Probability forecasts in the market of tennis betting: the CaSco normalization

The probability odds, obtained as the inverse of the betting odds, represent the most accurate proxy of the bookmaker forecasts associated to each player/team victory. However, these probability odds cannot be defined as actual forecasts because they incorporate the bookmaker margin and the longshot bias such that their summation is greater than one. In literature, different normalization methods have been proposed in order to close the gap between probability odds and the underlying forecasts. This paper proposes a new method of normalization, named CaSco (Candila-Scognamillo) normalization, for the fixed odds offered on sports with only two possible outcomes. The performances of the new procedure are evaluated using the betting odds provided by one of the most important on-line professional bookmaker on over 27.000 male tennis matches. The results show that the CaSco normalization has a better forecasting ability than that of the other approaches presented in literature.