Talk:Elo rating system/@comment-188.178.187.14-20120126081725/@comment-3014924-20120126093630

Now saying that the law of large numbers doesn't apply is false: Law of large numbers:

"In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed."

And it even validates the fact that ELO isn't that bad.

Want a proof? Look at ranked win/losses of the masses (that is, not among the best, not the worsts) and now check their win/loss ratio. Pretty close to 50%, isn't it?

The "extarnal factors", that adds up to you're win chances are equally likely to reduce your win chances, and hence, doesn't change the probability that much.

so yes, it's 50%, LLN applies. Period.

(And why do I exclude Real High Players, Real Bad Players? I don't, it's just as they are at the very top/bottom, their win probability p ISN'T equal to 50%, so according to LLN, at infinite, their mean value won't be 50%.)