The Bobby Cox Effect

Thomas Lake has a nice retrospective article on Bobby Cox’s ejections in the current issue of Sports Illustrated. If you have read it, you might have seen my brief contribution.

FEW HUMAN endeavors have been studied so closely by so many people with such fascination for such a long time as the game of baseball. Historians, economists and statisticians scrutinize everything that happens and compare it with everything else that already happened, going back to 1871. This ocean of numbers can tell us a lot about Bobby Cox. For example: He makes pitchers better. J.C. Bradbury, author of the 2008 book The Baseball Economist: The Real Game Exposed, looked at pitchers who had thrown for multiple teams and compared their performances for Cox with their performances for other teams. Using a sophisticated technique called multiple regression analysis, Bradbury factored out variables such as hitter-friendly ballparks, league ERA differences, team defense and pitchers’ ages. What remained was a meaningful Cox Effect, worth about a quarter of a run every nine innings. (True, the Leo Mazzone Effect was even larger, but the Cox Effect existed even in the 14 years Mazzone wasn’t Cox’s pitching coach.)

I looked at pitchers with more than 30 innings pitched in a season and hitters with more than 100 plate appearances who played for Bobby Cox and at least one other manager. The tables below report the estimates. The performance numbers are park corrected.


        	ERA
Bobby Cox       -0.256
        	(3.95)**

Career ERA      0.833
        	(16.36)**

LgERA   	0.249
        	(2.71)**

Tm BABIP        10.839
        	(4.12)**

Age     	-0.341
        	(6.10)**

Age2    	0.006
        	(6.28)**

Constant        1.686
        	(1.61)

Observations    1519
R-squared       0.29
Robust t statistics in parentheses      
* significant at 5%; ** significant at 1%  
        	OPS
Bobby Cox       -0.006
        	(1.24)

Career OPS      0.935
        	(42.88)**

LgOPS   	0.415
        	(6.48)**

Age     	0.028
        	(4.98)**

Age2    	-0.00046
        	(5.01)**

Constant        -0.670
        	(7.00)**

Observations    1833
R-squared       0.52
Robust t statistics in parentheses      
* significant at 5%; ** significant at 1%   

4 Responses “The Bobby Cox Effect”

  1. Marc Schneider says:

    Any ideas as to why Bobby Cox (as opposed to Leo Mazzone) would have such an effect?

  2. Melvin says:

    Would it make sense to perform the same study on other longtime managers as a control?

  3. Mike says:

    Perhaps a “Tony La Russa” effect on OPS.

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