A set is already the first to 7 games (with some contingencies) and a game is the first to 4 points (again with contingencies). So n is way more than 3.

Another thought coming soon.

]]>The law of large numbers holds when $n$ is large (you state 12) so that as long as n<12 we are still approximating. The larger $n$ is the better the approximation. Hence 5 is a much better approximation than 3 which will then mean that strong players will win more 5-sets than 3-sets.

As for teasing out multiple factors *if* they exist it is pretty easy to quantify the effect of experiment size and hence if anything remains it is fair game. The sample size (this time in terms of number of matches) is likely to be huge though.

Not being a fan of tennis I do not know if such a sample exists. ]]>

Well yes. (That Occam dude is such a square.) So the question is how to factor out the two reasons. I think that a 3 set match is already pretty long so that the variance factor is going to be negligible. (In practice the law of large numbers is usually the law of numbers larger than about twelve.)

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