Hockey Outsider
Registered User
- Jan 16, 2005
- 9,123
- 14,311
Talk me through your math, yeah? I calculate the odds at less than 2%, not 12.
Sure. A player with 300 points in 82 games scores 3.66 points per game, on average.
Probability of scoring 0 points = [(e ^ [-1 *lambda]) * (lambda ^ x)] / (factorial x)
= [(e ^ [-1 *3.66]) * (3.66 ^ 0)] / (factorial 0)
= 0.0257 * 1 / 1
= 0.0257
You can also type "=poisson(0,3.66,false)" into Excel.
Probability of scoring at least one point in a game = 1- probability of scoring 0 points
= 1 - 0.0257
= 0.9743
So there's a 97.4% probability of scoring at least one point in any game.
Probability of scoring at least once, in all 82 games = 0.9743 ^ 82
= 0.11825
= 12%
You mentioned certain statistical flaws which can't easily be dealt with, but there's another one too ... any more than 9 or 10 points in a single game is basically impossible. While the odds that 300 randomly distributed points would end up clustered in 8 games is extremely low, the chances of it are present in my formula, and I don't know how to deal with it.
Well, the probability of a 300-point player scoring 10 points in a game is 0.3%. That's quite remote and, again, the NHL has never seen anybody close to a 300-point scorer.
Weird things do happen, though. Sittler scored 10 points in a game and he was only a 100 point scorer.
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