statistically significant?

[tjd2001]

I should remember this from college statistics, but can’t for the life of me…any help is greatly appreciated: Over the past 5/6 years, my office football pool has produced one very odd result: one participant has a 756-524 record over that time (compared to the next best record of 690-590, I think his performance is pretty amazing). How statistically significant is his performance….can it all be placed on luck….or is he out picking the “50/50” spread? Is this a large enough sample size? If not, what would be a large enough sample size?

If someone could give me the basic math as a starting point, I’d like to be able to figure out similar situations myself.

Thanks!

[BruceZ]

[ QUOTE ]
I should remember this from college statistics, but can’t for the life of me…any help is greatly appreciated: Over the past 5/6 years, my office football pool has produced one very odd result: one participant has a 756-524 record over that time (compared to the next best record of 690-590, I think his performance is pretty amazing). How statistically significant is his performance….can it all be placed on luck….or is he out picking the “50/50” spread? Is this a large enough sample size? If not, what would be a large enough sample size?

If someone could give me the basic math as a starting point, I’d like to be able to figure out similar situations myself.

Thanks!

[/ QUOTE ]

The probability of getting at least 756 out of 1280 correct with a 50% probability of being correct on each one is given by the Excel function

=1-BINOMDIST(755,1280,0.5,TRUE).

If you have a newer version of Excel, you can evaluate this. Mine cannot. So we approximate this with a normal distribution of mean 640 and standard deviation sqrt(1280*0.5*0.5), and say that we are 115.5 above the average which is 115.5/sqrt(1280*0.5*0.5) =~ 6.4566 standard deviations above the average. The probability of being this many standard deviations above the mean or higher is given by the Excel function =1-NORMSDIST(6.4566) or about 1 in 18.6 BILLION.

Note that this is the probability of a given 50% player having this result, not the probability that someone in your office would have this result which would be higher, but still highly improbable if each pick is 50%.

[tjd2001]

Thanks BruceZ! That's exactly what I was looking for. Much appreciated.

[PantsOnFire]

I'm not a sportsbook guy but to me it looks like that guy's 756-524 record is right up there with football experts (i.e. the people who get paid to give advice).

[SunOfBeach]

59% vs the spread over 1200+ games? Wowsa...