Bear of Bad News
Your Third or Fourth Favorite HFBoards Admin
- Sep 27, 2005
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In the first case, I would calculate a z-score of 0.54 (the goaltender has performed about a half-standard deviation better than average). A league-average goaltender will stop three out of three shots about once in every 3.4 times.
(Note - if you calculate this value empirically, you'll see that it actually happens about 75% of the time - that's because the normal distribution doesn't approximate the binomial distribution very well when n=3. Also, I'd want to use a z-score corresponding to 2.5 out of 3 - or greater - since the normal distribution is a continuous one.)