Friday, 21 December 2012

Sports commentators and zero sum games

England have beaten India in India at cricket! Which for those of you who know nothing about cricket is about as good as it gets. But, this post was not prompted by Englands success. Instead it was prompted by a discussion I heard on the TMS commentary of the penultimate day of the series.
   A bit of background info first: Cricket, like most sports, relies on an umpire to make decisions – and they sometimes get them wrong. Technology has been progressively introduced over the last decade in order to reduce errors. The latest development is a Decision Review System. India, however, said that they did not want to use the system against England. And the International Cricket Council Regulations say that it can only be used if both sides agree. The commentators were discussing India’s decision not to use the system after England captain Alastair Cook was wrongly given out for the second time in the game. If the Decision Review System had been in use both decisions could have been corrected. On the basis of this the commentators were questioning why a team would not use the system. They basically said that it’s surely to the advantage of both teams to use it.
   This made me chuckle. It made me chuckle because cricket is a zero-sum-game, and in a zero-sum-game there cannot be anything that is advantageous to both sides. So, the claim is perverse (a Colemanballs). Let me explain: A zero-sum-game is one where payoffs add to zero meaning one team can only gain at another expense. Sport contests are effectively zero-sum-games because winning and losing is what it is all about – and only one team can win. You might want to argue at this point that winning fairly, in an exciting contest is preferred to winning by bending the rules in a dull contest, etc. That’s true, and it would mean that sports contests are not strictly zero-sum-games. This, however, is surely a very minor effect. Sport is about winners and losers and so we shall not be far wrong in modelling sports contests as zero-sum.
   In a zero-sum-game, given that one team’s gain is another’s loss, it is simple impossible to do something that benefits both teams. So, the commentators on test match special were wrong to suggest that the Decision review System could help both teams. It’s not uncommon, however, to hear similar sentiments. For example, we hear that the referral system in tennis has helped all players. We hear that putting the roof on to stop the weather effecting a football, rugby, or tennis match will help both teams. This suggests that sports commentators have a slight bias in understanding zero-sum-games.
   Interestingly, however, the bias has its limits. Sometimes commentators are very good at recognising the zero-sum nature of contests. For example, we hear that windy weather will favour the less talented tennis player. Or we hear that rain and mud will benefit the less talented rugby team. These comments are spot on – bad weather has to benefit one player or team, and by making the contest more of a lottery it will help close the gap between the less and more talented.
   So, what’s going on? Things like the review system, referral systems, and putting a roof on are under our control. The weather is out of our control. My conjecture, based entirely on anecdotal evidence, is that people are good at seeing the essential zero-sum nature of things when it comes to events out of our control, but are less good when it comes to things under our control. Why? Having a review system, or putting a roof on the stadium looks like progress – and progress must be good - so, we are biased to think it must help both teams. In truth, progress will almost always help the most talented to the disadvantage of the least talented, because it takes elements of luck and chance out of the equation. Which is bad news for those who favour the underdog.         

1 comment:

  1. Another example of the zero-sum fallacy came at the 2013 British Grand Prix ( In the race four of the cars experienced a puncture. That shouldn't happen! Pirelli and the teams new there were problems with the tyres then being used. But, the rules state that the type of tyre can only be changed if all teams agree. Given that this is a zero-sum game, there is no way that all teams will agree! Fortunately, there is also the possibility to unilaterally change the type of tyre if there are safety concerns.