Thursday, May 3, 2007

Simpson's Paradox

In my last post, I discussed the impact of special teams on goaltending. Here is an interesting example of that effect at work.

One of the main arguments for Brodeur as Vezina Trophy winner is that he leads Luongo and the other nominees in wins, goals against average, and save percentage. Wins are very team dependent, and goals against average is basically save percentage times the number of shots against, so these two are not very good measures. If Brodeur, however, ranks ahead of Luongo in save percentage, that is a good argument to use on his behalf. During the 2006-07 season, he did just that, with a .922 save percentage to Luongo's .921.

A closer look shows that this was not because Brodeur played better, but rather was caused by a large discrepancy in special team play between the Canucks and Devils. Here are the save percentage splits for Brodeur and Luongo for each game situation (even strength / penalty kill / power play):

Martin Brodeur: .927 / .904 / .888
Roberto Luongo: .928 / .906 / .910

Luongo ranks ahead of Brodeur in every game situation. How can he possibly end up behind Marty in overall save percentage? The reason is that Vancouver took more penalties, meaning Luongo had to face 199 more shots on the penalty kill than Brodeur. If Luongo had faced Brodeur's shots, and vice versa, and both of them stopped the puck at exactly the same rates, Luongo's save percentage would have been .923, and Brodeur's would have been .920.

In statistics, this is called Simpson's Paradox, where the ranking of several groups changes when they are combined. Luongo ranks ahead of Brodeur in each special team state, but then ends up behind in the overall rate. This is yet another example of hidden team effects, and how they can impact goaltenders.

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