abersonc;1429615 said:
Again, this isn't a sample. It is data from all the games that were played. Inferential statistics focus on drawing inferences about populations based on samples. This is not a sample. It is all of the games that went to OT. That's the population. We know exactly how correct the 52% is because it is based on the entire population.
You have a sample, and you are using inferential statistics (i.e., trying to reach conclusions that extend beyond the immediate data). You have a sample because the population is the infinite set of games that could be played under this rule. You are inferring because you are using the results from past games to infer the fairness of the coinflip rule in all games, including future games - games that haven't been played and can't possibly be in your data set.
Think about it this way. If you limit your population to include only games that have already been played, then you can make statements with certainty about only those games. If you want to extend your population to all games that could ever be played (the question of fairness), then you need to consider computing the likelihood that a fair process could generate the results we have to date.
I think you are letting the fact that you have a reasonable number of data points cloud your judgement on this matter. Would you still argue this strongly if there were only ten results and the coinflip winner had only won four of the games?
I don't understand why you think this problem is any different than the problem of determining whether a coin is a fair coin from the results of a given number of flips.