____ ____ / _/___ / __/__ _________ _ / // __ \/ /_/ _ \/ ___/ __ `/ _/ // / / / __/ __/ / / /_/ / /___/_/ /_/_/ \___/_/ \__,_/Infera is a tool for figuring out how good teams are from the results of a limited number of games between those teams.

It is intended to be useful

- for ranking teams in single tournaments and
- for integration of results from multiple tournaments.

Infera is also able to offer predictions of outcomes of games.

Infera is expected to work best if the scores of all games are supplied, rather than just who won every game. Scores are better because the program will give more accurate rankings if close games are distinguished from games with a big goal difference. Also if one team easily beats several teams, then the margin by which it wins in each case gives useful information about how good those lesser teams are *relative to each other*.

Infera only takes into account information from actual game results and completely ignores supposed `final placings' generated by standard tournament formats. Infera is very different from any sports ranking systems I have come across.

**
Teams playing in events for which Infera is being used as
originally intended should be informed
that every point in every game counts towards their inferred ranking.
**
The user may, however, use Infera in a variety of other ways.
You can designate certain games alone as being games that will be
included in the analysis. You can alter the "weight" attached to
each game. You can feed Infera just the win/lose outcomes if you want.

I call this number the `potential' of the team.

Infera thus may be harsh on teams that are inconsistent, sometimes losing games badly that they could easily win `on a good day'. If this is viewed as a problem then the easiest hack is to modify the data that is fed to Infera in some way; for example, the user may choose to omit each team's worst result and compute rankings based on the results of the other games. I'd say, "tough, if a team can't perform consistently then they don't deserve to be ranked as high as their best performance".

Obviously, if a tournament director knows who is playing on a given team and has prior knowledge of their skills, they will be able to give better predictions of teams' performance. The Infera program effectively assumes that the team's roster is unchanging.

Infera is built on the assumption that the probability distribution of the score depends only on the *difference* in potential between the two teams. I might add more details here if people wanted to know.

If, on using Infera for a time, it becomes evident that the assumed relationship between potentials and scores is too simple, then I could code up more advanced inference engines.

Let's consider a game of first-to-fifteen.

If team A's potential is 0.1 greater than team B's, then the probability that A will win is 0.61, with the most probable score being 15:12 (A:B). Thus teams with a difference of 0.1 in potential are expected to have close games with the better team winning 3 games out of 5. Potential differences smaller than 0.1 correspond to teams that are very hard to distinguish in just one game.

If team A's potential is 0.3 greater than team B's, then the probability that A will win is 0.79, with the most probable score being 15:10.

If team A's potential is 0.5 greater, then the probability that A will win is 0.91, with the most probable score being 15:8.

If team A's potential is 1.0 greater, then the probability that A will win is 0.996, with the most probable score being 15:5.

If the potential difference is 2.0, then the most probable score is 15:1, and the probability that team B will score more than 4 points is 0.07.

Another example: maybe you'd like the final results in a tournament to depend only weakly on the first day's results (when teams are finding their feet) and more strongly on the last day's results (which are the crucial games in many standard tournaments). If so, you can give lesser weight to the early games.

**
The author makes
no representations about the suitability of this software
for any purpose. It is provided `as is' without express
or implied warranty and without technical support.
**

David MacKay <mackay@mrao.cam.ac.uk>Strange Blue (Cambridge Ultimate) home page Last modified: Tue Feb 3 22:43:54 1998