The Affect of Uncertainty

[Utah]

How does the uncertainty surrounding handicapping parameters affect expected value?

Lets say that I am handicapping an NFL game that has had the line vetted by the public for a week. It is a pretty accurate line but I think I am a better handicapper and I can get a 5% edge on my bet.

Now, lets say I am also handicapping live match lines for Yugoslavian 2nd Division Badminton. The lines are known to be way off and the markets are thinly traded. I have much trouble handicapping these events but I believe that my bets are a 5% edge.

Is there any difference between these 2 bets? Is my expected return different?

Intuitively, I think that in the second case all the crazy randomness will be evenly distributed and eventually cancel out leaving me with my 5% expected. But, there is a high chance there is some flaw in my thinking.

Thanks in advance

[Ganchrow]

Assuming your estimate of 5% edge to be accurate, then your expected return in either case is by definition the same -- 5%.

And going a step further, for a binary bet, edge = p * decimal_odds - 1, and variance = (1 + Edge) * (1 - decimal_odds - Edge). Hence if your edge estimate is an unbiased estimator of actual edge then not only will your expectation be invariant to the noise of that estimate but so to will your outcome variance in addition to every other higher order moment. This is why Kelly stake isn't a function of forecast volaitility under the assumption of unibased forecasts.

[Ganchrow]

I should probably add that over a series of bets autocorrelation of forecast error would be relevant to bet sizing decisions even if the initial forecast estimate were unbiased.

[Utah]

Assuming your estimate of 5% edge to be accurate, then your expected return in either case is by definition the same -- 5%.

And going a step further, for a binary bet, edge = p * decimal_odds - 1, and variance = (1 + Edge) * (1 - decimal_odds - Edge). Hence if your edge estimate is an unbiased estimator of actual edge then not only will your expectation be invariant to the noise of that estimate but so to will your outcome variance in addition to every other higher order moment. This is why Kelly stake isn't a function of forecast volaitility under the assumption of unibased forecasts.

Thanks a lot. Much appreciated.