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 statistics.
Beginner Part 1
Learn
Statistics, maths and machine learning, each one introduced through a football question.
Statistics Through Football
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 a slump.
Beginner Part 2
How many goals will we score? The Poisson distribution
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
How long until the next goal? The Exponential distribution
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
How many shots until he scores? The Geometric distribution
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
How many shots until his hat-trick? The Negative Binomial distribution
The Geometric distribution waits for the first goal. The Negative Binomial waits for the third, or the fifth. It shows how long a hat-trick really takes, and it has a second job modelling goals that vary more than Poisson allows.
Intermediate Part 6
Win, draw or lose? The Multinomial distribution
A match has three possible results, not two. The Multinomial distribution handles any number of outcomes, and shows why a team's "expected" record over ten games almost never happens exactly.
Beginner Part 7
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 probability, and how that changes as the evidence grows.
Intermediate Part 8
Will the third goal come before full time? The Gamma distribution
The Exponential distribution waits for one goal. The Gamma waits for several. It shows why a team that averages two goals a game gets its third before full time only about one match in three.
Intermediate Part 9
How fast is fast? The Normal distribution
Ranking players from fastest to slowest tells you the order, not how unusual anyone is. The Normal distribution, and its standard deviation, measures how far a player stands out from the rest.
Beginner Part 10
Is a goal equally likely in any minute? The Uniform distribution
The Uniform distribution says every outcome is equally likely. It's the fairest-sounding model in statistics, and testing it against 28,016 goals shows football isn't that fair.
Beginner Part 11
Why the average transfer fee misleads. The Log-Normal distribution
Transfer fees, wages and market values can't go below zero, cluster low and have a few enormous outliers. The Log-Normal distribution describes them, and shows why the average fee is a poor guide to a typical one.
Intermediate Part 12
Linear Algebra Through Football
A midfielder's match in five numbers. Vectors
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
Four players, four numbers each. The whole team becomes a matrix
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
Who plays most like him? Measuring player similarity with distance
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
Bayesian Football
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 should nudge your opinion, not replace it.
Beginner Part 1
Top after five games. Are they really the best? Where priors come from
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