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Thursday, September 23, 2010
Simple example of regression toward the mean
Hawerchuk takes the scoring records of the top 20 scorers for the last 9 (qualifying) seasons:
......... GP G A Pts
Year 0 79 34 49 83
This is the important part: because he selected based on the metric he is studying, this is a selection bias. This group of players will not perform the same in Year T+1. And indeed, they don’t:
......... GP G A Pts
Year 0 79 34 49 83
Year 1 71 27 40 67
This is unsurprising in terms of direction, and could be surprising in terms of magnitude. Could we have guessed what T+1 should have been? Why yes, it should be the same as T-1:
......... GP G A Pts
Year -1 73 29 40 69
Year 0 79 34 49 83
Year 1 71 27 40 67
Once you have your selection bias, in order to figure out what you actually have, you need to look at the out-of-sample data. I have no doubt at all that if you repeat this in baseball, top 20 in OBP for the last 10 years, top 20 in SLG, top 20 in HR/PA, top 20 in ERA, top 20 in SB/time on base, top 20 in your high school math competition, top 20 in stock performance over the last 12 months and doing so for the previous 10 seasons (though in this case we’ll need to do it relative to the index *), etc, you will find this: the rates in T+1 will match those in T-1.
To the extent that it doesn’t, then either you have a sample of really young or really old players, or just bad luck. We’ve been beating this drum for a long time. In order to believe this, you need to roll up your sleeves and prove me right (or wrong). It’s time to take out your fishing rods.
(*) The reason that it won’t necessarily work in stocks is that companies may genuinely change. Not to mention stock prices is not something intrinsic but perceived. The “performance” of the stock is really not a true performance. With players, they don’t change that much, and their performance is their performance. Anyway, I’m sure there are some stock guys reading this, and are looking to do some work for an hour, learn something, and teach their colleagues something. Go for it.
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