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The "Hot Hand" and Coaches as Goalie Evaluators

Let's say that every NHL goaltender had the same talent level (.910 save %), but that no one knew this.  Coaches start the season with their #1 guy, but if he posts five bad games in a row (save % < 880) after the 15th game, then they switch to their backup and ride him until he has five bad games in a row.  In other words, the coach rides the "hot hand" until it's not hot anymore.

So what happens? 


Goalie 1 Hot 9.5 916 0 916
Goalie 2 Hot 15.0 908 918 913
Other 75.5 909


In the first category, I included situations where the starter never had a bad five-game stretch.  In the second group, I count every time that the starter gets benched and the backup plays the rest of the season (at least 20 games) without having his own bad five-game stretch.  So one-quarter of the time, the coach looks like a genius goaltender evaluator - purely by luck.  And over the course of two seasons, two out of 30 NHL coaches will look like multi-year geniuses, again, purely by luck.

Now I'm not saying that coaches have no talent for evaluating goaltenders.  And I'm not saying that goaltenders aren't streaky - I believe they exhibit more variation in their save percentage than we would expect purely by luck alone.  But it's important to keep in mind that what appears to be brilliant talent evaluation may very well be blind luck.