A statistical philosophy for sports modeling that treats observed game data as fixed truth and probability distributions as adaptive — updating beliefs as new evidence arrives. The alternative (frequentist) treats distributions as fixed and data as random, which is the wrong framing for the small-sample environment of sports.
You choose Bayesian approaches because sports data is inherently small-N: an EPL team plays 38 games, a Champions League team may play ~10. Every single observation must update the model — including "outlier" results like a 6-0 scoreline, which a frequentist would discard as an aberration but which actually happened and must inform team strength estimates. You use Monte Carlo simulation to build probability distributions as outputs (not point estimates). For player props, you use mixed distributions — simulate one distribution for efficiency (e.g., points per minute) combined with a separate distribution for playing time (e.g., minutes played) to produce a full probability distribution for the outcome.
Standard statistics (frequentist) assumes large samples. Sports gives you 38 EPL games per team, ~10 CL games, and sometimes far fewer. In small-N environments, frequentist models produce unstable estimates and throw away real data as "outliers." Bayesian models treat every observation as fixed truth that updates the distribution — exactly the right behavior when you have almost no data.
A player's point total depends on two independent sources of variance: efficiency (points per minute) and playing time (minutes). Point-estimate models collapse this into one number and miss the variance from playing time fluctuation. A player averaging 1.2 pts/min who plays anywhere from 15-35 minutes has enormous outcome variance that a single "projected 28 points" can't capture.
Most bettors assume a full season of data overrides priors. In college football (12 games), even after a full season "we're still regressing a large amount to our priors." Without strong priors, a model would pick the Minnesota Vikings to win the Super Bowl based on a negative point differential.
When your model shows a huge edge (e.g., 29% on a single game), naive model-market averaging is dangerous because the situations where your model disagrees most with the market are precisely the situations where YOUR model is most likely wrong. A horse your model prices at 3/1 going off at 25/1 is a debugging signal, not confirmation of a huge opportunity.