[Rupert Pupkin]

Originally Posted by Dunbar

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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Excellent work as always Dunbar!