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Bayesian Instinct

44 Pages Posted: 15 Feb 2017 Last revised: 5 Apr 2017

Etan A. Green

Wharton - Operations, Information and Decisions

David P. Daniels

Stanford Graduate School of Business

Date Written: April 3, 2017


Do experts form rational beliefs when making split-second, sophisticated judgments? A long literature suggests not: individuals often form prior beliefs from biased sampling and update those beliefs by improperly weighting new information. This paper studies belief formation by professional umpires in Major League Baseball. We show that the decisions of umpires reflect an accurate, probabilistic, and state-specific understanding of their rational expectations—as well as an ability to integrate those prior beliefs in a manner that approximates Bayes rule. Given that umpires have barely a second to form beliefs and make a decision, we conclude that the instincts of professional umpires mimic a sophisticated level of rationality remarkably well.

Keywords: beliefs, rational expectations, Bayes rule, field study, experts

JEL Classification: D81, D83, D84

Suggested Citation

Green, Etan A. and Daniels, David P., Bayesian Instinct (April 3, 2017). Available at SSRN: or

Etan A. Green (Contact Author)

Wharton - Operations, Information and Decisions ( email )

Philadelphia, PA 19104
United States

David P. Daniels

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305
United States

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