Let us first say this about referees: they have evolved into marvellous species, worthy of an Attenborough voiceover, with lungs as deep as a blacksmith's bellows and the 4D-vision of a teacher on a school outing. Even in the hyper-accelerated, scheming-cheating thrash of modern football – where these sheriffs with headsets make roughly 600 decisions every match – they get an enormous amount right.

Yet the following is also true: they are unwittingly and incontrovertibly biased towards home teams – especially those with larger crowds.

"The evidence is overwhelming," says professor Alan Nevill, a specialist in biostatistics at Wolverhampton University. "And it is across a range of sports including football."

We can all cite oven-fresh examples from the past week. That bite and a shin-rake missed at Anfield. An offside goal and buttocky bodycheck ignored in Munich. A phantom penalty in Basel. Another offside goal waved through at the Emirates. In isolation these events tell us little. But by probing the issue from multiple angles, using large data sets and advanced statistical techniques, a pattern emerges. Referees subconsciously favour home teams.

A decade ago, Nevill led a study in which 40 qualified referees were asked to judge 47 incidents from a 1998-99 match between Liverpool v Leicester; half watched with crowd noise, the control group in silence. The results were surprising: those viewing the footage with crowd noise awarded significantly fewer fouls (15.5%) against the home team compared with those watching in silence.

In the NBA, fewer fouls are given against star players at home, while when Bundesliga matches are played in stadiums with running tracks the bias referees usually show the home team halves. Another paper – The 12th Man? Refereeing bias in English and German soccer – shows that home teams receive fewer yellow and red cards, even when accounting for them being disproportionately the favoured team and disproportionately ahead during games.

One of the authors, Dr Babatunde Buraimo – a senior lecturer in sports economics at the University of Central Lancashire – talks me through the "sophisticated statistical model" involving "minute-by-minute bivariate probit analysis". It is impressive stuff, although you don't need a maths degree to know the likely consequences of being reduced to 10 men by a home-town decision. Forthcoming research also suggests that referees favour home teams by adding more injury time in addition to the amount the fourth official holds up – when a match is closer and when any additional time would favour the home team.

You might think improved referee training could change this. But Nevill's latest article, in the Psychology of Sport and Exercise last month, suggests it is not that simple. It is true that home advantage has declined in England and Scotland – something Nevill says is due to a "systematic improvement" in referees' decision-making accuracy because of better training and monitoring. There is, however, a caveat. The steepest decline in home advantage is to be found in the lower leagues and shallowest in the Premier League. "I think it's the first scientific proof that it's the crowd having the influence," Nevill says. "Referees' objective capabilities are still not immune to the unconscious influence of the crowd."

Psychologists call this influence conformity. And you can see how it happens. If 70,000 fans scream for a decision it can reinforce the referee's first impression of an incident. Or it can make them subconsciously decide to get the crowd off their backs by giving them what they want.

It has long been mooted that home advantage is partly down to playing in a familiar stadium, or the adverse effects of travelling. Maybe for an NFL team playing across the other side of America. But in the Premier League?

Another myth we cling to – that shouting until your tonsils are red-raw can somehow inspire your team – also has little to back it up. One example cited by Tobias Moskowitz and Jon Wertheim, the authors of Scorecasting, is that in 624 NHL shootouts between 2005-09 – when you might expect the home crowd to be more vociferous and therefore more inspiring – the home team won 304 (49.4%) times and the away team 316 (50.6%).

When looking at reasons for home advantage we first direct our attention to the man in the middle. We assume that whatever the terraces spit at referees runs off, like water off Gore-Tex. Research suggests otherwise.

So what should be done? One view is to just lump it. As David Forrest, professor of economics at Salford University, points out. "Statisticians think justice is everything. But randomness and noise create uncertainty of outcome, which is one of the appeals of sport."

On the other end of the scale, video evidence – while not to everyone's taste – can help. When the instant-replay challenge was introduced to the NFL in 1999 it led to a 29.4% drop in home advantage. In football the effect could be even greater: because the game is low scoring, one decision – a penalty, red card or offside goal – is more likely to affect the result.

Whatever your view, doesn't this issue deserve a little more attention? As it is, any discussion of referee bias rarely goes beyond weary laments involving Manchester United and the lack of away penalties at Old Trafford – something, incidentally, that silicon chips are yet to show has any statistical significance.