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I'm trying to adapt something like this association football prediction approach to 2v2 foosball games at our office.

For football, they basically have an offense score and a defense score for each time. The game is a fixed length of time. They then use Poisson regression based on the scoring history to try to find out each team's offensive/defensive values.

The problem is different for foosball, and I think Poisson may not be the correct distribution to use. For the following reasons:

  1. We play first to 10 points, not for a fixed length of time
  2. Players switch positions after their team scores 5 points

Can anyone recommend a better distribution or a way of approaching the problem? We don't need a 100% optimal solution, but we are aiming for something that is reasonably ok.

Bonus points for ideas on how to split the offense/defense ratings among the players.

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    $\begingroup$ Here is a very similar recent question. $\endgroup$
    – cardinal
    Oct 19, 2011 at 8:57
  • $\begingroup$ When thinking about the other question, I sketched out a scheme for a model of playing to a set number of points, but I never posted it to that question. I ended up with a curved exponential family, which had some similarities to a generalized linear model. If you would like to see that, I can try to dig out those notes and post it. $\endgroup$
    – cardinal
    Oct 19, 2011 at 9:00
  • $\begingroup$ On trying to find a distribution - if all games are complete, obviously the winning score is 10; the distribution is on the losing score (and you'd also need to model the probability of winning of course). For that it seems to me a quasi-binomial GLM would be an obvious first choice, though perhaps something like a beta-binomial model might do if you have the resources to pursue it. $\endgroup$
    – Glen_b
    May 29, 2013 at 22:01
  • $\begingroup$ What do you mean by "switch positions"? $\endgroup$ Jul 29, 2013 at 10:14

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Here is an explanation of how Elo rankings are used in an actual foosball league. It goes into quite a lot of depth.

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    $\begingroup$ The Elo rating system is named after Arpad Elo, and therefore isn't capitalized all the way through. $\endgroup$ Mar 21, 2012 at 1:19

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