[Ganchrow]

Originally Posted by VideoReview

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Your question actually has little to do with Kelly per se. Given stated payout odds, then the mapping of probability to Kelly stake will be injective (i.e., one-to-one) for all positive expectation. As such, once you determine a confidence interval for your forecast probability, converting that to a confidence interval for Kelly is trivial.

I'm a little unclear as to why you're using R² as an estimator of probability. Loosely speaking, the R² of a model corresponds to the percent of the variability of your data set that's explained by that model. Unless I've misunderstood the nature of your regression, that's going to be very different from the win probability you're attempting to estimate.

Typically when trying to estimate a probability (which is obviously only defined on the interval [0,1]) using regression analysis one uses the logarithim of the inverse of "fair" payout odds (i.e., "fair" decimal odds - 1, or b in your Kelly equation given an edge of 0) as the dependent variable, which is defined across the entire set of real numbers. This is know as a "logistic regression".

It's also not strictly correct to use ±0.98/sqrt(n) as your interval. While this does correspond to a 95% confidence interval, this would only really be strictly true were your data set drawn from a single binomial distribution with p=50% (.98 = 2*50%*(1-50%)*1.96). In the context of your particular problem the confidence interval would be better expressed using the standard error of the regression.

Specific mechanics aside I suspect I'd probably tend to agree with RickySteve in his analysis. That said, why don't you e-mail me your spreadsheet along with a description of each of the columns and we can take it from there.