Bayesian inference meets racket sports: we model player skill as a dynamic normal distribution, continuously updated from match outcomes. Z-scores, star ratings, and vanishingly rare 10-star outliers — the math is worth a look.
We use Bayesian statistics and advanced mathematical models to quickly estimate play levels based on match results. Our proprietary algorithms operate on normal distributions to update a player's estimated level mean and variance. We transform all player levels into a standard normal distribution with mean 0. From this, we regularly compute the overall standard deviation for each sport, which allows us to determine each player's Z-factor. The Z-factor determines a player's star rating: A Z-factor of 0 corresponds to a 4-star rating, while a Z-factor of 0.75 corresponds to a 5-star rating, and so on. As any aspiring statistician will quickly notice, a 10-star player (Z = 4.5) is extremely rare. If you ever meet one, take a picture — they're rarer than players who don't blame a bad shot on their gear!