Pretty football and the Nash equilibrium


Ignore Barcelona. Ignore Spain. Ignore 1982 Brazil, Total Football Holland, and the Invincibles. What if the real footballing lesson about aspiration and beauty lies not in art, but in economics? This I have learned from John Forbes Nash, the Nobel Laureate depicted by Russell Crowe in A Beautiful Mind. In the movie version, Crowe/Nash advises his friends to “ignore the blonde” if they want a dance. The blonde will shoot down each maths nerd who asks her to dance and the blonde’s friends will bristle at being second-choice. This story is Hollywood’s version of the discovery of Nash equilibrium. In brief, pursuing naked self-interest does not advance the greater good, but pursuing self-interest once you take into account everyone else’s decisions, does.

Any football competition is a structured Nash equilibrium game. In the Premier League we can watch the physical play of Stoke City, the scrappy direct play of Everton, or the defensive organisation of Sunderland. From an aesthetic perspective, these teams may not compare to Barcelona’s play. But if you think of these styles as part of a whole, a competitive environment in which failure means relegation, then the tactical choices of the entire Premier League table becomes a web of strategic decisions as intricate and beautiful as a twelve-pass Barcelona move finished off with an audacious Lionel Messi chip.

Of course, Barcelona, Spain and Brazil should be appreciated for the football they have produced and the moments in history they have provided. But history is biased towards the new. And the new is frequently driven by conflict and adaption boiling just beneath the dominant trends of football at any given time. Appreciating Barcelona and Spain is not, for most of us, an issue. What we might have a tendency to do is admire such teams at the expense of the remarkable accomplishments of so many other subtle, important adaptations that make the entire world of football today the way that we find it. Sometimes, we may find ourselves so interested in what new idea might be the next chapter in Jonathan Wilson’s wonderful book Inverting the Pyramid might be that we lose sight of how impressive it might be to run out a side that plays a solid 4-4-2 because that’s like, so chapter five.

But, as Stephen Jay Gould once wrote, the tail in evolution is never the bulk of the story, only what is different. The most common form of life on Earth is bacteria and without all that bacteria the story of the whole planet would be a different one. The diversity of the world makes each of its unique pieces possible. Try to remember that before shuddering in memory of the Juventus-Milan 2003 Champions League final.

Stories like Greece winning Euro 2004 or Fulham making the final of the Europa League are every bit as amazing as the ones that dominate our global football press. Many observers, however, dismiss these accomplishments as random, or retrograde because they do not contribute to the great narrative of football tactics. We see artistic beauty in the Barcelona style, and thus we conclude that the majesty of their play corresponds to some sort of auteur-ish quality that, if our favorite club, nation, whatever, simply hired the right director with the right artistic vision, then everything would come right for our side too. The result of this mentality has not been the proliferation of beauty, but the rather comical proclamations of “Welsh Barcelonas,” “Scottish Barcelonas,” or “City of Saint Paul Recreation League Barcelonas” as a descriptor that indicates high aspiration, but guarantees to under-deliver on the description’s promise. 

Nash equilibrium says that each side needs to make the most out of what they can do, given that their opponents are trying to do the same.  For some teams that means that they have to mix and match what they are trying to do to avoid being overrun by stronger opponents. For others, that means playing consistently the same way every time because no one is good enough to stop it. For others still, it means playing the same way every time because the gains from consistency give some sides a better chance than trying to get gains by adjusting to different matchups. Nash equilibrium also suggests that the debate between zonal and the man-marking corner kick defending does not have a winner because it might depend on the specifics of the kinds of teams you are going to be facing and the kinds of risks you will be exposed to over the course of an entire year. 

Perhaps most importantly of all, Nash equilibrium suggests that when our teams forget about the beauty ideal and pursue their own self-interest in the strategic context of knowing that all competitors are doing the same, the greater good benefits from the strategic diversity. Next time you hear someone complain about how Stoke are too defensive, or how Swansea and Wigan are not defensive enough, stop and catch yourself for a moment. Would the Premier League be more or less interesting if it was a league of Manchester City and 19 cheap imitators? Go ahead, enjoy the dance for what it is.

Read the entire article by Steve Maloney at Football Ramble, “Ugly tactics and A Beautiful Mind”, and let us hear your opinion on the topic. You can interact with us in the comments section below, on Facebook and Twitter (@toknowthegame).

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