Those of you who read my posts over on the Statistical Analyses journal will know that I've been fairly active these past few months investigating Bookmaker Overround, how it appears to be levied differentially on the Home and the Away teams, and what this means for determining the Bookmaker's Implicit Probabilities.

Based on this I've come up with three different ways of inferring the Bookmaker's Implicit victory probability for the Home team given his head to head prices: 

• Overround-Equalising Implicit Home Team Probability = Away Team Price / (Home Team Price + Away Team Price)
• Risk-Equalising Implicit Home Team Probability = 1 / Home Team Price - Total Overround / 2 (where Total Overround = 1/ Home Team Price + 1 / Away Team Price - 1)
• Log Probability Score Optimised Home Team Probability = 1 / Home Team Price - 1.0281%

The Overround-Equalising approach is the one I've been using since MAFL started, and it's only been during the current off-season that I've given any serious thought to seeking alternatives. The Risk-Equalising approach is, in hindsight, a more logical, Bookmaker-centric way of considering the issue of allocating overround, and the Log Probability Score Optimised approach is an empirically-motivated extension of that more logical approach.

You can read more about each of the approaches in the blogs that I've linked to, but for the purposes of this blog all you need know is that the Risk-Equalising and Log Probability Score Optimised (LPSO) Probability Predictor will be joining the list of Probability Predictors that I'll be tracking this season. As its name suggests, the LPSO Probability Predictor is in some sense "optimised" so it will be interesting to see if its optimisation persists into 2013.

The LPSO Probability Predictor can be used as input to create a Margin Predictor, which I've done to create the Bookie_LPSO Margin Predictor. It will be joining the band of Margin Predictors on the MAFL Leaderboard along with two new ensemble Margin Predictors based on what I've called Really Simple Margin Predictors (RSMPs). Each of the 11 RSMPs uses as input a single variable derived either from Bookmaker prices or MARS Ratings and the new Margin Predictors, RSMP_Simple and RSMP_Weighted, combine the opinions of these 11 RSMPs in different ways.

SUMMARY

So, in short, there are four new Predictors for 2013: 

• Two Probability Predictors, Bookie_RE and Bookie_LPSO (Bookie_OE will also appear on the MAFL Leaderboard too, but it's just the Probability Predictor from last season renamed for clarity)
• Two Margin Predictors, RSMP_Simple and RSMP_Weighted

 

In total that means we'll have 27 Head-to-Head Predictors, 16 Margin Predictors, 7 Head-to-Head Probability Predictors and 1 Line Probability Predictor.

The downloadable PDF has been updated to include these new Predictors.