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Was the referee against us?

Your team's card count says less than you think. Here is the arithmetic.

Nottingham Forest were booked 8 times in a match. They average 2.2 under every other referee that season. That is the biggest gap in 2,280 club-matches — and gaps that size happen about as often as pure chance makes them.

The arithmetic, so you can check it

2.06
cards a side, on average
1.436
how much that bounces on its own — √2.06
1.418
how much it actually bounces

A count of about two, arriving at random, varies by roughly its own square root. That is 1.436. What we measure is 1.418 — across 2,280 club-matches from 2023-24 onward. Simulating the same matches with the referee removed entirely gives 1.437 [1.369, 1.492] over 200 runs.

How often a gap that big happens, against how often chance makes it

Gap in cardsObservedChance Difference
1.5+30.1%29.4%+0.7
2.0+15.7%15.5%+0.2
2.5+6.0%6.6%-0.6
3.0+3.0%3.3%-0.3
3.5+1.4%1.9%-0.5
4.0+0.7%1.0%-0.3

Observed is at or below chance at every threshold. There is no size of gap at which "we were booked far more than usual" happens more often than randomness alone would make it.

The biggest gaps we hold

ClubSeasonBookedTheir averageGap Other matches
Nottingham Forest2024-2582.2+5.836
Chelsea2024-2582.5+5.533
Crystal Palace2023-2471.8+5.236
Aston Villa2024-2571.8+5.236
Nottingham Forest2023-2472.1+4.934
Arsenal2025-2661.2+4.834
Sheffield Utd2023-2472.5+4.536
Arsenal2023-2461.5+4.535

Each average is that club's own rate under every OTHER referee in the same season, so the referee being asked about is never in his own baseline. Each club-match compares the cards that club took to its own average under every OTHER referee in the same season, with at least 10 such matches.

This is not a defence of referees

It is a statement about what a card count can detect, and nothing more. A referee could be biased in ways this measure cannot see — in fouls not given, in advantage played, in which challenges draw a word instead of a card — and every number on this page would look exactly the same. What the page rules out is the specific inference people draw from the specific number they can see. It does not rule out the thing they suspect.

One measure does come out above chance

Reported because leaving it out would be the selective quoting this page argues against. Take the total cards in a match against what both clubs average, and the spread is 2.189 where chance gives 2.029 — about 0.82 cards of real excess. Some matches genuinely are carded more than the two teams' habits predict.

It still cannot carry a claim about one match. At a gap of 4+ cards it fires on about 25 matches a season, and roughly 17 of those would fire by chance anyway. Two firings in three are noise, and nothing tells you which is which. A per-match line built on it would be wrong about most of the matches it appeared on.

Your club's actual ledger

Arsenalevery confirmed error for and against themEvery club's ledgererrors for and against, sortable

Other questions

Who is the strictest referee?The question has a real answer, and it is not a name.What are bookings actually for?More than a quarter are not for a foul.Does the season start lenient?Fouls peak in round one. Cards do not peak until round six.What happened when the league cracked down on dissent?Both halves sagged in the first season. Only one came back.