Who's the best signing? It depends what you're optimising
Beginner Part 1 of Decision Science Through Football
Football Data Science
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.
How likely is each scoreline?
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.
- Home win
- Draw
- Away win
Each cell is the chance of that exact score, in percent. The outlined cell is the most likely.
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Where should he put it? Penalties and the Nash equilibrium
Intermediate Part 1 of Game Theory Through Football
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Bottom at Christmas, down in May?
Beginner Myth or Maths
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Are derbies unpredictable?
Beginner Myth or Maths
Featured investigation
Bottom at Christmas, down in May?
One of football's oldest sayings is that the side bottom at Christmas goes down. In the Scottish Premiership it's mostly true. Of 26 sides bottom on Christmas Day, 18 finished bottom, and every one that escaped was within a point of the side above.
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Read the analysis
Myth or Maths
All claims testedThings football people say, checked against the data.
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Are derbies unpredictable?
Form goes out of the window in a derby, or so they say. Across 297 Scottish Premiership derbies with bookmakers' odds, the favourites won about as often as the odds said. Derbies are different in one way. They're feistier, with about three-quarters of a yellow card more a game.
Beginner
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Is second-season syndrome real?
Promoted sides are said to struggle in their second year, once the novelty wears off. Of 23 that stayed up, 12 did better in year two and 11 worse. Sides with a great first season do fall back, but so does everyone else who over-performs.
Beginner
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Is midweek football different?
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
Learn through football
All learning pathsEach series starts at part 1, and every piece builds on the one before.
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 1Linear 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.
1 part 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.
1 part Beginner
Start at part 1Interactive models
All modelsChange the inputs and watch the answer move. That is the quickest way to understand a model.
Poisson Match Predictor
Set each side's expected goals and see every scoreline's probability, plus win, draw and loss.
Form or luck?
A striker who never gets better or worse still has droughts and hot streaks. See how long, and how often, by chance alone.
Did we deserve to win?
Enter each side's shots as xG and see who the chances favoured, and the points each side deserved.
SPFL Lab
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.
Latest research
All researchDo the bookmakers get Scottish football right?
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
How many points is a goal worth?
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
When is the title decided?
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.”
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