Statistics Through Football
Probability distributions from the ground up, from penalties and goals to streaks and transfer fees, one football question at a time.
12 parts Beginner to Intermediate
Start at part 1Learn
Statistics, maths and machine learning, each one introduced through a football question.
Each series starts at part 1, and every piece builds on the one before. New to the notation? The glossary explains every symbol.
Linear Algebra Through Football
Vectors and matrices, and the maths behind player similarity, runs and passes, formations, ratings and PCA.
10 parts Beginner to Advanced
Start at part 1Bayesian Thinking Through Football
How to update what you believe about a team or a player as the evidence comes in, and where the starting beliefs come from.
6 parts Beginner to Advanced
Start at part 1Machine Learning Through Football
How models learn from past matches to predict the next one: features and targets, training and testing, and the traps in between.
14 parts Beginner to Advanced
Start at part 1Calculus Through Football
Rates of change, from how quickly a winger gets up to speed to how models learn: derivatives and integrals without the fear.
6 parts Beginner to Intermediate
Start at part 1Game Theory Through Football
Football as a contest of choices: penalties, tactics and the rules themselves, and what the best decision looks like when the other side is thinking too.
3 parts Intermediate
Start at part 1Decision Science Through Football
Operations research on the pitch and in the boardroom: signings under a budget, squads, schedules and set pieces, and how to choose well when you can't try every option.
2 parts Beginner to Intermediate
Start at part 1Latest parts
How far forward should we push? Attack, defence and the price of a rule
Push more players forward and you score more, but you concede more too. Calculus finds the best setting, and when the board sets a limit on goals conceded, it puts a price on that limit, in points a season for every goal.
Intermediate Part 2 of Decision Science Through Football
Why Gijón wasn't a prisoner's dilemma
In 1982 West Germany and Austria knew a 1–0 win for West Germany put them both through, and for 80 minutes nobody tried to change it. Game theory's most famous puzzle, the prisoner's dilemma, explains why deals fall apart. Gijón shows the other kind, the deal that needs no one to agree to it.
Intermediate Part 3 of Game Theory Through Football
Why don't keepers just stand still? The middle, the Panenka and three choices
Keepers almost never stay put for a penalty, and takers rarely go down the middle. Add the middle to the penalty game and the maths explains both, says how often each should happen, and shows why a perfect Panenka gets used less, not more.
Intermediate Part 2 of Game Theory Through Football
Who's the best signing? It depends what you're optimising
Five players on a shortlist, £10m to spend. Chase goals and you sign the striker. Chase points and three cheaper players beat him. Add one rule and the answer changes again. The three parts of every optimisation problem, with a transfer window.
Beginner Part 1 of Decision Science Through Football