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10-11-2013, 11:27 PM
#41
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Join Date: Sep 2005
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Quote:
 Originally Posted by Laos Just being curious on how you get your numbers like" one every 75000 seasons" from your standard deviation?
Good question. If we assume that shots on net follow a binomial distribution (admittedly a stretch), then as the number of shots faced increases, the distribution can be approximated by a normal distribution.

At that point, and with a z-score, it's just a matter of measuring the area to the right (in the case of a positive z-score) or to the left (in the case of a negative z-score).

For instance, consider a goaltender with a z-score of -1.48 (since that's an image that I was able to swipe online ):

There is 6.94% of the curve to the left of the goaltender's performance, so we would expect a goaltender to do as poorly as he did (or worse) 6.94% of the time. So it would happen about every 14.4 seasons (since 1/6.94% = 14.4).

Does that make sense? Once we assume a binomial distribution (which isn't perfect, but it's not horrible), then it's just probability theory.