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.
12 parts Beginner to Advanced
New to this? These parts are Beginner level: 8.
Start at part 1The cleanest game in football: one kicker, one keeper, and why the best plan is to be unpredictable. Parts 1 and 2.
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 often. The professionals turn out to do almost exactly that.
Intermediate Part 1
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 often each should happen, and shows why a perfect Panenka gets used less, not more.
Intermediate Part 2
What happens when both sides could do better, when one moves first, when they meet again, and when the rules themselves are the choice. Parts 3 to 6.
In 1982 West Germany and Austria knew a 1–0 win for West Germany put them both through, and for 80 minutes nobody tried to change it. Game theory's most famous puzzle, the prisoner's dilemma, explains why deals fall apart. Gijón shows the other kind, the deal that needs no one to agree to it.
Intermediate Part 3
When one manager makes a change, the other sees it and answers. Drawing the match as a game tree and solving it from the end shows why, in some games, the side that waits does better, and why it pays to keep a substitution in hand.
Advanced Part 4
Kick the ball out for an injured player and the other side gives it back, though no law makes them. Played once, a deal like that falls apart. Played again and again, it can hold. Repeated games explain why, what tit-for-tat has to do with it, and why penalty takers should never fall into a pattern.
Advanced Part 5
Every part of this series took the rules as fixed. The people who write them are playing a game too, choosing payoffs so that players' own best moves give the football they want. Three points for a win shows how, and 25 Scottish seasons re-scored at two points show what it changed.
Intermediate Part 6
Bluffs, signals, threats and trust: the 50/50, contract talks, feigned injuries, dummy runs, the offside trap and the transfer race. Parts 7 to 12.
Two players chase a loose ball. Go in hard and you might win it, or collide. Pull out and you're safe, but beaten. Game theory says there's no best choice, only a best mix, and a simple rule about who got there first beats both.
Intermediate Part 7
A player and a club both gain from a new deal; the only question is how they split the gain. Game theory's answer is that it depends on what each could get by walking away, and on who's in more of a hurry.
Beginner Part 8
A player goes down. The referee can't see whether he's hurt or wasting time, only that he went down. Game theory shows when a signal like that tells you anything, and why one rule in the Laws of the Game makes it honest.
Intermediate Part 9
A striker who only runs when the pass is coming is easy to mark. Mix in runs that are never meant to get the ball and the defender can't tell which to follow. Game theory says exactly how often to bluff, and shows the dummy runs pay off through the real ones.
Intermediate Part 10
The offside trap is all or nothing. If every defender steps up, the striker is caught; if one holds, he plays him on and the rest are stranded. Game theory calls this a stag hunt, and it shows why a settled back four can run the trap and a patched-up one shouldn't try.
Intermediate Part 11
When several clubs chase the same striker, the one that gets him is usually the one whose scouts rated him highest, and that often means it paid too much. Auction theory calls this the winner's curse, and it says the more clubs are in the race, the less you should offer.
Intermediate Part 12