Gambling Odds To Outcome probabilities Conversion (goto_conversion) and Faster Shin's Method (efficient_shin_conversion)

The most common method used to convert gambling 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.

Our proposed method, Gambling Odds To Outcome probabilities Conversion (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.

Our table of experiment results shows goto_conversion converts gambling odds to probabilities more accurately than all three of these existing methods.

This package is an implementation of goto_conversion as well as efficient_shin_conversion. The Shin conversion is originally a numerical solution but according to Kizildemir 2024 [6], we can enhance its efficiency by reduction to an analytical solution. We have implemented the enhanced Shin conversion proposed by Kizildemir 2024 as efficient_shin_conversion in this package.

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.

Presentation at the Royal Statistical Society

• Link to Presentation Recording: https://youtu.be/M00osEjcp_4?si=_WZv09311q3UoS9t&t=411

Applications on Kaggle

To the best of my knowledge, on Kaggle, at least four gold medal solutions and many other medal solutions have publicly stated that they applied goto_conversion in their solution:

• Gold Medal Winning (3rd out of 821) Solution from 2024 March Mania Kaggle Competition
• Gold Medal Winning (4th out of 821) Solution from 2024 March Mania Kaggle Competition
• 1xGold and 2xSilver Medal Winning Solution from 2019 to 2022 March Mania Kaggle Competition
• 15xBronze Medal Winning (86th to 100th place out of 821) Solution from 2024 March Mania Kaggle Competition
• Silver Medal Winning (38th out of 821) Solution from 2024 Match Mania Kaggle Competition
• Most Voted Solution from 2023 Optiver Kaggle Competition
• Gold Medal Winning (14th out of 3225) Solution from 2023 Optiver Kaggle Competition (the zero_sum variant)

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]

Numpy array inputs will return numpy array outputs

import goto_conversion
import numpy as np
goto_conversion.goto_conversion(np.array([1.2, 3.4, 5.6]))

[0.77535282 0.17479473 0.04985245]

Test cases for efficient_shin_conversion

import goto_conversion
print(goto_conversion.efficient_shin_conversion([1.22,4.57,6.54]))
print(goto_conversion.efficient_shin_conversion([1.22,4.63,6.38]))
print(goto_conversion.efficient_shin_conversion([1.17,4.97,7.57]))

[0.8005889182988829, 0.13614976602243348, 0.0632613156786835]
[0.8004787158953608, 0.1325348922189233, 0.0669863918857159]
[0.8396249156189404, 0.11832615760257503, 0.04204892677848464]

Notice the printed probability lists match the first three rows of table 1 in Kizildemir 2024 [6].

Pseudo Code

Experiment Results

The experiment results table below evaluates each conversion method's predicted probabilities based on ~200,000 football matches' gambling odds (home win, draw or away win) across 8 different bookmakers that had at least 12 seasons of data on football-data.co.uk [5].

goto_conversion significantly outperforms all other conversion methods for all 8 bookmakers with just one exception. goto_conversion outperforms efficient_shin_conversion for only 6 out of the 12 seasons under the Pinnacle Sports (PS) bookmaker which implied an insignificant p-value of exactly 0.5.

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 gambling 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.

[5] Football-Data

[6] Kizildemir, M., Akin, E., & Alkan, A. (2024). A Family of Solutions Related to Shin’s Model For Probability Forecasts. Cambridge Open Engage

Contact Me

via LinkedIn Message: https://www.linkedin.com/in/goto/

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.