An exercise in Small Data. These programs estimate players' table-football performance ratings from the results of first-to-N-goals games. (Of course, these programs don't have to be used for foosball. There's no reason they wouldn't work for any other two-sided, no-draw games with discrete scoring.) Complicating the statistical problem is the heterogeneity of the games: some are singles games, others are doubles games; some games are first-to-4 victories, others are first-to-6, and still others are first-to-3.
The heart of the program is a statistical model implemented with Stan, and the data-processing pipeline as a whole goes like this.
fooscore.stan defines the statistical model as a Stan model, which Stan compiles into the sampler program fooscore. Running fooscore fits the model with a Markov-chain Monte Carlo method, generating estimates of the model's parameters' values (i.e. the performance ratings one actually wants).
The model assumes players' ratings come from some statistical distribution with a mean of zero and standard deviation σ. It puts a lognormal prior on σ, assuming it'll be of order 1. The default distribution is a boring normal distribution, but I've played with a logistic distribution (which makes no obvious difference) and a t distribution with 3 degrees of freedom (which allows for a more fat-tailed rating distribution, making a bit of difference at the extremes).
To turn rating differences into expected scores, the model assumes a player or team's chance p of scoring the next goal/point is a logistic function of their rating advantage over the opposition. (If both sides have equal ratings that chance is of course 50%.) To connect this fact to the actual outcome of a game, the model assumes the winner's final score was the number of goals needed to win (e.g. a 7-3 game must have been a first-to-7 game), then treats the loser's score as a negatively binomially distributed variable, where the distribution's parameters are the winner's score and p. (Wikipedia expresses the NB distribution's parameters differently to Stan, incidentally, hence the (1 - nb_p) / nb_p circumlocution in the Stan model.)
The effective rating of a team is simply taken to be the sum of its players' ratings. That just seemed like the intuitive way to do it, but I have no rigorous justification for it!
Someone else logs the game results in spreadsheets. I just pull out the results into the somewhat cleaner text file dump.txt for ease of processing, and the table of players' names into names.dat. (The names here are fake, by the way.)
extract-from-dump.py reads dump.txt and turns it into data-from-dump.R, a score data file in an R-like format the Stan-compiled sampler can use.
Finally the actual fooscore sampler runs, reading the results of games from data-from-dump.R and recording Bayesian posterior distributions for the players' ratings in fooscore-out.csv. This typically needs a minute or so.
The R script fooscore.R reads fooscore-out.csv to make a dot plot of players' ratings, with standard error bars. See fooscore.pdf.