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Keynes Society

Keynes Society
Professor Stefan Szymanski (Cass Business School)
on Game Theory and Penalty Shoot-outs

Professor Stefan Szymanski from the Cass Business School London treated a packed house at the Egerton Room to an enthralling analysis of the economics of the penalty shoot out.  After running through the usefulness of ideas drawn from game theory in looking at the best strategies for penalty takers and goalkeepers he then turned to a class example of the genre. The 2008 Champion’s League penalty shoot out in the early hours of the morning in a rain-sodden Moscow stadium is set to become a classic mini case study in the economics of game theory
applied to sport. We are told that the then Chelsea coach Avram Grant may have been in receipt of some advice on strategy from LSE Professor and football fan Ignacio Palacios-Huerta is reputed to have sent some written advice to Grant before the final in case a penalty shoot out took place.

The advice was as follows:
1. Ronaldo sometimes stops when approaching the kick; when he does this he tends to shoot to his left most of the time
2. Van der Sar (Manchester’s goalkeeper) tends to dive more often to kicker’s natural side than his optimal mixed strategy would suggest and therefore Chelsea kickers should kick more often to their unnatural side (i.e. kick right if right-footed, kick left if left-footed)

We can never be sure whether Grant followed through the advice by telling his Chelsea players to go for their unnatural side when taking their penalties. But the evidence in front of us is fairly clear. The five right-footed Chelsea players who took spot-kicks in the first six penalties (Ballack, Belliti, Lampard, Terry and Kalou) all chose to aim right (their unnatural side). Van der Sar guessed correctly three times but was unable to stop the strikers scoring. But as we all know John Terry missed his kick with the score at 4-4 and blew a chance to win the Champion’s League. Up steps Anelka in the sudden death stanza and with the score 6-5 to Manchester United. In a smart piece of psychology Van der Sar uses his left hand to point Anelka towards a right-sided spot kick (again the unnatural side for a right-footed striker). Anelka refuses the bluff and send his kick to his natural side, and watches in grim disbelief as Van der Sar stretches to his left to make a match-winning save.

For Professor Szymanski Chelsea’s downfall was the result of failing to appreciate the importance of randomness - their penalties had become predictable and Van der Sar perhaps cottoned on to this. The lecture carried important lessons for economists in general and Chelsea fans in particular who will nowe never be able to watch another shoot-out without thinking of this rich and memorable Keynes Society meeting.

Our next meeting is on the 11th February with Dr Andrew Sentance from the Monetary Policy Committee of the Bank of England.


DATE POSTED: 28 January 2010

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