Vectors and matrices, and the maths behind player similarity, runs and passes, formations, ratings and PCA.
10 parts Beginner to Advanced
Start at part 1A 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
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
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
Distance says how far apart two players' numbers are. Cosine similarity asks whether they point the same way, which compares playing style rather than volume. It only works once the stats are standardised.
Intermediate Part 4
A run from one spot on the pitch to another is a vector, how far forward and how far across. From that pair of numbers you get the length of the run, its direction, its speed and whether it was heading for goal.
Beginner Part 5
Every pass has a start and an end, so every pass is a vector. That turns "he never passes forward" from an opinion into a number, and shows why a player's average pass can hide half of what he does.
Beginner Part 6
A formation is a set of player positions, and the change from the defensive shape to the attacking one is a transformation. Measure it and you can see how far the team moves, how much it stretches, and which player's job is different.
Intermediate Part 7
A weighted rating turns a player's scores into one number, but the weights decide what matters. Matrix multiplication rates a whole squad for several roles at once, and shows why "best" always means "best at what".
Intermediate Part 8
Football stats overlap. Principal component analysis finds the few directions that carry most of the information. On 26 seasons of Scottish Premiership data, one component built from eight stats explains 56% of the variation and tracks points per game better than any single stat.
Advanced Part 9
Write down who passes to whom and you have a matrix. Its rows and columns count passes made and received, and multiplying it by itself shows how the ball travels in two passes, who links defence to attack, and who plays the one-twos.
Intermediate Part 10