For probabilities between about 30% and 70%, which approximately equates to prices in the $1.35 to $3.15 range, all four models give roughly the same margin prediction for a given bookie probability. They differ, however, outside that range of probabilities, by up to 10-15 points. Since only about 37% of games have bookie probabilities in this range, none of the models is penalised too heavily for producing errant margin forecasts for these probability values.

So far then, the best model we've produced has used only bookie probability and a MARS modelling approach.

Let's finish by adding the other MARS back into the equation - my MARS Ratings, which bear no resemblance to the MARS algorithm, and just happen to share a name. A bit like John Howard and John Howard.

This gives us the following model:

*Predicted Margin = 14.487934 + if(Prob > 0.6898155, 78.090701 x (Prob - 0.6898155),0) + if(Prob < 0.6898155, -75.579198 x (0.6898155 - Prob),0) + if(MARS_Diff < -7.29, 0, 0.399591 x (MARS_Diff + 7.29)*

The model described by this equation is kinked with respect to bookie probability in much the same way as the previous model. There's a single kink located at the same probability, though the slope to the left and right of the kink is smaller in this latest model.

There's also a kink for the MARS Rating variable (which I've called MARS_Diff here), but it's a kink of a different kind. For MARS Ratings differences below -7.29 Ratings points - that is, where the home team is rated 7.29 Ratings points or more below the away team - the contribution of the Ratings difference to the predicted margin is 0. Then, for every 1 Rating point increase in the difference above -7.29, the predicted margin goes up by about 0.4 points.

This final model, which I think can still legitimately be called a simple one, has an R-squared of 23.5%. That's a further increase of 0.8%, which can loosely be thought of as the contribution of MARS Ratings to the explanation of game margins over and above that which can be explained by the bookie's probability assessment of the home team's chances.