# Looking for correct distribution for modelling foosball scoring

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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Here is a very similar recent question. –  cardinal Oct 19 '11 at 8:57
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. –  cardinal Oct 19 '11 at 9:00
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. –  Glen_b May 29 at 22:01
What do you mean by "switch positions"? –  Peter Ellis Jul 29 at 10:14