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[Dunbar]

Originally Posted by jman5581

Just finished all my law school finals, so I've got time back on my hands...

dunbar, about a month ago you wrote... "I've got to catch a plane in a few hours, but at some point I'd like to write some more about the statistical significance of jman's results."

I'd be interested in hearing what it is you have to say.

jman, I finally got around to looking at this again. Let me see if I can produce some statistics without (1) making a mistake, or (2) putting you to sleep.

Here's what I did:

1. I calculated the average result of your 119 show bets. You lost an average of $0.008 per $2 show bet.

2. I calculated the standard deviation of your 119 show bets. The standard deviation is 0.94, based on $2 bets.*

3. I calculated the "standard error", which is the standard deviation divided by the square root of the number of bets. 0.94/sqrt(119) = 0.09.

Armed with this data, the challenge is to tell whether your good performance was just a matter of luck. (like a roulette player who just happens to hit a few numbers.)

Consider these two "tests":

Test 1: Can we distinguish jman's record from someone who loses at the track take, say 16%?

A -16% bettor would lose $0.32 per bet compared to jman's $0.008. A 32 cent loss is more than 3 standard errors worse than jman's loss. A 3-standard error result should occur by luck in about one in 700 cases. I think we can assume that jman's picks were clearly better than the track take.

Test 2: Can we distinguish jman from someone who picks well enough to lose at just 5%?

A -5% capper would lose $0.10 per $2 bet. That's about $0.09 worse than jman's result. The difference between a -5% capper and jman result for his 119 bets is about one standard error. That kind of difference occurs by luck about 1 time in 6. We can't really rule out the luck element at that level.

Bottom Line: Your picks clearly showed that the difference between your results and a dart-thrower is statistically significant. But we'd need more picks to say that you're doing better (in a statistically significant sense) than a capper who has a 5% average loss.

Bottom Line, version 2: There's less than 1 chance in 700 that a dart-throwing capper could have produced results as good as yours. There's about 1 chance in 6 that a capper who averages a 5% loss could have produced results as good as yours over the course of 119 bets.

--Dunbar

* one easy way to do this is use the Excel function, =STDEVA(C1:C119), where the payoffs are in cells C1 down to C119.
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