The worlds of football and particle physics may seem poles apart, but both are wrestling with the same conundrum: when is enough enough?
Fans of the English Premiership have been mesmerised by the sight of current league champions Chelsea languishing near the relegation zone, while Manchester United rack up their worst run of defeats since 1961.
That, in turn, has sparked controversy about how to tell when enough is enough, and radical change is called for – such as the sacking of the manager.
Meanwhile, a strikingly similar debate is raging among scientists about the underperformance of a cosmic theory with a huge fanbase.
Known as supersymmetry, it is supposed to be a key player in attempts to create the Theory of Everything, describing all the forces and particles in the universe.
Yet despite being given chances to shine in the famous arena of the Large Hadron Collider in Switzerland, supersymmetry has failed to score a single goal in the form of the detection of any of the particles it predicts.
That has prompted the same question as that facing the boards of football clubs: is it time to say enough is enough, and think about radical change?
We have all faced similar conundrums, in everything from financial planning to relationships. But despite its ubiquity, the problem of deciding when enough is enough remains one of the trickiest to solve. One major sticking point is that it’s always tempting to wait for more evidence – yet by the time we have it, the situation may have become irretrievably dire.
Then there is the problem that every decision involves not just data but also a judgment call about the implications – and there is no guarantee of making the right one.
Even so, there is plenty of scope for making better use of the evidence we do have – especially when it comes to decisions like when to fire football managers.
The first question that has to be asked is whether the run of failures could be put down to bad luck.
The ability of chance to imitate evidence of genuine success or failure is astonishing. Studies have shown that most of us have a poor grasp of what randomness is capable of.
For example, asked to write down the outcomes of tossing a coin 50 times, people typically come up with sequences containing runs of no more than a few consecutive heads or tails. After all, everyone knows that randomness means a pretty even spread of the various possibilities.
In fact, the theory of randomness shows that clustering is far more likely than we think. Even just 50 coin tosses are likely to include at least one run of five heads or tails. Only if one witnesses at least eight or so should one start to suspect something odd about the coin.
While the outcome of a football match is not a matter of pure chance, it is clear we need to be wary of reading too much into a run of bad form.
Deciding when chance is no longer a viable explanation is one of the key tasks of statistics. And in the case of football managers, a technique that might reveal when “enough is enough” exists.
Known as the sequential probability ratio test (SPRT), it was invented by mathematicians in the Second World War to tell when factory output was falling below standard.
In essence, the SPRT involves monitoring what comes off the production line, and keeping tally of the number of failures.
Clearly, that total number will grow over time, but it is possible to put limits on how fast it should grow if the manufacturing process is meeting standards.
The SPRT makes maximum use of the evidence emerging from production lines, thus drastically reducing the amount of sampling needed to reveal any problems. This made the technique so valuable to the war effort that its existence remained classified until the late 1940s.
Since then, it has been used to keep tabs on everything from the side effects of newly launched vaccines to the performance of pest-control methods.
It has even been put forward as a means of detecting serial killers. In 1998, Harold Shipman, a family doctor working near Manchester, England, was arrested on suspicion of murder.
At his trial, he was found guilty of killing 15 of his elderly patients, but an official inquiry concluded Shipman probably murdered more than 200 in a period of 20 years.
A team of statisticians later showed that Shipman’s murderous activity could have been spotted years earlier if medical records had been analysed using the SPRT. While all doctors experience occasional blips in patient death rates by chance alone, the use of the SPRT could have revealed the soaring rates among Shipman’s patients as early as 1985, saving dozens of lives.
The same idea could be used to spot football managers who are underperforming.
Given a target hit rate – set by, say, the need to qualify for at least the Uefa Europa League – SPRT would give early warning of when a team’s performance is going seriously awry.
That still leaves the problem of ascribing blame, but it does help cut through claims of a team just having some bad luck.
Avoiding being fooled by chance events has long been an obsession among scientists.
But in the case of supersymmetry, they face a more basic problem: the theory can always be tweaked to explain away failures.
That makes it akin to a football team with an army of managers. Deciding when enough is enough then involves telling the difference between failures of management or players.
This year could well be the one where supersymmetry runs out of excuses.
The Large Hadron Collider will start collecting more data in the spring, and if that fails to reveal any new particles, it is likely that the theory’s backers will start to drift away.
It won’t be a rational decision – just one based on a feeling that money and effort might be better spent elsewhere.
To which the owners of Chelsea and Manchester United might justifiably respond: welcome to our world.
Robert Matthews is a visiting professor of science at Aston University, Birmingham
