[grndmstr_c]

endrity, the catch is this. Winners of multi-possession games can be approximately determined by taking stock of which team had a higher proportion of won possessions. As the number of possessions that go into that per-game sample proportion increases, the difference between that sample proportion and the true probability of winning a given possession will tend to decrease, with the net result being that the better team will win a majority of the possessions more and more often. You're correct about the sample proportion zeroing in on the true mean probability of winning a single possession, but the standard deviation of that sample proportion is shrinking at a root N rate (the same root N that I noted in my last post), and that's what ends up making the difference.