Football is a simple game. Twenty-two players chase a ball for 90 minutes, and at the end the team with the highest wage bill wins. My version of Gary Lineker’s original line on the inevitability of German victory may be less witty than his, but it captures something of English football’s growing credibility crisis.

The association between spending power and success on the pitch has been established for some time in academic circles, and went mainstream in the 2009 book Soccernomics, co-authored by my colleague Simon Kuper. On average, the more money a football club spends on its staff — both players and coaches — the better its results.

It’s an inconvenient truth for a sport that has always styled itself as belonging to everybody. For the most part this has been tolerated by fans and owners of the less wealthy clubs — this is partly because there has always been space for a meritocratic interpretation in which the clubs with the most money have earned it through superior performances, rewarded by prize money and more paying fans. And partly because the gaps in performance tracked the gaps in spending — which is to say they have been merely large, rather than vast.

But neither of those factors holds true now. First, there is the torrent of money poured into elite clubs by billionaire individuals, states and latterly US private equity, which few outside of the recipients’ most diehard fans would claim has been earned on the pitch. And second, the gaps in performance have become gulfs. By my calculations, over the past 26 years, the gap between the top and bottom clubs has widened by 19 points, and the team that tops the table has improved its goal difference by an average of one goal every year.

None of these breaches of football’s social contract are exclusive to Manchester City, but there is a reason the Abu Dhabi-owned club has become the lightning rod for criticism of so-called financial doping. Where other billionaire-owned sides have generally shifted themselves along the trendline — spending more money and enjoying a commensurate improvement in performance — City have sheared away entirely, dominating even opponents with similarly substantial wage bills.

Averaged over the last nine seasons, most Premier League clubs have fared roughly as well as we would expect based on the historical relationship between wages and performance. There are of course exceptions — Brighton have earned about seven more points per season than their wage bill would indicate, while Manchester United have underperformed by about six points — but City are an outlier. The club has bludgeoned its way to 15 more points per season than we would expect based on the wage bill relative to other clubs.

Such an extreme divergence from the historical trend raises an obvious question: how have they managed to reach a level of performance that would typically be associated with a team spending tens of millions more?

One possibility is that just like other, more modest over-performers Brighton and Liverpool, City have mastered the arts of data-driven recruitment to maximise the on-pitch value of every pound they spend. The additional factor of employing arguably the best coach in the world, Pep Guardiola, provides a substantial extra boost. This is certainly plausible — since Guardiola’s arrival, the “Citizens” have been the best-performing team in the league every year across a raft of different metrics.

However, among the more than 100 allegations of financial rule-breaking levelled at City by the Premier League last week is a more ominous possible explanation of the club’s outsized success: that it could have been paying some of its playing and coaching staff additional fees not disclosed in its accounts.

To be clear, the club has denied any wrongdoing and the statistics presented here provide the what, not the why or the how. But for as long as the Premier League allows a meritocracy to become a plutocracy, its integrity and credibility will be in jeopardy.

Whatever the independent commission adjudicating the club’s case concludes, Manchester City have helped to break English football, even if they haven’t broken the rules., @jburnmurdoch

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