The Thumb Came Off the Scale

For one season, football across Europe was played to empty stands. The experiment nobody would ever have been allowed to run got run anyway, and the record of it is public: every result, every card, every referee's name. This page takes 243,134 matches apart to ask what a crowd is actually worth, and to whom it was speaking.

Artificial Wasteland · 2026-08-02 · 243,134 matches · 22 divisions · 33 seasons

Home teams win more than away teams. They have done so for as long as anyone has counted, in every league, at every level, in most sports. The standard explanation has four parts: the away side travels, the away side plays on an unfamiliar pitch, the home side has a crowd, and the referee has that crowd in his ears. Untangling the four is impossible in the normal run of things, because they arrive together and leave together.

Then in March 2020 they came apart. Leagues shut, restarted behind locked gates, played a whole season to nobody, and let the crowds back in. The travel stayed. The pitch stayed. The noise went and then returned. That is a switch, thrown on a scale no laboratory could reach, and it is the reason this page exists.

Everything below is computed in your browser from a bundle of sums this page carries, built from the football-data.co.uk archive: every league match in 22 European divisions from the 1993-94 season to 2025-26. Nothing is quoted from a paper except where a paper is named.

1. A long slide, and one season that falls off it

The standard measure of home advantage, due to Pollard, is the share of all points won in a match that went to the home side. Fifty per cent is no advantage. Over the 33 seasons in this archive it has been sliding, slowly and steadily, from 61.93% in 1993-94 to 57.29% in 2018-19, which is about a fifth of a percentage point a season. Fit a straight line to those 26 pre-pandemic seasons and every one of them sits close to it.

One season does not.

The home side took 53.99% of the points in 2020-21. The trend fitted to every season from 1993-94 to 2018-19 predicts 56.57%. The gap is 2.58 percentage points, or 5.6 times the root-mean-square error of that fit. No other season in the record is more than 2.2 away. And the four seasons since the stands refilled sit back on the line.

This matters more than it looks, because the most serious objection to the whole ghost-game literature is that home advantage was already falling and a naive before-and-after would mistake the trend for the treatment. Reade, Schreyer and Singleton put it plainly in 2022: the drop after the restart did not obviously deviate from the pre-pandemic trend over the few seasons they had. With 33 seasons and five more on the far side, it does. The ghost season is the largest residual in the record, and the recovery is as sharp as the fall.

2. Nobody had to tell us when the crowds went

There is a temptation, in a study like this, to type in the dates: this league shut here, that one reopened there. Every typed date is a place where the study can quietly become wrong. So we did not type them. We asked the fixture list where the hole was.

For each division, take every match date in 2019-20 and find the longest gap between consecutive dates. In a normal season the biggest gap is a winter break: two or three weeks. In 2019-20 eleven divisions have a gap of between 66 and 104 days, and the other eleven simply stop in the second week of March and never resume. The suspension is not an assumption here. It is a shape in the data.

The restart dates the fixture list hands back are the ones the record reports independently: the Bundesliga on 16 May 2020, first back in Europe; Portugal on 3 June; Greece on the 6th; Spain on the 10th and 11th; Turkey on the 12th; England and Italy on the 17th and 20th. France, the Netherlands, Belgium and all four Scottish divisions never came back that season.

That gives the tightest comparison available anywhere in this problem: the same season, the same squads, the same table, the same referees, with a crowd and then without one. To keep the comparison clean we throw away everything from 15 February 2020 onward on the crowd side, because Italy and Greece had already begun locking gates in late February and Turkey played a week of closed-door matches before it suspended. What is left is 2,537 matches with spectators and 1,040 without.

Read the significance column and the page's whole argument is already visible. The scoreline measures move in the expected direction and cannot be told from noise: home points share falls from 56.9% to 54.7% at p = 0.17, goal difference from 0.295 to 0.204 at p = 0.16. The discipline measures move like a switch: the yellow-card gap goes from +0.344 to −0.131, a swing of nearly half a card a match at t = −7.3, and the foul gap flips sign at t = −4.1.

This is exactly the split the published literature has been arguing about. Bryson, Dolton, Reade, Schreyer and Singleton, working on 2019-20 alone, concluded that an absent crowd had no effect on the final scoreline and reduced the away side's yellow cards by about a third of a card. Wunderlich and colleagues titled their paper Home advantage remains and reported the referee measures moving at p < .001 while points and goals came in at p = .068 and p = .056. Scoppa, pooling ten seasons rather than one, found home advantage roughly halved and highly significant.

They are all looking at the same world. The disagreement is a power problem, and this page can show it in one dataset: the within-season design has 1,040 empty matches and cannot resolve the scoreline effect; the season-long design below has 7,648 and can. Nobody was wrong. The scoreline effect is smaller relative to its own noise than the refereeing effect is, so it takes about seven times as much football to see.

3. Everything that moved, moved on one side. Except the cards.

Widen out from the one interrupted season to the whole ghost season, 2020-21, when every league in this panel played essentially the entire campaign to empty stands. Set it against the six clean crowd seasons around it: 2017-18, 2018-19, and 2022-23 through 2025-26. That is 46,455 matches with spectators against 7,648 without.

Now ask the question that a difference-of-differences hides: which side of the pitch actually changed?

The pattern is almost too tidy. The home team got worse and the away team did not change. Home shots fell by 1.16 a match at t = −18.4; away shots moved by 0.06, which is nothing. Home corners fell; away corners did not. Home goals fell by 0.10; away goals rose by 0.007, which is also nothing. Whatever the crowd was doing for the home side, it was not doing anything to the visitors.

And then the cards break the pattern, in the other direction. Home yellows did not move (−0.02, p = 0.18). Away yellows fell by 0.27 (t = −16.35). The one measure where the away side changed is the one the away side does not control.

Fouls, meanwhile, went up for everybody: home fouls by 1.25, away fouls by 0.68. More fouls were being given and fewer of them were being carded, which is a level shift in how the season was refereed, not a home-and-away story. That is why the ratio matters more than the count.

4. What a foul was worth, depending on who committed it

Divide cards by fouls and you get the only number on this page that is really about the official: the rate at which a foul became a booking. This is the measure Endrich and Gesche used in German football in 2020, conditioning the card on the foul so that a change in play cannot masquerade as a change in judgement.

With a crowd in the ground, an away foul was 11.8% more likely to be punished with a card than a home foul. With the ground empty, 2.6%. The same offence, the same competition, the same officials, and a different verdict depending on which shirt committed it, until there was nobody there to hear it.

Three of the 22 divisions are left out of that ratio, and the reason is a single sentence in the archive's own notes: for France's second division, Belgium and Greece it records free kicks conceded rather than fouls, which is a wider category. The rate is computed on the other 19, over 44,050 matches that carry both a foul count and a card count for both sides.

This has a laboratory ancestor. In 2002 Nevill, Balmer and Williams sat 40 qualified referees in front of video of 47 challenges from a Premier League match and split them into two groups: one heard the crowd, one heard silence. The group with the noise gave 12.5 fouls against the home side; the silent group gave 14.8, which is 15.5% more. Away fouls barely differed. Their conclusion, in their own words, was that the dominant effect of crowd noise was to reduce the number of fouls awarded against the home team, rather than increase the number against the away team. Two decades later the same experiment ran itself, at a scale no ethics committee could have granted, and the conditional rate moved the same way.

5. The same men

An objection survives all of the above: perhaps the officials changed. New referees, a new directive, a quiet instruction. The English and Scottish files, alone in this archive, name the referee for every match, and the German and Italian ones do for part of it. That is enough to ask a much harder question: did individual referees change, against themselves?

Take every named official with at least 20 matches in the crowd seasons and at least 20 in the ghost season. There are 84 of them, across 12 divisions. For each, compute his own home-favouring card gap in each window.

Their average gap goes from +0.274 cards a match to −0.006. It falls for 65 of the 84. The paired t is −6.97. These are not different men applying a different standard. They are the same men, and the standard they applied moved when the noise stopped.

6. Is it just the run-in?

The 1,040 empty matches in section 2 were all end-of-season matches, and end-of-season matches are strange: dead rubbers, decided titles, teams with nothing to play for. If a normal June behaves like that on its own, the whole comparison collapses.

So run it as a placebo. The restart left each division a specific number of matches: 92 in the Premier League, 124 in Serie A, and so on. In every other season, take that same division's last 92 or 124 matches and compare them with its pre-February matches, exactly as before. If a run-in by itself moves the card gap, it will show up in every year.

It shows up a little. Run-ins do drift: the average placebo swing across the 25 other seasons is −0.078 cards, with a standard deviation of 0.071 and a worst case of −0.213. The 2019-20 restart swings −0.474, more than twice the most extreme run-in in 26 seasons and 5.6 standard deviations below the placebo mean. It ranks first of 26, which is the smallest rank the test can return.

7. Twenty-one of twenty-two

An effect that appears in one league is a story about that league. Here is every division in the panel, ghost season against crowd seasons, sortable by any column.

The yellow-card gap fell in 21 of 22 divisions. The single exception is Scottish League One, on 110 ghost matches, where it rose from 0.187 to 0.218. Under a sign test that is p = 1.1 × 10⁻⁵. Home points share fell in 18 of 22, p = 0.004. Red cards fell in 12 of 22, which is exactly what a coin does: red cards are too rare, at about one per ten matches, for this design to say anything, and the papers that claim a red-card effect are on thinner ice than the ones that claim a yellow-card effect.

8. The part the headlines skipped

Everything so far says the referee's thumb came off the scale. Here is the arithmetic that says it was never a very heavy thumb.

Home advantage, measured as points per match, was 0.4085 in the crowd seasons and 0.2393 in the ghost season. The home side lost 0.1692 points a match. Over the same windows, its net yellow-card advantage fell by 0.2524 cards and its net red-card advantage by 0.0117.

So: how much is a card worth? For a red card there are real estimates. Ridder, Cramer and Hopstaken, in 1994, built the design that removes the obvious trap, which is that red cards go disproportionately to teams already in trouble; their conditional estimate is that a sending-off raises the other side's scoring rate by 88% and barely moves the ten-man team's own. Badiella and colleagues, in 2023, put the expected impact of a red card with 30 minutes left at 0.39 to 0.50 goals. Call a goal worth roughly a point and a red card lands somewhere near half a point, perhaps a whole one if it comes early.

For a yellow card there is essentially nothing, and that absence is itself informative. The one study we found that models goals and bookings jointly, Titman and colleagues on 1,864 English matches, reports no direct effect of yellow cards on goal-scoring rates at all. The yellow-card literature that does exist is about deterrence rather than outcomes: a booked player fouls less because he fears the next one. If a yellow card is worth nothing on the scoreboard, the whole disciplinary channel collapses to the red-card term, and the red-card term is very small.

Rather than pick a number, pick your own.

At the values most people would defend, a yellow at 0.05 points and a red at 0.9, the disciplinary channel buys about 14% of what the home side lost. Set the yellow to zero, as Titman's result suggests you should, and it buys 6%. To pay for the whole of it on yellows alone you would have to price a caution at 0.67 points a card, which is a quarter of a win. To pay for it on red cards alone you would have to price a sending-off at 14.5 points, and a football match contains three.

That is the finding this page most wants you to leave with, because it is the one that runs against the easy story. The bias was real, it was unanimous across leagues, it was visible inside individual referees, and it vanished completely when the stands emptied. It was also never large enough to be most of home advantage. Most of what the home side lost, it lost in its own play: a shot a match, half a corner, a tenth of a goal. The crowd was talking to the referee, and the referee was listening, and it mattered less than the fact that the crowd was also talking to the players.

The bound above is a bound, not a decomposition. Cards and play are not independent: a card changes how a team plays, and how a team plays draws cards. What the arithmetic rules out is the strong version of the story, in which refereeing bias is home advantage. It cannot be.

9. Two clubs, one ground

There is a second, older way to pull the four causes apart, and it does not need a pandemic. In a handful of cities two clubs share a single stadium. When they play each other, the away side travels nowhere and plays on the pitch it trains on. Travel and familiarity are exactly zero. What remains is the crowd, which still favours the nominal home club through its season-ticket allocation, and the designation itself.

Ponzo and Scoppa built this design in 2018 on 22 seasons of Serie A and 128 such derbies. This archive holds 33 seasons and seven shared grounds: four in Italy, the Jan Breydel in Bruges, which was purpose-built in 1975 as a home for both Club Brugge and Cercle Brugge, the Munich Olympiastadion for the Bundesliga seasons after 1860 moved in alongside Bayern in 1995, and Selhurst Park for the seasons Crystal Palace and Wimbledon were both there and in the same division. Because each pair hosts the other exactly once a season, any difference in the two clubs' strength cancels out of the pooled figure by construction. The ghost season is left out of this arm, since the question here is what a shared ground is worth with a crowd in it.

Across all seven grounds the home side takes 55.8% of the points, against 59.8% in the same division-seasons at large. Restricted to Serie A up to 2012-13, close to Ponzo and Scoppa's window, this archive gives home points 1.708 and away 1.005 in the league as a whole, against their published 1.707 and 1.001: an independent reproduction from a different source, to three decimal places.

But the derby arm cannot carry much weight, and we will not pretend otherwise. Two hundred and fifty-two matches give a standard error of 2.7 percentage points on that 55.8%, so the honest reading is that a shared ground removes somewhere between all of home advantage and none of it. Ponzo and Scoppa read their version as crowd support accounting for roughly 60% of the effect. Van de Ven, in 2011, used the same design and titled his paper Supporters are not necessary for the home advantage. The design is good; the sample it can reach is small.

10. What came back, and what did not

The strongest thing about a switch is that it can be thrown twice. Anything that only ever went one way, and stayed, cannot explain a change that reversed.

Video assistant referees arrived in these leagues between the 2017-18 and 2019-20 seasons, and in Scotland later still, in 2022-23. None of them adopted it in the ghost season and none of them gave it back. Home advantage had been declining for three decades and continued to. Neither can produce a card gap that is 0.282 across the six crowd seasons, 0.029 in the ghost season, and 0.271 the very next season, when the turnstiles opened again.

The five-substitute rule is the confounder that deserves a test rather than an argument, because it did arrive in 2020. It arrived unevenly. The Premier League's clubs voted against keeping it twice, in August and September 2020, and played the entire ghost season on three substitutes while most of the continent played on five. If the vanishing card gap were a substitution effect, the one league that did not change its substitutions should not show it. It shows it: the Premier League's yellow-card gap went from 0.250 in the crowd seasons to 0.024 in the ghost season, t = −2.60 on 380 empty matches.

One honest complication, which we found by going looking for it. Fischer and Haucap reported that the Bundesliga's home advantage collapsed after the 2020 restart and that the effect decayed within about six matchdays; a 2024 preprint by Schank, Voigt and Orthey reports that it rebounded to near normal in 2020-21 while the stands were still empty, and reads that as adaptation. In this archive the German result reproduces exactly: Bundesliga home point share was 55.8% before the suspension, 43.3% after the restart, and back to 55.4% the following, entirely empty, season.

It does not generalise. Pooled over the eleven divisions that restarted, home point share was 57.5% with crowds, 54.7% in the first empty weeks and 54.5% across the whole empty season that followed. There is no rebound outside Germany. The adaptation story is a real finding about one league, and the fleet of studies built on the Bundesliga alone should be read with that in mind.

11. What the crowd was for

Put it together and the four classical causes separate, unevenly and with different confidence attached to each.

Travel and familiarity look small. Two clubs sharing a stadium still show most of a normal home advantage, though the sample is thin enough that this is the least secure claim here.

The crowd acting on the players is the biggest measurable piece, and it acts in one direction only: it raises the home side's attacking output and leaves the visitors alone. A shot, half a corner, a tenth of a goal per match, all of it on one side of the pitch.

The crowd acting on the official is the cleanest, most unanimous and most completely reversible effect in the whole record: 21 of 22 divisions, 65 of 84 individual referees, gone in an empty stadium and back within a season. It is also, on any defensible accounting, a minority of what home advantage is made of.

Which leaves a nice small irony to finish on. The part of home advantage that everybody argues about, the referee, is the part we can measure best and the part that matters least. The part nobody can argue with, the ball going in the net more often at one end, is the part we understand worst. The stands emptied, the thumb came off the scale, and the scale kept tilting anyway.