# Prospect Theory and the Favorite Long-Shot Bias in Baseball

## Abstract

**:**

## 1. Introduction

## 2. Bookmaker Odds and Efficient Markets

## 3. Conditions for Inefficiency

#### A Difference of Mean Run Differentials

## 4. Results

## 5. A Betting Strategy

## 6. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | Referred to there as a misestimation of probabilities. |

2 | https://sports-statistics.com/sports-data/mlb-historical-odds-scores-datasets/, accessed on 4 May 2023. |

3 | https://www.retrosheet.org/, accessed on 4 May 2023. |

## References

- Agresti, Alan, and Brent A. Coull. 1998. Approximate is better than “exact” for interval estimation of binomial proportions. The American Statistician 52: 119–26. [Google Scholar]
- Brown, Lawrence D., T. Tony Cai, and Anirban DasGupta. 2001. Interval estimation for a binomial proportion. Statistical Science 16: 101–33. [Google Scholar] [CrossRef]
- Gandar, John M., Richard A. Zuber, R. S. Johnson, and W. Dare. 2002. Re-examining the betting market on major league baseball games: Is there a reverse favourite-longshot bias? Applied Economics 34: 1309–17. [Google Scholar] [CrossRef]
- Kahneman, Daniel, and Amos Tversky. 1979. Prospect theory: An analysis of decision under risk. Econometrica 47: 263–91. [Google Scholar] [CrossRef]
- Krieger, Kevin, Justin L. Davis, and James Strode. 2021. Patience is a virtue: Exploiting behavior bias in gambling markets. Journal of Economics and Finance 45: 735–50. [Google Scholar] [CrossRef]
- Levy, Jack S. 1992. An introduction to prospect theory. Political Psychology 13: 171–86. [Google Scholar]
- Miller, Steven J. 2007. A derivation of the Pythagorean won-loss formula in baseball. Chance 20: 40–48. [Google Scholar] [CrossRef]
- Newall, Philip W. S., and Dominic Cortis. 2021. Are sports bettors biased toward longshots, favorites, or both? A literature review. Risks 9: 22. [Google Scholar] [CrossRef]
- Ottaviani, Marco, and Peter Norman Sørensen. 2008. The favorite-longshot bias: An overview of the main explanations. Handbook of Sports and Lottery Markets, 83–101. [Google Scholar] [CrossRef]
- Snowberg, Erik, and Justin Wolfers. 2010. Explaining the favorite–long shot bias: Is it risk-love or misperceptions? Journal of Political Economy 118: 723–46. [Google Scholar] [CrossRef]
- Woodland, Bill M., and Linda M. Woodland. 2016. Additional evidence of heuristic-based inefficiency in season wins total betting markets: Major league baseball. Journal of Economics and Finance 40: 538–48. [Google Scholar] [CrossRef]
- Woodland, Linda, and Bill Woodland. 1994. Market efficiency and the favorite-longshot bias: The baseball betting market. The Journal of Finance 49: 269–79. [Google Scholar] [CrossRef]
- Woodland, Linda, and Bill Woodland. 2003. The reverse favourite-longshot bias and market efficiency in major league baseball: An update. Bulletin of Economic Research 55: 113–23. [Google Scholar] [CrossRef]
- Yu, Dian, Jianjun Gao, and Tongyao Wang. 2022. Betting market equilibrium with heterogeneous beliefs: A prospect theory-based model. European Journal of Operational Research 298: 137–51. [Google Scholar] [CrossRef]

**Figure 1.**Implied probability (green), true probability (purple), and the difference (red) as the mean run differential increases. These plots are calculated using ten-day (

**above**) and twenty-day (

**below**) means. The colored bands show 95% confidence intervals.

**Figure 2.**Implied probability (green), true probability (purple), and the difference (red) as the mean run differential increases. These plots are calculated using forty-day (

**above**) and sixty-day (

**below**) means. The colored bands show 95% confidence intervals.

**Figure 3.**Implied probability (green), true probability (purple), and the difference (red) as the mean run differential decreases. These plots are calculated using ten-day (

**above**) and twenty-day (

**below**) means. The colored bands show 95% confidence intervals.

**Figure 4.**Implied probability (green), true probability (purple), and the difference (red) as the mean run differential decreases. These plots are calculated using forty-day (

**above**) and sixty-day (

**below**) means. The colored bands show 95% confidence intervals.

**Figure 5.**Probability of a win, expressed as a money line, when the difference of mean run differentials exceeds a given threshold.

Month/Day | Visitor @ Home | Visitor Runs–Home Runs |
---|---|---|

5/23 | Cubs @ Reds | 7–4 |

5/23 | Dodgers @ Nationals | 10–1 |

5/22 | Diamondbacks @ Cubs | 4–5 |

5/22 | Nationals @ Brewers | 8–2 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Nutaro, J.
Prospect Theory and the Favorite Long-Shot Bias in Baseball. *Risks* **2023**, *11*, 95.
https://doi.org/10.3390/risks11050095

**AMA Style**

Nutaro J.
Prospect Theory and the Favorite Long-Shot Bias in Baseball. *Risks*. 2023; 11(5):95.
https://doi.org/10.3390/risks11050095

**Chicago/Turabian Style**

Nutaro, James.
2023. "Prospect Theory and the Favorite Long-Shot Bias in Baseball" *Risks* 11, no. 5: 95.
https://doi.org/10.3390/risks11050095