Once upon a time, there was a book called The Numbers Game, by David Sally and Chris Anderson. In it, among other things, was a chapter on football and O-ring theory, teaching a young generation of nerdy football watchers two things.
One: the story of the Challenger disaster, which tragically exploded, killing seven crew members, due to a tiny component failing in cold weather, the O-ring. Two: that football is a sport where the weak links make the difference.
The theory — which started off in that most sporting of realms, economics — is that if you have a bunch of workers who each have tasks to do in a project, one person who’s worst has the most effect of the bunch. If you have someone who’s half as good as the rest, they’re going to hold everyone else up; but if you have a worker who’s twice as good, their work will still need to rely on the normies pulling their weight.
The book’s application of the idea to football took hold, appearing in FourFourTwo magazine and an episode of the Revisionist History podcast. In a sense, it’s echoed by José Mourinho and other coaches who are said to believe that the team who makes fewest mistakes wins. In this school of thought, football is a ‘weak link’ sport, and if there’s a trade-off to be made between maximising a star player and covering a frailty then it’s the frailty that must be protected and patched.
But there’s a problem.
In 2016, Stefan Szymanski and Guy Wilkinson published a paper which argued exactly the opposite: it’s not the worst players on the team who count most, it’s the best. (Wilkinson’s doctoral dissertation is available online, the first section of which is essentially the 2016 paper).
Their work isn’t quite a case of ‘superstar theory’ — which would be that the best player on the team matters most — as it argues that the top two players are equally important, with the third-best close behind. But these top few are clearly the ones that matter in their work. Their ‘optimal strategy’ says that these three should account for around 70% of the wages on the team.
Hopefully that last sentence made you go ‘…wait, what?’.
Because now we exit the ‘these are the technical papers’ phase of this post and into the ‘what do the technical papers actually mean’ phase.
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One reason why Szymanski and Wilkinson’s optimal strategy may have had so much of the wage bill focused on so few players is that they just used starting XIs. They note that, in reality, teams may choose to spread their spending a bit more evenly in case their top players get injured. Or that it might be good management of a workforce not to spend 70% of the wages on less than 30% of the starting line-up.
Neither study used any hugely sophisticated methods for gauging ‘player value’ because, to be fair to them, they couldn’t. Football still doesn’t have an all-in-one performance metric that can be used for work like this. Possession value models are promising but are still very much in the ‘iteration’ phase, and I’m not sure how many deal well with the Valley of Meh issue. Also, running the model for the number of seasons and competitions that would be needed for this work may be beyond the scope of many researchers.
This doesn’t mean that Sally and Anderson or Szymanski and Wilkinson’s work is fundamentally flawed, just that they would appear more as works of theory than works of experimentation. That said, when you have two studies that say completely contradictory things, the method does kinda matter.
It’s also kind of a problem that both theories seem plausible. You could quite easily argue in either direction.
- For O-ring: “Teams regularly build game-plans, in part, around protecting their worst players, and quite often their better players have to limit themselves to accommodate worse players. Besides, Messi at Burnley wouldn’t make Burnley into world-beaters.”
- For ‘get a good main trio, forget the rest’: “Better players don’t just add their own skill to a team, they help unlock talent in others. And, y’know, good players are good! Besides, Chelsea had the worst goalkeeper in the league in 2019/20 and still finished fourth; if your top players are good enough you can mask a weak link.”
To me, football is too much of an inter-connected sport for things to be as simple as coming down to the strongest link or weakest link.
If a team plays an intricate possession-style, it would probably do them good to avoid a weak link in midfield. But a team playing a zonal defensive system might find it better to have one or two stronger links to help organise the players around them than improve the weakest player. A poor finisher in a strong attacking team might be better than a very strong poacher in a weak attacking team. A weak link at full-back might be less serious than a weak link at centre-back.
Maybe instead of the theory argument being strong link vs weak link it should be strong selection vs weak selection, or maybe strong unit vs weak unit. Anyway, it seems not to be as simple as O-rings after all. But at least I still know what the Challenger disaster is, I guess.
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 || "Possession value models..." ||They do what they say on the tin, model the value of actions in a spell of possession. Examples include American Soccer Analysis’ Goals Added, Opta’s Possession Value added, Karun Singh’s Expected Threat, KU Leuven and SciSports’ Valuing Actions by Estimating Probabilities