Statistics, maths and machine learning, each one introduced through a football question.
Every intermediate piece, series by series, in part order.
The Geometric distribution waits for the first goal. The Negative Binomial waits for the third, or the fifth. It shows how long a hat-trick really takes, and it has a second job modelling goals that vary more than Poisson allows.
Intermediate Part 6 of Statistics Through Football
A striker scores 8 of his 10 penalties. Calling him an 80% taker is overconfident. The Beta distribution describes how sure we can really be about a probability, and how that changes as the evidence grows.
Intermediate Part 8 of Statistics Through Football
The Exponential distribution waits for one goal. The Gamma waits for several. It shows why a team that averages two goals a game gets its third before full time only about one match in three.
Intermediate Part 9 of Statistics Through Football
Transfer fees, wages and market values can't go below zero, cluster low and have a few enormous outliers. The Log-Normal distribution describes them, and shows why the average fee is a poor guide to a typical one.
Intermediate Part 12 of Statistics Through Football
Distance says how far apart two players' numbers are. Cosine similarity asks whether they point the same way, which compares playing style rather than volume. It only works once the stats are standardised.
Intermediate Part 4 of Linear Algebra Through Football
A formation is a set of player positions, and the change from the defensive shape to the attacking one is a transformation. Measure it and you can see how far the team moves, how much it stretches, and which player's job is different.
Intermediate Part 7 of Linear Algebra Through Football
A weighted rating turns a player's scores into one number, but the weights decide what matters. Matrix multiplication rates a whole squad for several roles at once, and shows why "best" always means "best at what".
Intermediate Part 8 of Linear Algebra Through Football
Write down who passes to whom and you have a matrix. Its rows and columns count passes made and received, and multiplying it by itself shows how the ball travels in two passes, who links defence to attack, and who plays the one-twos.
Intermediate Part 10 of Linear Algebra Through Football
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 of Bayesian Thinking Through Football
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 of Bayesian Thinking Through Football
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 of Bayesian Thinking Through Football
Three numbers known before kick-off, one model trained by gradient descent, and a probability for every result. Tested on five SPFL seasons it beats every model in the series so far and gets close to the bookmakers.
Intermediate Part 8 of Machine Learning Through Football
A decision tree predicts a match the way a pundit reasons, with a string of yes-or-no questions, and it learns which questions to ask from the data. On five SPFL test seasons two questions nearly match logistic regression; twelve fall apart.
Intermediate Part 9 of Machine Learning Through Football
One decision tree is jumpy, so grow a hundred, each on a slightly different set of matches, and average what they say. On five SPFL test seasons the forest fixes most of a single tree's wild guesses, and still finishes just behind logistic regression.
Intermediate Part 10 of Machine Learning Through Football
Start with a rough guess, look at what it got wrong, and fix a little of it with a small tree. Repeat a few hundred times. On five SPFL test seasons gradient boosting draws level with logistic regression, and shows where three numbers run out.
Intermediate Part 11 of Machine Learning Through Football
Machine learning models learn by measuring how their error changes as they adjust a setting, then stepping downhill. That's the derivative at work. 25 SPFL seasons show it finding how much of last season's scoring carries into this one.
Intermediate Part 6 of Calculus Through Football
A penalty taker and a goalkeeper choose at almost the same moment, and any habit gets punished. Game theory says both should mix it up, and says exactly how often. The professionals turn out to do almost exactly that.
Intermediate Part 1 of Game Theory Through Football
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
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
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