Statistics, machine learning and mathematics explained through football.
Explore models, test football myths and learn how data can help us understand the game.
Move the sliders. Every number below is recalculated with a Poisson model.
Expected goals from 0.1 to 5.
Each cell is the chance of that exact score, in percent. The outlined cell is the most likely.
Featured investigation
Fans, pundits and managers all say home advantage is worth a goal. Over 18,000 Scottish league matches since 2000/01 say it is worth about a quarter of one.
Things football people say, checked against the data.
"They've had eight corners, they're all over them." Over 5,877 Scottish Premiership matches, the side with more corners won only 44% of the time, and once you know the shots, corners add nothing.
Beginner
"Forget the stats, look at the form." Over 26 Scottish Premiership seasons, a side's shot difference predicted its next six games better than its recent points did, and a gap of eight points in form shrank to under one.
Intermediate
"The table never lies," they say at the end of every season. Over 26 Scottish Premiership seasons, luck alone moves a team's points total by about eight either way: enough to reshuffle mid-table, but not enough to fake a title.
Intermediate
Each series starts at part 1, and every piece builds on the one before.
A penalty has two outcomes and nothing in between. That simple idea, the Bernoulli trial, is the building block of expected goals and of most football statistics.
Beginner Part 1
One penalty is a Bernoulli trial. Five penalties, each with the same chance, is the Binomial distribution, and it shows why missing one in five is normal, not a slump.
Beginner Part 2
A team averages two goals a game. How likely is it to score exactly three? The Poisson distribution turns an average into a probability for every score, and it sits underneath most football prediction models.
Beginner Part 3
Poisson counts goals. The Exponential distribution times the wait between them, and shows why "we're due a goal" isn't how probability works.
Beginner Part 4
A striker scores with one shot in five. How many shots until his first goal? The Geometric distribution answers it, and shows why a three-match drought is often just bad luck.
Beginner Part 5
A player's performance can be written as a list of numbers in a fixed order. That list is a vector, and it's the first step to comparing players, finding replacements and feeding football into machine learning.
Beginner Part 1
One player's performance is a vector. Stack several players together and you have a matrix, the grid that almost all of data science starts from. Multiply it by a set of weights and every player gets a rating.
Beginner Part 2
Two players' stats are two vectors, and the distance between them measures how alike they are. It's how recruitment teams shortlist replacements, and it only works once every stat is put on the same scale.
Beginner Part 3
A 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
Change the inputs and watch the answer move. That is the quickest way to understand a model.
Set each side's expected goals and see every scoreline's probability, plus win, draw and loss.
A striker who never gets better or worse still has droughts and hot streaks. See how long, and how often, by chance alone.
Enter each side's shots as xG and see who the chances favoured, and the points each side deserved.
Eleven predictors forecast every Scottish Premiership match. Each is scored against the results on log loss, Brier score and calibration, not just how often it picked the winner.
Eleven predictors, 5,258 Scottish Premiership matches. Picking the most winners is the wrong test. Log loss, Brier score and calibration tell you which models actually understand football, and the bookmaker still beats them all.
Intermediate
“I've spent much of my career working with data, statistics and modelling. Football gives me a far more interesting place to use them.”
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