Sunday, August 16, 2015

Doubling Rate Entropy And Kullback-Leibler Divergence

Cover and Thomas (2006) show that, in a horse race, a handicapper has an expected wealth growth-rate equal to that of an investor who wins every race minus a measure of uncertainty of the race and minus the difference in the win probability distribution used by the handicapper and the distribution of true win probabilities. Intuitively, this makes sense. To reduce the race uncertainty, we should focus on open betting markets with as few runners as possible. To reduce the win estimates difference, we should meld our betting line estimates with that of the crowd (Benter, 2004). In terms of a simplistic equation:

   Long-Term Profit = Clairvoyance – Race Uncertainty – Win Estimate Divergence.

My experience is that most handicappers focus too much on trying to become clairvoyant and not enough on selecting open races and factoring in the “wisdom of crowds”.