The Sacking Fallacy: Managerial Turnover and Regression to the Mean in Franchise Cricket

When a sports team enters a competitive slump, firing the head coach is frequently seen as decisive leadership. While economists have extensively investigated managerial dismissals across European football and American leagues, empirical work on professional cricket remains non-existent. This paper provides the first empirical test of head coach turnover in elite franchise cricket, tracking all six franchises across the nine editions of the Pakistan Super League from 2016 to 2024 (N = 52 team-seasons). Adapting the econometric framework of Farnell (2014), we test whether hiring a new head coach drives genuine performance recovery or represents a costly overreaction to short-term variance. At first glance, franchises bringing in a new coach register an average win rate improvement of +1.70 percentage points. However, once we estimate an econometric model that controls for the severity of the prior-season slump, this recovery is entirely explained by statistical regression to the mean (beta = -0.8708, p < 0.0001, R^2 = 43.3%). In fact, after accounting for natural mean reversion, the estimated impact of replacing a coach turns negative (beta = -4.43, p = 0.384). Furthermore, franchises with the highest coaching turnover (Karachi Kings, with 5 changes in 9 editions) hold the lowest historical win rates in the league (38.6%), whereas teams with institutional and analytical continuity (Multan Sultans and Islamabad United) dominate titles and playoff appearances. These results demonstrate that coaching sackings in short-tournament cricket are classic examples of executive scapegoating and the illusion of control under small-sample noise.