Table 2 Generalized linear model results...

Table 2

Generalized linear model results for performance evaluation bias*

DV: Overrecognition	Model 1		Model 2		Model 3		Model 4		Model 5		Model 6		Model 7
DV: Overrecognition	b(s.e.)	p-val.	b(s.e.)	p-val.	b(s.e.)	p-val.	b(s.e.)	p-val.	b(s.e.)	p-val.	b(s.e.)	p-val.	b(s.e.)	p-val.
Pitcher's past performance			0.034	[0.000]	0.052	[0.000]	0.028	[0.000]	0.042	[0.000]	0.034	[0.000]	0.053	[0.000]
Pitcher's past performance			(0.003)		(0.005)		(0.004)		(0.004)		(0.003)		(0.006)
Pitcher's past performance × Inning					−0.004	[0.000]							−0.004	[0.000]
Pitcher's past performance × Inning					(0.001)								(0.001)
Pitcher's past performance × Run expectancy							0.015	[0.010]					0.014	[0.014]
Pitcher's past performance × Run expectancy							(0.006)						(0.006)
Pitcher's past performance × One strike									−0.012	[0.009]			−0.012	[0.009]
Pitcher's past performance × One strike									(0.005)				(0.005)
Pitcher's past performance × Two strikes									−0.009	[0.050]			−0.009	[0.051]
Pitcher's past performance × Two strikes									(0.005)				(0.005)
Pitcher's past performance × Batter: All-Star											0.001	[0.395]	0.001	[0.537]
Pitcher's past performance × Batter: All-Star											(0.002)		(0.002)
Inning	0.034	[0.000]	0.039	[0.000]	0.044	[0.000]	0.039	[0.000]	0.039	[0.000]	0.039	[0.000]	0.044	[0.000]
Inning	(0.001)		(0.001)		(0.002)		(0.001)		(0.001)		(0.001)		(0.002)
Run expectancy	−0.097	[0.000]	−0.095	[0.000]	−0.095	[0.000]	−0.112	[0.000]	−0.095	[0.000]	−0.095	[0.000]	−0.112	[0.000]
Run expectancy	(0.009)		(0.009)		(0.009)		(0.012)		(0.009)		(0.009)		(0.012)
One strike	0.611	[0.000]	0.611	[0.000]	0.611	[0.000]	0.611	[0.000]	0.626	[0.000]	0.611	[0.000]	0.626	[0.000]
One strike	(0.007)		(0.007)		(0.007)		(0.007)		(0.009)		(0.007)		(0.009)
Two strikes	0.613	[0.000]	0.611	[0.000]	0.611	[0.000]	0.611	[0.000]	0.623	[0.000]	0.611	[0.000]	0.622	[0.000]
Two strikes	(0.007)		(0.007)		(0.007)		(0.007)		(0.009)		(0.007)		(0.009)
Batter: All-Star	−0.033	[0.000]	−0.033	[0.000]	−0.033	[0.000]	−0.033	[0.000]	−0.033	[0.000]	−0.035	[0.000]	−0.035	[0.000]
Batter: All-Star	(0.003)		(0.003)		(0.003)		(0.003)		(0.003)		(0.004)		(0.004)
Pitcher: All-Star	0.097	[0.000]	0.064	[0.000]	0.065	[0.000]	0.064	[0.000]	0.064	[0.000]	0.064	[0.000]	0.065	[0.000]
Pitcher: All-Star	(0.004)		(0.005)		(0.005)		(0.005)		(0.005)		(0.005)		(0.005)
Rookie	−0.073	[0.000]	−0.033	[0.001]	−0.034	[0.001]	−0.033	[0.001]	−0.033	[0.001]	−0.033	[0.001]	−0.034	[0.001]
Rookie	(0.010)		(0.010)		(0.010)		(0.010)		(0.010)		(0.010)		(0.010)
Pitcher (right-handed)	0.049	[0.000]	0.050	[0.000]	0.050	[0.000]	0.050	[0.000]	0.049	[0.000]	0.050	[0.000]	0.050	[0.000]
Pitcher (right-handed)	(0.007)		(0.007)		(0.007)		(0.007)		(0.007)		(0.007)		(0.007)
Pitcher: White	−0.036	[0.000]	−0.035	[0.000]	−0.035	[0.000]	−0.035	[0.000]	−0.035	[0.000]	−0.035	[0.000]	−0.035	[0.000]
Pitcher: White	(0.008)		(0.008)		(0.008)		(0.008)		(0.008)		(0.008)		(0.008)
Pitcher age	−0.005	[0.000]	−0.005	[0.000]	−0.006	[0.000]	−0.005	[0.000]	−0.005	[0.000]	−0.005	[0.000]	−0.006	[0.000]
Pitcher age	(0.001)		(0.001)		(0.001)		(0.001)		(0.001)		(0.001)		(0.001)
Edge pitch	0.392	[0.000]	0.392	[0.000]	0.392	[0.000]	0.392	[0.000]	0.392	[0.000]	0.392	[0.000]	0.392	[0.000]
Edge pitch	(0.068)		(0.068)		(0.068)		(0.068)		(0.068)		(0.068)		(0.068)
Batter: White	−0.008	[0.202]	−0.008	[0.213]	−0.008	[0.213]	−0.007	[0.217]	−0.008	[0.213]	−0.008	[0.213]	−0.007	[0.217]
Batter: White	(0.006)		(0.006)		(0.006)		(0.006)		(0.006)		(0.006)		(0.006)
Batter age	−0.014	[0.000]	−0.014	[0.000]	−0.014	[0.000]	−0.014	[0.000]	−0.014	[0.000]	−0.014	[0.000]	−0.014	[0.000]
Batter age	(0.001)		(0.001)		(0.001)		(0.001)		(0.001)		(0.001)		(0.001)
Batter (right-handed)	0.140	[0.000]	0.139	[0.000]	0.139	[0.000]	0.139	[0.000]	0.139	[0.000]	0.139	[0.000]	0.139	[0.000]
Batter (right-handed)	(0.007)		(0.007)		(0.007)		(0.007)		(0.007)		(0.007)		(0.007)
Small score difference	0.056	[0.000]	0.050	[0.000]	0.053	[0.000]	0.050	[0.000]	0.050	[0.000]	0.050	[0.000]	0.053	[0.000]
Small score difference	(0.011)		(0.011)		(0.011)		(0.011)		(0.011)		(0.011)		(0.011)
Attendance	0.000	[0.068]	0.000	[0.206]	0.000	[0.214]	0.000	[0.207]	0.000	[0.205]	0.000	[0.207]	0.000	[0.214]
Attendance	(0.000)		(0.000)		(0.000)		(0.000)		(0.000)		(0.000)		(0.000)
Bases loaded	0.189	[0.000]	0.194	[0.000]	0.193	[0.000]	0.196	[0.000]	0.194	[0.000]	0.194	[0.000]	0.196	[0.000]
Bases loaded	(0.021)		(0.021)		(0.021)		(0.021)		(0.021)		(0.021)		(0.021)
Home team	0.019	[0.003]	0.019	[0.004]	0.018	[0.005]	0.019	[0.004]	0.019	[0.004]	0.019	[0.004]	0.018	[0.005]
Home team	(0.007)		(0.007)		(0.007)		(0.007)		(0.007)		(0.007)		(0.007)
Degrees	0.001	[0.000]	0.001	[0.000]	0.001	[0.000]	0.001	[0.000]	0.001	[0.000]	0.001	[0.000]	0.001	[0.000]
Degrees	(0.000)		(0.000)		(0.000)		(0.000)		(0.000)		(0.000)		(0.000)
Wind speed	−0.003	[0.000]	−0.003	[0.000]	−0.003	[0.000]	−0.003	[0.000]	−0.003	[0.000]	−0.003	[0.000]	−0.003	[0.000]
Wind speed	(0.001)		(0.001)		(0.001)		(0.001)		(0.001)		(0.001)		(0.001)
Constant	−2.536	[0.000]	−2.583	[0.000]	−2.604	[0.000]	−2.575	[0.000]	−2.592	[0.000]	−2.582	[0.000]	−2.605	[0.000]
Constant	(0.066)		(0.065)		(0.065)		(0.065)		(0.065)		(0.065)		(0.065)
Log-likelihood	−445737.58		−445620.75		−445607.42		−445617.09		−445617.20		−445620.38		−445600.24
Umpire × year FE	Yes		Yes		Yes		Yes		Yes		Yes		Yes
Observations	1,452,180		1,452,180		1,452,180		1,452,180		1,452,180		1,452,180		1,452,180

DV: Overrecognition	Model 1		Model 2		Model 3		Model 4		Model 5		Model 6		Model 7
DV: Overrecognition	b(s.e.)	p-val.	b(s.e.)	p-val.	b(s.e.)	p-val.	b(s.e.)	p-val.	b(s.e.)	p-val.	b(s.e.)	p-val.	b(s.e.)	p-val.
Pitcher's past performance			0.034	[0.000]	0.052	[0.000]	0.028	[0.000]	0.042	[0.000]	0.034	[0.000]	0.053	[0.000]
Pitcher's past performance			(0.003)		(0.005)		(0.004)		(0.004)		(0.003)		(0.006)
Pitcher's past performance × Inning					−0.004	[0.000]							−0.004	[0.000]
Pitcher's past performance × Inning					(0.001)								(0.001)
Pitcher's past performance × Run expectancy							0.015	[0.010]					0.014	[0.014]
Pitcher's past performance × Run expectancy							(0.006)						(0.006)
Pitcher's past performance × One strike									−0.012	[0.009]			−0.012	[0.009]
Pitcher's past performance × One strike									(0.005)				(0.005)
Pitcher's past performance × Two strikes									−0.009	[0.050]			−0.009	[0.051]
Pitcher's past performance × Two strikes									(0.005)				(0.005)
Pitcher's past performance × Batter: All-Star											0.001	[0.395]	0.001	[0.537]
Pitcher's past performance × Batter: All-Star											(0.002)		(0.002)
Inning	0.034	[0.000]	0.039	[0.000]	0.044	[0.000]	0.039	[0.000]	0.039	[0.000]	0.039	[0.000]	0.044	[0.000]
Inning	(0.001)		(0.001)		(0.002)		(0.001)		(0.001)		(0.001)		(0.002)
Run expectancy	−0.097	[0.000]	−0.095	[0.000]	−0.095	[0.000]	−0.112	[0.000]	−0.095	[0.000]	−0.095	[0.000]	−0.112	[0.000]
Run expectancy	(0.009)		(0.009)		(0.009)		(0.012)		(0.009)		(0.009)		(0.012)
One strike	0.611	[0.000]	0.611	[0.000]	0.611	[0.000]	0.611	[0.000]	0.626	[0.000]	0.611	[0.000]	0.626	[0.000]
One strike	(0.007)		(0.007)		(0.007)		(0.007)		(0.009)		(0.007)		(0.009)
Two strikes	0.613	[0.000]	0.611	[0.000]	0.611	[0.000]	0.611	[0.000]	0.623	[0.000]	0.611	[0.000]	0.622	[0.000]
Two strikes	(0.007)		(0.007)		(0.007)		(0.007)		(0.009)		(0.007)		(0.009)
Batter: All-Star	−0.033	[0.000]	−0.033	[0.000]	−0.033	[0.000]	−0.033	[0.000]	−0.033	[0.000]	−0.035	[0.000]	−0.035	[0.000]
Batter: All-Star	(0.003)		(0.003)		(0.003)		(0.003)		(0.003)		(0.004)		(0.004)
Pitcher: All-Star	0.097	[0.000]	0.064	[0.000]	0.065	[0.000]	0.064	[0.000]	0.064	[0.000]	0.064	[0.000]	0.065	[0.000]
Pitcher: All-Star	(0.004)		(0.005)		(0.005)		(0.005)		(0.005)		(0.005)		(0.005)
Rookie	−0.073	[0.000]	−0.033	[0.001]	−0.034	[0.001]	−0.033	[0.001]	−0.033	[0.001]	−0.033	[0.001]	−0.034	[0.001]
Rookie	(0.010)		(0.010)		(0.010)		(0.010)		(0.010)		(0.010)		(0.010)
Pitcher (right-handed)	0.049	[0.000]	0.050	[0.000]	0.050	[0.000]	0.050	[0.000]	0.049	[0.000]	0.050	[0.000]	0.050	[0.000]
Pitcher (right-handed)	(0.007)		(0.007)		(0.007)		(0.007)		(0.007)		(0.007)		(0.007)
Pitcher: White	−0.036	[0.000]	−0.035	[0.000]	−0.035	[0.000]	−0.035	[0.000]	−0.035	[0.000]	−0.035	[0.000]	−0.035	[0.000]
Pitcher: White	(0.008)		(0.008)		(0.008)		(0.008)		(0.008)		(0.008)		(0.008)
Pitcher age	−0.005	[0.000]	−0.005	[0.000]	−0.006	[0.000]	−0.005	[0.000]	−0.005	[0.000]	−0.005	[0.000]	−0.006	[0.000]
Pitcher age	(0.001)		(0.001)		(0.001)		(0.001)		(0.001)		(0.001)		(0.001)
Edge pitch	0.392	[0.000]	0.392	[0.000]	0.392	[0.000]	0.392	[0.000]	0.392	[0.000]	0.392	[0.000]	0.392	[0.000]
Edge pitch	(0.068)		(0.068)		(0.068)		(0.068)		(0.068)		(0.068)		(0.068)
Batter: White	−0.008	[0.202]	−0.008	[0.213]	−0.008	[0.213]	−0.007	[0.217]	−0.008	[0.213]	−0.008	[0.213]	−0.007	[0.217]
Batter: White	(0.006)		(0.006)		(0.006)		(0.006)		(0.006)		(0.006)		(0.006)
Batter age	−0.014	[0.000]	−0.014	[0.000]	−0.014	[0.000]	−0.014	[0.000]	−0.014	[0.000]	−0.014	[0.000]	−0.014	[0.000]
Batter age	(0.001)		(0.001)		(0.001)		(0.001)		(0.001)		(0.001)		(0.001)
Batter (right-handed)	0.140	[0.000]	0.139	[0.000]	0.139	[0.000]	0.139	[0.000]	0.139	[0.000]	0.139	[0.000]	0.139	[0.000]
Batter (right-handed)	(0.007)		(0.007)		(0.007)		(0.007)		(0.007)		(0.007)		(0.007)
Small score difference	0.056	[0.000]	0.050	[0.000]	0.053	[0.000]	0.050	[0.000]	0.050	[0.000]	0.050	[0.000]	0.053	[0.000]
Small score difference	(0.011)		(0.011)		(0.011)		(0.011)		(0.011)		(0.011)		(0.011)
Attendance	0.000	[0.068]	0.000	[0.206]	0.000	[0.214]	0.000	[0.207]	0.000	[0.205]	0.000	[0.207]	0.000	[0.214]
Attendance	(0.000)		(0.000)		(0.000)		(0.000)		(0.000)		(0.000)		(0.000)
Bases loaded	0.189	[0.000]	0.194	[0.000]	0.193	[0.000]	0.196	[0.000]	0.194	[0.000]	0.194	[0.000]	0.196	[0.000]
Bases loaded	(0.021)		(0.021)		(0.021)		(0.021)		(0.021)		(0.021)		(0.021)
Home team	0.019	[0.003]	0.019	[0.004]	0.018	[0.005]	0.019	[0.004]	0.019	[0.004]	0.019	[0.004]	0.018	[0.005]
Home team	(0.007)		(0.007)		(0.007)		(0.007)		(0.007)		(0.007)		(0.007)
Degrees	0.001	[0.000]	0.001	[0.000]	0.001	[0.000]	0.001	[0.000]	0.001	[0.000]	0.001	[0.000]	0.001	[0.000]
Degrees	(0.000)		(0.000)		(0.000)		(0.000)		(0.000)		(0.000)		(0.000)
Wind speed	−0.003	[0.000]	−0.003	[0.000]	−0.003	[0.000]	−0.003	[0.000]	−0.003	[0.000]	−0.003	[0.000]	−0.003	[0.000]
Wind speed	(0.001)		(0.001)		(0.001)		(0.001)		(0.001)		(0.001)		(0.001)
Constant	−2.536	[0.000]	−2.583	[0.000]	−2.604	[0.000]	−2.575	[0.000]	−2.592	[0.000]	−2.582	[0.000]	−2.605	[0.000]
Constant	(0.066)		(0.065)		(0.065)		(0.065)		(0.065)		(0.065)		(0.065)
Log-likelihood	−445737.58		−445620.75		−445607.42		−445617.09		−445617.20		−445620.38		−445600.24
Umpire × year FE	Yes		Yes		Yes		Yes		Yes		Yes		Yes
Observations	1,452,180		1,452,180		1,452,180		1,452,180		1,452,180		1,452,180		1,452,180

Note(s): *Robust standard errors clustered at the game level are reported in parentheses; p-values are rounded to three decimal places and reported in brackets

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