Bookmaker Implicit Probabilities: Empirical Value of the Risk-Equalising Approach

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A few blogs back I developed the idea that bookmakers might embed overround in each team's price not equally but instead such that the resulting head-to-head market prices provide insurance for a fixed (in percentage point terms) calibration error of equivalent size for both teams. Since then I've made only passing comment about the empirical superiority of this approach (which I've called the Risk-Equalising Approach) relative to the previous approach (which I've called the Overround-Equalising Approach).
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The Calibration of the Head-to-Head Fund Algorithm

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In the previous blog we considered the logarithmic probability score on ProPred, WinPred and the TAB bookie and found that the TAB bookie was the best calibrated of the three and that relative tipping performance was somewhat unrelated to relative probability scores. For the Head-to-Head Fund, whose job in life is to make money, the key question is to what extent do its probability scores relative to the TAB bookie's shed light on its money-making prowess.
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