Maybe this is a bit too much towards math, but we have Noam :-)
If you view the final point standings of any tournament, you'll probably see many players with an average number of points, but few with a very high or low score. For Swiss this is almost by construction, but for a round robin (easier to analyze) it also resembles a Gaussian distribution.
My question is whether it is actually one, or something only similar, assuming some simplifications:
- n players play a round robin with n-1 rounds. n is assumed to be a very large number (ideally infinite).
- Each player is assumed to have equal strength.
- Thus the result of each game is (independently) 1, 1/2, 0 with probability p,1-2*p,p with p in [0,1/2].
This should be homework for a statistics student...and I can immediately claim the mean of the score distribution is (n-1)/2 in any case.