Who's Best? It's All About The Base(s)
/Simple question: which of MoS' 17 Margin Predictors has been best-performed over the past two seasons?
Read MoreSimple question: which of MoS' 17 Margin Predictors has been best-performed over the past two seasons?
Read MoreWith the exception of Combo_NN_2, all of the Margin Predictors rely on an algorithm that takes Bookmaker Implicit Probabilities as an input in some form:
For this short blog I've switched, in all of the underlying algorithms, the Implicit Probabilities calculated using the Risk-Equalising Approach as replacements for those calculated using the Overround-Equalising Approach and then compared the resulting MAPEs for seasons 2007 to 2012 for all the Margin Predictors.
Overall, all Margin Predictors except Bookie_3 benefit from the switch, however modestly. Bookie_9, which now will serve as a co-predictor in the MAFL Margin Fund, benefits most, knocking over one quarter of a point per game off its MAPE.
The uniformity of these improvements is made slightly more remarkable by the realisation that the Margin Predictors, built using Eureqa, were optimised for the probability outputs of the underlying algorithms when those algorithms were using Overround-Equalising Implicit Probabilities. So, for example, the equation for Bookie_9, which is:
Predicted Home Team Margin = 2.2205129 + 17.729506 * ln(Home Team Bookmaker Probability/(1-Home Team Bookmaker Probability)) + 2*Home Team Bookmaker Probability
was created by Eureqa to minimise the historical MAPE of this equation when the Home Team Bookmaker Probabilities being used were those calculated assuming Overround-Equalisation. The 0.26 points per game reduction in the MAPE is being achieved without re-optimising this equation but, instead, simply by replacing the Home Team Probabilities with those calculated using a Risk-Equalising Approach.
Bookie_3 is the one Margin Predictor that responds poorly to the switch of probabilities without an accompanying re-optimisation in Eureqa. When I performed such a re-optimisation, Eureqa came up with this remarkably simple equation:
Predicted Home Team Margin = 21 * ln(Home Team Bookmaker Probability/(1-Home Team Bookmaker Probability))
This predictor has an MAPE of 29.22 points per game, which is extraordinarily low for such an easy-to-use predictor.
CONCLUSION
Virtually every algorithm used in MAFL has now been shown to benefit, however slightly, from using Implicit Probabilities calculated using the Risk-Equalising instead of the Overround-Equalising Approach. Naturallly, this makes me wonder if there's an even better way ...
Maybe next year I'll look for it.
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