Punching a Ticket to Cooperstown

Figures & data

Table 1 Description of variables.

Variable name	Variable description
Name	Name of the player—identifies the case in the data.
HoF	A “Yes”/“No” indicator on whether or not the player is in the Hall of Fame.
Yrs	Number of seasons played in player’s career.
WAR	Baseball Reference’s measure of Wins Above Replacement.
	This is a single number that describes the number of wins the player added to their teams over the course of their career.
WAR7	The sum of the seven best seasons of WAR in the player’s career.
	It may not be seven seasons in a row.
JAWS	Developed by Baseball Prospectus. It contains a combination of career and 7-year peak WAR totals allowing for comparison to average Hall of Fame players by position.
Jpos	The average JAWS score for all Hall of Fame players at this position plus overall Hall of Fame averages for positions with fewer inducted players.
JAWSratio	JAWS divided by Jpos and multiplied by 100.
G	Games played during a player’s career.
AB	At bats during a player’s career.
R	Runs scored during a player’s career.
H	Hits during a player’s career.
HR	Home runs hit during a player’s career.
RBI	Runs batted in during a player’s career.
SB	Stolen bases during a player’s career.
BB	Walks (bases on balls) during a player’s career.
BA	Batting average. This is H divided by AB.
OBP	On base percentage. This is the sum of H, BB, and times hit by a pitch divided by the sum of AB, BB, times hit by a pitch, and sacrifice flies.
SLG	Slugging percentage. This is the number of bases divided by AB.
	Every single is one base, double is two bases, triple is three bases, and HR is four bases in the numerator of this calculation.
OPS	The sum of OBP and SLG.
OPSadj	OPS adjusted to the player’s ball park. 100 is an “average” hitter.

Table 2 Summary statistics.

Not in Hall of Fame
n = 447
	Mean	SD	Min.	Q1	Median	Q3	Max.
Yrs	14.96	3.37	4.00	13.00	15.00	17.00	24.00
WAR	30.58	17.67	–5.30	17.60	29.10	40.80	162.80
WAR7	24.12	10.35	0.00	16.75	24.40	30.95	72.20
JAWSratio	50.239	25.05	–4.55	31.24	50.35	65.19	220.19
G	1662	486.11	67	1337	1673	1996	3592
AB	5836	1872.89	186	4588	5923	7129	14053
R	824.6	325.17	25.0	617.5	832.0	1031.5	2227.0
H	1622	549.82	54	1252	1621	1992	4256
HR	145.5	127.47	1.0	39.0	105.0	231.5	762.0
RBI	776.7	344.26	24.0	513.5	728.0	1026.5	1996.0
SB	125.7	129.99	2.0	37.5	80.0	172.0	752.0
BB	600.2	306.18	7.0	382.5	559.0	792.5	2558.0
BA	0.277	0.020	0.208	0.264	0.276	0.290	0.356
OBP	0.345	0.029	0.254	0.326	0.345	0.364	0.444
SLG	0.413	0.060	0.256	0.369	0.411	0.455	0.607
OPS	0.758	0.081	0.529	0.704	0.760	0.811	1.051
OPSadj	107.1	19.85	22.0	94.0	109.0	120.0	182.0
Hall of Fame
n = 155
	Mean	SD	Min.	Q1	Median	Q3	Max.
Yrs	18	3.46	10.00	16.00	18.00	20.00	27.00
WAR	67.05	26.88	16.20	49.50	63.00	75.45	162.10
WAR7	42.25	11.59	18.90	34.65	41.30	48.00	84.70
JAWSratio	99.68	33.04	30.45	76.41	96.49	114.09	213.49
G	2162	480.99	1211	1792	2164	2499	3308
AB	8001	1796.00	4205	6623	8134	9282	12364
R	1336	325.01	579	1092	1291	1592	2295
H	2418	568.11	1161	2045	2386	2826	4189
HR	225.3	181.52	11.0	74.0	169.0	360.0	755.0
RBI	1234	386.20	530	951	1208	1526	2297
SB	227.5	223.16	8.0	68.0	153.0	333.0	1406.0
BB	916.5	391.11	308.0	644.0	848.0	1118.5	2190.0
BA	0.302	0.024	0.253	0.284	0.303	0.319	0.366
OBP	0.377	0.030	0.299	0.357	0.376	0.395	0.482
SLG	0.465	0.065	0.316	0.427	0.462	0.505	0.690
OPS	0.841	0.086	0.653	0.797	0.837	0.888	1.164
OPSadj	128.8	20.95	82.0	115.0	128.0	141.0	206.0

Table 3 Correlation matrix for the 17 quantitative variables of interest (lower triangle).

	Yrs
Yrs	1.000	WAR
WAR	0.595	1.000	WAR7	JAWS
WAR7	0.504	0.954	1.000	ratio
JAWSratio	0.580	0.984	0.968	1.000	G
G	0.847	0.733	0.679	0.712	1.000	AB
AB	0.779	0.734	0.691	0.710	0.973	1.000	R
R	0.675	0.849	0.804	0.814	0.849	0.896	1.000	H
H	0.743	0.786	0.742	0.759	0.927	0.972	0.927	1.000	HR
HR	0.409	0.567	0.579	0.574	0.558	0.512	0.541	0.478	1.000	RBI
RBI	0.651	0.773	0.750	0.764	0.792	0.796	0.811	0.818	0.807	1.000
SB	0.303	0.368	0.320	0.328	0.346	0.409	0.512	0.423	–0.126	0.117
BB	0.589	0.794	0.751	0.773	0.738	0.688	0.793	0.672	0.635	0.699
BA	0.143	0.487	0.508	0.482	0.216	0.307	0.496	0.507	0.106	0.428
OBP	0.204	0.637	0.663	0.640	0.282	0.288	0.568	0.425	0.328	0.482
SLG	0.224	0.576	0.633	0.593	0.345	0.351	0.520	0.439	0.792	0.755
OPS	0.237	0.647	0.698	0.660	0.352	0.359	0.582	0.472	0.694	0.722
OPSadj	0.273	0.704	0.744	0.713	0.367	0.371	0.588	0.480	0.624	0.692
	SB
SB	1.000	BB
BB	0.262	1.000	BA
BA	0.211	0.226	1.000	OBP
OBP	0.175	0.665	0.729	1.000	SLG
SLG	–0.095	0.499	0.579	0.655	1.000	OPS
OPS	–0.006	0.601	0.683	0.835	0.963	1.000	OPSadj
OPSadj	0.096	0.601	0.645	0.812	0.873	0.926	1.000

Table 4 Estimated coefficients for the logistic regression model: all predictors.

	Estimate	SE	z-value	p-value	VIF
Intercept	–29.521	10.324	2.859	0.004
Yrs	0.196	0.107	1.827	0.068	5.265
WAR	–0.045	0.044	–1.021	0.307	24.771
WAR7	0.092	0.053	1.732	0.083	8.949
JAWSratio	0.075	0.029	2.628	0.009	18.262
G	–0.004	0.003	–1.294	0.196	70.577
AB	0.002	0.002	1.378	0.168	305.547
R	0.002	0.002	1.157	0.247	16.338
H	–0.005	0.004	–1.148	0.251	217.261
HR	–0.003	0.004	–0.818	0.413	17.582
RBI	0.004	0.001	3.022	0.003	9.339
SB	–0.001	0.001	–0.537	0.591	2.786
BB	–0.005	0.002	–2.229	0.026	23.187
BA	30.070	37.774	0.796	0.426	24.439
OBP	124.293	115.247	1.078	0.281	391.423
SLG	60.916	112.795	0.540	0.589	2083.015
OPS	–71.714	112.334	–0.638	0.523	3217.564
OPSadj	–0.031	0.022	–1.385	0.166	6.715

Table 5 Eigenvalue for the correlation matrix of the quantitative variables of interest.

Component	Eigenvalue	Percent of variance	Cumulative percent
1	10.6494	62.64	62.64
2	2.6160	15.39	78.03
3	1.4537	8.55	86.58
4	0.7307	4.30	90.88
5	0.4824	2.84	93.72
6	0.4314	2.54	96.26
7	0.2936	1.73	97.98
8	0.0988	0.58	98.56
9	0.0770	0.45	99.02
10	0.0520	0.31	99.32
11	0.0473	0.28	99.60
12	0.0278	0.16	99.77
13	0.0185	0.11	99.87
14	0.0109	0.06	99.94
15	0.0079	0.05	99.99
16	0.0024	0.01	100.00
17	0.0001	0.00	100.00
	17.0000

Table 6 Results of backward selection procedure: z-statistic p-values with $\alpha =0.05$.

Principal	Iterations
component	#1	#2	#3	#4	#5	#6	#7	#8	#9	#10
z1	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
z2	0.624	0.635
z3	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
z4	0.082	0.084	0.083	0.084	0.057	0.041	0.016	0.012	0.017	0.019
z5	0.000	0.000	0.000	0.000	0.001	0.001	0.001	0.001	0.002	0.003
z6	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
z7	0.214	0.206	0.218	0.231	0.295
z8	0.231	0.221	0.239	0.239
z9	0.177	0.143	0.154	0.147	0.231	0.259
z10	0.140	0.139	0.144	0.158	0.113	0.097	0.062	0.094
z11	0.003	0.003	0.003	0.004	0.001	0.001	0.000	0.001	0.001	0.002
z12	0.041	0.042	0.044	0.047	0.044	0.035	0.025	0.036	0.052
z13	0.161	0.158	0.152	0.150	0.097	0.110	0.108
z14	0.042	0.042	0.040	0.045	0.031	0.018	0.009	0.005	0.007	0.012
z15	0.837
z16	0.190	0.197	0.155	0.151	0.085	0.046	0.010	0.011	0.021	0.046
z17	0.525	0.517	0.526

NOTE: A bold value represents the p-value from the z-test for the estimated logistic regression coefficient of the variable eliminated at that specific iteration of the backward selection procedure using a significance level of 0.05.

Table 7 Eigenvectors for the correlation matrix for the retained components.

		Eigenvectors from R
	Variable	${\mathbf{a}}_1$	${\mathbf{a}}_3$	${\mathbf{a}}_4$	${\mathbf{a}}_5$	${\mathbf{a}}_6$	${\mathbf{a}}_{11}$	${\mathbf{a}}_{14}$	${\mathbf{a}}_{16}$
y1	Yrs	0.203	–0.128	0.141	0.254	–0.268	–0.101	–0.202	–0.024
y2	WAR	0.284	0.094	–0.258	0.131	0.339	0.281	0.595	–0.155
y3	WAR7	0.279	0.091	–0.259	0.096	0.442	–0.419	0.165	0.056
y4	JAWSratio	0.281	0.078	–0.272	0.164	0.397	0.099	–0.685	0.061
y5	G	0.251	–0.135	0.114	0.089	–0.084	0.149	0.274	0.141
y6	AB	0.252	–0.053	0.212	–0.005	0.013	–0.061	–0.174	–0.711
y7	R	0.282	0.109	0.053	–0.129	–0.109	–0.424	0.008	0.030
y8	H	0.268	0.059	0.308	0.046	0.047	0.072	–0.060	0.652
y9	HR	0.215	–0.512	–0.090	–0.355	–0.002	0.391	0.006	0.006
y10	RBI	0.278	–0.243	0.212	–0.112	0.059	–0.089	0.014	–0.017
y11	SB	0.098	0.536	–0.166	–0.703	–0.121	0.091	–0.006	0.006
y12	BB	0.257	–0.075	–0.443	0.157	–0.472	0.221	–0.155	0.015
y13	BA	0.174	0.432	0.531	0.160	0.075	0.401	–0.046	–0.124
y14	OBP	0.215	0.293	–0.148	0.279	–0.433	–0.112	0.098	–0.027
y15	SLG	0.226	–0.188	–0.168	–0.273	0.016	–0.228	–0.014	0.001
y16	OPS	0.241	–0.032	–0.071	–0.100	–0.144	–0.210	0.037	0.007
y17	OPSadj	0.242	0.040	–0.049	–0.104	–0.030	0.163	–0.051	0.004

Table 8 Correlation matrix for the 17 quantitative variables of interest and retained principal components.

	z1	z3	z4	z5	z6	z11	z14	z16
Yrs	0.664	–0.155	0.121	0.177	–0.176	–0.022	–0.002	–0.001
WAR	0.926	0.113	–0.220	0.091	0.222	0.061	0.062	–0.008
WAR7	0.912	0.109	–0.221	0.067	0.277	–0.091	0.017	0.003
JAWSratio	0.917	0.094	–0.233	0.114	0.261	0.022	–0.071	0.003
G	0.817	–0.163	0.097	0.062	–0.055	0.032	0.029	0.007
AB	0.824	–0.064	0.181	–0.003	0.009	–0.013	–0.018	–0.035
R	0.921	0.132	0.045	–0.090	–0.071	–0.092	0.001	0.002
H	0.875	0.071	0.264	0.032	0.031	0.016	–0.006	0.032
HR	0.703	–0.618	–0.077	–0.247	–0.001	0.085	0.001	0.000
RBI	0.906	–0.293	0.181	–0.077	0.039	–0.019	0.001	–0.001
SB	0.319	0.646	–0.142	–0.488	–0.080	0.020	–0.001	0.000
BB	0.837	–0.091	–0.379	0.109	–0.310	0.048	–0.016	0.001
BA	0.568	0.521	0.454	0.111	0.050	0.087	–0.005	–0.006
OBP	0.700	0.353	–0.126	0.194	–0.285	–0.024	0.010	–0.001
SLG	0.736	–0.226	0.144	–0.189	0.011	–0.050	–0.001	0.000
OPS	0.787	–0.038	0.061	–0.069	–0.095	–0.046	0.004	0.000
OPSadj	0.792	0.048	–0.042	–0.072	–0.020	0.035	–0.005	0.000

Fig. 1 Scatterplots of the principal components scores versus their “interpretation”.

Table 9 Estimated coefficients for the logistic regression model.

		Estimate	Std. Error	z-value	p-value	VIF
	Intercept	–2.382	0.225	–10.600	$<2\times {10}^{-16}$
z1	Component #1	0.939	0.090	10.483	$<2\times {10}^{-16}$	1.596
z3	Component #3	0.796	0.122	6.529	$6.64\times {10}^{-11}$	1.252
z4	Component #4	0.399	0.170	2.344	0.019	1.131
z5	Component #5	0.588	0.200	2.937	0.003	1.070
z6	Component #6	1.200	0.226	5.314	$1.08\times {10}^{-7}$	1.120
z11	Component #11	–2.274	0.727	–3.129	0.002	1.164
z14	Component #14	–3.317	1.320	–2.513	0.012	1.092
z16	Component #16	–7.000	3.515	–1.992	0.046	1.194

Fig. 2 Deviance residual plots versus fitted values and retained principal components.

Table 10 Player classification: logistic regression model results.

	Model prediction
Actual	No HoF	HoF
No HoF	425	22
HoF	40	115

Table 11 Player classification: predicted Hall of Famers not in the Hall of Fame.

Name	$\widehat{P}\left(\text{HoF}\right)$	Name	$\widehat{P}\left(\text{HoF}\right)$
Pete Rose	0.990	Edgar Martinez	0.671
Barry Bonds	0.986	Vada Pinson	0.660
Shoeless Joe Jackson	0.982	Buddy Bell	0.660
Bill Dahlen	0.888	Ken Boyer	0.624
Lave Cross	0.800	Sherry Magee	0.611
Nomar Garciaparra	0.765	Minnie Minoso	0.590
Kenny Lofton	0.740	Keith Hernandez	0.582
Larry Walker	0.709	Manny Ramirez	0.571
Bobby Veach	0.688	Dick Allen	0.531
Scott Rolen	0.688	Thurman Munson	0.515
Ted Simmons	0.678	Ken Williams	0.508

Table 12 Player classification: Hall of Famers predicted not to be in the Hall of Fame.

Name	Years	$\widehat{P}\left(\text{HoF}\right)$	Name	Years	$\widehat{P}\left(\text{HoF}\right)$
Red Schoendienst^†	1945–1963	0.490	Jim Thome*	1991–2012	0.226
Gabby Hartnett*	1922–1941	0.467	Ross Youngs^†	1917–1926	0.225
Dave Winfield*	1973–1988	0.463	Ralph Kiner*	1946–1955	0.225
	1990–1995
Bobby Doerr ^†	1937–1944,	0.419	Lloyd Waner^†	1927–1942,	0.203
	1946–1951			1944–1945
Dave Bancroft ^†	1915–1930	0.417	Freddie Lindstrom^†	1924–1936	0.202
Jim Bottomley^†	1922–1937	0.410	Larry Doby^†	1947–1959	0.200
Tony Perez*	1964–1986	0.395	George Kell^†	1943–1957	0.194
Enos Slaughter^†	1938–1942,	0.395	Ernie Lombardi^†	1931–1947	0.182
	1946–1959
Max Carey^†	1910–1929	0.381	Willie McCovey*	1959–1980	0.174
Lou Brock*	1961–1979	0.368	Joe Tinker^†	1902–1916	0.132
Travis Jackson^†	1922–1936	0.349	Roy Campanella*	1948–1957	0.109
Reggie Jackson*	1967–1987	0.335	Roger Bresnahan^†	1897, 1900–1915	0.107
Harry Hooper^†	1909–1925	0.305	High Pockets Kelly^†	1915–1917,	0.103
				1919–1930, 1932
Joe Gordon^†	1938–1943,	0.302	Phil Rizzuto^†	1941–1942,	0.096
	1946–1950			1946–1956
Tony Lazzeri^†	1926–1939	0.295	Johnny Evers^†	1902–1917,	0.092
				1922, 1929
Hack Wilson^†	1923–1934	0.290	Harmon Killebrew*	1954–1975	0.069
Orlando Cepeda^†	1958–1974	0.275	Bill Mazeroski^†	1956–1972	0.042
Frank Chance^†	1898–1914	0.259	Rick Ferrell^†	1929–1945, 1947	0.028
Willie Stargell*	1962–1982	0.257	Tommy McCarthy^†	1884–1896	0.025
Chick Hafey^†	1924–1935, 1937	0.239	Ray Schalk^† 1912–1929	0.008

† Elected by one of the veterans or eras committees.

* Elected by the BBWAA.