Edelman Sharpe Ratio

David Edelman, Quantitative Finance lecturer, handicapper, and author derives a sports trading version of the Sharpe Ratio on page 28 of "The Compleat Horseplayer".
SR = (ProbWin - (1 / DecimalOdds)) / Sqrt(ProbWin * (1 - ProbWin))
For example, with the following 'investments', A is judged to be slightly better than B in terms of expected return per unit of risk:
A: ProbWin = 45%, DecimalOdds = 2.60
SR = (0.45 - (1 / 2.6)) / Sqrt(0.45 * (1 - 0.45))
= 0.13142
B: ProbWin = 31%, DecimalOdds = 4.00
SR = (0.31 - (1 / 4.0)) / Sqrt(0.31 * (1 - 0.31))
= 0.12973