Why your team's star player is nowhere near as important as you think

Cristiano Ronaldo, Portugal

With Alex Buttner insisting this week that he wasn't a weak link at Manchester United, David Sally – co-author of The Numbers Game – explains why it's actually a side's worst player that may matter most

In May of last year, Crystal Palace were not one of the surprise packages of the 2015/16 Premier League season. In fact, they limped over the line to finish in 15th place.

That wasn’t the case over Christmas, however. As they tucked into their turkey dinners, Alan Pardew’s team found themselves in the unprecedented position of rubbing shoulders with the top four, kept out of the Champions League spots only by goal difference. Then a 14-match winless streak, featuring five consecutive defeats, transformed the sugar-plum tale of sixth place into the dire depth-plumbing of 16th.

Alan Pardew

Pardew's Palace slid down the Premier League table in 2016

No match was more representative of Palace’s shattering season than their 1-0 defeat at Villa Park in January, which gifted the Midlanders their first victory since the opening day in August. Joleon Lescott headed a corner tamely at goalkeeper Wayne Hennessey but the ball spun from between the palms of his hands to between the heels of his boots, ricocheting about like a housefly pinging between screening and glass in a window. The ball dribbled fractionally over the line. Hennessey’s mistake (along with the bad luck endured by Eagles forward Wilfried Zaha in hitting the post) cost Palace a point or even three, and did less than nothing to boost the squad’s sickly morale.

O-ring Theory

If an organisation produces goods or services in which the qualities of each worker’s contributions are multiplied, then mistakes can be catastrophic

The significance of errors is one of the key facts employed in The Numbers Game to deduce that football is a ‘weakest-link’ sport. A weakest-link sport is essentially one in which the weakest elements of a team do more than the strongest elements to determine the result of a match or a season.

This theory can also help to explain some of the biggest surprises of the previous campaign: Leicester's Premier League title win, Chelsea’s rapid slump to mid-table, the continued success of Diego Simeone’s Atletico Madrid and a Cristiano Ronaldo-less Portugal winning the Euro 2016 final against the hosts and favourites, France.

The conclusion was drawn with the help of an economic model called the ‘O-ring Theory’, which says that if an organisation produces goods or services in which the qualities of each worker’s contributions are multiplied, then mistakes can be catastrophic and success is determined more by the worst employee than the best.

The name refers to the 1986 Challenger shuttle disaster, in which the seven crew members of the NASA Space Shuttle orbiter were killed when the craft exploded 73 seconds into its flight. The cause of the tragedy? A faulty O-ring less than half an inch in diameter.

Arrigo Sacchi agreed with the theory without quite realising it, when the architect of Milan’s success in the 1980s said that the point of tactics is to “multiply the players’ qualities exponentially”.

Arrigo Sacchi

Sacchi was a big believer in multiplying his players' qualities

Player rankings

The O-ring Theory has a couple of important implications for understanding football. For a start, players of similar ability tend to cluster together: squads of galacticos and squads of galoots arise naturally. Because of the higher quality of the surrounding talent, Luis Suarez is even more valuable to Barcelona than he was during his time at Liverpool.

A rating of -0.5 means the player is a serious problem, and -1.0 causes the manager to shake his head, sigh and take a look at options present in the youth team

This clustering was visible in last season’s Premier League squads. Using a statistical model called the ‘Anderson Sally Meta-Scout’, driven primarily by match data, every Premier League player’s performance in 2015/16 was rated. A rating of zero means that a player is average within the Premier League for his position; a rating of +0.5 is good, +1.0 is a star, and +2.0 is a superstar.

By contrast, a rating of -0.5 means the player is a serious problem, and -1.0 causes the manager to shake his head, sigh and take a look at options in the youth team. The 11 players who played the most minutes for their club in the 2015/16 Premier League are selected (making sure every position is represented), and the top-rated player is the ‘strong link’ while the 11th is the ‘weak link’.

In general, the better strong links are teamed with the better weak links, and the worse clustered with the worse. The top three teams in the league had weak links who were above average. So, did Leicester succeed against all odds because Riyad Mahrez was phenomenal, or because Danny Simpson performed well as the side’s ‘weak link’?

Luis Suarez

The O-ring Theory states that Suarez is even more important at Barcelona than he was at Liverpool

Best of the worst

The connections between people are as important, or perhaps more important, than the individuals themselves

The second key implication of the O-ring Theory on football is that, all else being equal, you are much better off improving the tail end of your squad than trying to shoehorn in an expensive superstar. An improvement of equal measure in the quality of your weakest link, as opposed to your strongest, yields a better goal differential, more points and a bigger leap up the table. In other words, even though Mahrez scored and assisted significantly more goals than Marc Albrighton, the former Aston Villa man’s performances relative to his position in Leicester’s hierarchy may have been more valuable.

A big part of Atletico Madrid’s success under Diego Simeone is that he implicitly embraces ‘weakest link’ philosophy. “Football is a game of errors,” he has said. “The fewer mistakes you make, the closer you are to a victory. It’s a lie that he who attacks the most is closer to winning. It’s he who makes the fewest mistakes. And for that, we work on what we feel are the opposition weak points.”

Simeone knows he can’t sign the world’s best players, thanks to his club’s relatively meagre resources, but he realises that he can have the ‘best worst player’ of any club in La Liga or the Champions League, and that he can multiply the qualities of the players he has more dramatically than any other manager.

Then there’s Charles Horton Cooley. Yes, he sounds like a wing-half who represented Sunderland and District Teachers A.F.C. with some distinction at the turn of the last century, but he wasn’t a sportsman. In fact, he was a rather withdrawn, yet renowned, American sociologist.

Diego Simeone

Simeone is a manager who seems to believe in the theory of the weakest link

Still, this unathletic teacher would surely have admitted that football was part of society, and accordingly he might have permitted this variation on one of his most famous quotations. “[Football] is an interweaving and interworking of mental selves. I imagine your mind, and what your mind thinks about my mind, and what my mind thinks about what your mind thinks about my mind […] whoever cannot or will not perform these feats is not properly in the game.”

Still with us? What Cooley’s saying is that the connections between people are as important, or perhaps more important, than the individuals themselves. It is easy to conceptualise the ‘weakest link’ model as focusing just on individual player quality, but that’s the equivalent of capturing tactics in terms of a static formation of 11 single players arrayed in space, the way you’d see them in a newspaper preview of an upcoming match. These atomised pictures are devoid of all of the interweavings Cooley said are so essential to society – and, by extension, to football.

Visualising the network

These linkages could be the mental interworkings of motivation, cultural difference, personal liking, disapproval, understanding and anticipation

A more realistic picture of the joined network that truly comprises a football team would have all of the connections, with different lengths and widths representing closeness and importance.

These connections might be actions such as passes or even touching (one academic study actually found that NBA teams who shared more high fives, fist bumps and hugs enjoyed greater success), or they could be the mental interworkings of motivation, cultural difference, personal liking, disapproval, understanding and anticipation. So, while it is simplest to think of a ‘weak link’ as merely the least talented player in the team, a more complex view would be that the ‘weak link’ might actually be a thin, stretched or non-existent link between two players.

Anne Robinson

Think of a thin, stretched or non-existent link between two players, rather than Anne Robinson

Like many a prolific striking partnership, Liverpool duo John Toshack and Kevin Keegan were routinely labelled ‘telepathic’. That tag stuck to the pairing so firmly that they once took part in a televised test for ESP (extrasensory perception). Writing on fansite The Liverpool Offside decades later, Trevor Downey described it thus: “The men were sat back-to-back and given cards with symbols on them. Each had to guess what the other’s card displayed. There was stunned silence in the studio as they made the right call repeatedly [...] Then Keegan collapsed giggling and admitted he could see the big Welshman’s cards reflected in the camera lens.

“Since then, an array of football pundits have continued, undeterred, to pontificate about telepathy between players. It’s a concept that has become embedded in the culture of cliché that constantly lingers around football like a cheap, pungent cologne.”

Josh Toshack, Kevin Keegan

Toshack and Keegan had an excellent understanding at Liverpool