History-Dependent Mixed Strategies: Evidence From Major League Baseball

Abstract

This article analyzes to what extent baseball players adjust mixed strategies depending on the history by which the batting count is realized, then tests if these adjustments are aligned with best-response play. Two situations are examined: (1) pitches preceded by a borderline ball or strike at which the batter did not swing and (2) batters taking a strike as opposed to swinging and missing. Adjustments in batter and pitcher strategy on the following pitch are identified as statistically significant, however, of small magnitude. Analysis considers the effects of these adjustments on the expected runs scored during the plate appearance.