1977 Toronto Blue Jays
Baseball Player Won-Loss Records
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1977 Toronto Blue Jays
*
Traditional Statistics and Splits (Retrosheet)
Toronto Blue Jays -
Franchise Page
(Regular Season)
(
1977 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
Ron Fairly
12.7
12.9
-0.8
0.6
13.5
12.0
1.0
2.4
Otto Velez
12.4
12.7
-0.8
0.6
13.2
11.9
0.8
2.2
Roy Howell
10.4
10.9
-0.7
0.4
11.1
10.1
0.8
1.9
Steve Bowling
7.1
7.2
-0.4
0.4
7.3
7.0
0.0
0.8
Doug Rader
8.2
9.1
-1.0
-0.0
9.0
8.3
0.5
1.5
Phil Roof
0.1
0.2
-0.1
-0.1
0.1
0.2
-0.1
-0.1
Pedro Garcia
2.9
3.9
-0.8
-0.4
3.0
3.9
-0.6
-0.3
Hector Torres
7.3
9.3
-1.3
-0.5
7.8
8.8
-0.4
0.4
Tim Nordbrook
1.8
2.8
-0.8
-0.6
2.0
2.6
-0.5
-0.3
Rick Cerone
2.0
2.9
-0.8
-0.6
2.1
2.8
-0.6
-0.3
Ernie Whitt
0.6
1.5
-0.8
-0.7
0.9
1.2
-0.3
-0.2
Jim Mason
1.6
2.9
-1.0
-0.8
1.8
2.7
-0.7
-0.5
Gary Woods
6.1
7.5
-1.5
-0.8
6.1
7.5
-1.6
-0.9
Steve Staggs
7.9
10.2
-1.8
-0.9
8.4
9.7
-0.8
0.1
Bob Bailor
13.3
16.4
-2.6
-1.1
14.9
14.8
0.4
1.9
Doug Ault
11.6
13.7
-3.0
-1.8
12.2
13.1
-1.7
-0.4
Sam Ewing
5.9
8.6
-2.9
-2.1
6.6
8.0
-1.6
-0.8
Dave McKay
6.9
10.4
-3.1
-2.3
7.4
9.8
-2.0
-1.2
Alan Ashby
7.5
11.8
-3.9
-3.0
8.4
10.9
-2.2
-1.2
John Scott
5.1
8.7
-3.7
-3.0
5.6
8.3
-2.8
-2.1
Al Woods
12.3
17.1
-5.6
-4.1
14.2
15.2
-1.6
-0.1
------
------
------
------
------
------
------
------
SUB-TOTAL
143.8
180.7
-37.4
-20.8
155.6
168.9
-13.9
2.7
Basic Player Won-Lost Records
Pitchers
(Sorted by pWORL)
Player
pWins
pLosses
pWOPA
pWORL
eWins
eLosses
eWOPA
eWORL
Pete Vuckovich
7.4
7.5
-0.2
1.0
7.7
7.3
0.3
1.5
Dave Lemanczyk
12.9
13.9
-0.9
0.9
13.2
13.7
-0.4
1.4
Jerry Garvin
13.9
15.7
-1.6
0.4
14.6
15.0
-0.3
1.6
Jerry Johnson
3.8
4.2
-0.6
0.2
3.7
4.3
-0.7
-0.0
Tom A. Murphy
1.9
2.0
-0.2
0.1
1.9
2.1
-0.2
0.1
Mike Willis
4.1
4.6
-0.6
0.1
4.4
4.4
-0.1
0.7
Dennis DeBarr
0.3
0.4
-0.1
-0.0
0.4
0.4
-0.0
0.1
Steve Hargan
1.2
1.6
-0.4
-0.2
1.3
1.5
-0.2
0.0
Tom Bruno
0.5
1.0
-0.6
-0.4
0.5
1.0
-0.5
-0.4
Mike Darr Sr.
0.1
0.8
-0.7
-0.6
0.1
0.7
-0.6
-0.6
Jim Clancy
4.9
6.4
-1.4
-0.6
5.1
6.3
-1.1
-0.4
Jesse Jefferson
11.9
14.4
-2.4
-0.7
12.9
13.3
-0.3
1.5
Chuck Hartenstein
0.4
1.4
-1.1
-0.9
0.7
1.1
-0.5
-0.3
Bill Singer
3.6
5.4
-1.8
-1.2
3.9
5.2
-1.3
-0.7
Jeff Byrd
4.2
7.8
-3.5
-2.7
5.3
6.7
-1.4
-0.6
------
------
------
------
------
------
------
------
SUB-TOTAL
71.2
87.3
-15.9
-4.7
75.4
83.1
-7.4
3.8
pWins
pLosses
pWOPA
pWORL
eWins
eLosses
eWOPA
eWORL
TEAM TOTALS
215.0
268.0
-53.3
-25.5
231.0
252.0
-21.2
6.5
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.
Ron Fairly
11.1
9.5
0.540
0.6
0.8
0.460
0.0
0.0
0.000
1.8
1.8
0.498
Otto Velez
9.5
7.9
0.545
0.7
0.6
0.532
0.0
0.0
0.000
3.1
3.5
0.471
Roy Howell
7.6
6.5
0.540
0.8
0.7
0.540
0.0
0.0
0.000
2.6
3.0
0.467
Steve Bowling
3.2
4.0
0.441
0.3
0.3
0.499
0.0
0.0
0.000
3.9
2.7
0.586
Doug Rader
6.6
6.5
0.506
0.7
0.5
0.560
0.0
0.0
0.000
1.7
1.3
0.557
Phil Roof
0.0
0.2
0.002
0.0
0.0
0.000
0.0
0.0
0.000
0.1
0.1
0.643
Pedro Garcia
1.8
2.6
0.410
0.2
0.2
0.494
0.0
0.0
0.000
1.1
1.1
0.499
Hector Torres
4.5
5.5
0.451
0.4
0.5
0.448
0.0
0.0
0.000
2.9
2.9
0.502
Tim Nordbrook
1.0
1.7
0.371
0.1
0.1
0.527
0.0
0.0
0.000
0.8
0.9
0.490
Rick Cerone
1.5
2.1
0.420
0.1
0.2
0.317
0.0
0.0
0.000
0.5
0.4
0.536
Ernie Whitt
0.7
1.0
0.409
0.1
0.0
0.701
0.0
0.0
0.000
0.1
0.2
0.375
Jim Mason
1.0
1.6
0.374
0.2
0.3
0.391
0.0
0.0
0.000
0.7
0.8
0.445
Gary Woods
3.4
4.8
0.412
0.6
0.5
0.549
0.0
0.0
0.000
2.1
2.1
0.499
Steve Staggs
5.5
5.9
0.482
0.5
0.8
0.392
0.0
0.0
0.000
2.5
3.0
0.454
Bob Bailor
8.8
9.5
0.482
1.4
0.9
0.601
0.0
0.0
0.000
4.6
4.5
0.510
Doug Ault
9.5
9.7
0.494
0.6
1.1
0.367
0.0
0.0
0.000
2.1
2.2
0.493
Sam Ewing
4.7
5.1
0.478
0.5
0.2
0.650
0.0
0.0
0.000
1.5
2.6
0.365
Dave McKay
4.2
6.2
0.404
0.4
0.5
0.463
0.0
0.0
0.000
2.9
3.1
0.485
Alan Ashby
6.0
8.2
0.423
0.5
0.8
0.397
0.0
0.0
0.000
1.9
1.9
0.507
John Scott
3.2
4.3
0.427
0.4
1.0
0.283
0.0
0.0
0.000
2.1
2.8
0.431
Al Woods
8.3
9.0
0.481
0.9
0.8
0.524
0.0
0.0
0.000
5.0
5.3
0.488
------
------
------
------
------
------
------
------
------
------
------
------
SUB-TOTAL
102.0
111.7
0.477
9.9
10.7
0.479
0.0
0.0
0.000
44.1
46.1
0.489
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.
Pete Vuckovich
0.0
0.0
0.000
0.0
0.0
0.000
7.4
7.0
0.512
0.3
0.3
0.460
Dave Lemanczyk
0.0
0.0
0.000
0.0
0.0
0.000
12.9
13.3
0.493
0.3
0.4
0.471
Jerry Garvin
0.0
0.0
0.000
0.0
0.0
0.000
14.3
14.8
0.492
0.3
0.2
0.609
Jerry Johnson
0.0
0.0
0.000
0.0
0.0
0.000
3.6
4.2
0.462
0.1
0.1
0.500
Tom A. Murphy
0.0
0.0
0.000
0.0
0.0
0.000
1.8
2.0
0.475
0.1
0.0
0.680
Mike Willis
0.0
0.0
0.000
0.0
0.0
0.000
4.2
4.2
0.501
0.1
0.1
0.489
Dennis DeBarr
0.0
0.0
0.000
0.0
0.0
0.000
0.4
0.4
0.499
0.0
0.0
0.448
Steve Hargan
0.0
0.0
0.000
0.0
0.0
0.000
1.3
1.5
0.467
0.0
0.0
0.769
Tom Bruno
0.0
0.0
0.000
0.0
0.0
0.000
0.5
0.9
0.376
0.0
0.2
0.077
Mike Darr Sr.
0.0
0.0
0.000
0.0
0.0
0.000
0.2
0.7
0.184
0.0
0.0
0.068
Jim Clancy
0.0
0.0
0.000
0.0
0.0
0.000
5.0
5.9
0.460
0.2
0.2
0.447
Jesse Jefferson
0.0
0.0
0.000
0.0
0.0
0.000
12.7
12.9
0.495
0.3
0.4
0.448
Chuck Hartenstein
0.0
0.0
0.000
0.0
0.0
0.000
0.7
1.1
0.389
0.0
0.0
0.654
Bill Singer
0.0
0.0
0.000
0.0
0.0
0.000
3.9
5.1
0.438
0.0
0.0
0.562
Jeff Byrd
0.0
0.0
0.000
0.0
0.0
0.000
5.3
6.4
0.451
0.1
0.2
0.433
------
------
------
------
------
------
------
------
------
------
------
------
SUB-TOTAL
0.0
0.0
0.000
0.0
0.0
0.000
74.2
80.3
0.480
1.9
2.1
0.475
Batting
Baserunning
Pitching
Fielding
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
eWins
eLoss
Win Pct.
TEAM TOTALS
102.0
111.7
0.477
9.9
10.7
0.479
74.2
80.3
0.480
46.0
48.2
0.488
eWin, eLoss, eWOPA by Position
Catcher
Player
eWins
eLosses
eWOPA
Alan Ashby
8.4
10.9
-2.0
Rick Cerone
2.1
2.8
-0.5
Ernie Whitt
0.7
0.8
-0.1
Phil Roof
0.1
0.2
-0.1
------
------
------
TOTAL
11.4
14.7
-2.8
First Base
Player
eWins
eLosses
eWOPA
Doug Ault
11.9
12.9
-1.9
Ron Fairly
3.3
4.3
-1.3
Doug Rader
0.4
0.5
-0.2
Sam Ewing
0.0
0.0
-0.0
------
------
------
TOTAL
15.6
17.7
-3.3
Second Base
Player
eWins
eLosses
eWOPA
Steve Staggs
8.5
9.7
-0.7
Dave McKay
3.5
4.2
-0.4
Pedro Garcia
3.0
3.7
-0.5
Hector Torres
2.0
2.7
-0.5
------
------
------
TOTAL
17.0
20.2
-2.2
Third Base
Player
eWins
eLosses
eWOPA
Roy Howell
10.5
9.5
0.9
Doug Rader
5.8
4.5
1.2
Dave McKay
2.7
3.7
-1.0
Hector Torres
0.1
0.1
0.0
------
------
------
TOTAL
19.0
17.8
1.0
Shortstop
Player
eWins
eLosses
eWOPA
Bob Bailor
5.9
6.2
0.3
Hector Torres
5.6
6.1
-0.0
Tim Nordbrook
2.0
2.6
-0.5
Jim Mason
1.8
2.7
-0.7
Dave McKay
1.3
1.7
-0.2
------
------
------
TOTAL
16.6
19.3
-1.1
Left Field
Player
eWins
eLosses
eWOPA
Al Woods
12.8
13.4
-1.2
John Scott
2.0
2.7
-0.8
Bob Bailor
1.7
1.9
-0.3
Sam Ewing
1.2
1.3
-0.2
Ron Fairly
1.5
0.8
0.6
Steve Bowling
1.0
1.2
-0.2
------
------
------
TOTAL
20.2
21.3
-2.1
Center Field
Player
eWins
eLosses
eWOPA
Gary Woods
6.0
7.5
-1.6
Bob Bailor
6.3
5.7
0.5
John Scott
3.5
5.2
-1.8
Steve Bowling
2.4
2.5
-0.2
------
------
------
TOTAL
18.2
20.9
-3.2
Right Field
Player
eWins
eLosses
eWOPA
Otto Velez
9.6
9.3
-0.2
Steve Bowling
3.8
3.3
0.4
Sam Ewing
2.7
4.2
-1.7
Ron Fairly
3.0
2.6
0.2
Al Woods
1.0
1.4
-0.5
Bob Bailor
0.4
0.3
0.1
Doug Rader
0.1
0.0
0.0
------
------
------
TOTAL
20.5
21.0
-1.6
Designated Hitter
Player
eWins
eLosses
eWOPA
Ron Fairly
5.5
4.4
0.9
Doug Rader
2.2
2.7
-0.6
Otto Velez
2.8
2.0
0.8
Sam Ewing
2.0
1.8
0.1
Roy Howell
0.6
0.6
-0.1
Bob Bailor
0.4
0.6
-0.3
Al Woods
0.1
0.2
-0.1
Pedro Garcia
0.0
0.0
0.0
------
------
------
TOTAL
13.5
12.4
0.8
Pinch Hitter
Player
eWins
eLosses
eWOPA
Otto Velez
0.6
0.9
-0.1
Sam Ewing
0.8
0.6
0.3
Doug Rader
0.4
0.5
-0.0
Doug Ault
0.3
0.2
0.2
Ernie Whitt
0.1
0.4
-0.3
Al Woods
0.4
0.1
0.3
Ron Fairly
0.2
0.1
0.1
Bob Bailor
0.2
0.1
0.1
Pedro Garcia
0.0
0.2
-0.2
Gary Woods
0.1
0.0
0.1
Steve Bowling
0.1
0.0
0.0
Jim Mason
0.1
0.0
0.1
Hector Torres
0.0
0.0
0.0
John Scott
0.0
0.0
-0.0
Roy Howell
0.0
0.0
0.0
Alan Ashby
0.0
0.0
0.0
Dave McKay
0.0
0.0
-0.0
Steve Staggs
0.0
0.0
-0.0
------
------
------
TOTAL
3.3
3.1
0.5
Pinch Runner
Player
eWins
eLosses
eWOPA
John Scott
0.1
0.2
-0.1
Dave McKay
0.0
0.1
-0.1
Steve Bowling
0.1
0.0
0.0
Hector Torres
0.0
0.0
0.0
Pedro Garcia
0.0
0.0
-0.0
Ernie Whitt
0.0
0.0
-0.0
Sam Ewing
0.0
0.0
-0.0
Otto Velez
0.0
0.0
0.0
Al Woods
0.0
0.0
0.0
------
------
------
TOTAL
0.3
0.4
-0.1
Pitcher Offense
Player
eWins
eLosses
eWOPA
------
------
------
TOTAL
0.0
0.0
0.0
Starting Pitching
Player
eWins
eLosses
eWOPA
Jerry Garvin
14.6
15.0
-0.2
Dave Lemanczyk
13.2
13.6
-0.3
Jesse Jefferson
13.0
13.3
-0.2
Jeff Byrd
5.4
6.6
-1.1
Jim Clancy
5.2
6.1
-0.9
Bill Singer
4.0
5.0
-1.0
Pete Vuckovich
3.5
3.4
0.1
Steve Hargan
1.2
1.4
-0.2
Mike Willis
0.8
1.2
-0.4
Mike Darr Sr.
0.2
0.7
-0.5
Tom A. Murphy
0.4
0.3
0.1
------
------
------
TOTAL
61.5
66.7
-4.6
Relief Pitching
Player
eWins
eLosses
eWOPA
Pete Vuckovich
4.2
3.9
0.2
Jerry Johnson
3.7
4.3
-0.7
Mike Willis
3.5
3.2
0.2
Tom A. Murphy
1.5
1.7
-0.2
Chuck Hartenstein
0.7
1.1
-0.4
Tom Bruno
0.5
1.0
-0.5
Dennis DeBarr
0.4
0.4
-0.0
Steve Hargan
0.1
0.1
0.1
Bill Singer
0.0
0.0
-0.0
------
------
------
TOTAL
14.6
15.7
-1.4
Team eWins over Positional Average by Position
P
C
1B
2B
3B
SS
LF
CF
RF
Oth
1977 Toronto Blue Jays
-6.0
-2.8
-3.3
-2.2
1.0
-1.1
-2.1
-3.2
-1.6
1.2
pWin, pLoss, pWOPA by Position
Catcher
Player
pWins
pLosses
pWOPA
Alan Ashby
7.5
11.8
-3.9
Rick Cerone
2.0
2.9
-0.8
Ernie Whitt
0.5
1.0
-0.5
Phil Roof
0.1
0.2
-0.1
------
------
------
TOTAL
10.1
16.0
-5.3
First Base
Player
pWins
pLosses
pWOPA
Doug Ault
11.3
13.4
-3.1
Ron Fairly
3.2
4.3
-1.4
Doug Rader
0.3
0.6
-0.4
Sam Ewing
0.0
0.0
-0.0
------
------
------
TOTAL
14.8
18.4
-4.8
Second Base
Player
pWins
pLosses
pWOPA
Steve Staggs
7.9
10.2
-1.8
Dave McKay
3.4
4.3
-0.7
Pedro Garcia
2.9
3.7
-0.6
Hector Torres
2.0
2.7
-0.5
------
------
------
TOTAL
16.2
20.9
-3.7
Third Base
Player
pWins
pLosses
pWOPA
Roy Howell
9.9
10.1
-0.3
Doug Rader
5.7
4.7
0.9
Dave McKay
2.2
4.1
-2.0
Hector Torres
0.1
0.1
0.0
------
------
------
TOTAL
17.8
19.0
-1.4
Shortstop
Player
pWins
pLosses
pWOPA
Bob Bailor
5.3
6.8
-0.9
Hector Torres
5.1
6.6
-0.8
Tim Nordbrook
1.8
2.8
-0.8
Jim Mason
1.6
2.9
-1.1
Dave McKay
1.3
1.8
-0.3
------
------
------
TOTAL
15.1
20.8
-3.9
Left Field
Player
pWins
pLosses
pWOPA
Al Woods
10.9
15.3
-5.1
John Scott
1.8
3.0
-1.4
Bob Bailor
1.4
2.2
-0.9
Sam Ewing
1.2
1.3
-0.2
Ron Fairly
1.5
0.8
0.6
Steve Bowling
1.1
1.2
-0.1
------
------
------
TOTAL
17.8
23.8
-7.1
Center Field
Player
pWins
pLosses
pWOPA
Gary Woods
6.0
7.5
-1.6
Bob Bailor
5.8
6.2
-0.5
John Scott
3.2
5.4
-2.3
Steve Bowling
2.4
2.5
-0.2
------
------
------
TOTAL
17.5
21.6
-4.6
Right Field
Player
pWins
pLosses
pWOPA
Otto Velez
9.1
9.8
-1.3
Steve Bowling
3.6
3.5
-0.1
Sam Ewing
2.3
4.5
-2.4
Ron Fairly
2.7
2.9
-0.4
Al Woods
1.0
1.3
-0.4
Bob Bailor
0.3
0.3
-0.0
Doug Rader
0.1
0.0
0.1
------
------
------
TOTAL
19.1
22.5
-4.6
Designated Hitter
Player
pWins
pLosses
pWOPA
Ron Fairly
5.2
4.6
0.4
Doug Rader
1.9
3.1
-1.3
Otto Velez
2.6
2.2
0.3
Sam Ewing
1.8
2.0
-0.2
Roy Howell
0.4
0.8
-0.4
Bob Bailor
0.3
0.7
-0.4
Al Woods
0.1
0.2
-0.2
Pedro Garcia
0.0
0.0
0.0
------
------
------
TOTAL
12.3
13.6
-1.8
Pinch Hitter
Player
pWins
pLosses
pWOPA
Otto Velez
0.8
0.7
0.1
Sam Ewing
0.6
0.8
-0.1
Doug Rader
0.2
0.6
-0.3
Doug Ault
0.3
0.3
0.0
Ernie Whitt
0.0
0.4
-0.4
Al Woods
0.3
0.2
0.1
Ron Fairly
0.1
0.2
0.0
Bob Bailor
0.2
0.1
0.1
Pedro Garcia
0.0
0.2
-0.2
Gary Woods
0.1
0.0
0.1
Steve Bowling
0.1
0.0
0.0
Jim Mason
0.1
0.0
0.1
Hector Torres
0.0
0.0
-0.0
John Scott
0.0
0.0
-0.0
Roy Howell
0.0
0.0
0.0
Alan Ashby
0.0
0.0
0.0
Dave McKay
0.0
0.0
-0.0
Steve Staggs
0.0
0.0
-0.0
------
------
------
TOTAL
2.8
3.6
-0.4
Pinch Runner
Player
pWins
pLosses
pWOPA
John Scott
0.1
0.2
-0.0
Dave McKay
0.0
0.1
-0.1
Steve Bowling
0.1
0.0
0.0
Hector Torres
0.0
0.0
0.0
Pedro Garcia
0.0
0.0
-0.0
Ernie Whitt
0.0
0.0
-0.0
Sam Ewing
0.0
0.0
-0.0
Otto Velez
0.0
0.0
0.0
Al Woods
0.0
0.0
-0.0
------
------
------
TOTAL
0.3
0.4
-0.1
Pitcher Offense
Player
pWins
pLosses
pWOPA
------
------
------
TOTAL
0.0
0.0
0.0
Starting Pitching
Player
pWins
pLosses
pWOPA
Jerry Garvin
13.9
15.7
-1.6
Dave Lemanczyk
12.9
13.9
-0.9
Jesse Jefferson
11.9
14.4
-2.4
Jeff Byrd
4.2
7.8
-3.5
Jim Clancy
4.9
6.4
-1.4
Bill Singer
3.6
5.4
-1.8
Pete Vuckovich
3.3
3.6
-0.2
Steve Hargan
1.0
1.6
-0.5
Mike Willis
0.6
1.4
-0.8
Mike Darr Sr.
0.1
0.8
-0.7
Tom A. Murphy
0.5
0.2
0.3
------
------
------
TOTAL
57.1
71.1
-13.4
Relief Pitching
Player
pWins
pLosses
pWOPA
Pete Vuckovich
4.1
4.0
0.1
Jerry Johnson
3.8
4.2
-0.6
Mike Willis
3.5
3.2
0.2
Tom A. Murphy
1.4
1.9
-0.5
Chuck Hartenstein
0.4
1.4
-1.1
Tom Bruno
0.5
1.0
-0.6
Dennis DeBarr
0.3
0.4
-0.1
Steve Hargan
0.2
0.0
0.1
Bill Singer
0.0
0.0
-0.0
------
------
------
TOTAL
14.1
16.2
-2.5
Team pWins over Positional Average by Position
P
C
1B
2B
3B
SS
LF
CF
RF
Oth
1977 Toronto Blue Jays
-15.9
-5.3
-4.8
-3.7
-1.4
-3.9
-7.1
-4.6
-4.6
-2.3
*
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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