goto-conversion 0.2.0

Novel Conversion of Betting Odds to Probabilities

goto_conversion: Novel Conversion of Betting Odds to Probabilities

The most common method used to convert betting odds to probabilities is to normalise 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] maximises 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 standard error. This attempts to consider the favourite-longshot bias by utilising the proportionately wider standard errors implied for inverses of longshot odds and vice-versa.

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

The favourite-longshot bias is not limited to gambling markets, it exists in stock markets too. Thus, we applied the original goto_conversion to stock markets by defining the zero_sum variant. Under the same philosophy as the original goto_conversion, zero_sum adjusts all predicted stock prices (e.g. weighted average price) by the same units of standard error to ensure all predicted stock prices relative to the index price (e.g. weighted average nasdaq price) sum to zero. This attempts to consider the favourite-longshot bias by utilising the wider standard errors implied for predicted stock prices with low trade volume and vice-versa.

Citations (not limited to, unofficial)

Most Voted Public Solution from 2024 Optiver Kaggle Competition

1xGold and 2xSilver Medal Winning Public Solution from 2019 to 2022 March Mania Kaggle Competition

Bronze Medal Winning Public Solution from 2024 March Mania Kaggle Competition

Installation

Requires Python 3.7 or above.

pip install goto-conversion

Usage

Decimal Odds

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

[0.7753528189788175, 0.17479473292721065, 0.04985244809397199]

American Odds

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

[0.7753528189788175, 0.17479473292721065, 0.04985244809397199]

Pseudo Code

Experiment Results

The experiment results table directly below is based on the same 6,000 football matches' betting odds (home win, draw or away win) 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

References

[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.

Contact Me

via kaggle message: https://www.kaggle.com/kaito510/competitions

Q&A

Q1. I want to know whether the teams in the csv file named mensProbabilitiesTable in the 538 data you created are in 2024 or 2023?

A1. 2024 but it is NOT 538 data, it is my data displayed in a format inspired by 538.