[Dark Horse]

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[Ganchrow]

Originally Posted by Dark Horse

Hey amigo. I was wondering if you had a math formula for translating Z-factor (which you seem to use) into bet size.

What the p-value of a Z-score tells us is the probability of observing a particular result at random, assuming the distribution from which it's drawn to be normally distributed. In this manner, Z-scores may be used to determine confidence intervals about particular estimates so that we might be able to say that we were perhaps 95% certain that the "true" success rate of a particular strategy were within 2% of 55%.

So when estimating win probabilities of given strategies how does this impact Kelly? The short answer is that it doesn't. Given some betting odds, then as long as our estimates of the win probability are unbiased, the Kelly stake given that win probability would be the same were the Z-score 0.1 or 7.

I can see why this at first blush might seem confusing or illogical, but the consistency should quickly become apparent when you consider that irrespective of risk preferences a bettor would be indifferent between placing a bet with a win probability of X%, and selecting randomly between two bets ... one with win probability (X+Y)% and the other with win probability (X-Y)%.

Just remember this ... if you come up with 1,000 different strategies, the observed win frequencies of your 10 best strategies will not be unbiased estimators of the underlying respective win probabilities. In such case neither the "raw" Z-score nor the Kelly stake based on the observed frequencies will be accurate in the manner intended.

[Dark Horse]

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[RickySteve]

I don't think he'd be risking his money on any team because they've covered 10 of the last 12 games as a favorite on the Tuesday following Arbor Day in the first game of a back-to-back coming off 2 straight ATS wins on the road against non-division opponents, or whatever other iron pyrite angles you're dredging up.

[Dark Horse]

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[Dark Horse]

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[maxpower79]

Optimal bet size is based on expected winning percentage.

I can't imagine you would risk as much on a 12-4 strategy (75%, Z-factor 2.00) as on a strategy with a Z-factor of 3.00.

But how can you risk anything on a strategy at all? If you had some reason to believe that the event you're going to bet on has an outcome that will be determined exclusively by the exact same factors that determined the outcome of the 16 observations, then your expected win percentage might be 75%. But are there any sports events where that is the case?

So the question remains. Why base bet size on percentage and not on Z-factor? They're not the same thing, so how could it not make a difference?

Because you can get an estimated win percentage for a specific game, e.g. the probability the Pats win by more than 11 this weekend. How you do that is not normally a purely statistical process. But you can't get a Z-score for a game, because that exact game has never happened before, and will never happen again. You only get to observe the outcome once.

[Dark Horse]

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[Dark Horse]

I just prefer a stunned silence here.

memo to self.
Don't f*cking bother.