2  5  8 11
     13 -  B  3  6  9 12  2  5  8 11  1  4  7 10
    
     1 v  2   3 v 13   4 v 12   5 v 11   6 v 10   7 v  9
     1 v  5   2 v  4   6 v 13   7 v 12   8 v 11   9 v 10
     1 v  8   2 v  7   3 v  6   4 v  5   9 v 13  10 v 12
     1 v 11   2 v 10   3 v  9   4 v  8   5 v  7  12 v 13
     2 v 13   3 v 12   4 v 11   5 v 10   6 v  9   7 v  8
     1 v  4   2 v  3   5 v 13   6 v 12   7 v 11   8 v 10
     1 v  7   2 v  6   3 v  5   8 v 13   9 v 12  10 v 11
     1 v 10   2 v  9   3 v  8   4 v  7   5 v  6  11 v 13
     1 v 13   2 v 12   3 v 11   4 v 10   5 v  9   6 v  8
     1 v  3   4 v 13   5 v 12   6 v 11   7 v 10   8 v  9
     1 v  6   2 v  5   3 v  4   7 v 13   8 v 12   9 v 11
     1 v  9   2 v  8   3 v  7   4 v  6  10 v 13  11 v 12
     1 v 12   2 v 11   3 v 10   4 v  9   5 v  8   6 v  7
    

    Table 13.2. Seeding An 8-Team Bracket From Three Pools

            A1 ----_
                 A _---------_
            WC*----          _
                           E _----------_
            C2 ----_         _          _
                 B _---------           _
            B2 ----                     _
                                      I _---------------
            C1 ----_                    _  (1st place)
                 C _---------_          _
            A2 ----          _          _
                           F _----------
            B1 ----_         _
                 D _---------
            A3 ----
    
            * WC - Wild Card - the winner of the playoff between B3 and C3.
    

    14. Fourteen Teams

    I have yet to find a solution to either the Fourteen or Fifteen team problem. The following solution was devised for the 1991 Central Plains Sectional.

    14.1. The First Day Of Play

    14.1.1. Overview:
    In all of the formats described below, the first days' play is as follows:

    Start off with three pools: two of five teams, the other pool has four teams. Round-robin within each pool. Eight teams qualify for the next day's elimination. Those eight teams are: two from each of the three pools, a wild-card, and the winner of the "eighth spot play-in." In this way, the top three teams from each pool each have a shot at making the next day's bracket.

    The question, of course, is how to figure out which third place team is the wild-card, and which of the other two teams must play the "eighth spot play-in." The following scenario is one such possibility.

    First, we recognize that the third place teams in Pools A and B each had to win two games (or, more precisely, finish ahead of two other teams) in order to finish in third place. This is one potential objective reason for letting one of those two teams be the wild card. The other team must play the "play-in" with the third place team from Pool C.

    Point differentials are used to choose one third place team from the other. The two third place teams from Pool A and Pool B have four round-robin games, giving them four games' worth of point differentials. Exclude the high and the low, and combine the other two point differentials for a total point differential. (If the teams are still tied, use all four games). This exclusion is based on the fact that it is possible that a team who has to play the top seed (and/or the bottom seed) of the entire tournament may be at an unfair advantage (or disadvantage), and that the top and bottom seeds are in Pools A and B.

    The team with the better point differential becomes the wild card, the other teams must "play-in" against the third place team from Pool C.

    This solution, of course, leaves a lot to be desired. Chief among the problems are using point differentials with differing opponents. On the other hand, no one gets eliminated by a point differential. The worst that can happen is that a third place team must play against another third place team. At least the fate is in the teams' own hands.

    14.1.2. Seeding:
    The initial seeds should be as follows:
                    Pool A          Pool B          Pool C
                    Seed #1         Seed #2         Seed #3
                    Seed #6         Seed #5         Seed #4
                    Seed #7         Seed #8         Seed #9
                    Seed #12        Seed #11        Seed #10
                    Seed #13        Seed #14
    
    14.1.3. Schedule:
    The following is a good schedule to use:

    Assume that pool A has five teams, and pools B and C have four teams each.

                    Fields:  1      2      3      4      5
                    9:00   B1-B3  B2-B4  C1-C4  A1-A3  A4-A5
                    10:45  B1-B2  C1-C3  C2-C4  A1-A5  A2-A4
                    12:30  B3-B4  C1-C2  C3-C4  A2-A5  A3-A4
                    2:15   B1-B4  B2-B3  C2-C3  A1-A4  A2-A3
                    4:45                 3B-3C* A1-A2  A3-A5
    
    (* this game is the one between the third place finishers of pools B and C)
    
    Note that the round-robin for the two pools of four (B and C) are played over four rounds on three fields. They could be played on three rounds on four fields, but there are two disadvantages of that method. First, it takes up an extra field. Second, most of the teams would be done after the third round while pool A still has two more rounds to go. The schedule above uses less fields and keeps more players around.

    Last minute suggestions: take the top team from each pool. They are the top three, and they can play their own round-robin to determine first through third.

    Next, determine the next eight teams: the three second and third place teams, the fourth place team from pool A, and one other team. I don't know how to get this other team. Perhaps the last place team with the smallest losing differential between themselves and the second-to-last place team. Or, how about the two teams with the smallest losing differentials play off? The best scenario, of course, is if during the course of the first day, one of the teams decides that they don't want to go on to the next tournament. Whatever is decided, however, make sure all the captains agree on it.

    Then, these eight teams go into the double elimination, see Table 8.1.1. Of course, the teams will not be playing for 1st through 8th, like in the table. Take the top five teams from the bracket (1st through 5th in the table), and they are 4th through 8th in this format.

    Good luck

    Table 14.1. Fourteen Team Round-Robin Grid

           1  2  3  4  5  6  7  8  9 10 11 12 13
           -  -  -  -  -  -  -  -  - -- -- -- --
      1 - 13  2  5  8 11  3  6  9 12 14  4  7 10
      2 - 12  1  4  7 10 13 14  5  8 11  3  6  9
      3 - 11 14  6  9 12  1  4  7 10 13  2  5  8
      4 - 10 13  2  5  8 11  3  6  9 12  1 14  7
      5 -  9 12  1  4  7 10 13  2 14  8 11  3  6
      6 -  8 11  3 14  9 12  1  4  7 10 13  2  5
      7 - 14 10 13  2  5  8 11  3  6  9 12  1  4
      8 -  6  9 12  1  4  7 10 13  2  5 14 11  3
      9 -  5  8 11  3  6 14 12  1  4  7 10 13  2
     10 -  4  7 14 13  2  5  8 11  3  6  9 12  1
     11 -  3  6  9 12  1  4  7 10 13  2  5  8 14
     12 -  2  5  8 11  3  6  9 14  1  4  7 10 13
     13 -  1  4  7 10 14  2  5  8 11  3  6  9 12
     14 -  7  3 10  6 13  9  2 12  5  1  8  4 11
    
     1 v  2   3 v 14   4 v 13   5 v 12   6 v 11   7 v 10   8 v  9
     1 v  5   2 v  4   3 v  6   7 v 13   8 v 12   9 v 11  10 v 14
     1 v  8   2 v  7   3 v  9   4 v  5   6 v 14  10 v 13  11 v 12
     1 v 11   2 v 10   3 v 12   4 v  8   5 v  7   6 v  9  13 v 14
     1 v  3   2 v 13   4 v 11   5 v 10   6 v 12   7 v  8   9 v 14
     1 v  6   2 v 14   3 v  4   5 v 13   7 v 11   8 v 10   9 v 12
     1 v  9   2 v  5   3 v  7   4 v  6   8 v 13  10 v 11  12 v 14
     1 v 12   2 v  8   3 v 10   4 v  9   5 v 14   6 v  7  11 v 13
     1 v 14   2 v 11   3 v 13   4 v 12   5 v  8   6 v 10   7 v  9
     1 v  4   2 v  3   5 v 11   6 v 13   7 v 12   8 v 14   9 v 10
     1 v  7   2 v  6   3 v  5   4 v 14   8 v 11   9 v 13  10 v 12
     1 v 10   2 v  9   3 v  8   4 v  7   5 v  6  11 v 14  12 v 13
     1 v 13   2 v 12   3 v 11   4 v 10   5 v  9   6 v  8   7 v 14
    

    15. Fifteen Teams

           1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
           -  -  -  -  -  -  -  -  - -- -- -- -- -- --
      1 - 14  3  7 11 15  4  8 12  B  5  9 13  2  6 10
      2 - 13  B  6 10 14  3  7 11 15  4  8 12  1  5  9
      3 - 12  1  5  9 13  2  6 10 14  B  7 11 15  4  8
      4 - 11 15  B  8 12  1  5  9 13  2  6 10 14  3  7
      5 - 10 14  3  7 11 15  4  8 12  1  B  9 13  2  6
      6 -  9 13  2  B 10 14  3  7 11 15  4  8 12  1  5
      7 -  8 12  1  5  9 13  2  6 10 14  3  B 11 15  4
      8 -  7 11 15  4  B 12  1  5  9 13  2  6 10 14  3
      9 -  6 10 14  3  7 11 15  4  8 12  1  5  B 13  2
     10 -  5  9 13  2  6  B 14  3  7 11 15  4  8 12  1
     11 -  4  8 12  1  5  9 13  2  6 10 14  3  7  B 15
     12 -  3  7 11 15  4  8  B  1  5  9 13  2  6 10 14
     13 -  2  6 10 14  3  7 11 15  4  8 12  1  5  9  B
     14 -  1  5  9 13  2  6 10  B  3  7 11 15  4  8 12
     15 -  B  4  8 12  1  5  9 13  2  6 10 14  3  7 11
    
     1 v  3   4 v 15   5 v 14   6 v 13   7 v 12   8 v 11   9 v 10
     1 v  7   2 v  6   3 v  5   8 v 15   9 v 14  10 v 13  11 v 12
     1 v 11   2 v 10   3 v  9   4 v  8   5 v  7  12 v 15  13 v 14
     1 v 15   2 v 14   3 v 13   4 v 12   5 v 11   6 v 10   7 v  9
     1 v  4   2 v  3   5 v 15   6 v 14   7 v 13   8 v 12   9 v 11
     1 v  8   2 v  7   3 v  6   4 v  5   9 v 15  10 v 14  11 v 13
     1 v 12   2 v 11   3 v 10   4 v  9   5 v  8   6 v  7  13 v 15
     2 v 15   3 v 14   4 v 13   5 v 12   6 v 11   7 v 10   8 v  9
     1 v  5   2 v  4   6 v 15   7 v 14   8 v 13   9 v 12  10 v 11
     1 v  9   2 v  8   3 v  7   4 v  6  10 v 15  11 v 14  12 v 13
     1 v 13   2 v 12   3 v 11   4 v 10   5 v  9   6 v  8  14 v 15
     1 v  2   3 v 15   4 v 14   5 v 13   6 v 12   7 v 11   8 v 10
     1 v  6   2 v  5   3 v  4   7 v 15   8 v 14   9 v 13  10 v 12
     1 v 10   2 v  9   3 v  8   4 v  7   5 v  6  11 v 15  12 v 14
     1 v 14   2 v 13   3 v 12   4 v 11   5 v 10   6 v  9   7 v  8
    

    16. Sixteen Teams

    16.1. One Team Advances, Or Other Non-UPA Tournaments

    If you are simply running a 16-team tournament, without having to worry about teams qualifying to the next level, you have all kinds of flexibility. An easy format is simply four pools of four. The top two of each pool advance to a quarterfinal single-elimination, and the bottom two of each pool advance to a "Division II" quarterfinal single-elimination. This way everyone gets lots of games. What follows (this page and the next) is a sample format you can use:
              20-team format                            16-team format
    
        Rnd   Odd      Even                     Rnd     Odd     Even
    
        10   1 v  5   2 v  4                    10:00   1-3     2-4
        12   1 v  3   4 v  5                    12:30   1-4     2-3
         2   2 v  5   3 v  4                     3:00   1-2     3-4
         4   1 v  2   3 v  5
    
        10   1 v  4   2 v  3                    10:00   quarterfinals
        12    quarterfinals                     12:30   semifinals
         2      semifinals                       3:00   finals
         4        finals
    
                                Pool A: Fields 1 & 2
                                Pool B: Fields 3 & 4
                                Pool C: Fields 5 & 6
                                Pool D: Fields 7 & 8
    
    For 16-game schedule: All games to 17 cap 19. Games should be capped at 30 minutes before the next round. If a game runs into the cap, the next game is scheduled for 20 minutes after the preceeding game ends, and is capped at 2:00 past the new scheduled start time.

    (NOTE - this is not to be used for UPA qualifying tournaments; however it is an excellent format for other tournaments where the object is to pick a single winner, while giving all teams as many games as possible).

    SUNDAY'S ELIMINATION ROUNDS
    DIVISION I
    
    Round #1   Rnd 2      Rnd 3                             Rnd 3
    
    A1 ----_                                           LE ----------_
         A _---------_                                            K _---------
    D2 ----          _                                 LF ----------  3rd place
                   E _----------_
    B2 ----_         _          _                      LG ----------_
         B _---------           _                                 M _---------
    C1 ----                     _                      LH ----------  7th place
                              I _---------------
    A2 ----_                    _  (1st place)
         C _---------_          _
    D1 ----          _          _
                   F _----------
    B1 ----_         _
         D _---------
    C2 ----
    
           LA---------_
                    G _----------_
           LB---------           _
                               J _ --------
           LC---------_          _  5th place
                    H _----------
           LD---------
    
    ----------------------------------------------------------------------
    
    DIVISION II
    Round #1   Rnd 2      Rnd 3                             Rnd 3
    
    A3 ----_                                           LE ----------_
         A _---------_                                            K _---------
    D4 ----          _                                 LF ----------  3rd place
                   E _----------_
    B4 ----_         _          _                      LG ----------_
         B _---------           _                                 M _---------
    C3 ----                     _                      LH ----------  7th place
                              I _---------------
    A4 ----_                    _  (1st place)
         C _---------_          _
    D3 ----          _          _
                   F _----------
    B3 ----_         _
         D _---------
    C4 ----
    
           LA---------_
                    G _----------_
           LB---------           _
                               J _ --------
           LC---------_          _  5th place
                    H _----------
           LD---------
    
    All games to 15, except Division I games E, F, and I, which are to 17, and
    I to 19 by mutual agreement.  For the sixteen game schedule, all games to
    17, and Division I finals to 19 by mutual agreement.
    

    16.2. Two Teams Advance

    UPA STANDARD DOUBLE ELIMINATION FORMAT

    This format must be used for Regional tournaments when two teams advance. See the next page. Note that teams that lose the first two rounds play a third game (see games #30 and #31). In this particular example of a schedule (used at the Mid-Atlantic Regionals in 1991), fields 1, 4, 10, and 11 were the best fields. Obviously, you will want to move some games around to match your particular field configuration.

    Additionally, games #30 and #31 can be moved to the fourth round if you need those fields for other games (e.g., Women's or Master's Divisions). Note that in this case, this format only uses six fields in the third round, four fields in the fourth round, and only three and then two fields for all of Sunday.

    UPA STANDARD DOUBLE ELIMINATION FORMAT
    
    1  ----------_
              #1 _-----------_
    16-----------         #9 _
    8 -----------_           _---------_
              #2 _-----------          _
    9 -----------                  #17 _
    4 -----------_                     _------------_
              #3 _-----------_         _            _
    13-----------        #10 _         _            _
    5 -----------_           _---------             _
              #4 _-----------                       _
    12-----------                               #23 _
    2 -----------_                                  _---------------
              #5 _-----------_                      _   1st place
    15-----------        #11 _                      _
    7 -----------_           _---------_            _
              #6 _-----------          _            _
    10-----------                  #18 _            _
    6 -----------_                     _------------
              #7 _-----------_         _
    11-----------        #12 _         _
    3 -----------_           _---------
              #8 _-----------
    14-----------
                        L11 --------_                   L23  --------_
               L1 ---------_    #19 _-------_                        _
                       #13 _--------    #24 _                        _
               L2 ---------                 _-------_            #29 _
                        L12 --------_       _   #26 _                _---
               L3 ---------_    #20 _-------        _-------_        _2nd
                       #14 _--------                _       _        _
               L4 ---------              L17 -------        _        _
                         L9 --------_                  #28  _        _
               L5 ---------_    #21 _-------_               _--------
                       #15 _--------    #25 _               _  L13 ------_
               L6 ---------                 _-------_       _        #30 _
                        L10 --------_       _   #27 _       _  L14 ------
               L7 ---------_    #22 _-------        _-------_  L15 ------_
                       #16 _--------                _                #31 _
               L8 ---------              L18 -------           L16 ------
    
    ----------------------------------------------------------------------
     start cap  Flds 1   3   4   7   8   9  10  11 - All first round     -
      9:00 10:40     2   1   4   3   8   7   5   6 -   games to 15/17.   -
     11:00 12:55     9  13  10  14  12  16  11  15 - All other games to  -
      1:15  3:10    21      22      30  31  19  20 -   17/19, except:    -
      3:30  5:25*   17      25              18  24 - #17 & #18: to 19/21 -
    Sunday:                                      -   #23 is to 21/23.    -
      9:00 11:00                            26  27 - Note: cap starts    -
     10:30  1:15            23                     - after the "next     -
     11:30  1:30                            28     - completed pass."    -
      2:00  4:15                            29     -                     -
    ----------------------------------------------------------------------
     NOTE: In games #26 & #27, opponents will be switched if it avoids a
     repetitive game.  This is the only possible deviation from the schedule.
     *In games #17 and #18, the cap is at 5:45.
    

    16.3. Five Thru Eight Teams Advance

            Fields  1-2     3-4     7-8
    10am            A1      B1      C1              field:          odd  even
    12noon          A2      B2      D1              Round 1:        1-3, 2-4
     2pm            A3      C2      D2              Round 2:        1-4, 2-3
     4pm            B3      C3      D3              Round 3:        1-2, 3-4
     6pm            A,B & C,D crossovers
    
            Above, A1 means Pool A-round 1, etc.
            Below, A2 means Pool A-second place, etc.
    
    Saturday  Sunday . . .              +----------------------------------+
    6pm     11am            3pm         | Sunday schedule for pool winners:|
                                        | (fields 5 & 6)                   |
    A2 ----_                            | 12noon:  A1-D1, B1-C1            |
         A _---------_                  | 2:15 pm: winners play losers     |
    B3 ----          _                  | 4:30 pm: remaining games         |
                   E _----------_       +----------------------------------+
    D2 ----_         _          _
         B _---------           _
    C3 ----                     _                           +--------------------+
                              I _---------------            | winner I: 5th      |
    C2 ----_                    _  (5th place)              | winner N: 6th      |
         C _---------_          _                           | loser  N: 7th      |
    D3 ----_         _          _                           | loser  M: 8th      |
                   F _----------                            | winner P: 9th      |
    B2 ----_         _                                      | loser  P: 10th     |
         D _---------                                       | loser G,H: 11-12th |
    A3 ----                                                 | winner S: 13th     |
              11am           1pm     3pm             5pm    | loser S: 14th      |
             LA---------_                                   +--------------------+
                      G _----------_                        +-------------------+
             LB---------         J _---------_              | SUNDAY'S FIELDS:  |
                                   _         _              | Field: 1  2  3  4 |
                      LF ----------          _              | 11am   E  F  G  H |
             LC---------_                  M _--------_     | 1pm    R  Q  J  K |
                      H _----------_         _        _     | 3pm    S  P  M  I |
             LD---------         K _         _        _     | 5pm             N |
                                   _---------         _     +-------------------+
                      LE ----------                 N _---------------
                1pm    3pm               LI ----------
          A4 --------_                3pm
                   Q _-----_       LJ ---------_
          D4 --------    S _                   _
          B4 --------_     _-----           P  _-------
                   R _-----        LK ---------
          C4 --------
    
    Notes on specific games:  Games J & K: Opponents will be switched if it
    avoids repetitive games.  This is the only possible deviation from the
    schedule.  Game N does not have to take place, if neither team desires to
    play.  Losers of games G and H can play each other for 11th and 12th place.
    Losers of games Q and R can play each other for 15th and 16th place.
    

    Table 16.1. Sixteen team round-robin grid

           1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
           -  -  -  -  -  -  -  -  - -- -- -- -- -- --
      1 - 15  2  5  8 11 14 16  4  7 10 13  3  6  9 12
      2 - 14  1  4  7 10 13  3  6  9 12 15 16  5  8 11
      3 - 13 16  6  9 12 15  2  5  8 11 14  1  4  7 10
      4 - 12 15  2  5  8 11 14  1 16  7 10 13  3  6  9
      5 - 11 14  1  4  7 10 13  3  6  9 12 15  2 16  8
      6 - 10 13  3 16  9 12 15  2  5  8 11 14  1  4  7
      7 -  9 12 15  2  5  8 11 14  1  4 16 10 13  3  6
      8 - 16 11 14  1  4  7 10 13  3  6  9 12 15  2  5
      9 -  7 10 13  3  6 16 12 15  2  5  8 11 14  1  4
     10 -  6  9 12 15  2  5  8 11 14  1  4  7 16 13  3
     11 -  5  8 16 14  1  4  7 10 13  3  6  9 12 15  2
     12 -  4  7 10 13  3  6  9 16 15  2  5  8 11 14  1
     13 -  3  6  9 12 15  2  5  8 11 14  1  4  7 10 16
     14 -  2  5  8 11 16  1  4  7 10 13  3  6  9 12 15
     15 -  1  4  7 10 13  3  6  9 12 16  2  5  8 11 14
     16 -  8  3 11  6 14  9  1 12  4 15  7  2 10  5 13
    
     1- 2   3-16   4-15   5-14   6-13   7-12   8-11   9-10
     1- 5   2- 4   3- 6   7-15   8-14   9-13  10-12  11-16
     1- 8   2- 7   3- 9   4- 5   6-16  10-15  11-14  12-13
     1-11   2-10   3-12   4- 8   5- 7   6- 9  13-15  14-16
     1-14   2-13   3-15   4-11   5-10   6-12   7- 8   9-16
     1-16   2- 3   4-14   5-13   6-15   7-11   8-10   9-12
     1- 4   2- 6   3- 5   7-14   8-13   9-15  10-11  12-16
     1- 7   2- 9   3- 8   4-16   5- 6  10-14  11-13  12-15
     1-10   2-12   3-11   4- 7   5- 9   6- 8  13-14  15-16
     1-13   2-15   3-14   4-10   5-12   6-11   7-16   8- 9
     1- 3   2-16   4-13   5-15   6-14   7-10   8-12   9-11
     1- 6   2- 5   3- 4   7-13   8-15   9-14  10-16  11-12
     1- 9   2- 8   3- 7   4- 6   5-16  10-13  11-15  12-14
     1-12   2-11   3-10   4- 9   5- 8   6- 7  13-16  14-15
     1-15   2-14   3-13   4-12   5-11   6-10   7- 9   8-16
    

    17. Seventeen Teams

    Three pools of four, one pool of five. The top two in each pool play an eight-team double elimination the second day. Games are to 15; teams in the pool of five play games to 13.

    This is not unreasonably unfair to the teams in the pool of five. Presumably, the 17th seed is in that pool which ought to be easy victories for any team that has a chance at finishing in the top two of the pool. There could be a problem, however, if not much is known about the teams, and the seeding is very inaccurate.

    A possible nightmare occurs if there is a three-way tie for first, thus relegating a team with one loss to finish out of the top eight. This is a serious problem for which I haven't come up with a satisfactory solution (except for some sort of cross-over between 2d and 3d place teams the next day).

    The schedules for five and four-game round-robins appear in Tables 5.1.1 and 4.1 respectively. You could simply give each pool two fields, and let them go at it. This would take up eight fields. A better schedule might be one below:

            Fields:  1      2      3      4      5      6      7
            9:00   D1-D3  D2-D4  C1-C4  A1-A3  A2-A4  B1-B3  B4-B5
            10:45  D1-D2  C1-C3  C2-C4  A1-A2         B1-B5  B2-B4
            12:30  D3-D4  C1-C2  C3-C4  A3-A4         B2-B5  B3-B4
            2:15   D1-D4  D2-D3  C2-C3  A1-A4  A2-A3  B1-B4  B2-B3
            4:45                                      B1-B2  B3-B5
    
    Note that the round-robin for two of the pools of four (pools C and D in this example) are played over four rounds on three fields. They could be played on three rounds on four fields, but there are two disadvantages of that method. First, it takes up an extra field. Second, the teams in the pool of five (pool A) would be done after the third round while pools A and B still had two more rounds to go. The schedule above uses less fields and keeps more players around. The schedule for Pool B tries to mimic pool D, for the same reasons, but it's kind of awkward.

    If you are simply running an 18-team tournament, without having to worry about teams qualifying to the next level, you have all kinds of flexibility. An easy format for the second day for the top two of each pool advance to a quarterfinal single-elimination, and the next two (third and fourth place teams) of each pool advance to a "Division II" quarterfinal single-elimination. (This 16-team Division I & II elimination is shown in Section 16.1.) Schedule the two remaining fifth place teams for a game on the second day, also.

           1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17
           -  -  -  -  -  -  -  -  - -- -- -- -- -- -- -- --
      1 - 16  2  5  8 11 14 17  3  6  9 12 15  B  4  7 10 13
      2 - 15  1  4  7 10 13 16  B  5  8 11 14 17  3  6  9 12
      3 - 14 17  B  6  9 12 15  1  4  7 10 13 16  2  5  8 11
      4 - 13 16  2  5  8 11 14 17  3  6  9 12 15  1  B  7 10
      5 - 12 15  1  4  7 10 13 16  2  B  8 11 14 17  3  6  9
      6 - 11 14 17  3  B  9 12 15  1  4  7 10 13 16  2  5  8
      7 - 10 13 16  2  5  8 11 14 17  3  6  9 12 15  1  4  B
      8 -  9 12 15  1  4  7 10 13 16  2  5  B 11 14 17  3  6
      9 -  8 11 14 17  3  6  B 12 15  1  4  7 10 13 16  2  5
     10 -  7  B 13 16  2  5  8 11 14 17  3  6  9 12 15  1  4
     11 -  6  9 12 15  1  4  7 10 13 16  2  5  8  B 14 17  3
     12 -  5  8 11 14 17  3  6  9  B 15  1  4  7 10 13 16  2
     13 -  4  7 10  B 16  2  5  8 11 14 17  3  6  9 12 15  1
     14 -  3  6  9 12 15  1  4  7 10 13 16  2  5  8 11  B 17
     15 -  2  5  8 11 14 17  3  6  9 12  B  1  4  7 10 13 16
     16 -  1  4  7 10 13  B  2  5  8 11 14 17  3  6  9 12 15
     17 -  B  3  6  9 12 15  1  4  7 10 13 16  2  5  8 11 14
    
     1- 2   3-17   4-16   5-15   6-14   7-13   8-12   9-11
     1- 5   2- 4   6-17   7-16   8-15   9-14  10-13  11-12
     1- 8   2- 7   3- 6   4- 5   9-17  10-16  11-15  12-14
     1-11   2-10   3- 9   4- 8   5- 7  12-17  13-16  14-15
     1-14   2-13   3-12   4-11   5-10   6- 9   7- 8  15-17
     1-17   2-16   3-15   4-14   5-13   6-12   7-11   8-10
     1- 3   4-17   5-16   6-15   7-14   8-13   9-12  10-11
     1- 6   2- 5   3- 4   7-17   8-16   9-15  10-14  11-13
     1- 9   2- 8   3- 7   4- 6  10-17  11-16  12-15  13-14
     1-12   2-11   3-10   4- 9   5- 8   6- 7  13-17  14-16
     1-15   2-14   3-13   4-12   5-11   6-10   7- 9  16-17
     2-17   3-16   4-15   5-14   6-13   7-12   8-11   9-10
     1- 4   2- 3   5-17   6-16   7-15   8-14   9-13  10-12
     1- 7   2- 6   3- 5   8-17   9-16  10-15  11-14  12-13
     1-10   2- 9   3- 8   4- 7   5- 6  11-17  12-16  13-15
     1-13   2-12   3-11   4-10   5- 9   6- 8  14-17  15-16
     1-16   2-15   3-14   4-13   5-12   6-11   7-10   8- 9
    

    18. Eighteen Teams

    Two pools of five, two pools of four. The top two in each pool play an eight-team double elimination the second day. Games are to 15; teams in the pools of five play games to 13.

    This is not unreasonably unfair to the teams in the pools of five. Presumably, the 17th and 18th seeds are in that pool which ought to be easy victories for any team that has a chance at finishing in the top two of the pool. There could be a problem, however, if not much is known about the teams, and the seeding is very inaccurate.

    A possible nightmare occurs if there is a three-way tie for first, thus relegating a team with one loss to finish out of the top eight. This is a serious problem. This format was used at the 1989 South Fall Sectional in the Mid-Atlantic, and we simply crossed our fingers and hoped for the best. We were constrained by having only seven fields available, at three different locations. And we couldn't think of anything else that would fit. The three-way tie did not happen for us.

    The schedules for five and four-game round-robins appear in Tables 5.1.1 and 4.1 respectively. You could simply give each pool two fields, and let them go at it. This would take up eight fields. A better schedule might be one below:

            Fields:  1      2      3      4      5      6      7
            9:00   D1-D3  D2-D4  C1-C4  A1-A3  A4-A5  B1-B3  B4-B5
            10:45  D1-D2  C1-C3  C2-C4  A1-A5  A2-A4  B1-B5  B2-B4
            12:30  D3-D4  C1-C2  C3-C4  A2-A5  A3-A4  B2-B5  B3-B4
            2:15   D1-D4  D2-D3  C2-C3  A1-A4  A2-A3  B1-B4  B2-B3
            4:45                        A1-A2  A3-A5  B1-B2  B3-B5
    
    Note that the round-robin for the two pools of four (pools C and D in this example) are played over four rounds on three fields. They could be played on three rounds on four fields, but there are two disadvantages of that method. First, it takes up an extra field. Second, half of the teams would be done after the third round while pools A and B still had two more rounds to go. The schedule above uses less fields and keeps more players around.

    If you are simply running an 18-team tournament, without having to worry about teams qualifying to the next level, you have all kinds of flexibility. An easy format for the second day for the top two of each pool advance to a quarterfinal single-elimination, and the next two (third and fourth place teams) of each pool advance to a "Division II" quarterfinal single-elimination. (This 16-team Division I & II elimination is shown in Section 16.1.) Schedule the two remaining fifth place teams for a game on the second day, also.

    Table 18.1. Eighteen team round-robin grid

           1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17
           -  -  -  -  -  -  -  -  - -- -- -- -- -- -- -- --
      1 - 17  4  9 14 18  6 11 16  3  8 13  5 10 15  2  7 12
      2 - 16  3  8 13  5 10 15 18  7 12 17  4  9 14  1  6 11
      3 - 15  2  7 12 17  4  9 14  1  6 11 16 18  8 13  5 10
      4 - 14  1  6 11 16  3  8 13  5 10 15  2  7 12 17 18  9
      5 - 13 18 10 15  2  7 12 17  4  9 14  1  6 11 16  3  8
      6 - 12 17  4  9 14  1 18 11 16  3  8 13  5 10 15  2  7
      7 - 11 16  3  8 13  5 10 15  2 18 12 17  4  9 14  1  6
      8 - 10 15  2  7 12 17  4  9 14  1  6 11 16  3 18 13  5
      9 - 18 14  1  6 11 16  3  8 13  5 10 15  2  7 12 17  4
     10 -  8 13  5 18 15  2  7 12 17  4  9 14  1  6 11 16  3
     11 -  7 12 17  4  9 14  1  6 18 16  3  8 13  5 10 15  2
     12 -  6 11 16  3  8 13  5 10 15  2  7 18 17  4  9 14  1
     13 -  5 10 15  2  7 12 17  4  9 14  1  6 11 16  3  8 18
     14 -  4  9 18  1  6 11 16  3  8 13  5 10 15  2  7 12 17
     15 -  3  8 13  5 10 18  2  7 12 17  4  9 14  1  6 11 16
     16 -  2  7 12 17  4  9 14  1  6 11 18  3  8 13  5 10 15
     17 -  1  6 11 16  3  8 13  5 10 15  2  7 12 18  4  9 14
     18 -  9  5 14 10  1 15  6  2 11  7 16 12  3 17  8  4 13
    
     1- 4   2- 3   5-18   6-17   7-16   8-15   9-14  10-13  11-12
     1- 9   2- 8   3- 7   4- 6   5-10  11-17  12-16  13-15  14-18
     1-14   2-13   3-12   4-11   5-15   6- 9   7- 8  10-18  16-17
     1-18   2- 5   3-17   4-16   6-14   7-13   8-12   9-11  10-15
     1- 6   2-10   3- 4   5- 7   8-17   9-16  11-14  12-13  15-18
     1-11   2-15   3- 9   4- 8   5-12   6-18   7-10  13-17  14-16
     1-16   2-18   3-14   4-13   5-17   6-11   7-15   8- 9  10-12
     1- 3   2- 7   4- 5   6-16   8-14   9-13  10-17  11-18  12-15
     1- 8   2-12   3- 6   4-10   5- 9   7-18  11-16  13-14  15-17
     1-13   2-17   3-11   4-15   5-14   6- 8   7-12   9-10  16-18
     1- 5   2- 4   3-16   6-13   7-17   8-11   9-15  10-14  12-18
     1-10   2- 9   3-18   4- 7   5- 6   8-16  11-13  12-17  14-15
     1-15   2-14   3- 8   4-12   5-11   6-10   7- 9  13-16  17-18
     1- 2   3-13   4-17   5-16   6-15   7-14   8-18   9-12  10-11
     1- 7   2- 6   3- 5   4-18   8-13   9-17  10-16  11-15  12-14
     1-12   2-11   3-10   4- 9   5- 8   6- 7  13-18  14-17  15-16
     1-17   2-16   3-15   4-14   5-13   6-12   7-11   8-10   9-18
    

    19. Nineteen Teams

           1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19
           -  -  -  -  -  -  -  -  - -- -- -- -- -- -- -- -- -- --
      1 - 18  2  5  8 11 14 17  B  4  7 10 13 16 19  3  6  9 12 15
      2 - 17  1  4  7 10 13 16 19  3  6  9 12 15 18  B  5  8 11 14
      3 - 16 19  B  6  9 12 15 18  2  5  8 11 14 17  1  4  7 10 13
      4 - 15 18  2  5  8 11 14 17  1  B  7 10 13 16 19  3  6  9 12
      5 - 14 17  1  4  7 10 13 16 19  3  6  9 12 15 18  2  B  8 11
      6 - 13 16 19  3  B  9 12 15 18  2  5  8 11 14 17  1  4  7 10
      7 - 12 15 18  2  5  8 11 14 17  1  4  B 10 13 16 19  3  6  9
      8 - 11 14 17  1  4  7 10 13 16 19  3  6  9 12 15 18  2  5  B
      9 - 10 13 16 19  3  6  B 12 15 18  2  5  8 11 14 17  1  4  7
     10 -  9 12 15 18  2  5  8 11 14 17  1  4  7  B 13 16 19  3  6
     11 -  8  B 14 17  1  4  7 10 13 16 19  3  6  9 12 15 18  2  5
     12 -  7 10 13 16 19  3  6  9  B 15 18  2  5  8 11 14 17  1  4
     13 -  6  9 12 15 18  2  5  8 11 14 17  1  4  7 10  B 16 19  3
     14 -  5  8 11  B 17  1  4  7 10 13 16 19  3  6  9 12 15 18  2
     15 -  4  7 10 13 16 19  3  6  9 12  B 18  2  5  8 11 14 17  1
     16 -  3  6  9 12 15 18  2  5  8 11 14 17  1  4  7 10 13  B 19
     17 -  2  5  8 11 14  B  1  4  7 10 13 16 19  3  6  9 12 15 18
     18 -  1  4  7 10 13 16 19  3  6  9 12 15  B  2  5  8 11 14 17
     19 -  B  3  6  9 12 15 18  2  5  8 11 14 17  1  4  7 10 13 16
    
     1- 2   3-19   4-18   5-17   6-16   7-15   8-14   9-13  10-12
     1- 5   2- 4   6-19   7-18   8-17   9-16  10-15  11-14  12-13
     1- 8   2- 7   3- 6   4- 5   9-19  10-18  11-17  12-16  13-15
     1-11   2-10   3- 9   4- 8   5- 7  12-19  13-18  14-17  15-16
     1-14   2-13   3-12   4-11   5-10   6- 9   7- 8  15-19  16-18
     1-17   2-16   3-15   4-14   5-13   6-12   7-11   8-10  18-19
     2-19   3-18   4-17   5-16   6-15   7-14   8-13   9-12  10-11
     1- 4   2- 3   5-19   6-18   7-17   8-16   9-15  10-14  11-13
     1- 7   2- 6   3- 5   8-19   9-18  10-17  11-16  12-15  13-14
     1-10   2- 9   3- 8   4- 7   5- 6  11-19  12-18  13-17  14-16
     1-13   2-12   3-11   4-10   5- 9   6- 8  14-19  15-18  16-17
     1-16   2-15   3-14   4-13   5-12   6-11   7-10   8- 9  17-19
     1-19   2-18   3-17   4-16   5-15   6-14   7-13   8-12   9-11
     1- 3   4-19   5-18   6-17   7-16   8-15   9-14  10-13  11-12
     1- 6   2- 5   3- 4   7-19   8-18   9-17  10-16  11-15  12-14
     1- 9   2- 8   3- 7   4- 6  10-19  11-18  12-17  13-16  14-15
     1-12   2-11   3-10   4- 9   5- 8   6- 7  13-19  14-18  15-17
     1-15   2-14   3-13   4-12   5-11   6-10   7- 9  16-19  17-18
     1-18   2-17   3-16   4-15   5-14   6-13   7-12   8-11   9-10
    

    20. Twenty Teams

    If you are simply running a 20-team tournament, without having to worry about teams qualifying to the next level, you have all kinds of flexibility. An easy format is simply four pools of five. The top two of each pool advance to a quarterfinal single-elimination, and the bottom two of each pool advance to a "Division II" quarterfinal single-elimination. (This 16-team Division I & II elimination is shown in Section 16.1.) This way everyone gets lots of games. What follows is a sample format you can use:
                            20-team format
    
                    Rnd   Odd      Even
    
                    10   1 v  5   2 v  4
                    12   1 v  3   4 v  5
                     2   2 v  5   3 v  4
                     4   1 v  2   3 v  5
    
                    10   1 v  4   2 v  3
                    12    quarterfinals
                     2      semifinals
                     4        finals
    
                    Pool A: Fields 1 & 2
                    Pool B: Fields 3 & 4
                    Pool C: Fields 5 & 6
                    Pool D: Fields 7 & 8
    
    For 20-game schedule: All games to 15/cap 17. Games should be capped at 20 minutes before the next round. If a game runs into the cap, the next game is scheduled for 20 minutes after the preceeding game ends, and is capped at 1:40 past the new scheduled start time.

    For the second day,

    Table 20.1. Twenty team round-robin grid

           1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19
           -  -  -  -  -  -  -  -  - -- -- -- -- -- -- -- -- -- --
      1 - 19  2  5  8 11 14 17  3  6  9 12 15 18 20  4  7 10 13 16
      2 - 18  1  4  7 10 13 16 19 20  5  8 11 14 17  3  6  9 12 15
      3 - 17 20  6  9 12 15 18  1  4  7 10 13 16 19  2  5  8 11 14
      4 - 16 19  2  5  8 11 14 17  3  6  9 12 15 18  1 20  7 10 13
      5 - 15 18  1  4  7 10 13 16 19  2 20  8 11 14 17  3  6  9 12
      6 - 14 17  3 20  9 12 15 18  1  4  7 10 13 16 19  2  5  8 11
      7 - 13 16 19  2  5  8 11 14 17  3  6  9 12 15 18  1  4 20 10
      8 - 12 15 18  1  4  7 10 13 16 19  2  5 20 11 14 17  3  6  9
      9 - 11 14 17  3  6 20 12 15 18  1  4  7 10 13 16 19  2  5  8
     10 - 20 13 16 19  2  5  8 11 14 17  3  6  9 12 15 18  1  4  7
     11 -  9 12 15 18  1  4  7 10 13 16 19  2  5  8 20 14 17  3  6
     12 -  8 11 14 17  3  6  9 20 15 18  1  4  7 10 13 16 19  2  5
     13 -  7 10 20 16 19  2  5  8 11 14 17  3  6  9 12 15 18  1  4
     14 -  6  9 12 15 18  1  4  7 10 13 16 19  2  5  8 11 20 17  3
     15 -  5  8 11 14 17  3  6  9 12 20 18  1  4  7 10 13 16 19  2
     16 -  4  7 10 13 20 19  2  5  8 11 14 17  3  6  9 12 15 18  1
     17 -  3  6  9 12 15 18  1  4  7 10 13 16 19  2  5  8 11 14 20
     18 -  2  5  8 11 14 17  3  6  9 12 15 20  1  4  7 10 13 16 19
     19 -  1  4  7 10 13 16 20  2  5  8 11 14 17  3  6  9 12 15 18
     20 - 10  3 13  6 16  9 19 12  2 15  5 18  8  1 11  4 14  7 17
    
     1- 2   3-20   4-19   5-18   6-17   7-16   8-15   9-14  10-13  11-12
     1- 5   2- 4   3- 6   7-19   8-18   9-17  10-16  11-15  12-14  13-20
     1- 8   2- 7   3- 9   4- 5   6-20  10-19  11-18  12-17  13-16  14-15
     1-11   2-10   3-12   4- 8   5- 7   6- 9  13-19  14-18  15-17  16-20
     1-14   2-13   3-15   4-11   5-10   6-12   7- 8   9-20  16-19  17-18
     1-17   2-16   3-18   4-14   5-13   6-15   7-11   8-10   9-12  19-20
     1- 3   2-19   4-17   5-16   6-18   7-14   8-13   9-15  10-11  12-20
     1- 6   2-20   3- 4   5-19   7-17   8-16   9-18  10-14  11-13  12-15
     1- 9   2- 5   3- 7   4- 6   8-19  10-17  11-16  12-18  13-14  15-20
     1-12   2- 8   3-10   4- 9   5-20   6- 7  11-19  13-17  14-16  15-18
     1-15   2-11   3-13   4-12   5- 8   6-10   7- 9  14-19  16-17  18-20
     1-18   2-14   3-16   4-15   5-11   6-13   7-12   8-20   9-10  17-19
     1-20   2-17   3-19   4-18   5-14   6-16   7-15   8-11   9-13  10-12
     1- 4   2- 3   5-17   6-19   7-18   8-14   9-16  10-15  11-20  12-13
     1- 7   2- 6   3- 5   4-20   8-17   9-19  10-18  11-14  12-16  13-15
     1-10   2- 9   3- 8   4- 7   5- 6  11-17  12-19  13-18  14-20  15-16
     1-13   2-12   3-11   4-10   5- 9   6- 8   7-20  14-17  15-19  16-18
     1-16   2-15   3-14   4-13   5-12   6-11   7-10   8- 9  17-20  18-19
     1-19   2-18   3-17   4-16   5-15   6-14   7-13   8-12   9-11  10-20