Penalty taking: some game theory and hypothesis testing

One of my colleagues sent me an article in the Financial Times from March 17 entitled “How to save a penalty: the truth about football’s toughest shot. On star goalie Diego Alves, game theory and the science of the spot kick.” I found the article interesting for two reasons.

  1. It has a fun discussion of the psychology and game theory of taking penalty kicks. It points to the paper by Ignacio Palacios-Huerta in which he shows that professional soccer players take penalties in a way that is consistent with Nash equilibrium (or minmax) behavior. The FT article also includes an interesting interview with Ignacio Palacios-Huerta and his “analysis of ideal penalty-taking strategies for the then Chelsea manager Avram Grant before the Champions League final against Manchester United in 2008.”
  2. The FT article highlights Diego Alves, Valencia’s goalkeeper, and argues that he is particularly good at stopping penalties. The FT article argues that Diego Alves’ stopping record (he stopped 22 of 46 penalties – a very high number compared to the average stopping rate of 25% of all goalkeepers combined) cannot be explained by chance alone.

In this blog post I want to comment on the 2nd point. It is actually wrong. And it is wrong for an interesting reason. Moreover the mistake made is very easy to make and is a very common one.

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