Adjusting true odds to allow for vigorish

A mathematical model predicting sporting outcomes produces probabilities that sum to one, whereas the probabilities implied by bookmaker's odds sum to more than one. Vigorish or over-round is the excess probability that supplies the bookies margin, and could typically range from 2% to over 20%. If the probabilities from a mathematical model are to be used for supplying real time odds they need to be adjusted for the bookmaker's vigorish. In the reverse situation, when testing models from past data, bookmaker's odds need to be adjusted so that the implied probabilities sum to one. Schembri et al (2011) discusses two methods - normalisation and equal distribution. However neither of these suitably allow for the fact that the margin on outsiders is usually greater than favourites. A true price of $1.05 can be reduced to $1.03 for less than 2% margin, whereas a $100 true price could be set at $50 for a $50% margin. This paper discusses an alternativeapproach using a power function to transform probabilities. This was successfully used when supplying real time odds to a leading bookmarker (Clarke, 2007).