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Week 3 — The lever nobody pulls

Published: 2026-08-31 · Snapshot: 2026-W37 · Claim level: L1 (descriptive)

What the data says

Whether a foul is punished depends enormously on where and when it happens. A foul in your own defensive fifth is carded 31.4% of the time; the same offence in the attacking fifth, 8.9%. A foul in the opening quarter of an hour is carded 6.5% of the time; after ninety minutes, 25.6%.

That is a large, exploitable difference, and it is not exploited. Across 98 clubs in five leagues, the average position of a club's fouls spans 48 to 58 on a hundred-point pitch, a tenth of the range over which the gradient is measured. Where a club fouls does not predict how often it is carded.

The lever is real. Nobody appears to be pulling it.

Where this question came from

Study 02 found that a club's booking index is a persistent property, repeating season to season at r = +0.32 across eleven leagues. Something club-level is stable. The obvious candidate is that clubs differ in which fouls they commit, and that the good ones foul where cards are cheap.

That mechanism was unverifiable here until recently, because football-data.co.uk records fouls as a count and nothing else. It is testable now because a peer-reviewed, openly licensed source of foul-level data exists, which this project had wrongly recorded as not existing. See DATA_SOURCES.md.

This analysis was not pre-registered. It is exploratory, the question was formed after seeing study 02's persistence result, and it is reported at L1 accordingly.

The metric

Card rate per foul LITERATURE. The share of fouls followed by a yellow or red card. Azmat and Yi (2024) model the same quantity at the level of an individual foul and call it expected booking; this report uses observed rates rather than a fitted model, so nothing here is their xB.

1. Where you foul

Card risk by pitch location

The map is drawn in the fouling team's attacking direction, so the left edge is their own goal line. Card risk concentrates hard in front of goal and falls away steadily upfield. Central fouls draw 19.0% against 13.0% out wide.

None of that is surprising in direction. The size is: a threefold difference between one end of the pitch and the other, on the same nominal offence.

2. When you foul

Card risk by minute

The rise across a match is steeper than the spatial effect: roughly fourfold from the opening minutes to stoppage time.

The interesting part is the discontinuity. Card rate climbs through the first half to 16.1% in its final five minutes, then drops to 12.8% in the first five minutes of the second. A 3.3 point fall across the interval, p = 4×10⁻⁴.

Whatever accumulates during a half is therefore partly discharged at half time, which points at match tension and referee escalation rather than at fatigue or the running foul count. This report does not attempt to distinguish those, and the search that would establish whether the reset is already known in the literature could not be run.

3. What state you are in

Fouling team Card rate
Behind 18.1%
Ahead 16.2%
Level 13.3%

Teams are treated more harshly when losing than when level. That is confounded in an obvious way: a team chasing a game fouls differently, not just more. Nothing here separates the referee's response from the team's behaviour.

4. The gradient is steep, and every club stands in the same place

The unused lever

This is the result. The card-rate gradient runs the length of the pitch. Club averages occupy 48 to 58 of it.

Foul context, meaning position and minute and score state together, explains 30.8% of the spread in cards per foul between clubs. So context matters a great deal to whether a foul is carded, and clubs differ enough in aggregate for it to matter to a club.

They just do not differ in the direction that would help.

Placement against card rate

A club's mean foul position against its card rate gives r = −0.14, 95% interval [−0.33, +0.06]. The sign points the way the mechanism predicts and that is all that can be said for it. The test can find a correlation of 0.28 at 80% power, so a moderate relationship is ruled out and a small one is not.

Clubs do differ genuinely in where they foul: 70% of the between-club variation in mean foul position survives correcting for the sampling error of a club average. They barely differ in when, at 14%. Moving from the worst to the best observed foul mix would be worth about 18% of the base card rate.

What this does and does not show

It does not show that tactical fouling is a myth. A season average is a blunt instrument. A club could foul cynically in exactly the situations that matter — protecting a lead, killing a counter — without shifting its season mean position by a tenth of a pitch. That is the most likely way a real effect would hide from this test, and this data cannot rule it out.

It does not establish causation in either direction. Where a team fouls is a consequence of how it defends, which is a consequence of who it is playing. None of that is randomised.

It does show that referees respond to context far more strongly than to anything about the club in front of them, and that the aggregate differences between clubs in foul placement are small enough to leave most of the available advantage unclaimed.

For the club in study 02

Porto's adjusted booking index is 0.989. Their league is not in this data and one season could not support a club-level claim if it were. But if no club among 98 in the five largest leagues measurably converts foul placement into a lower card rate, the prior that any particular club is doing so should be low, and an average index is what that predicts.

The data lesson

A large effect at the level of an event can be nearly invisible at the level of an actor, and the reason is not statistical subtlety. It is that the actors do not vary much on the axis where the effect lives.

The gradient here spans a factor of three. The actors span a tenth of it. Anyone reasoning from the first number to a claim about the second is skipping the step where you check how much the actors actually differ. The whole premise of the original viral post was exactly that.

The general form: before attributing an outcome gap to a behaviour, measure the spread in the behaviour. Pricing tiers, staffing patterns, model thresholds, retry policies. A steep response curve is worth nothing if everyone is standing on the same point of it.

Tri-anchor

Anchor Source
Data 47,955 fouls across 1,826 matches and 98 clubs, five leagues 2017-18, Pappalardo et al. (2019), CC BY 4.0
Football Azmat & Yi (2024) on P(card | foul context); Wright & Hirotsu (2003) on when a professional foul is rationally worthwhile
Data science Cronbach (1951) for the reliability correction separating true club variation from the sampling error of a club mean; Simpson (1951) on why a within-level effect need not appear between levels

References

Open questions

The situations a season average hides. The obvious next test is card rate per foul restricted to the situations where cynical fouling is supposed to happen: leading by one, last twenty minutes, opponent breaking. If clubs differ anywhere, it is there. The data supports it and this report did not run it.

Whether the half-time reset is known. A 3.3 point drop across the interval is either a documented feature of refereeing or it is not, and no search was possible here to find out. It is recorded as an observation, not a discovery.

Portugal. Neither open event source covers it, so the question that started this project stays out of reach at foul level.

Reproduce this

Every number above is written to facts.json by the second command, so nothing here is typed by hand.

uv run python scripts/ingest_events.py    # downloads and reduces the event logs
uv run python scripts/build_week03.py     # figures and facts, offline