Search: penalties | Football Data Science

Statistics #2

Five penalties, how many go in? The Binomial distribution

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…

Statistics #8

Eight from ten. Is he an 80% penalty taker? The Beta distribution

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…

Game Theory #1

Where should he put it? Penalties and the Nash equilibrium

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…

Bayesian Thinking #1

Four from four. How good is he really? Bayesian thinking

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…

Game Theory #2

Why don't keepers just stand still? The middle, the Panenka and three choices

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…

Game Theory #5

Why do teams give the ball back? Repeated games and the shadow of the future

…explain why, what tit-for-tat has to do with it, and why penalty takers should never fall into a pattern.

Model

Penalty Shootout Simulator

Set each side's penalty conversion rate and see how often each wins the shootout, sudden death included.

Model

Penalty Game Solver

Set how often a taker scores on each side, with the keeper guessing right or wrong, and see how often each should go which way.

Statistics #1

Goal or miss? The Bernoulli distribution

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…

Game Theory #10

Why make the dummy run? Bluffing, decoys and how often to fake

…send a false one. The answer uses the same trick as the penalty equilibrium in part 1: mix your choices so the other side gains nothing by guessing either way.…

Glossary

Gambler's fallacy

…a keeper diving the other way because the last three penalties went to the same side.

Model

How good is he really?

A new signing scores four penalties from four. Combine what you believed before with his record and see how good he is likely to be.

Glossary

Nash equilibrium

…neither side can do better by changing only its own. At a penalty, the mix of kicks and dives that leaves nothing to exploit.

Glossary

Payoff matrix

…combination of choices is worth, such as the chance a penalty goes in for each place the taker aims and each way the keeper dives.

Glossary

Zero-sum game

…where one side's gain is exactly the other's loss. Every penalty scored is one the keeper didn't save.

Glossary

n choose k

…k things from n. There are 10 ways to score exactly 2 penalties from 5.

Glossary

p

…one thing happening, written as a number from 0 to 1. A penalty taker with p = 0.75 scores three in four.

Glossary

theta

The true value you're trying to learn, such as a penalty taker's real conversion rate. In the vector articles it's an angle instead.

Game Theory #4

Who should change first? Substitutions, game trees and backward induction

…Parts 1 to 3, both sides chose at the same moment: the penalty taker and the keeper, two teams at Gijón. A substitution is different. Everyone can see it, and…

Machine Learning #20

Expected goals from scratch. Where everyone stood

…data. The analysis is ours, not StatsBomb's. Leaving out penalties, free kicks and corners, which are different problems, leaves 95,162 open-play shots with…

Bayesian Thinking #8

Four from six. Is the new manager really better?

…good is he really? model does this kind of updating for penalty takers, and it works for managers too: read "penalties" as games and "scored" as won. Set the…

Machine Learning #5

Stubborn or jumpy? Bias and variance

…the part of football no model can predict. Deflections, penalties, a keeper's bad day. Flexibility trades the first two against each other. The third never…

Bayesian Thinking #2

Top after five games. Are they really the best? Where priors come from

…before) with evidence (what you've just seen). For a penalty taker, the prior was a sensible guess: most takers score about three in four. For a league table…

Game Theory #6

Who designs the game? Three points for a win and the rules behind the football

…foresee. The series in one page Part The game The idea 1 Penalty, two choices Mix, and the Nash equilibrium 2 Penalty, with the middle Minimax with three…

Bayesian Thinking #3

1–0 up at half-time. Will they hold on? Bayes' theorem

…theorem does. Bayesian updating showed the idea with a penalty taker's record, and where priors come from showed where the starting belief comes from. This is…

Research

Do referees favour the home side?

…not a count of how many fouls were booked. Cards only. Penalties, free kicks, added time and offside calls might show a home lean too; this data doesn't have…

Myth or Maths

Does form matter more than underlying performance?

…games is a short run. A couple of deflections, a missed penalty or a red card can swing it, and they don't carry over. This is regression to the mean: extreme…

Myth or Maths

Does sacking the manager bring a bounce?

…side's level and partly bad luck: the deflections, the penalties, the late goals. The luck doesn't carry on, so results drift back towards the side's real…

Myth or Maths

Does winning the corner count mean you're on top?

…halfway line counts the same as one whipped onto the penalty spot. The model is simple. It's a straight-line fit on individual matches, and doesn't allow for…

Bayesian Thinking #4

Eleven goals in five games. Can they keep it up? Updating a team's scoring rate

…estimate a little. Bayesian updating did this with a penalty taker, and Bayes' theorem with a half-time score. Here it runs all season. The concept Start each…