The stats behind the ‘beautiful game’

In the beautiful game, statistics show that home advantage truly does make a difference. The bigger teams also have an edge as their larger fan bases, and the noise they make, could possibly influence a decision on the field.

Arsenal kicks off their Premier League campaign today when they host Liverpool. Getty Images

The outcome of Sunday’s clash between Arsenal and Liverpool, the first big Premiership game of the season, may be uncertain, but one thing’s for sure: it will trigger an outbreak of Monday Morning Manager syndrome.

Anyone who works in an office knows the symptoms: the resident “experts” banging on about why the outcome was actually inevitable, given the … well, you name it. Team selection, formation, substitutions, lucky breaks, bad refereeing – the list is endless.

It’s this mix of the random and the predictable that attracts millions to the Beautiful Game, and not just the armchair pundits. It’s long fascinated researchers, among them statisticians who have set about putting the long-held beliefs of amateur pundits to the test.

One thing that is sure to be on the minds of fans watching tonight’s game is the Law of Home Advantage: that teams playing in their own stadium have an edge over the visiting side.

According to this, Arsenal should benefit from the fact that tonight’s match takes place at their home ground, London’s Emirates Stadium.

Folklore is one thing, but is it actually true? And how big is the advantage anyway? This is where the statisticians come in, gathering real-life evidence and putting such claims to the test.

In a landmark paper published in 1998, statisticians Dr Mark Dixon and Dr Michael Robinson analysed the outcome of more than 4,000 matches played by English league clubs during the 1990s.

They confirmed the folklore about home advantage, and showed it’s a strikingly strong effect, with 45 per cent of games being won by the home team, almost double the win rate achieved by the visiting side.

Dr Dixon and Dr Robinson also found evidence for another long-standing belief of fans: that games come to life with a first goal scored just before half-time.

Analysis of the data showed that scoresheets were often blank until about five minutes before half-time, at which point the chances of a first goal spiked.

Once the deadlock had been broken, the scoring rate in the match rose significantly, with every extra goal increasing the chances of yet more going in. In particular, if the scoreline reached 2-2, a high-scoring thriller of a match often ensued.

Not all the cliches of the terraces stood up to scrutiny, however.

Many fans believe in the theory of Immediate Strike-Back, according to which a team that has just conceded a goal is likely to respond with a sudden spurt that leads them to get a goal themselves.

Dr Dixon and Dr Robinson not only failed to confirm the theory, but found evidence for the opposite.

The team that scores first typically works hard to defend that goal and avoid seeing it quickly cancelled out.

Since the Britons’ paper, others have applied the same approach to other time-honoured claims in football.

The UK Royal Statistical Society journal Significance recently published a study of a notorious source of arguments among fans: does having a player given a red card and sent off make a team easier or harder to beat?

There are perfectly good arguments on both sides.

Being reduced to 10 players means that those remaining have to work harder and smarter to keep up with the opposition, let alone beat them. On the other hand, the psychological impact of being behind may make players try harder.

At a slightly more sophisticated level, there is the resulting loss of shape of the 10-member team, which often leads managers to retrench in defence, making them harder to score against.

To see which effect wins, study author Adam Greenberg analysed the outcome of games over four seasons of Premiership football in which red cards had been issued.

No matter how the data was analysed, the result was the same. As perhaps anyone rational enough to avoid following football would think obvious, a team of 10 players really is easier to beat.

No special magic kicks in when a player is shown a red card, nor can managers make up for the deficit.

But Mr Greenberg did find something to keep the Monday Morning Managers chattering. While both teams suffer if one of their players is sent off, the home sides suffer far more.

Exactly why isn’t clear. Mr Greenberg suggests that maybe the home team feels more vulnerable to having its advantage undermined in front of its fans, and loses confidence.

Mr Greenberg also found evidence for another cause of countless arguments: big teams do seem to have fewer refereeing decisions going against them, and fewer red cards.

While the effect is not strong, there does seem to be a link between where teams end up at the end of the season, and how many red cards they get.

Mr Greenberg warns of the well-known statistical trap here: correlation is not causation, and it is hard to tell which comes first: the red cards, or the lowly league position.

But a clue may come from research into that much better-attested “law” of football, the home advantage.

Research has shown that this depends on the size of the crowd: the bigger, the better for the home side. And the big clubs have the biggest crowds of all.

So could it be that the fans themselves are affecting the decisions?

Some years ago, researchers at Liverpool John Moores University carried out an intriguing study that may explain what is happening.

They asked experienced referees, players and coaches to judge over 50 tackles recorded on videotape, with only half of them allowed to hear the crowd reaction.

The results were remarkable. Of the tackles, which weren’t clear-cut fouls, those that were both seen and heard were over 40 per cent more likely to be judged favourably for the home team than those judged with no sound.

In other words, the roar of the home team really can influence decisions.

Thus it seems that, even in these days of billion-pound teams, whose players earn millions, there’s still a role for the fans on the terraces.

Those unable to turn up in person should be aware, however, that there’s no evidence that yelling at the TV affects anyone other than the neighbours.

Robert Matthews is visiting professor of science at Aston University, Birmingham.