, and it’s awfully tempting to jump on a bandwagon before checking the facts. But since one of my roles in the world is being a data scientist, I have a habit of wanting to run the numbers before I form an opinion.
Lately, I’ve turned this into a routine: whenever a debate sparks up over something we can measure, I track down the data to get the facts straight. I finally reached my limit with the wild guessing people rely on to make their points, so I decided to use my skills to let the numbers do the talking instead. And since I’m already going down these rabbit holes just to shut up my friends, I figured it would be cool to start sharing my findings with you.
This weekend, with the World Cup barely cold and half the planet still arguing about it — the US included, now that they’ve apparently discovered soccer exists (it’s football, if you’re reading this from the right side of the Atlantic) — I got into a long argument with a friend.
His theory: big teams are favoured because the referees fold under pressure and respect those clubs more. My theory: that’s his perception because of a strong home bias — refs may feel under pressure due to home crowds.
As you may know, most football fans are not exactly rational about referees. Two people supporting different clubs can watch the exact same tackle and see two completely different fouls. But my friend’s argument left me with a question. Do big teams really get favored by referees? Are there other factors creating this perception? Or is no one favored at all?
Normally, I’d be just as biased as anyone else. But since I recently stopped following football after some club elections left me totally disillusioned about my club, I think I finally have the emotional maturity and detachment to investigate this purely through the data.
Gather around, folks. Let’s find out if referees fold under pressure.
First, the data
Data from Football Data – Image by Author
Everything here comes from football-data.co.uk, which is a small miracle of a website: free, tidy, and maintained by people who clearly love data (Joseph Buchdahl is a legend in the sports analytics space). It has results, odds, fouls, cards – the whole grammar of a football match, going back decades.
There’s one catch with this data for our purpose. Fouls and bookings only show up consistently from the 2017/18 season for a chunk of the leagues, so for those competitions we start the clock there and throw out anything earlier.
Small sample from our data
Now, the temptation (and this is exactly where most bar-stool arguments fall apart) is to just count yellow cards/fouls as the referee punishment. Big team gets fewer cards at home, case closed, referees are bought.
Except cards on their own tell you almost nothing, because they depend on how much you foul in the first place. A team that dominates the ball and camps in the opponent’s half commits fewer fouls, and fewer fouls means fewer chances to get booked.
So the real unit of this whole study isn’t cards. It’s cards per foul — the referee’s conversion rate. Of all the fouls you commit, how many actually get punished? And even that number must be looked with caution.
Two pairs of columns carry the referee intervention in our dataset:
- HY / AY — yellow cards, home and away.
- HF / AF — fouls committed, home and away. The denominator. Cards per foul is the entire question.
A referee’s whistle doesn’t happen in a vacuum, though, so before I blame the crowd I have to strip out everything else that could explain the pattern. Maybe the big teams get the calls because they’re simply better, not because they’re home — so I take the betting odds, strip out the bookmaker’s margin, and use them to measure how lopsided each match was on paper. Maybe the away team just fouls more because it spends ninety minutes defending so we’ll use shots and possession to account for territory. And maybe it’s game state: chasing a 0–1 at half-time changes how recklessly you tackle, so the half-time score goes in too. We’ll take this into account in our analysis.
My bet (and the argument I had with my friend) is that home bias (clubs that play at home) has a much larger impact on the ref than “bigger clubs”. On the data, I’ll also use two important angles to see that:
- The first is reverse fixtures. Every pair of teams plays twice a season, once at each ground. Line those two matches up side by side and the teams are very similar — just the moment of the season and coach switches may carry some changes — so whatever’s left over when you flip home and away can’t be blamed on one side simply being better. It’s one of the best clean comparisons we get.
- Buried in the data is a natural experiment nobody designed on purpose: the COVID seasons, when matches were played in empty stadiums. If the home crowd is what bends the referee, then take the crowd away and the effect should shrink. So every match gets flagged as CROWD, EMPTY, or EXCLUDED.
The rest is bookkeeping: which league, which season, which two clubs, plus the raw results and shot counts kept around in case we need them.
Exploring the data
Home and Away Fouls per Game
With the data in hand, the first thing worth looking at is which leagues foul the most.
No surprise to me: the portuguese Primeira Liga is one of the most foul-heavy top flight in the dataset at 29.4 fouls a game, second only to Italy’s Serie B across all fourteen divisions. And Portugal is top of the lot for fouls committed by the home team.
The pattern is geographic. Italy, Portugal and Spain fill the top five, while the Eredivisie, the Premier League and the Championship sit at the bottom on 21 to 22. Southern European games get stopped far more often than northern ones.
Fouls per Game – Image by Author
The next thing that jumps out is that home and away teams foul ratio has a gap that changes between every league.
Fouls per Game per League (Home Team vs. Away Team) – Image by Author
In Spain, Portugal and Turkey the home side actually fouls more. Everywhere else the away side edges it, but the possible explanation is that home teams spend more of the match attacking, so they get fewer opportunities to foul in the first place. The difference is there, though. But that spread between leagues may be about playing culture, not about a referee benefitting home teams.
Note: I’ve excluded COVID-era matches from all of this. They come back later, when empty stadiums turn into the most useful thing in the whole dataset.
So referees call slightly more fouls against the away team. But calling a foul and punishing it are two different things. Cards are the punishment, so do away sides collect more of them?
Yellow Cards per Match (Home vs. Away) – Image by Author
Now this is interesting. In every single league, the home team is booked less. And the gap is remarkably steady: between 0.15 and 0.34 extra yellows per game for the away side, with most leagues sitting near 0.30.
Plenty of confounders are still in the way. We don’t know where on the pitch those fouls happened, or what kind they were. Away teams might, by playing style, commit more dangerous fouls simply because more of the game is happening in their own half.
I have a suspicion, and one obvious thing to rule out before I go anywhere near the crowd. If home teams spend the match camped in the opposition half, then the fouls committed against them happen in more dangerous places, and dangerous fouls deserve cards. That alone could explain everything, with no referee bias required.
To test it, I need to know who was actually on top during each match.
Controlling for team strength
football-data website records no possession figures, but it does record three things that gesture at the same idea: shots, shots on target, and corners. Turn each into a share of the match total (for example, the home team’s shots divided by all shots taken) and average the three. The result runs from 0 to 1, where 0.5 is a perfectly balanced game and anything above it means a team spent the afternoon camped in the other half.
Across more than 50.000 matches the home side averages 0.548 and the away side 0.452. Home advantage turns up in the run of play before a referee blows anything.
The teams at the top of that index are who you’d expect: Teams like Celtic and Rangers, Bayern, all three of Portugal’s big clubs, Manchester City, PSV and Ajax, Barcelona.
Most dominant clubs according to our index
Corners and shot share usually agree, which makes them a solid proxy for which team dominated. It isn’t possession, and it isn’t time spent in the opponent’s half, but it captures domination well.
Correlation between Shots and Corners – Image by Author
The index isn’t flawless, though. Atlético Madrid are the obvious case: cynical, low-risk football that wins about a quarter of a point per game more than their territory says it should. They do dominate the shot count, third-best in La Liga, but the index still understates them, because efficiency in front of goal is invisible to it.
Territorial Dominance Index vs. Points per Game – Image by Author
Some clubs, Atlético Madrid or PSG before Luis Enrique, dominate games by taking their chances rather than by controlling territory. The index can’t see that.
Still, it correlates at 0.93 with points per game, which tells me it’s capturing something real about who controlled a match.
So now we can ask the question properly. Does home protection depend on territorial dominance? Again, if a home side spends the afternoon camped in the opposition half, does the gap between the fouls it commits and the cards it collects look different from a home side that’s being overrun?
That’s the test that separates two very different stories. If the home advantage only appears when the home team is on top, then this was never about the venue at all. It’s home teams simply being good more often and spending more time in opposition’s field (therefore, fouls from the away team are more deserving of a punishment). If the gap between cards and fouls survives even when the home side is being battered, something else is going on.
The referee folds under pressure
One cool finding: As the home team takes control of a game, the fouls dry up. A match where the home side is heavily outplayed produces about 26 fouls; one where it’s heavily on top produces closer to 25. Domination means fewer interruptions, and a more open game.
Fouls Commited per Match according to Home Team Dominance – Image by Author
Fouls move, then. But now let’s look at the card gap.
Yellow Cards per Match according to Home Team Dominance – Image by Author
Incredible. The card gap refuses to go anywhere. In every single band, the home side is booked less per foul it commits, and it isn’t a marginal thing. When the home team is heavily outplayed, pinned back and out-shot for ninety minutes, it’s still punished 7% less often than an away team having exactly as bad an afternoon.
If anything, the gap grows the more the home side dominates, from around 6% when it’s second best to nearly 11% when it’s on top. Dominating your opponent buys you extra leniency. But it surely isn’t where the leniency comes from, because the home team gets it either way.
If we apply a confidence interval on the distribution of this data, home bias always shows up in cards per foul, in every scenario:
Home Advantage in Cards Per Foul – Image by Author
There’s one more way to check this, and it’s the cleanest one football gives us for free. In almost every league, two teams play each other twice a season, once at each ground. Same two squads, same two styles, same manager in the vast majority of cases — the exceptions being sides that sacked their coach in between and other factors that affect some games.
But line the two fixtures up and flip home for away, and there’s little left to explain a difference except the venue itself. The home advantage holds there too:
Softer Whistle for Home Teams per League – Image by Author
Team strength only justifies a bit
Finally, let us do one last statistical test to isolate team strength.
Does the home card-foul advantage survive once we control for team strength, or does it collapse into noise?
The model takes one match at a time and asks whether the cards were shared out the way the fouls were:
home cards ~ Binomial(total cards in the match, p)
If cards simply followed fouls, a side committing 45% of a match’s fouls would collect 45% of its bookings. That proportionality is the model’s starting assumption, and what I measure is how far reality departs from it. Then I remove the controls one at a time, so that when a gap does show up I can see how much of it each factor accounts for, and how much is left over when they’ve all had their turn.
Two teams in one match still aren’t in identical positions, so the model makes four adjustments: for who dominated the play, who led at half time, who was the better side on the pre-match odds, and who won the corner count.
Binomial model per factor
Overall, home teams collect 11.3% fewer cards per foul than the side they’re playing. Home teams really are the better side more often, they really do dominate more of the play, they really are ahead at the break more often. The coefficients show each of those buys a softer whistle in its own right, so each of them could be doing the work.
Take out team strength (measured by pre-match odds) and the gap falls from 11.3% to 7.1%. Take out territory (possession play) and it goes to 6.4%. Half-time state and corners barely move it at all.
Which leaves 6.3% that none of those factors can account for. Two teams, same match, same referee, equally matched on the odds, equally dominant on the pitch, equally placed on the scoreboard — and the one wearing the home shirt is still punished 6.3% less for the fouls it commits.
The answer from this model are in line with the former conclusions: home teams are punished 6.3% less often per foul than their opponents in the same match, with a 95% confidence interval running from 5.0% to 7.6%. Across 54,000 matches, the chance of that being a fluke is roughly one in fifty billion billion.
Is it a Crowd Effect?
Unless every referee in Europe is on the take, something else has to explain this. And the most obvious candidate is the thing clubs sell tickets for in the first place: the crowd.
Forty thousand people reacting to the same tackle at the same moment is a lot of pressure to be standing in the middle of. Cards are one of the few tools a referee has to keep control of a game, which makes them exactly the decision you’d expect that pressure to bend.
The problem is that you can’t randomise a crowd. You can’t ask half of Europe to play in front of 40,000 people and the other half in front of nobody, then compare the bookings.
Except that in 2020, a virus did it for us.
For a season and a half (due to Covid), matches across the continent were played in empty stadiums. If the crowd is what bends the whistle, then the home advantage should have walked out of the ground with the fans. And, surprise, surprise:
Home Whistle Advantage through time – Image by Author
In 2018/19, the last full season with crowds, the home advantage ran at 11.1%, (before the controls strip it back to 6.3%), so it’s the bigger number from earlier. It fell to 7.6% as 2019/20 was interrupted, then to 4.0% across the empty 2020/21. In 2021/22, with the turnstiles open again, it came back to 12.2%. Higher than before it left.
Crowds aren’t only working on the officials, and the next section separates that out, but this is the biggest single thing they move.
Football itself was different behind closed doors. Home teams lost whatever it is a crowd gives them and played worse for it, so maybe the cards simply followed the football, fewer home attacks, fewer away defenders scrambling to stop them, fewer bookings.
That’s testable. Take every measure of home advantage in the data and ask how much of it survived in an empty stadium. Shots, shots on target, corners and goals are what the players did. Cards per foul are what the referee gave.
Changes in different factors during Covid – Image by Author
On the pitch, home teams kept roughly half of what they had. They lost 38% of their edge in goals, 47% in shots, 48% in shots on target and 54% in corners. Diminished, but still recognisably home teams.
Their card advantage lost 101% of it.
Are stronger teams benefited?
Now, for my friend’s argument.
The dataset comes with bookmakers’ odds, which means I can measure how lopsided each match was expected to be before kick-off. Split every game by that and a pattern emerges on the cards per foul:
Expectation to win vs. Referee Leniency – Image by Author
When the home side is a heavy favourite, it’s booked 4.1 fewer times per 100 fouls than its opponent. When the away side is the heavy favourite, that flips: the home team is now booked 1.02 times more. Being expected to win buys you leniency, and the bigger the gap, the more it buys. On this chart, my friend is right.
Except that “heavy favourite” and “big club” aren’t the same thing, and neither is the same as “gets protected.” A side expected to win 4–0 plays a completely different match from one hanging on for a point. It has the ball more, defends less, and commits the kind of fouls that don’t need a card — the factors that justify the leniency that we’ve seen before.
So my friend was half right in a way that doesn’t help him. Favourites do get a softer whistle. But it isn’t respect for the badge, it’s probably because of the style of football they play.
Conclusion
So, let’s see some of the conclusion from this blog post:
- The home whistle is real, and it’s worth about 6.3%. In the same match, with the same referee, against an opponent equally strong on the odds, equally dominant on the pitch and equally placed on the scoreboard, the home side is punished 6.3% less often for the fouls it commits.
- It isn’t about fouling less. Home teams commit 49.3% of a match’s fouls, but they collect 45.9% of its cards. The card gap is six times the foul gap. Whatever is happening, it happens after the foul, not before it.
- It doesn’t need the home team to be good. A home side being heavily outplayed, pinned back and out-shot for ninety minutes, is still booked 7% less often than an away side having exactly as bad an afternoon. Dominance roughly doubles the advantage, from 6% to 11%, but it never creates it.
- My friend may be wrong about big clubs. Being a favourite does buy a softer whistle, but that’s the style of football favourites play, not respect for the badge.
- It’s the crowd. Empty the stadiums and the entire 6.3% disappears, in 13 of 14 divisions. In 2019/20 alone home sides went from 5.6% less booked before the suspension to 8.6% more after the restart.
- The crowd moved the referee more than it moved the players. Home teams kept about half their edge in goals, shots and corners without their fans. They kept none of their card advantage.
The home bias isn’t the badge on the shirt. It’s the twenty or forty thousand people behind the goal, and referees, being human, hear them.
Which question do you want me to address next?
Some caveats worth mentioning about the analysis:
- Cards per foul controls foul volume, not foul severity. A team under pressure commits more cynical, more bookable fouls. The reverse-fixture design handles the team-level version of this; it cannot fully handle the within-match version.
- “Behind closed doors” is approximate. It is defined by date windows, not by attendance records. Some 2020/21 matches had partial crowds, which biases the estimate toward finding no effect — the true collapse is, if anything, sharper.
- No referee name, so nothing here is about individual officials. The claim is about refereeing as a system under crowd pressure.
References
[1] J. Buchdahl, Football-Data.co.uk (2026), https://www.football-data.co.uk
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