litehoof wrote:


1) "+95 kills" doesn't mean anything statistically

2) The current statistics

http://www.youplay.it/play/bm_Stats.asp?ID=ED11610

is 707 kills vs. 609 kills, which means that the black Camel scored about 53.7% of the total kills, which does not seem so much w.r.t. the 50% one would expect.

Assume that the planes have a priori the same chance of winning. Then, given a total of 1316 kills, the expected value is 658 kills, with a variance* of sqrt((707+609)/4)=18 kills. That is, one would "expect" 658+/-18 kills (within one sigma).

707 kills is about 2.7 sigmas away from the mean, which is not so surprising, particularly in light of the following point.

3) The problem is that in any case the chances for the two planes to win the match are not a priori the same: better pilots might prefer the black camel.

And, in fact, this is the case. Pokerguy was in 341 of these games, with stats of:

91 kills, 24 deaths on the allied camel (79%)

157 kills, 46 deaths on the black camel (77%)
So these numbers, which are much more homogenous statistically, tell us that Pokerguy is favoured when playing on the allied(!) camel.

So, if we remove Pokerguy's statistics from the above numbers (because Pokerguy is a really good pilot, and he *can* screw the statistics), we get:

707 - 24 - 157 = 526 kills for the black Camel

609 - 91 - 46 = 472 kills for the allied Camel

So this means 52.7% kills for the black Camel when we take into account that a very good player plays more often with the black camel than with the allied one... even though he does slightly better on the allied plane than on the black one!

The expected number of kills would be 499 in this case, and the variance* is 16, so with these improved statistics we are at 1.7 sigmas from the expected result. I am pretty sure that, if one takes into account the fact that many players have played more on different sides, the deviation will be even lower. (This is left as an an exercise to the reader).

The final lesson is: think twice before claiming that a statistics is screwed up

*) When computing the variance, I was neglecting the possibility of a double kill, which does decrease the variance, but by an amount which is in any case neglectable, I believe, since the variance depends on the square-root of the sample size.

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