Moments after Arsenal’s Champions League ambitions were brutally coldcocked by Barcelona, their manager, Arsène Wenger, estimated his side’s chances of a miracle at the Camp Nou at 5%. He should be so lucky. Their hopes of qualifying for the quarter-finals are now barely one in 100.

I say this with some confidence based on a new piece of academic wizardry in the European Journal of Operational Research, with a distinctly unacademic title: “What is a good result in the first leg of a two-leg football match?” We know the answer: a thumping great shellacking. But the academics were searching for deeper truths. For the first time they wanted to quantify the effect of the away goals rule – and to show how a first-leg result affected a team’s chances of qualification.

The boffins began by analysing 6,975 two-legged Champions and Europa League ties, and their predecessor competitions, between the 1960s and 2012-2013. From this they found the importance of home advantage had slipped over time. Between 1965-66 and 1980-81, 56.2% of first legs were won by the home team. That dropped to 46.1% from 1997-98 to 2012-13.

That came as no great surprise. It mirrors what is happening in European domestic football. All sorts of theories have been advanced for this decline, including better refereeing decisions and improvements in travel, making for less fatigue, but no one knows for sure.

The academics then asked another question: how great is the damage when a club at home in the first leg concedes an away goal? This takes us back neatly to Arsenal v Barcelona. For 70 minutes the match was in the balance. Then Arsenal got frisky and were ripped apart by Lionel Messi on the counter. A few minutes later, a Messi penalty doubled Barça’s lead. Game over.

Beforehand Wenger had warned that “if you concede a goal at home in the Champions League it’s a knife in your heart every time”, adding that “even at home 0-0 is not a bad score”.

The Frenchman’s wounded reaction at the defeat showed much he was bleeding. His team were chastised for being “naive”, the implication being they should have kept it tight. The academics’ research suggests he was probably on to something.

They found that if two teams of equal strength face each other and the first leg finishes 0-0, a home side has a 46.7% chance of progressing. A 1-0 victory lifts that to 65.3%. But losing 0-1 drops it like a stone, to only 12.5%. Arsenal may have done better to stick rather than twist. The academics also found the most balanced result going into a second leg is 2-1 – a score that leaves the home side with a 55.3% chance of progressing. By contrast, a 1-0 win would give the home side a 63.5% chance of going through.

It means that winning 2-1 gives a probability of advancement to the next round of exactly 8% less compared with 1-0. As two of the report’s authors, David Forrest and Juan de Dios Tena of the University of Liverpool Management School, point out, this is the first time the impact of the away goals rule has been quantified.

There is one other thing worth noting. What constitutes a good first-leg result is not static. It changes over time. As Forrest points out: “A 0-0 used to be a bad result for the home team. Up to 1980, a goalless draw meant a home team had just a 27.3% chance of going through. Now it’s nearly half.” Again, that’s the lessening effect of home advantage at play.

So where does all this number crunching leave us? First, it again opens up the debate about whether the away goals rule should be scrapped, either because it is unfair or has the opposite outcomes of what it supposed to do. As Wenger noted last week, the rules of the modern European Cup “encourage you to defend at home and attack away because of the importance of the away goal”.

He has beaten this drum before. As he pointed out in 2008: “Instead of having a positive effect it has been pushed too far tactically in the modern game.”

But this latest research, published in December 2015, backs up Wenger again. The away goal is essentially an arbitrary rule to either avoid having a play-off, or reduce the chance of a penalty shootout, yet it skews the way teams play and sometimes the result too.

Of course you could counter this by arguing that slow-burn tension in the first leg often explodes in the return tie, making up for any initial cageyness. But given the effect of the away goals rule is so strong, Uefa might be wise to follow the League Cup’s lead by introducing it only after extra-time.

For now Wenger is trying to pick up the pieces of another Arsenal defeat at Manchester United. But after a rush of games against Swansea City, Tottenham Hotspur, Hull City and West Bromwich Albion in the coming days he will soon have another big decision when the Gunners travel to Barcelona for the return leg on 16 March. To shoot for the stars, or accept the cold-stone reality that a comeback is surely beyond his side. All the evidence suggests it is an easy decision.