For football fans who've wondered what the numbers really say. Each idea starts with a football question and builds up from there, and you don't need a maths background.
Written by Bryan McGuire, a data scientist with more than 35 years' experience, using real match data.
Tell the model how many goals each side usually scores, and it works out the chance of every scoreline. It's the classic starting point for predicting football results.
Try a match-up, or move the sliders:
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.
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 1Vectors and matrices, and the maths behind player similarity, runs and passes, formations, ratings and PCA.
10 parts Beginner to Advanced
Start at part 1How to update what you believe about a team or a player as the evidence comes in, and where the starting beliefs come from.
2 parts Beginner to Intermediate
Start at part 1Change 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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