1946 St. Louis Cardinals
Baseball Player Won-Loss Records
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1946 St. Louis Cardinals
*
Traditional Statistics and Splits (Retrosheet)
St. Louis Cardinals -
Franchise Page
(Regular Season)
(
1946 National League
)
Postseason
Positional Average
(Weighted Avg of Options): 0.500
(1-Year)
(9-Year)
(Long-Run)
Positional Averages for Pitchers
(Wgted Avg of Options): "0.500
"vs. Different Values for Starting vs. Relief Pitchers: (Empirical)
(Based on Pitchers who Do Both)
Basic Player Won-Lost Records
Position Players
(Sorted by pWORL)
Player
pWins
pLosses
pWOPA
pWORL
eWins
eLosses
eWOPA
eWORL
Enos Slaughter
25.9
18.4
6.0
8.3
24.9
19.4
4.0
6.3
Stan Musial
22.9
16.1
5.1
7.2
22.6
16.4
4.5
6.5
Whitey Kurowski
19.2
15.0
3.9
5.6
18.8
15.4
3.1
4.9
Erv Dusak
12.3
7.8
4.0
5.0
11.0
9.1
1.2
2.3
Marty Marion
18.1
16.5
2.0
3.8
17.1
17.4
0.3
2.1
Red Schoendienst
17.9
16.5
1.6
3.4
16.8
17.5
-0.3
1.4
Harry Walker
11.4
10.3
0.7
1.8
10.9
10.8
-0.3
0.8
Dick Sisler
7.9
6.4
1.0
1.8
7.1
7.2
-0.7
0.0
Joe Garagiola
4.8
4.7
0.2
0.7
4.5
5.0
-0.3
0.2
Terry Moore
9.3
9.3
-0.3
0.7
9.2
9.5
-0.5
0.5
Walter Sessi
0.9
0.3
0.6
0.6
0.6
0.6
0.0
0.1
Lou Klein
2.8
2.5
0.3
0.6
2.6
2.7
0.0
0.3
Nippy Jones
0.5
0.2
0.3
0.3
0.3
0.4
0.0
0.1
Jeff Cross
2.1
2.1
0.0
0.3
2.0
2.3
-0.3
-0.0
Clyde Kluttz
2.6
2.8
-0.1
0.2
2.5
2.9
-0.3
-0.0
Bill Endicott
0.7
0.7
-0.0
0.1
0.6
0.8
-0.2
-0.1
Del Rice
2.5
2.8
-0.2
0.0
2.6
2.7
-0.1
0.2
Danny Litwhiler
0.0
0.1
-0.0
-0.0
0.0
0.1
-0.0
-0.0
Emil Verban
0.0
0.1
-0.1
-0.0
0.0
0.1
-0.1
-0.0
Del Wilber
0.0
0.2
-0.2
-0.2
0.1
0.2
-0.1
-0.1
Ken O'Dea
0.8
1.4
-0.5
-0.4
0.9
1.3
-0.4
-0.3
Buster Adams
4.7
6.3
-1.8
-1.2
5.3
5.7
-0.6
-0.0
------
------
------
------
------
------
------
------
SUB-TOTAL
167.4
140.6
22.7
38.7
160.3
147.6
9.0
25.0
Basic Player Won-Lost Records
Pitchers
(Sorted by pWORL)
Player
pWins
pLosses
pWOPA
pWORL
eWins
eLosses
eWOPA
eWORL
Howie Pollet
18.6
14.5
4.9
7.1
17.3
15.9
2.4
4.6
Harry Brecheen
17.1
14.0
3.8
5.9
16.3
14.8
2.8
4.8
Murry Dickson
12.3
8.3
4.4
5.9
11.2
9.4
2.4
3.8
Max Lanier
4.1
2.0
2.3
2.7
3.6
2.5
1.5
1.9
Ken Burkhart
6.3
4.8
1.7
2.4
5.4
5.7
-0.1
0.7
Red Munger
2.7
1.6
1.2
1.5
2.5
1.8
0.9
1.2
Al Brazle
8.4
8.6
0.2
1.4
8.7
8.3
0.9
2.1
Ted Wilks
4.1
3.9
0.3
1.0
3.6
4.4
-0.6
0.1
Fred Martin
1.9
1.1
0.8
1.0
1.6
1.3
0.4
0.6
Red Barrett
3.5
3.7
-0.1
0.4
3.2
4.0
-0.5
-0.0
Johnny Beazley
6.7
7.7
-0.7
0.2
6.4
7.9
-1.2
-0.2
Freddy Schmidt
0.3
0.4
-0.1
-0.0
0.3
0.4
-0.0
0.0
Johnny Grodzicki
0.1
0.4
-0.3
-0.3
0.1
0.3
-0.2
-0.1
Blix Donnelly
0.4
1.0
-0.6
-0.5
0.5
0.8
-0.3
-0.1
Howie Krist
0.2
1.4
-1.2
-1.0
0.6
1.0
-0.4
-0.2
------
------
------
------
------
------
------
------
SUB-TOTAL
86.6
73.4
16.6
27.7
81.6
78.5
7.9
19.0
pWins
pLosses
pWOPA
pWORL
eWins
eLosses
eWOPA
eWORL
TEAM TOTALS
254.0
214.0
39.2
66.4
241.9
226.1
16.8
44.0
Basic Player Won-Lost Records
Position Players
(Sorted by pWORL)
Batting
Baserunning
Pitching
Fielding
Player
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
Enos Slaughter
15.7
12.0
0.568
1.6
1.1
0.579
0.0
0.0
0.000
7.5
6.5
0.536
Stan Musial
17.0
11.1
0.605
1.5
1.3
0.551
0.0
0.0
0.000
3.8
4.3
0.470
Whitey Kurowski
12.9
10.1
0.562
1.1
0.9
0.558
0.0
0.0
0.000
4.6
4.6
0.497
Erv Dusak
6.5
6.1
0.518
0.6
0.4
0.613
0.0
0.0
0.000
3.8
2.7
0.584
Marty Marion
8.4
9.8
0.462
0.6
0.5
0.538
0.0
0.0
0.000
8.2
7.0
0.538
Red Schoendienst
9.6
10.9
0.468
1.7
1.2
0.584
0.0
0.0
0.000
5.7
5.3
0.515
Harry Walker
5.8
6.5
0.472
1.0
0.8
0.562
0.0
0.0
0.000
4.1
3.5
0.542
Dick Sisler
5.1
4.9
0.508
0.3
0.4
0.385
0.0
0.0
0.000
1.7
1.8
0.491
Joe Garagiola
3.5
4.2
0.459
0.2
0.2
0.552
0.0
0.0
0.000
0.8
0.7
0.529
Terry Moore
6.0
6.3
0.488
0.9
0.4
0.665
0.0
0.0
0.000
2.4
2.6
0.473
Walter Sessi
0.6
0.6
0.476
0.0
0.0
0.657
0.0
0.0
0.000
0.0
0.0
0.000
Lou Klein
1.4
1.8
0.441
0.2
0.1
0.557
0.0
0.0
0.000
1.0
0.7
0.589
Nippy Jones
0.3
0.3
0.477
0.0
0.0
0.481
0.0
0.0
0.000
0.0
0.0
0.655
Jeff Cross
0.8
0.9
0.464
0.4
0.4
0.518
0.0
0.0
0.000
0.8
1.0
0.448
Clyde Kluttz
1.9
2.2
0.465
0.2
0.2
0.471
0.0
0.0
0.000
0.4
0.5
0.469
Bill Endicott
0.5
0.6
0.456
0.0
0.0
0.074
0.0
0.0
0.000
0.1
0.2
0.265
Del Rice
2.0
2.2
0.474
0.1
0.0
0.683
0.0
0.0
0.000
0.5
0.5
0.509
Danny Litwhiler
0.0
0.1
0.264
0.0
0.0
0.569
0.0
0.0
0.000
0.0
0.0
0.000
Emil Verban
0.0
0.1
0.000
0.0
0.0
0.000
0.0
0.0
0.000
0.0
0.0
0.000
Del Wilber
0.1
0.2
0.277
0.0
0.0
0.843
0.0
0.0
0.000
0.0
0.0
0.226
Ken O'Dea
0.7
1.1
0.393
0.0
0.0
0.839
0.0
0.0
0.000
0.2
0.2
0.450
Buster Adams
3.5
3.6
0.495
0.3
0.2
0.633
0.0
0.0
0.000
1.5
1.9
0.435
------
------
------
------
------
------
------
------
------
------
------
------
SUB-TOTAL
102.3
95.4
0.518
10.8
8.3
0.566
0.0
0.0
0.000
47.0
44.1
0.516
Basic Player Won-Lost Records
Pitchers
(Sorted by pWORL)
Batting
Baserunning
Pitching
Fielding
Player
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
Howie Pollet
1.0
1.8
0.360
0.0
0.1
0.325
15.5
13.6
0.533
0.6
0.6
0.496
Harry Brecheen
0.8
1.7
0.304
0.0
0.0
0.460
14.8
12.4
0.545
0.7
0.7
0.513
Murry Dickson
0.9
1.0
0.488
0.2
0.1
0.683
9.3
8.1
0.534
0.7
0.4
0.653
Max Lanier
0.2
0.4
0.366
0.0
0.0
0.473
3.1
2.2
0.592
0.2
0.1
0.700
Ken Burkhart
0.4
0.5
0.423
0.0
0.1
0.190
4.9
5.0
0.492
0.1
0.1
0.631
Red Munger
0.2
0.3
0.496
0.0
0.0
0.349
2.1
1.5
0.575
0.1
0.0
0.740
Al Brazle
0.5
1.0
0.359
0.1
0.1
0.528
7.6
6.6
0.532
0.5
0.7
0.421
Ted Wilks
0.2
0.3
0.412
0.0
0.0
0.254
3.2
3.9
0.451
0.3
0.2
0.656
Fred Martin
0.0
0.1
0.329
0.0
0.0
0.301
1.5
1.1
0.584
0.1
0.2
0.345
Red Barrett
0.1
0.4
0.229
0.0
0.0
0.611
3.0
3.4
0.471
0.1
0.1
0.516
Johnny Beazley
0.6
0.6
0.474
0.0
0.0
0.421
5.8
6.9
0.459
0.1
0.3
0.332
Freddy Schmidt
0.0
0.0
0.000
0.0
0.0
0.000
0.3
0.3
0.482
0.0
0.0
0.395
Johnny Grodzicki
0.0
0.0
0.000
0.0
0.0
0.000
0.2
0.3
0.334
0.0
0.0
0.222
Blix Donnelly
0.0
0.0
1.000
0.0
0.0
0.352
0.5
0.8
0.390
0.0
0.0
0.667
Howie Krist
0.0
0.0
0.000
0.0
0.0
0.000
0.6
1.0
0.374
0.0
0.0
0.826
------
------
------
------
------
------
------
------
------
------
------
------
SUB-TOTAL
4.9
7.9
0.386
0.4
0.5
0.451
72.3
67.1
0.519
3.6
3.3
0.523
Batting
Baserunning
Pitching
Fielding
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
TEAM TOTALS
107.3
103.3
0.510
11.2
8.8
0.560
72.3
67.1
0.519
50.6
47.4
0.516
eWin, eLoss, eWOPA by Position
Catcher
Player
eWins
eLosses
eWOPA
Joe Garagiola
4.4
4.9
-0.3
Clyde Kluttz
2.4
2.9
-0.4
Del Rice
2.6
2.7
-0.1
Ken O'Dea
0.9
1.3
-0.3
Del Wilber
0.1
0.2
-0.1
------
------
------
TOTAL
10.3
12.0
-1.2
First Base
Player
eWins
eLosses
eWOPA
Stan Musial
15.9
11.1
3.7
Dick Sisler
3.2
3.2
-0.3
Harry Walker
0.7
0.6
0.0
------
------
------
TOTAL
19.8
14.8
3.4
Second Base
Player
eWins
eLosses
eWOPA
Red Schoendienst
15.1
15.8
-0.5
Lou Klein
2.7
2.7
0.0
Jeff Cross
0.5
0.8
-0.3
Erv Dusak
0.1
0.0
0.0
Nippy Jones
0.0
0.0
-0.0
------
------
------
TOTAL
18.3
19.3
-0.7
Third Base
Player
eWins
eLosses
eWOPA
Whitey Kurowski
18.5
15.5
2.7
Red Schoendienst
1.6
1.4
0.2
Erv Dusak
0.7
0.7
0.0
Jeff Cross
0.0
0.0
-0.0
------
------
------
TOTAL
20.9
17.7
2.9
Shortstop
Player
eWins
eLosses
eWOPA
Marty Marion
17.3
17.3
0.4
Jeff Cross
1.1
1.1
-0.0
Red Schoendienst
0.2
0.2
0.1
------
------
------
TOTAL
18.6
18.6
0.5
Left Field
Player
eWins
eLosses
eWOPA
Erv Dusak
9.3
7.8
0.7
Stan Musial
6.7
5.4
0.8
Dick Sisler
3.6
3.6
-0.3
Buster Adams
1.9
2.2
-0.4
Harry Walker
1.1
1.1
-0.1
Bill Endicott
0.2
0.4
-0.2
------
------
------
TOTAL
22.7
20.5
0.5
Center Field
Player
eWins
eLosses
eWOPA
Harry Walker
8.7
8.5
-0.2
Terry Moore
8.4
8.5
-0.5
Buster Adams
2.6
3.0
-0.5
Erv Dusak
0.0
0.1
-0.1
------
------
------
TOTAL
19.8
20.2
-1.3
Right Field
Player
eWins
eLosses
eWOPA
Enos Slaughter
24.9
19.4
3.9
------
------
------
TOTAL
24.9
19.4
3.9
Designated Hitter
Player
eWins
eLosses
eWOPA
------
------
------
TOTAL
0.0
0.0
0.0
Pinch Hitter
Player
eWins
eLosses
eWOPA
Terry Moore
0.8
0.9
-0.0
Buster Adams
0.8
0.5
0.3
Erv Dusak
1.0
0.2
0.8
Walter Sessi
0.6
0.6
0.0
Harry Walker
0.4
0.6
-0.1
Bill Endicott
0.4
0.4
-0.0
Nippy Jones
0.4
0.3
0.2
Dick Sisler
0.3
0.3
0.0
Joe Garagiola
0.1
0.2
-0.0
Whitey Kurowski
0.1
0.0
0.1
Danny Litwhiler
0.0
0.1
-0.0
Del Rice
0.0
0.0
-0.0
Emil Verban
0.0
0.1
-0.1
Jeff Cross
0.0
0.0
-0.0
Clyde Kluttz
0.0
0.0
0.0
Red Schoendienst
0.0
0.0
-0.0
Marty Marion
0.0
0.0
-0.0
------
------
------
TOTAL
5.1
4.3
1.2
Pinch Runner
Player
eWins
eLosses
eWOPA
Jeff Cross
0.3
0.3
0.0
Harry Walker
0.0
0.0
0.0
Erv Dusak
0.0
0.0
-0.0
Dick Sisler
0.0
0.0
-0.0
Nippy Jones
0.0
0.0
-0.0
Harry Brecheen
0.0
0.0
-0.0
Bill Endicott
0.0
0.0
0.0
------
------
------
TOTAL
0.4
0.4
0.0
Pitcher Offense
Player
eWins
eLosses
eWOPA
Howie Pollet
1.0
1.8
-0.0
Harry Brecheen
0.8
1.8
-0.2
Murry Dickson
1.0
1.1
0.4
Al Brazle
0.6
1.0
0.0
Johnny Beazley
0.6
0.7
0.2
Ken Burkhart
0.4
0.6
0.1
Max Lanier
0.2
0.4
0.0
Red Munger
0.3
0.3
0.1
Ted Wilks
0.2
0.3
0.0
Red Barrett
0.1
0.4
-0.1
Fred Martin
0.1
0.1
-0.0
Blix Donnelly
0.0
0.0
0.0
Freddy Schmidt
0.0
0.0
-0.0
------
------
------
TOTAL
5.4
8.4
0.5
Starting Pitching
Player
eWins
eLosses
eWOPA
Howie Pollet
14.7
13.1
1.6
Harry Brecheen
15.1
12.4
2.7
Murry Dickson
8.0
6.1
2.0
Johnny Beazley
5.9
7.1
-1.2
Al Brazle
5.7
5.3
0.4
Ken Burkhart
4.4
4.6
-0.2
Max Lanier
3.3
2.2
1.1
Red Barrett
2.4
3.0
-0.6
Red Munger
2.2
1.4
0.7
Fred Martin
1.3
0.9
0.4
Ted Wilks
0.6
1.1
-0.5
------
------
------
TOTAL
63.6
57.3
6.3
Relief Pitching
Player
eWins
eLosses
eWOPA
Ted Wilks
2.9
2.9
-0.0
Murry Dickson
2.1
2.4
-0.3
Al Brazle
2.3
2.0
0.4
Howie Pollet
1.4
1.1
0.4
Howie Krist
0.6
1.0
-0.4
Red Barrett
0.7
0.6
0.1
Blix Donnelly
0.5
0.8
-0.3
Harry Brecheen
0.4
0.7
-0.3
Ken Burkhart
0.6
0.5
0.1
Freddy Schmidt
0.3
0.4
-0.0
Fred Martin
0.3
0.3
0.0
Johnny Grodzicki
0.2
0.3
-0.2
Red Munger
0.1
0.1
-0.1
Johnny Beazley
0.1
0.1
0.0
------
------
------
TOTAL
12.4
13.1
-0.7
Team eWins over Positional Average by Position
P
C
1B
2B
3B
SS
LF
CF
RF
Oth
1946 St. Louis Cardinals
6.1
-1.2
3.4
-0.7
2.9
0.5
0.5
-1.3
3.9
1.2
pWin, pLoss, pWOPA by Position
Catcher
Player
pWins
pLosses
pWOPA
Joe Garagiola
4.7
4.6
0.3
Clyde Kluttz
2.6
2.8
-0.1
Del Rice
2.4
2.8
-0.3
Ken O'Dea
0.8
1.4
-0.5
Del Wilber
0.0
0.2
-0.2
------
------
------
TOTAL
10.6
11.7
-0.7
First Base
Player
pWins
pLosses
pWOPA
Stan Musial
15.9
11.0
3.7
Dick Sisler
3.4
3.1
-0.0
Harry Walker
0.7
0.6
0.1
------
------
------
TOTAL
20.0
14.7
3.7
Second Base
Player
pWins
pLosses
pWOPA
Red Schoendienst
15.8
15.1
0.9
Lou Klein
2.8
2.5
0.3
Jeff Cross
0.6
0.7
-0.1
Erv Dusak
0.1
0.0
0.1
Nippy Jones
0.0
0.0
-0.0
------
------
------
TOTAL
19.2
18.3
1.2
Third Base
Player
pWins
pLosses
pWOPA
Whitey Kurowski
19.0
15.0
3.8
Red Schoendienst
1.9
1.2
0.8
Erv Dusak
0.7
0.8
-0.1
Jeff Cross
0.0
0.0
-0.0
------
------
------
TOTAL
21.6
17.0
4.4
Shortstop
Player
pWins
pLosses
pWOPA
Marty Marion
18.1
16.5
2.0
Jeff Cross
1.2
1.1
0.1
Red Schoendienst
0.2
0.2
-0.0
------
------
------
TOTAL
19.4
17.8
2.1
Left Field
Player
pWins
pLosses
pWOPA
Erv Dusak
10.5
6.6
3.4
Stan Musial
7.0
5.1
1.5
Dick Sisler
4.3
3.0
1.1
Buster Adams
1.8
2.4
-0.8
Harry Walker
1.0
1.1
-0.2
Bill Endicott
0.2
0.4
-0.2
------
------
------
TOTAL
24.8
18.5
4.8
Center Field
Player
pWins
pLosses
pWOPA
Harry Walker
9.3
7.9
1.1
Terry Moore
8.5
8.5
-0.4
Buster Adams
2.4
3.2
-0.9
Erv Dusak
0.0
0.2
-0.2
------
------
------
TOTAL
20.2
19.7
-0.3
Right Field
Player
pWins
pLosses
pWOPA
Enos Slaughter
25.9
18.4
6.0
------
------
------
TOTAL
25.9
18.4
6.0
Designated Hitter
Player
pWins
pLosses
pWOPA
------
------
------
TOTAL
0.0
0.0
0.0
Pinch Hitter
Player
pWins
pLosses
pWOPA
Terry Moore
0.9
0.9
0.1
Buster Adams
0.5
0.8
-0.1
Erv Dusak
1.0
0.2
0.8
Walter Sessi
0.9
0.3
0.6
Harry Walker
0.3
0.7
-0.3
Bill Endicott
0.5
0.3
0.2
Nippy Jones
0.5
0.2
0.3
Dick Sisler
0.3
0.3
-0.0
Joe Garagiola
0.1
0.2
-0.0
Whitey Kurowski
0.1
0.0
0.1
Danny Litwhiler
0.0
0.1
-0.0
Del Rice
0.0
0.0
0.0
Emil Verban
0.0
0.1
-0.1
Jeff Cross
0.0
0.0
0.0
Clyde Kluttz
0.0
0.0
0.0
Red Schoendienst
0.0
0.0
-0.0
Marty Marion
0.0
0.0
-0.0
------
------
------
TOTAL
5.2
4.2
1.4
Pinch Runner
Player
pWins
pLosses
pWOPA
Jeff Cross
0.3
0.3
-0.0
Harry Walker
0.0
0.0
0.0
Erv Dusak
0.0
0.0
-0.0
Dick Sisler
0.0
0.0
-0.0
Nippy Jones
0.0
0.0
0.0
Harry Brecheen
0.0
0.0
-0.0
Bill Endicott
0.0
0.0
-0.0
------
------
------
TOTAL
0.4
0.4
-0.0
Pitcher Offense
Player
pWins
pLosses
pWOPA
Howie Pollet
1.2
1.7
0.2
Harry Brecheen
0.9
1.6
0.0
Murry Dickson
1.1
1.0
0.5
Al Brazle
0.6
1.0
-0.0
Johnny Beazley
0.7
0.6
0.3
Ken Burkhart
0.4
0.5
0.1
Max Lanier
0.3
0.4
0.1
Red Munger
0.3
0.3
0.1
Ted Wilks
0.3
0.3
0.1
Red Barrett
0.2
0.3
-0.0
Fred Martin
0.1
0.1
0.0
Blix Donnelly
0.0
0.0
0.0
Freddy Schmidt
0.0
0.0
-0.0
------
------
------
TOTAL
5.9
7.8
1.4
Starting Pitching
Player
pWins
pLosses
pWOPA
Howie Pollet
15.6
12.3
3.3
Harry Brecheen
15.7
11.7
4.1
Murry Dickson
9.0
5.1
3.9
Johnny Beazley
6.0
7.0
-1.0
Al Brazle
5.4
5.6
-0.2
Ken Burkhart
5.3
3.8
1.5
Max Lanier
3.9
1.7
2.2
Red Barrett
2.5
2.8
-0.3
Red Munger
2.4
1.2
1.2
Fred Martin
1.6
0.6
1.0
Ted Wilks
0.5
1.2
-0.7
------
------
------
TOTAL
67.9
53.0
15.0
Relief Pitching
Player
pWins
pLosses
pWOPA
Ted Wilks
3.3
2.4
0.9
Murry Dickson
2.2
2.2
0.0
Al Brazle
2.4
1.9
0.4
Howie Pollet
1.9
0.6
1.4
Howie Krist
0.2
1.4
-1.2
Red Barrett
0.8
0.6
0.2
Blix Donnelly
0.3
1.0
-0.6
Harry Brecheen
0.5
0.7
-0.2
Ken Burkhart
0.5
0.5
0.0
Freddy Schmidt
0.3
0.4
-0.1
Fred Martin
0.2
0.4
-0.2
Johnny Grodzicki
0.1
0.4
-0.3
Red Munger
0.1
0.2
-0.1
Johnny Beazley
0.1
0.1
-0.0
------
------
------
TOTAL
12.8
12.7
0.1
Team pWins over Positional Average by Position
P
C
1B
2B
3B
SS
LF
CF
RF
Oth
1946 St. Louis Cardinals
16.6
-0.7
3.7
1.2
4.4
2.1
4.8
-0.3
6.0
1.4
*
Player won-loss records are calculated using Retrosheet play-by-play data. For some seasons, Retrosheet does not have full play-by-play data for all games. In these cases, some games may be missing.
The number of Games shown here are the number of games for which Retrosheet play-by-play data exist and were used in these calculations.
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