A club that fouls with impunity, and the four ways I was wrong about it

What the data says

Across eleven European leagues, how often a team is booked per foul it commits depends mostly on how strong that team was expected to be that afternoon. Heavy underdogs are booked more, heavy favourites less, in all eleven leagues, and no club identity is involved.

In the Portuguese league, once you account for that, for the era and for the referee who was actually appointed, one club of twenty-six is booked measurably more than expected. It is Sporting, at 1.18. Porto and Benfica both sit at 1.00, indistinguishable from average.

A post had gone around implying Porto were being favoured by referees. That is where the question came from, and it is the last time the post appears here. The claim is the object of study; the person who made it is not, so it is neither linked nor named. See EDITORIAL.md.

The pre-registered question

Is there a measurable difference in how often a given club is booked, relative to the fouls it commits?

Written before the data was pulled. What follows reports what happened, including the parts where the answer changed under its own tests.

The metric

Booking index LITERATURE-adjacent, COINED in this form. Yellow cards received, divided by yellow cards expected from the team's own foul count. An index of 1.0 means booked exactly as often as the fouls imply.

The underlying quantity — cards conditioned on fouls — is standard. Phatak et al. (2021) use fouls-per-card across five leagues. The name and the specific expectation model here are mine, and neither appears in the literature under this label. Treating it as an established measure would be a mistake.

The first answer, which looked good and was wrong

Porto's raw booking index comes out at 0.890. Comfortably below 1.0, interval excluding it. Benfica sits at 0.885. On its face, two clubs booked around 12% less than their fouls imply.

That is roughly the shape the original claim predicted. It is also wrong three times over.

Wrong (1): most of it is being the favourite

Booking rate per foul depends heavily on how strong you were expected to be in that specific match. In Portugal, the league the question was about and the one the figure shows, a heavy underdog is booked at 1.121 times its foul count and a heavy favourite at 0.854. A 31% swing, with no club identity involved.

The pattern is not Portuguese. The underdog end sits above the favourite end in all eleven leagues, median 1.098 against 0.856. Per-league bands are in story.json, alongside every other number this study's figures carry.

Strict monotonicity across all five bands holds in seven of them. Germany, France, Italy and Spain each tick up by less than 0.01 between the two underdog bands, which are also their smallest samples. The direction is everywhere; the perfectly clean staircase is not.

Dominant clubs are favourites most weeks. So roughly half of Porto's apparent leniency was being the better side, which they share with every strong club in Europe.

Wrong (2): the expectation model was misspecified

The expectation assumed yellow cards are proportional to fouls: expected = rate × fouls. They are not.

Fitting yellows = a + b × fouls per league-season gives an intercept worth 13% to 47% of mean yellows, depending on the competition. Observed yellows per foul falls monotonically across the range, from 0.197 in matches where a side commits six fouls or fewer to 0.122 where it commits more than twenty. Every bin is in story.json.

That intercept is interpretable. It is the cards that have nothing to do with your foul count: dissent, delaying the restart, entering the field of play, simulation, plus whatever the data feed does or does not record as a foul. In Greece and Italy it is nearly half of all cards.

Forcing the line through the origin inflates every low-foul team and deflates every high-foul team, with no behaviour involved. A test on synthetic teams with identical card processes shows the proportional model inventing a gap of over 0.10 between them.

Dominant clubs foul less than average. The model was flattering exactly the clubs the finding was about.

Wrong (3): the effect is not the club's

This is the one that changed the conclusion, and the test is embarrassingly cheap. Compute the same index for the opponents.

All three from scripts/strength_effect.py, recorded in strength_effect.json.

When a dominant club plays, the other team is booked more per foul too, and the two are close to independent. A club-level story predicts the second correlation is zero. It is not.

The within-club version is cleaner still. Holding the club fixed and splitting its own matches by opponent quality:

It rises in 11 of 11 leagues. Club identity is differenced out here, so this is the same side, playing the same way, booked differently according to who is at the other end of it.

So the correct statement is not "dominant clubs are booked more." It is:

Yellows per foul scale with the quality of the fixture, for both teams.

A club's own quality is half of that fixture quality, so strong clubs genuinely do see a higher rate. They are not being singled out. They are playing in higher-quality matches, and those matches produce more yellows per foul.

If not the club, then the manager?

The natural next candidate. Managers set how a side presses and how it fouls, and Portuguese clubs change them often enough to test it: take every manager who worked at two or more clubs, measure each spell against that club's own baseline excluding them, and see whether the two spells agree.

They do not. Across 42 spell pairs the correlation is r = −0.076, and a permutation test that reshuffles which spell belongs to which manager gives p = 0.628. The observed value sits in the middle of the null. A manager who runs a disciplined side at one club is no more likely than chance to do it at the next.

Between-manager variance accounts for about 12% of the spread in spell effects, which is small enough that the honest reading is that this data cannot see a manager effect, rather than that none exists. Either way, the club-level story does not become a manager-level story. Every number in this section is in manager_travel.json.

Wrong (4), sort of: someone got there first

Dawson, Dobson, Goddard and Wilson published a gradient in cards by team strength in 2007 (JRSS-A 170(1)), on 2,660 Premier League matches, with a Nash-equilibrium model of aggression. Their reduced form is a subset of the one used here.

What may be new is conditioning on fouls: asking not "who gets more cards" but "who gets more cards for the same number of fouls". Rediscovering a known result on twenty-two times the data is worth doing. Presenting it as new is not.

So: was the club being favoured?

On this measure, no.

Portugal has no referee data in the standard source, so we assembled it. 2,737 match-official rows across ten seasons, 98.4% joined to our matches and validated on scorelines rather than names. Portuguese referees vary as much as English ones, with booking multipliers from 0.75 to 1.32 among the 32 with 40+ matches, but that variation is not concentrated on anyone. Every club's mean referee draw falls between 0.971 and 1.021.

Each club is judged against officials measured without that club. Otherwise a side that draws one official often helps set the baseline it is being judged against, and a real effect partly cancels itself.

Adjusting for era, match situation and the actual official on the pitch:

Produced by scripts/portugal_referee_table.py, with all 26 clubs in referee_table.json.

Porto sit at 1.002, indistinguishable from average. One club of twenty-six separates from expectation, and it is not the one in the original claim.

The figure shows the era-and-situation step only, which is why Porto reads 1.02 there against 1.00 in the table: the referee adjustment moves them slightly further down. The shape is the point. Almost every club that looked unusual on the raw index stops looking unusual once the situation is accounted for, and the hollow-to-solid movement is the size of that correction.

The multiplicity check, which is where most of these die

Testing twenty-six clubs and reporting the extreme one is how you manufacture a finding. One club clears an uncorrected p < 0.05, and the next two sit just outside it.

Under a Benjamini–Hochberg screen at FDR 0.10, one survives:

These p-values are two-sided, computed by the script alongside the table. They were previously typed in by hand and cannot be reproduced from any method recorded here, which is why they moved: the runner-up used to read 0.044 and now reads 0.081. Two-sided is the convention the 95% interval above already assumes, and no direction was specified in advance for a club sitting below expectation, so the screen and the interval now agree about which clubs are extreme.

Gil Vicente is the one a naive threshold would have published. Sporting survives Bonferroni too, which is the conservative correction and not one this result needed.

What this cannot say

It measures yellow cards relative to fouls committed and nothing else. It says nothing about penalties given or denied, offside calls, disallowed goals, red cards specifically, added time, or whether any individual decision was correct. If "favoured" means those things, this analysis is silent on it and should not be quoted as though it were not.

A high index is also not misconduct. Sporting commit fouls that draw cards more often than their foul count predicts. Why is a separate question this data cannot answer.

What happens next, and what the index is worth

Two questions this report raises are answered elsewhere, because neither is about Porto.

The season in progress has its own page, the Portuguese season as it stands. It is deliberately not part of this report: a live test with a resolution date in November would leave a dated document permanently unfinished, and the pre-registration deserves a surface that is expected to change.

Whether a one-season booking index means anything at all is study 04. It has to be asked, because Sporting separating and Porto not is only interesting if the measure carries a club property in the first place. It does, and it is small: 15% of the spread between clubs in a season is real and the rest is the Poisson noise of one season's cards.

The data lesson

The version that transfers, and the reason this report is in a repository about method rather than about football: when a metric is an average over a group, ask whether the effect belongs to the group or to the situations the group is in. Cohorts, segments, cost centres, model slices. The arithmetic is identical and so is the error.

Every attack run against this finding, and the two that killed part of it, are in the table below.

Pressure tests

METHODS.md §11 attacks a finding on six fronts before it is published. The point of tabulating them is that an attack never tried cannot pass as one tried and survived.

Two of the six killed something. Both deaths are in the body of this report rather than in a footnote, because the deaths are the finding.

Tri-anchor

References

• Dawson, P., Dobson, S., Goddard, J. & Wilson, J. (2007). Are Football Referees Really Biased and Inconsistent? JRSS-A 170(1), 231–250. doi:10.1111/j.1467-985X.2006.00451.x
• Phatak, A., Rein, R. & Memmert, D. (2021). The Dirty League. J. Human Kinetics 80, 263–276. doi:10.2478/hukin-2021-0095
• Efron, B. & Morris, C. (1975). Data Analysis Using Stein's Estimator. JASA 70(350), 311–319. doi:10.1080/01621459.1975.10479864
• Benjamini, Y. & Hochberg, Y. (1995). Controlling the False Discovery Rate. JRSS-B 57(1), 289–300. doi:10.1111/j.2517-6161.1995.tb02031.x

Open questions

Sporting. The one club still separating, at 1.177 across three managers and with no unusual referee draw. Nobody was arguing about Sporting, which is part of why it is interesting.

Absolute versus relative quality: tested, and still open. Our strength measure is standardised within league, so a Celtic–St Mirren fixture scores as "high quality" on the same scale as Barcelona–Getafe. The gradient does vary a lot between leagues, from −0.040 in Spain to −0.110 in Belgium, and that variation is real rather than noise: 91% of it survives correcting for how precisely each league's gradient is estimated.

Absolute quality looked like the explanation and is not. Against UEFA association coefficients the gradient correlates at +0.61, but the association does not survive controlling for home advantage (+0.50, p = 0.14). Home advantage itself correlates at +0.79 across the eleven leagues, which is stronger, stable under leave-one-out, and survives correcting for having tried seven league-level covariates.

It is also an artifact of aggregation.

Splitting the same data into three-season blocks and asking whether a league's own gradient moves when its own home advantage moves gives −0.086, p = 0.50, with the slope running the other way in five of the six leagues that have enough blocks to fit one. The test can detect a correlation of 0.35 at 80% power, so it is not simply underpowered against a claimed 0.79.

Produced by scripts/aggregation_levels.py, with each league's own slope in aggregation.json.

Home advantage fell across the panel from 0.349 goals per match in 2001 to 0.220 in 2025, with the crowd-free seasons visible as a trough. The gradient did not follow it.

So the question stays open, and the aggregation lesson is the same one as Wrong (3) above: a correlation across eleven leagues is a correlation between eleven things that differ in many ways at once. This is exploratory rather than pre-registered, and it is recorded here as a question not answered rather than as a finding.

What we cannot resolve at all. Whether the same foul is punished more harshly in a bigger match, or whether bigger matches simply contain more cardable fouls. Distinguishing those requires foul-level video coding. That is the honest limit here.

Reproduce this

uv run python scripts/build_discipline_story.py   # figures 1-7, and the club table
uv run python scripts/aggregation_levels.py       # figure 8, the aggregation test
uv run python scripts/strength_effect.py          # the cross-league association
uv run python scripts/portugal_referee_table.py  # the club table above
uv run python scripts/referee_decomposition.py
uv run python scripts/manager_travel.py