Are Winrates Normally Distributed?

[PTjvs]

My gut instinct says this is because the raw +$/hand won is greater than the -$/hand you lose (due to some pots being multiway). Generally speaking, your small chunks of hands will break down as follows:

1) Many where you don't win big pots and you are slightly -$

2) Slightly fewer where you win enough hands to have a small +$

3) A few where you win a big hand or two & are very +$.

4) A few where you lose a few big pots & are very -$ (less however than your big +$ chunks, since due to multiway pots, the amount you WIN if big pots is larger than the amount you LOSE in the same big pot)

This should leader to a bell curve is NOT evenly distributed, but peaks on the - side, with the difference being made up by the curve coming down less steeply on postive end.

I hope I described that well, I'd do one in MS paint, but I'm a very bad artist.

if i am correct however, if you took the same data from HU play, it SHOULD look like a normal bell curve, as the effect of multiway play is completely eliminated.

jvs

[sthief09]

one of the possible conclusions that justin a came up with is that maybe BB/100 is not the optimal measure for those who want to do tests on it. maybe we could get a more accurate standard deviation from BB/1000, though for most people, playing that many hands before getting a standard deviation would be infeasible and plain annoying

[felson]

I think PTjvs is dead on. Also, this effect is strongest when the blocks of hands are very small. If the block is just one hand in length, then (in a 10-handed game) around 90% of your sample points will be <= 0, and about 10% will be greater than zero. As the block size gets larger, the median block value tends towards the mean. You can see this reflected in the plots, which shift to the right as the block size gets larger.

[UprightCreature]

For the reason PTjvs states the winrate for one hand should not be normally distributed. There is an interesting fact though, that is the distribution of groups of a samples from a non-normal distribution aproach normal as the size of the group increases (Central Limit Theorem). Eg. winrate/1000 will be more normal than winrate /10.