For fans, players, coaches and analysts: anyone who's 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.
Tired legs, rotated squads, cold Tuesday nights. Midweek matches are supposed to be a different game. Over 10,000 Scottish league matches, they have the same results, the same upsets and, like for like, the same goals.
Beginner
Football is more attacking than ever, so the goalless draw must be disappearing. Over 10,000 Scottish league matches in 26 seasons, one match in 14 still ends 0–0, and the share hasn't budged.
Beginner
After 33 games the Scottish Premiership splits in two, and every spring someone calls it unfair. Over 25 seasons, the home games even out, but the fixtures don't. The side 7th at the split takes 2.6 more points from the last five than the side 6th.
Beginner
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.
5 parts Beginner to Intermediate
Start at part 1How models learn from past matches to predict the next one: features and targets, training and testing, and the traps in between.
8 parts Beginner to Intermediate
Start at part 1Rates 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 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.
Twenty-four seasons of Bet365 prices on 9,646 Scottish league matches. The odds are remarkably accurate in the middle, the margin has swung from 12% to 6.5% and back up, and backing outsiders is by far the worst bet.
Intermediate
Goal difference explains 93% of the points a Scottish side takes, at about 0.63 points per goal. Some teams beat their goals by four wins' worth in a season, but it barely carries into the next one. 572 team-seasons show why.
Intermediate
A title can be sealed in the table months after the numbers already know. Simulating 25 Scottish Premiership seasons from every third round, the model is typically 90% sure of the champion by round 12. The table doesn't settle it until round 34.
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.”
Why this site exists