1978 Milwaukee Brewers
Baseball Player Won-Loss Records
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1978 Milwaukee Brewers
*
Traditional Statistics and Splits (Retrosheet)
Milwaukee Brewers -
Franchise Page
(Regular Season)
(
1978 American League
)
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
Larry Hisle
20.0
15.2
4.3
6.2
19.8
15.4
3.9
5.7
Sal Bando
19.9
16.0
3.7
5.5
19.0
16.9
1.9
3.6
Robin Yount
18.3
16.4
3.0
4.7
17.6
17.0
1.7
3.4
Sixto Lezcano
17.6
14.7
2.1
3.7
18.1
14.2
3.2
4.7
Gorman Thomas
16.3
13.8
2.2
3.7
16.7
13.4
3.0
4.4
Don Money
15.1
12.7
2.2
3.6
14.8
12.9
1.8
3.1
Paul Molitor
16.0
15.1
1.7
3.2
15.4
15.6
0.7
2.2
Ben Oglivie
16.1
14.1
1.3
2.8
16.5
13.7
2.1
3.6
Jim Wohlford
3.7
2.8
0.7
1.0
3.2
3.2
-0.1
0.2
Charlie Moore
6.0
5.9
0.4
1.0
5.9
6.0
0.2
0.8
Dick Davis
5.5
5.6
-0.3
0.3
5.2
5.9
-0.9
-0.3
Cecil Cooper
10.7
10.9
-0.8
0.3
11.3
10.2
0.4
1.5
Andy Etchebarren
0.4
0.2
0.2
0.3
0.4
0.3
0.1
0.1
Larry Haney
0.3
0.1
0.2
0.2
0.2
0.2
-0.0
-0.0
Tim Johnson
0.1
0.0
0.1
0.1
0.1
0.1
0.1
0.1
Jim Gantner
2.4
2.8
-0.3
-0.0
2.3
2.9
-0.5
-0.3
Jeff Yurak
0.1
0.2
-0.1
-0.1
0.1
0.2
-0.1
-0.1
Tony Muser
0.4
0.5
-0.2
-0.1
0.4
0.5
-0.1
-0.1
Tim Nordbrook
0.1
0.4
-0.3
-0.2
0.1
0.3
-0.2
-0.1
Dave May
2.0
2.6
-0.6
-0.4
2.3
2.3
-0.1
0.2
Lenn Sakata
1.8
2.9
-0.9
-0.7
1.9
2.7
-0.7
-0.4
Buck Martinez
4.2
5.8
-1.3
-0.9
4.1
6.0
-1.6
-1.1
------
------
------
------
------
------
------
------
SUB-TOTAL
176.7
158.6
17.5
34.1
175.2
160.1
14.6
31.3
Basic Player Won-Lost Records
Pitchers
(Sorted by pWORL)
Player
pWins
pLosses
pWOPA
pWORL
eWins
eLosses
eWOPA
eWORL
Mike Caldwell
17.8
11.3
6.7
8.6
17.1
12.1
5.1
7.0
Lary Sorensen
15.2
12.2
3.2
4.9
15.6
11.8
3.9
5.7
Jerry Augustine
11.2
11.4
-0.1
1.4
11.3
11.3
0.1
1.6
Bill Castro
3.5
2.7
0.8
1.3
3.3
2.8
0.4
1.0
Ed Farmer
1.3
0.7
0.6
0.8
1.1
0.9
0.2
0.4
Eduardo R. Rodriguez
4.8
5.0
-0.2
0.5
5.1
4.7
0.4
1.1
Bill Travers
10.3
11.5
-1.2
0.2
10.2
11.5
-1.2
0.2
Willie Mueller
0.4
0.4
-0.0
0.0
0.3
0.4
-0.1
0.0
Andy Replogle
6.9
7.9
-1.0
0.0
6.7
8.0
-1.4
-0.4
Mark Bomback
0.0
0.2
-0.2
-0.2
0.1
0.2
-0.1
-0.1
Bob C. McClure
3.4
4.2
-0.9
-0.2
3.7
3.9
-0.3
0.4
Randy Stein
2.1
2.9
-0.8
-0.4
2.2
2.7
-0.6
-0.1
Moose Haas
1.4
2.2
-0.8
-0.6
1.6
2.0
-0.4
-0.1
------
------
------
------
------
------
------
------
SUB-TOTAL
78.3
72.4
6.2
16.5
78.4
72.3
6.3
16.6
pWins
pLosses
pWOPA
pWORL
eWins
eLosses
eWOPA
eWORL
TEAM TOTALS
255.0
231.0
23.6
50.6
253.6
232.4
20.9
47.9
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.
Larry Hisle
14.6
10.6
0.578
1.1
0.9
0.558
0.0
0.0
0.000
4.0
4.0
0.498
Sal Bando
13.0
11.3
0.537
0.9
0.8
0.513
0.0
0.0
0.000
5.0
4.9
0.505
Robin Yount
10.1
9.8
0.508
1.1
0.6
0.627
0.0
0.0
0.000
6.3
6.7
0.485
Sixto Lezcano
10.5
8.1
0.564
1.0
0.7
0.592
0.0
0.0
0.000
6.4
5.5
0.541
Gorman Thomas
11.3
8.4
0.575
0.7
0.5
0.552
0.0
0.0
0.000
4.6
4.7
0.494
Don Money
10.5
9.3
0.530
1.0
0.5
0.674
0.0
0.0
0.000
3.2
3.1
0.508
Paul Molitor
8.9
9.7
0.478
1.6
1.1
0.592
0.0
0.0
0.000
4.9
4.9
0.503
Ben Oglivie
11.4
8.9
0.562
1.1
1.0
0.513
0.0
0.0
0.000
3.9
3.9
0.501
Jim Wohlford
2.2
2.2
0.499
0.4
0.2
0.671
0.0
0.0
0.000
0.7
0.9
0.456
Charlie Moore
4.5
4.7
0.487
0.4
0.4
0.518
0.0
0.0
0.000
1.0
0.9
0.524
Dick Davis
3.6
4.2
0.463
0.3
0.3
0.493
0.0
0.0
0.000
1.3
1.4
0.482
Cecil Cooper
9.1
7.8
0.538
0.6
0.7
0.466
0.0
0.0
0.000
1.6
1.8
0.471
Andy Etchebarren
0.2
0.1
0.670
0.0
0.0
0.396
0.0
0.0
0.000
0.1
0.1
0.440
Larry Haney
0.2
0.2
0.421
0.0
0.0
0.397
0.0
0.0
0.000
0.0
0.0
0.990
Tim Johnson
0.1
0.1
0.671
0.0
0.0
0.315
0.0
0.0
0.000
0.0
0.0
0.000
Jim Gantner
1.3
1.7
0.429
0.2
0.2
0.415
0.0
0.0
0.000
0.9
1.0
0.470
Jeff Yurak
0.1
0.2
0.311
0.0
0.0
0.252
0.0
0.0
0.000
0.0
0.0
0.704
Tony Muser
0.2
0.4
0.377
0.0
0.0
0.497
0.0
0.0
0.000
0.2
0.1
0.587
Tim Nordbrook
0.1
0.1
0.334
0.0
0.1
0.012
0.0
0.0
0.000
0.1
0.1
0.428
Dave May
1.4
1.6
0.470
0.1
0.2
0.429
0.0
0.0
0.000
0.7
0.6
0.564
Lenn Sakata
1.1
1.7
0.388
0.1
0.1
0.563
0.0
0.0
0.000
0.7
0.9
0.448
Buck Martinez
3.0
4.5
0.403
0.2
0.3
0.419
0.0
0.0
0.000
0.8
1.1
0.433
------
------
------
------
------
------
------
------
------
------
------
------
SUB-TOTAL
117.4
105.6
0.527
10.7
8.6
0.553
0.0
0.0
0.000
46.5
46.5
0.500
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.
Mike Caldwell
0.0
0.0
0.000
0.0
0.0
0.000
16.0
12.2
0.568
0.6
0.3
0.648
Lary Sorensen
0.0
0.0
0.000
0.0
0.0
0.000
14.9
11.8
0.558
0.4
0.3
0.525
Jerry Augustine
0.0
0.0
0.000
0.0
0.0
0.000
10.9
11.1
0.496
0.4
0.2
0.620
Bill Castro
0.0
0.0
0.000
0.0
0.0
0.000
3.2
2.8
0.536
0.1
0.1
0.694
Ed Farmer
0.0
0.0
0.000
0.0
0.0
0.000
1.1
0.8
0.553
0.0
0.0
0.569
Eduardo R. Rodriguez
0.0
0.0
0.000
0.0
0.0
0.000
4.9
4.6
0.516
0.2
0.2
0.560
Bill Travers
0.0
0.0
0.000
0.0
0.0
0.000
10.0
11.0
0.476
0.4
0.4
0.474
Willie Mueller
0.0
0.0
0.000
0.0
0.0
0.000
0.3
0.4
0.464
0.0
0.0
0.891
Andy Replogle
0.0
0.0
0.000
0.0
0.0
0.000
6.6
7.6
0.465
0.1
0.3
0.268
Mark Bomback
0.0
0.0
0.000
0.0
0.0
0.000
0.1
0.2
0.244
0.0
0.0
0.000
Bob C. McClure
0.0
0.0
0.000
0.0
0.0
0.000
3.6
3.8
0.487
0.0
0.0
0.513
Randy Stein
0.0
0.0
0.000
0.0
0.0
0.000
2.2
2.7
0.451
0.1
0.1
0.489
Moose Haas
0.0
0.0
0.000
0.0
0.0
0.000
1.6
1.9
0.455
0.1
0.0
0.558
------
------
------
------
------
------
------
------
------
------
------
------
SUB-TOTAL
0.0
0.0
0.000
0.0
0.0
0.000
75.4
70.8
0.515
2.4
2.1
0.538
Batting
Baserunning
Pitching
Fielding
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
TEAM TOTALS
117.4
105.6
0.527
10.7
8.6
0.553
75.4
70.8
0.515
48.9
48.6
0.502
eWin, eLoss, eWOPA by Position
Catcher
Player
eWins
eLosses
eWOPA
Charlie Moore
5.9
6.0
0.2
Buck Martinez
4.1
5.9
-1.5
Andy Etchebarren
0.3
0.3
0.1
Larry Haney
0.2
0.2
-0.0
------
------
------
TOTAL
10.5
12.4
-1.3
First Base
Player
eWins
eLosses
eWOPA
Cecil Cooper
9.8
8.5
0.7
Don Money
6.1
5.0
0.8
Ben Oglivie
1.0
0.8
0.1
Tony Muser
0.4
0.4
-0.1
Sal Bando
0.2
0.3
-0.1
Jim Gantner
0.0
0.0
-0.0
------
------
------
TOTAL
17.5
15.1
1.5
Second Base
Player
eWins
eLosses
eWOPA
Paul Molitor
10.9
11.1
0.3
Don Money
3.9
4.1
0.0
Lenn Sakata
1.9
2.7
-0.6
Jim Gantner
1.5
1.8
-0.2
------
------
------
TOTAL
18.3
19.7
-0.5
Third Base
Player
eWins
eLosses
eWOPA
Sal Bando
17.8
15.7
2.0
Don Money
3.2
2.5
0.6
Jim Gantner
0.6
0.7
-0.1
Paul Molitor
0.1
0.1
-0.0
------
------
------
TOTAL
21.6
19.0
2.5
Shortstop
Player
eWins
eLosses
eWOPA
Robin Yount
17.5
17.1
1.6
Paul Molitor
4.3
4.4
0.3
Don Money
0.4
0.4
0.1
Tim Nordbrook
0.1
0.3
-0.1
Jim Gantner
0.0
0.3
-0.2
Tim Johnson
0.1
0.1
0.0
------
------
------
TOTAL
22.5
22.5
1.7
Left Field
Player
eWins
eLosses
eWOPA
Larry Hisle
10.8
8.1
2.3
Ben Oglivie
10.4
8.0
2.0
Dick Davis
2.1
2.7
-0.7
Jim Wohlford
1.6
1.8
-0.3
Dave May
0.5
0.5
-0.0
Jeff Yurak
0.0
0.0
0.0
------
------
------
TOTAL
25.4
21.1
3.4
Center Field
Player
eWins
eLosses
eWOPA
Gorman Thomas
16.5
13.5
2.8
Larry Hisle
3.3
2.5
0.8
Dave May
0.5
0.8
-0.3
Dick Davis
0.2
0.3
-0.0
Jim Wohlford
0.2
0.3
-0.0
------
------
------
TOTAL
20.8
17.3
3.2
Right Field
Player
eWins
eLosses
eWOPA
Sixto Lezcano
17.6
14.0
2.9
Ben Oglivie
3.1
2.3
0.7
Jim Wohlford
1.0
0.9
0.1
Dick Davis
0.5
0.5
0.0
Dave May
0.4
0.4
-0.1
Larry Hisle
0.0
0.1
-0.0
------
------
------
TOTAL
22.7
18.1
3.6
Designated Hitter
Player
eWins
eLosses
eWOPA
Larry Hisle
5.4
4.7
0.6
Dick Davis
2.1
2.2
-0.2
Ben Oglivie
1.7
2.4
-0.8
Cecil Cooper
1.2
1.6
-0.4
Sal Bando
0.9
0.9
0.0
Don Money
0.7
0.7
-0.0
Jim Wohlford
0.4
0.2
0.1
Dave May
0.3
0.3
0.1
Sixto Lezcano
0.2
0.3
-0.1
Paul Molitor
0.1
0.0
0.0
------
------
------
TOTAL
13.1
13.2
-0.5
Pinch Hitter
Player
eWins
eLosses
eWOPA
Dave May
0.6
0.4
0.2
Don Money
0.4
0.2
0.2
Ben Oglivie
0.2
0.3
-0.1
Cecil Cooper
0.3
0.2
0.1
Dick Davis
0.1
0.2
-0.1
Jeff Yurak
0.1
0.1
-0.0
Larry Hisle
0.1
0.1
-0.0
Jim Gantner
0.0
0.1
-0.1
Jim Wohlford
0.1
0.1
-0.0
Sixto Lezcano
0.1
0.1
0.1
Sal Bando
0.0
0.2
-0.1
Tony Muser
0.0
0.1
-0.1
Paul Molitor
0.0
0.1
-0.1
Charlie Moore
0.0
0.1
-0.1
Tim Johnson
0.0
0.0
0.0
Robin Yount
0.0
0.0
0.0
------
------
------
TOTAL
2.0
2.3
-0.1
Pinch Runner
Player
eWins
eLosses
eWOPA
Gorman Thomas
0.1
0.0
0.1
Jim Gantner
0.0
0.0
-0.0
Dave May
0.0
0.0
0.0
Jim Wohlford
0.0
0.0
0.0
Charlie Moore
0.0
0.0
-0.0
Tony Muser
0.0
0.0
-0.0
Paul Molitor
0.0
0.0
-0.0
Buck Martinez
0.0
0.0
0.0
Lenn Sakata
0.0
0.0
-0.0
Dick Davis
0.0
0.0
0.0
------
------
------
TOTAL
0.1
0.0
0.1
Pitcher Offense
Player
eWins
eLosses
eWOPA
------
------
------
TOTAL
0.0
0.0
0.0
Starting Pitching
Player
eWins
eLosses
eWOPA
Mike Caldwell
16.3
12.3
4.1
Lary Sorensen
15.1
12.1
3.2
Jerry Augustine
11.1
11.2
-0.1
Bill Travers
10.4
11.4
-0.9
Andy Replogle
5.4
6.1
-0.6
Eduardo R. Rodriguez
2.6
3.0
-0.4
Moose Haas
1.6
2.0
-0.4
Randy Stein
0.1
0.5
-0.4
Mark Bomback
0.0
0.2
-0.2
------
------
------
TOTAL
62.5
58.8
4.3
Relief Pitching
Player
eWins
eLosses
eWOPA
Bob C. McClure
3.7
3.9
-0.3
Bill Castro
3.3
2.8
0.4
Randy Stein
2.0
2.3
-0.4
Eduardo R. Rodriguez
2.4
1.9
0.5
Andy Replogle
1.4
1.9
-0.5
Ed Farmer
1.1
0.9
0.2
Willie Mueller
0.3
0.4
-0.1
Mike Caldwell
0.3
0.2
0.1
Jerry Augustine
0.2
0.1
0.1
Lary Sorensen
0.2
0.0
0.2
Moose Haas
0.0
0.0
0.0
Mark Bomback
0.0
0.0
0.0
------
------
------
TOTAL
15.0
14.4
0.3
Team eWins over Positional Average by Position
P
C
1B
2B
3B
SS
LF
CF
RF
Oth
1978 Milwaukee Brewers
4.6
-1.3
1.5
-0.5
2.5
1.7
3.4
3.2
3.6
-0.5
pWin, pLoss, pWOPA by Position
Catcher
Player
pWins
pLosses
pWOPA
Charlie Moore
6.0
5.8
0.5
Buck Martinez
4.2
5.8
-1.3
Andy Etchebarren
0.4
0.2
0.2
Larry Haney
0.3
0.1
0.2
------
------
------
TOTAL
10.9
11.9
-0.4
First Base
Player
pWins
pLosses
pWOPA
Cecil Cooper
9.5
8.8
0.1
Don Money
5.9
5.3
0.3
Ben Oglivie
0.9
0.9
-0.1
Tony Muser
0.4
0.4
-0.1
Sal Bando
0.2
0.3
-0.1
Jim Gantner
0.0
0.0
-0.0
------
------
------
TOTAL
16.9
15.8
0.0
Second Base
Player
pWins
pLosses
pWOPA
Paul Molitor
11.4
10.6
1.2
Don Money
4.0
3.9
0.2
Lenn Sakata
1.8
2.9
-0.9
Jim Gantner
1.6
1.7
-0.1
------
------
------
TOTAL
18.8
19.2
0.4
Third Base
Player
pWins
pLosses
pWOPA
Sal Bando
18.7
14.7
3.9
Don Money
3.4
2.2
1.2
Jim Gantner
0.7
0.6
0.1
Paul Molitor
0.1
0.1
0.0
------
------
------
TOTAL
23.0
17.6
5.2
Shortstop
Player
pWins
pLosses
pWOPA
Robin Yount
18.3
16.3
3.0
Paul Molitor
4.4
4.2
0.5
Don Money
0.5
0.3
0.2
Tim Nordbrook
0.1
0.4
-0.3
Jim Gantner
0.0
0.3
-0.2
Tim Johnson
0.1
0.0
0.1
------
------
------
TOTAL
23.4
21.6
3.4
Left Field
Player
pWins
pLosses
pWOPA
Larry Hisle
10.4
8.5
1.5
Ben Oglivie
11.0
7.5
3.2
Dick Davis
2.6
2.2
0.3
Jim Wohlford
1.9
1.5
0.3
Dave May
0.6
0.4
0.1
Jeff Yurak
0.0
0.0
0.0
------
------
------
TOTAL
26.4
20.2
5.4
Center Field
Player
pWins
pLosses
pWOPA
Gorman Thomas
16.2
13.8
2.2
Larry Hisle
3.3
2.4
0.8
Dave May
0.3
0.9
-0.6
Dick Davis
0.2
0.3
-0.2
Jim Wohlford
0.3
0.2
0.1
------
------
------
TOTAL
20.3
17.7
2.3
Right Field
Player
pWins
pLosses
pWOPA
Sixto Lezcano
17.4
14.2
2.4
Ben Oglivie
2.9
2.4
0.3
Jim Wohlford
1.0
0.9
0.1
Dick Davis
0.5
0.5
-0.1
Dave May
0.3
0.6
-0.3
Larry Hisle
0.0
0.1
-0.0
------
------
------
TOTAL
22.1
18.7
2.4
Designated Hitter
Player
pWins
pLosses
pWOPA
Larry Hisle
6.2
3.9
2.1
Dick Davis
2.2
2.2
-0.0
Ben Oglivie
1.1
2.9
-1.9
Cecil Cooper
1.0
1.8
-0.9
Sal Bando
1.0
0.8
0.1
Don Money
0.8
0.7
0.1
Jim Wohlford
0.5
0.1
0.3
Dave May
0.2
0.4
-0.2
Sixto Lezcano
0.1
0.3
-0.2
Paul Molitor
0.0
0.1
-0.0
------
------
------
TOTAL
13.1
13.3
-0.6
Pinch Hitter
Player
pWins
pLosses
pWOPA
Dave May
0.6
0.4
0.2
Don Money
0.4
0.2
0.2
Ben Oglivie
0.2
0.4
-0.2
Cecil Cooper
0.3
0.2
0.1
Dick Davis
0.0
0.3
-0.3
Jeff Yurak
0.1
0.2
-0.1
Larry Hisle
0.0
0.2
-0.1
Jim Gantner
0.0
0.1
-0.1
Jim Wohlford
0.1
0.1
-0.0
Sixto Lezcano
0.1
0.1
-0.0
Sal Bando
0.0
0.2
-0.1
Tony Muser
0.0
0.1
-0.1
Paul Molitor
0.0
0.1
-0.1
Charlie Moore
0.0
0.1
-0.1
Tim Johnson
0.0
0.0
0.0
Robin Yount
0.0
0.0
-0.0
------
------
------
TOTAL
1.7
2.6
-0.7
Pinch Runner
Player
pWins
pLosses
pWOPA
Gorman Thomas
0.1
0.0
0.1
Jim Gantner
0.0
0.0
-0.0
Dave May
0.0
0.0
0.0
Jim Wohlford
0.0
0.0
0.0
Charlie Moore
0.0
0.0
-0.0
Tony Muser
0.0
0.0
-0.0
Paul Molitor
0.0
0.0
0.0
Buck Martinez
0.0
0.0
-0.0
Lenn Sakata
0.0
0.0
-0.0
Dick Davis
0.0
0.0
0.0
------
------
------
TOTAL
0.1
0.1
0.1
Pitcher Offense
Player
pWins
pLosses
pWOPA
------
------
------
TOTAL
0.0
0.0
0.0
Starting Pitching
Player
pWins
pLosses
pWOPA
Mike Caldwell
17.6
11.0
6.7
Lary Sorensen
15.0
12.2
2.9
Jerry Augustine
10.9
11.4
-0.4
Bill Travers
10.3
11.5
-1.2
Andy Replogle
5.5
6.0
-0.4
Eduardo R. Rodriguez
2.6
2.9
-0.2
Moose Haas
1.4
2.2
-0.8
Randy Stein
0.1
0.6
-0.5
Mark Bomback
0.0
0.2
-0.2
------
------
------
TOTAL
63.3
58.0
5.8
Relief Pitching
Player
pWins
pLosses
pWOPA
Bob C. McClure
3.4
4.2
-0.9
Bill Castro
3.5
2.7
0.8
Randy Stein
2.1
2.3
-0.3
Eduardo R. Rodriguez
2.2
2.1
0.0
Andy Replogle
1.4
1.9
-0.5
Ed Farmer
1.3
0.7
0.6
Willie Mueller
0.4
0.4
-0.0
Mike Caldwell
0.3
0.3
0.0
Jerry Augustine
0.3
0.0
0.3
Lary Sorensen
0.2
0.0
0.2
Moose Haas
0.0
0.0
0.0
Mark Bomback
0.0
0.0
0.0
------
------
------
TOTAL
15.0
14.4
0.3
Team pWins over Positional Average by Position
P
C
1B
2B
3B
SS
LF
CF
RF
Oth
1978 Milwaukee Brewers
6.2
-0.4
0.0
0.4
5.2
3.4
5.4
2.3
2.4
-1.1
*
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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