The good news for Chelsea is that they are unbeaten since Guus Hiddink replaced José Mourinho as manager in December. The bad news is that 10 points from six league games is probably not a start that is going to close the gap on the top four – which stands at 14 points. The FA Cup remains a possibility but, unless Chelsea somehow win the Champions League, a change of manager alone will not have been enough to salvage the season.

The collapse of the champions is unprecedented in the Premier League era (which in this instance is a useful shorthand for saying since the economics of football dictated a self-perpetuating elite and rigid stratification). It is not necessarily to deny that Mourinho had become a toxic presence to point out that when something is not working at a club, the easiest solution is to sack the manager, who becomes a scapegoat, his slaughter symbolically absolving his people.

It is a ritual that has been enacted, as James Frazer demonstrates in The Golden Bough, by various groups with various degrees of literalness for millennia.

In The Manager Barney Ronay essentially argues that the role was invented to insulate the board of directors from blame.

There is a growing body of thought that believes that the manager is not as significant as football has made him. In Why England Lose, for instance, Simon Kuper and Stefan Szymanski argue that, in the 10 years beginning in 1998, a club’s total wage spend accounted for 89% of the variation in its average position in the league table. In The Numbers Game Chris Anderson and David Sally consider the decade from 2001-02 to 2010-11 and conclude that the actual figure is 81% – that a manager accounts for, at most, 19% of where a team finishes in the league.

The lesson appears to be that a club should concentrate its spending on players rather than the manager – the corollary, perhaps, being the argument that Chelsea’s struggles this season have been largely caused by transfer spending – a point Mourinho himself made obliquely at times and that is highlighted by the lack of attacking cover.

Perhaps that is true. But if we really have been deluded since the days of Herbert Chapman by the mystique of the manager, conforming, perhaps to Thomas Carlyle’s Great Man theory of history, there are some curiosities to consider. Only four managers (Tom Watson, Chapman, Brian Clough and Kenny Dalglish) have won the league with more than one club. It is true that managers used not to move as much as they do now, but that still suggests that it is rare for the right manager to find himself with the right players in the right circumstances.

Perhaps even more striking is that the same number of managers have won the league with Chelsea (Ted Drake, Mourinho and Carlo Ancelotti) as with Manchester United (Ernest Mangnall, Matt Busby, Alex Ferguson), despite United having been an economically powerful club for far more of their history than Chelsea. That suggests that even when conditions are favourable, it requires a certain genius to take advantage (it may be, of course, that, if the analysis were extended backwards to when the disparity between the richest and poorest was less pronounced, wage spending would be less significant. And wage spending of course, includes spending on the manager’s wages).

Richer clubs can hire better managers, just as they can hire better players: that there is a strong correlation between league position and wage spending then becomes at least partly a reflection of the quality of the manager.

José Mourinho in Shanghai earlier this week. Photograph: Imaginechina/Rex Shutterstock

But perhaps most significant is that the issues of wage spending and managerial quality are not discrete. How a player performs under a manager in part determines his wages. And in a very general sense the better the manager the more money there is to spend. Over time, as anybody would expect, the wealthy tend to prosper.

As Sally and Anderson point out, what is more significant – for once – is to take a smaller sample size and look at fluctuation from season to season. Between Mourinho’s first spell and Mourinho’s second spell Chelsea had five permanent managers, all working with roughly similar resources. Only one, Ancelotti, managed to do what Mourinho did in both spells and win the league, something that tends to confirm Mourinho’s specialness.

Yet despite that, Mourinho’s history, his regular failings in his third season at a club and the rumours leaking from the dressing room all supported his dismissal; the sense was of an irreconcilable fracture between the manager and at least some of his squad.

The question then is why there is such disparity between how Chelsea played last season and how they are playing this? There were those who saw in the apparent disparity between Chelsea’s performances in the Champions League and the Premier League evidence that their players had simply stopped playing for Mourinho. Perhaps that is true and it may be that, had Mourinho still been there, they would not have had the fight to get back (twice) into Saturday’s game against Everton.

But the broader question is about how they fell 2-0 and 3-2 behind in the first place. For long periods on Saturday Chelsea were dreadful.

It may be that the players regard the league as a lost cause and, so long as they do not get relegated, they cannot raise themselves to try to battle for eighth, and that a better Chelsea will emerge in the FA Cup and the Champions League (much as it did in 2012 when Chelsea won the competition in the midst of some very ordinary league form).

And the worry for Chelsea must be that the point Mourinho made after the defeat at Leicester in what turned out to be his last game as manager turns out to be correct. What if we are seeing not a great squad being brought low by a fractious relationship with their manager but their true level?

What if it was only Mourinho’s genius that elevated them last season?

Even if that is only partially accepted, another change of manager in the summer will probably not be enough. This is about the 81%, the players and how the squad is constructed, as much as it is about the 19%.