The most common method used to convert betting odds to probabilities is to normalize the inverse odds (Multiplicative conversion). However, this method does not consider the favourite-longshot bias.

To the best of our knowledge, there are two existing methods that attempt to consider the favourite-longshot bias. (i) Shin conversion [1, 2, 3] maximizes the expected profit for the bookmakers assuming a small proportion of bettors have inside information. (ii) Power conversion [4] raises all inverse odds to the same constant power. However, both of these methods require iterative computation to convert betting odds to probabilities.

Our proposed method (Goto conversion) is significantly more efficient than Shin and Power conversion because it converts betting odds to probabilities directly without iterative computation.

The Goto conversion reduces all inverse odds by the same units of margin of error. This attempts to consider the favourite-longshot bias by utilizing the wider margin of errors implied for inverses of longshot odds and vice-versa.

Furthermore, our tables of experiment results below show that the Goto conversion converts betting odds to probabilities more accurately than all three of these existing methods.

Requires Python 3.7 or above.

pip install goto-conversion

import goto_conversion
goto_conversion.goto_conversion([1.2, 3.4, 5.6])

[0.7753528189788175, 0.17479473292721065, 0.04985244809397199]

import goto_conversion
goto_conversion.goto_conversion([-500, 240, 460], isAmericanOdds = True)

[0.7753528189788175, 0.17479473292721065, 0.04985244809397199]

The experiment results table directly below is based on the same 6,000 football matches' betting odds across four different bookmakers.

Kaggle notebook to reproduce the table directly above: https://www.kaggle.com/code/kaito510/novel-conversion-of-football-betting-odds

The experiment results table directly below is based on 6,348 horse races' betting odds for the win and place markets.

Kaggle notebook to reproduce the table directly above: https://www.kaggle.com/code/kaito510/novel-conversion-of-horse-racing-odds

[1] H. S. Shin, “Prices of State Contingent Claims with Insider traders, and the Favorite-Longshot Bias”. The Economic Journal, 1992, 102, pp. 426-435.

[2] E. Štrumbelj, "On determining probability forecasts from betting odds". International Journal of Forecasting, 2014, Volume 30, Issue 4, pp. 934-943.

[3] M. Berk, "Python implementation of Shin's method for calculating implied probabilities from bookmaker odds"

[4] S. Clarke, S. Kovalchik, M. Ingram, "Adjusting bookmaker’s odds to allow for overround". American Journal of Sports Science, 2017, Volume 5, Issue 6, pp. 45-49.