That being said… yeah, you’re right. I’d only be right if we were talking about variables that aren’t essentially different sides of the same die. I was forgetting how much it changes things that LD%, FB%, and GB% are so dependent on each other — I mean, LD% = LD/(LD+GB+FB), which makes the standard deviation in LD% the same as the standard deviation of (GB+FB)%. I guess that’s what you were getting at earlier. Whoops, sorry.

]]>Example: there’s a 0.75 year-to-year correlation for playing in rainy games (OK, I made that up). Player skill has nothing to do with it — that’s more about where you play.

]]>I simulated 300 roulette wheel spins each year over a period of years, on a 0-36 wheel (no 00s), and tried to see how often 0’s came up each year. On this simulation that just popped up, I have 1% in one year followed by 6% in the next. Something like that would completely mess up a correlation. It can happen with rarer occurrences. Now contrast that with a coin flip — there’s no way you’ll get a Heads% 6 times higher than the previous year’s (e.g. 15% to 90%), over that many flips, and with the same coin.

]]>It doesn’t seem to me that there is any reason that having a different probability of success on a binomial trial would lead to the year to year correlation dropping (unless something else is different).

To use your coin example, it is not about flipping the coin 4 times vs 1000, but flipping a bunch of differently weighted coins 1000 times each and comparing the correlation of each coin’s results year after year.

]]>I think it’s a small part of what’s going on here, but the law of large numbers is in play, as always: http://en.wikipedia.org/wiki/Law_of_large_numbers

A rarer event is likelier to occur further from a certain expected rate — e.g.: flipping a coin 75% heads one year and 25% the next is not a shocker if you only flip it 4 times per year… it would be nearly impossible to do that if you flipped it 1,000 times per year (I mean, assuming it’s a normal coin…).

]]>The real issue is that the scorer bias and underlying randomness in the stat are higher. Could be wrong (or change my mind again), but this makes the most sense to me right now.

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