How to update what you believe about a team or a player as the evidence comes in, and where the starting beliefs come from.
8 parts Beginner to Advanced
New to this? These parts are Beginner level: 1, 3 and 8.
Start at part 1A new signing scores his first four penalties. Bayesian thinking combines what you believed before with what you've just seen, and shows why a perfect start should nudge your opinion, not replace it.
Beginner Part 1
Early-season league tables mislead. Over 550 Scottish team-seasons, only a third of a team's early form carried on. Bayesian thinking predicted exactly how much, using a prior measured from the data.
Intermediate Part 2
A half-time lead is evidence, and what it means depends on who's leading. Bayes' theorem combines the pre-match odds with the half-time score, and 5,419 SPFL matches show it working.
Beginner Part 3
Early-season goal averages swing wildly. Starting from last season and updating after every match, the Bayesian way, predicts the rest of the season about twice as well after five games. 25 SPFL seasons show how.
Intermediate Part 4
Take what we believe about every team, play the rest of the season thousands of times, and count who wins. Tested on 25 SPFL title races, the simulation's favourite won 20; the side top at halfway won 17.
Intermediate Part 5
Every club's home record says something about its ground, and a lot about luck. Partial pooling lets the data decide how far to trust each club's own figure. Over 26 Scottish Premiership seasons the clubs differ far less than the raw table suggests, and Hearts still come out on top.
Advanced Part 6
Seven times since 2001/02 a Scottish Premiership side has won 7–0. A Bayesian model says each was a long shot, but also that a league should see more of them than it does. Checking the model against every score shows where it goes wrong, and how far a simple fix gets.
Advanced Part 7
Rangers sacked Russell Martin after one win in seven league games; Danny Röhl won four of his first six. A Bayesian comparison puts the chance he's genuinely better at about nine in ten, not the near-certainty it felt like, and shows why more games couldn't settle it.
Beginner Part 8