No single event in the history of mankind has inspired more conspiracy theories than the assassination of John F. Kennedy. From Soviet snipers to a CIA-lead coup, the failings of the superficial investigation into the President’s death in Dallas created a void that countless amateur experts have attempted to fill as much with the powers of their imagination as rational thought processes.

But the prevailing argument against such theories, aside from questioning the legitimacy and integrity of the research they’re based around, is the concept of proportionality bias: in simple terms, the idea that a big event - such as the daylight murder of a President - must have an equally big cause.

The idea of someone as miniscule as proclaimed “lone nut” Lee Harvey Oswald having such a devastating impact on American and international politics is admittedly a difficult one to compute.

Which is perhaps why, amid a series of freak results in the Premier League this season, the immediate assumption has been that they could only come to fruition during the most unconventional period of the competition’s history in which games have been played out in empty stadia, in the absence of thousands of baying fans as the United Kingdom continues to unsuccessfully turn the tide in the war against Coronavirus.

Never more so than after a Super Sunday in which Manchester United conceded six goals for just the second time since the 1930s and Liverpool became the first reigning champions to concede seven goals in a game since Arsenal in 1953. Surely only an explanation as gargantuan as a global pandemic would suffice for two clubs so traditionally dominant to lose by such drastic margins within hours of each other. 

It would be foolish to think that changes to the Premier League environment haven’t impacted performance. It is an unusual, untraditional setting that every player in the division will have reacted to differently depending on their own internal psyche, and former Swansea and Sheffield Wednesday manager Carlos Carvajal believes the reduction of pressure from the stands could sway performance by 20%.

"The absence of fans in big clubs with big pressure on them reduces the focus and concentration of players. Fans open up your senses, increase the intensity of your muscular reaction. It has a huge influence in the head of players, I would say even 20%. The influence of fans of big clubs normally has a clear effect on opponents too as they feel more pressured. Without them it is 11 v 11 with a ball and a ref - everything balances out."

But statistically speaking, the overall impact of playing behind closed doors hasn’t been as staggering as the shocking nature of some of the results would have you believe.

According to a study conducted by bettingodds.com, the number of goals per game in the Premier League since the restart in June has only risen by 0.48. Undoubtedly, that’s a noteworthy margin - the kind of margin that would lead to less predictable flat out results (wins, draws and losses) if we assume all Premier League teams have a similar chance of scoring one extra goal every two games.

But in reality, we know that the teams who finished near the top of the table last season have a much greater chance of scoring that extra goal than those who didn’t, because they have naturally superior players and usually far more of them, which in itself contradicts some of the shock results inspiring theories of correlation between crowdless stadia and crazy scores - such as West Brom going three goals up against Chelsea and West Ham coming back from the opposite position against Tottenham.

In any case, even without trying to work out who those extra 0.48 goals per game are going to, while that surplus may be big enough to influence flat out results, it clearly isn’t so great as to explain how Liverpool and Manchester United managed to concede 13 goals between them on a single Sunday afternoon. There must be other factors at play than merely the absence of crowds making previously relegation-threatened Aston Villa a team capable of putting seven past a side that have won the Champions League and the Premier League over the last two seasons.

Ollie Watkins celebrates a hat-trick against Liverpool

So how exactly do we explain that? Well, perhaps the first thing to remember is that shock scorelines in the Premier League are uncommon but they aren’t unusual either. Take pre-lockdown last season, for example. Leicester City hammered Southampton 9-0 at St. Mary’s, Chelsea lost at home to relegated Bournemouth, Norwich City beat and outplayed Manchester City at Carrow Road, and in almost the exact same manner as the start of this season, Man United lost at home to Palace in August 2019.

What is clear, however, is that we’ve seen a much greater return of goals so far this season, with 3.58 per game representing a sizeable jump from last term’s 2.72. If just over half of that deficit (the aforementioned 0.48) is due to crowdless stadia, then there’s still a 0.38 increase down to other factors.

A big part of that is no doubt the controversial implementation of the handball law at the start of the campaign leading to an uplift in penalties, but even that should flatten out soon now that the traditional understanding of the rules has been reinstated.

And there are a further two influences worth bearing in mind; first and foremost, we are only a handful of games into a new season and it’s by no means unheard for the early stages of a fresh campaign to produce unlikely results - not all teams prepare as well as others, and that translates into inconsistent performances until every squad reaches a similar level of fitness. Accordingly, the statistics and averages could look very different once the remainder of the 2020/21 term has been played out, whether that’s behind closed doors or not.

Heung-min Son scores at Old Trafford

Secondly, United and Liverpool’s defeats contain their own personal causes, in addition to trends throughout the Premier League as a whole. In their prior away game, Tottenham put five past Southampton whereas United had previously been ripped apart by Palace and were fortunate to beat Brighton, while Liverpool had conceded three on the opening day against Leeds and Aston Villa entered the match off the back of a 3-0 romping of Fulham, their confidence sky-high.

Throw in the fact there’s a much greater emphasis on attacking football than ever before in the Premier League, and the shock scores we’ve seen this season are clearly down to a combination of factors - both club-specific and division-wide - rather than a simple equation of no fans in stadiums meaning more goals, massive upsets and crazy games.

Another aspect of crowdless football the statistics debunk is that the absence of crowds has significantly damaged home advantage, a theory which initially surfaced after results in the Bundesliga - the first domestic competition to recommence after Europe entered a period of nationwide lockdowns - appeared to dramatically swing in favour of visiting teams.

Indeed, while there has been some movement to the benefit of away sides, the actual gain per match has been just 0.09 points - so over the course of an entire season, Premier League teams will, on average, pick up an extra 1.71 points from their 19 away games. A miniscule difference. But how significant any swing towards away teams actually is anyway remains another debate altogether, because whatever teams lose collectively in home points, they’ll ultimately gain them by an almost identical amount on the road.

Old Trafford with empty seats

But what the numbers do make apparent is how the absence of supporters has affected teams differently, and while - again - there are likely a multitude of influences at play here, on the most-part it does make sense. The likes of Burnley, Crystal Palace and Sheffield United all employ defensive philosophies that play to the strengths of militant fanbases in tightly-packed, old-fashioned stadiums, creating a feeling that the whole crowd are quite literally right behind the team. Perhaps unsurprisingly then, they’ve seen the fourth-biggest, third-biggest and biggest drop-off respectively of points per game since the Premier League restarted, albeit this including both home and away results.

Anfield, too, produced some exceptional atmospheres as Liverpool chased down the Premier League crown last season and although there are some caveats to bear in mind, such as the fact the Reds were able to slowly but steadily march their way over the line towards the end of last season because they had such a healthy points lead, in addition to a pre-lockdown run of 18 consecutive wins being unsustainable, Jurgen Klopp will be concerned that in the absence of supporters, his side have suffered the second-biggest points drop of any Premier League team.

But if the statistics prove anything, it’s that placing uplifts, downturns and numerical swings on the single cause of the impact of supporter absence is something of a fallacy. There are numerous factors at play, from a team’s individual circumstances to the changing implementation of Premier League rules, and thus working out exactly why a team’s fortunes may have changed, or why there is greater unpredictability throughout the league since before lockdown, is a complex challenge.

For all the impact empty stadiums have inevitably had, there are equal, similar and arguably greater forces at play too.