Points Scored in Small Samples

Scoring of points in an NHL game is a essentially a Poisson process. With lambda = 1.0 (i.e. a point per game) and games = 20, we get



















Where "Probability" is the probability of that many points or fewer. 10% less than expected would be 18 or less. Simple randomness gives us a probability of 38.1% that a point per game player will have 18 points or less after 20 games. 20% less is 16 points. 22.1% probability of that happening.

Next issue. 31 players is a very small sample. 38% of 31 is about 12, but the 95% CI is 4 to 18. If 18 of the 31 have seen production drop, that is within randomness.

Regression to the mean

Two issues here. One is that 2012-13 was only 48 games. It is much more likely to see the effects of random fluctuations in 48 games than in 82 games. Some of the players identified as point per game players in 48 games would not have maintained that through a full season. The second is that even in a full season, some of the players who show up on the list are there because they performed at the high end of the expectation for their talent. The next season, their performance will most likely be closer to their average. They will "regress to their mean". One recent example was Brian Elliott. Career at ES he is 0.915. In 2011-12 he was 0.950. Predictably, in 2012-13 he regressed to 0.920.

On the list of the 31 players who produced a point per game last season, at least 10 are no where near that level for their career (Lupul, Letang, Kunitz, Ribeiro, Semin, Ladd, Voracek, Nash, Moulson, and Stepan). 3 more (Hall, Giroux, and Kadri) aren't at that level but don't have enough games to make a reliable prediction.

Why does that matter? Well, 38% would be down 10% or more if they were all really point per game players. If the group contains guys with less talent who are regressing to the mean, more than 38% will be down that much.

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