2015 New York Mets
Baseball Player Won-Loss Records
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2015 New York Mets*
Traditional Statistics and Splits (Retrosheet)
New York Mets - Franchise Page

(Regular Season)

(2015 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
21.417.92.3
4.2
20.918.41.5
3.4
8.25.33.1
3.8
7.56.01.7
2.3
15.912.91.7
3.1
15.413.40.7
2.1
16.614.91.5
3.0
16.015.50.1
1.6
7.75.22.3
2.9
7.55.31.9
2.6
5.84.01.6
2.0
5.54.31.1
1.5
15.715.90.1
1.6
15.616.1-0.2
1.4
4.03.10.9
1.2
3.53.6-0.1
0.2
11.011.10.0
1.1
10.911.2-0.2
0.8
3.63.20.4
0.7
3.43.4-0.1
0.2
3.73.40.3
0.6
3.83.40.3
0.7
12.812.8-0.6
0.6
12.413.2-1.3
-0.1
4.64.7-0.3
0.2
4.74.5-0.1
0.4
2.02.0-0.1
0.1
2.11.90.2
0.4
5.36.0-0.4
0.1
5.45.9-0.3
0.2
0.30.20.1
0.1
0.20.3-0.1
-0.0
11.411.9-1.2
-0.0
11.711.6-0.5
0.7
0.40.5-0.2
-0.1
0.30.6-0.2
-0.2
2.93.4-0.5
-0.2
3.03.2-0.1
0.2
0.81.4-0.5
-0.3
0.71.5-0.7
-0.6
1.21.8-0.6
-0.4
1.21.8-0.6
-0.4
5.26.2-1.1
-0.5
5.36.1-0.9
-0.4
2.83.6-1.0
-0.6
3.03.4-0.5
-0.2
------ ------ ------ ------ ------ ------ ------ ------
SUB-TOTAL
163.2151.47.9
23.2
160.1154.51.6
16.9


Basic Player Won-Lost Records
Pitchers
(Sorted by pWORL)
Player pWins pLosses pWOPA pWORL eWins eLosses eWOPA eWORL
13.310.14.3
5.8
13.310.24.2
5.6
7.04.02.8
3.8
6.34.71.4
2.5
11.19.72.4
3.7
10.99.82.0
3.3
10.49.51.5
2.8
10.49.51.6
2.9
3.31.81.6
1.9
2.72.40.5
0.8
12.613.9-0.4
1.3
12.713.8-0.1
1.6
10.611.5-0.2
1.2
10.511.6-0.3
1.1
0.60.10.5
0.6
0.60.20.4
0.5
1.41.10.3
0.5
1.11.4-0.3
-0.1
2.82.8-0.0
0.5
2.82.7-0.0
0.5
0.50.10.4
0.4
0.40.30.1
0.1
2.01.90.0
0.4
1.82.1-0.3
0.1
0.50.30.2
0.3
0.40.40.0
0.1
0.90.80.1
0.2
1.00.70.2
0.4
2.02.2-0.3
0.1
2.41.80.6
1.0
0.20.20.0
0.1
0.10.2-0.1
-0.0
0.20.10.0
0.0
0.10.2-0.1
-0.1
2.52.9-0.5
0.0
2.82.70.0
0.5
0.20.2-0.0
0.0
0.20.2-0.0
0.0
0.20.3-0.0
0.0
0.20.3-0.1
-0.1
0.81.0-0.2
0.0
1.20.60.5
0.7
0.60.7-0.1
0.0
0.70.60.1
0.2
0.00.0-0.0
-0.0
0.00.0-0.0
-0.0
2.12.8-0.5
-0.2
2.12.9-0.5
-0.2
1.72.5-0.7
-0.4
2.22.00.4
0.7
1.32.2-0.9
-0.5
1.61.9-0.4
-0.0
------ ------ ------ ------ ------ ------ ------ ------
SUB-TOTAL
88.882.610.3
22.6
88.383.19.7
22.0


pWins pLosses pWOPA pWORL eWins eLosses eWOPA eWORL
TEAM TOTALS
252.0234.018.2
45.9
248.3237.711.2
38.9


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.
13.911.0
0.558
1.41.1
0.545
0.00.0
0.000
5.66.3
0.473
6.65.2
0.556
0.20.2
0.512
0.00.0
0.000
0.60.6
0.507
12.610.0
0.558
0.50.9
0.386
0.00.0
0.000
2.22.6
0.462
11.210.6
0.513
0.80.8
0.488
0.00.0
0.000
4.04.1
0.491
5.23.6
0.589
0.40.2
0.629
0.00.0
0.000
1.91.6
0.542
3.83.1
0.550
0.30.2
0.548
0.00.0
0.000
1.51.0
0.596
10.310.5
0.497
0.30.5
0.391
0.00.0
0.000
4.95.0
0.495
2.52.5
0.501
0.20.1
0.558
0.00.0
0.000
0.81.0
0.456
7.06.8
0.506
0.50.7
0.417
0.00.0
0.000
3.43.7
0.480
2.32.3
0.505
0.10.1
0.466
0.00.0
0.000
1.01.0
0.495
2.72.5
0.520
0.10.1
0.555
0.00.0
0.000
0.90.8
0.542
7.58.5
0.470
0.70.7
0.526
0.00.0
0.000
4.24.0
0.509
3.32.7
0.547
0.30.3
0.549
0.00.0
0.000
1.11.6
0.402
1.21.3
0.482
0.10.1
0.517
0.00.0
0.000
0.70.5
0.619
4.44.9
0.475
0.20.3
0.401
0.00.0
0.000
0.80.7
0.524
0.00.1
0.138
0.20.1
0.536
0.00.0
0.000
0.10.0
0.730
8.38.3
0.502
0.70.5
0.606
0.00.0
0.000
2.72.9
0.485
0.30.5
0.373
0.00.0
0.330
0.00.0
0.000
0.10.1
0.407
1.81.8
0.490
0.10.1
0.351
0.00.0
0.000
1.21.2
0.498
0.61.3
0.315
0.10.1
0.377
0.00.0
0.000
0.00.1
0.413
0.91.4
0.387
0.10.1
0.496
0.00.0
0.000
0.20.3
0.438
3.54.0
0.466
0.40.4
0.542
0.00.0
0.000
1.41.7
0.457
2.02.7
0.428
0.20.1
0.601
0.00.0
0.000
0.80.7
0.553
------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------
SUB-TOTAL
111.9105.6
0.515
7.87.8
0.501
0.00.0
0.000
40.241.4
0.493


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.
1.01.7
0.365
0.00.1
0.156
11.48.6
0.571
0.40.2
0.658
0.00.0
0.000
0.00.0
0.000
6.24.6
0.574
0.10.1
0.395
0.61.7
0.277
0.00.0
0.310
9.98.3
0.544
0.20.2
0.473
0.60.8
0.397
0.00.0
0.219
9.48.3
0.530
0.30.4
0.400
0.40.4
0.479
0.00.0
0.375
2.12.0
0.517
0.10.0
0.864
0.61.4
0.291
0.00.1
0.154
11.812.0
0.497
0.30.3
0.513
0.71.1
0.395
0.10.0
0.661
9.210.0
0.479
0.50.4
0.555
0.00.0
0.000
0.00.0
0.000
0.50.2
0.770
0.00.0
0.806
0.00.0
0.000
0.00.0
0.000
1.11.4
0.445
0.00.0
0.639
0.00.0
0.000
0.00.0
0.000
2.82.7
0.507
0.00.0
0.746
0.00.0
0.000
0.00.0
0.000
0.40.3
0.564
0.00.0
0.000
0.00.0
0.007
0.00.0
0.000
1.82.1
0.463
0.00.0
0.848
0.00.0
0.000
0.00.0
0.000
0.40.4
0.531
0.00.0
0.000
0.00.0
0.000
0.00.0
0.000
1.00.7
0.583
0.00.0
0.559
0.10.1
0.445
0.00.0
0.179
2.31.7
0.576
0.00.0
0.465
0.00.0
0.000
0.00.0
0.000
0.10.2
0.374
0.00.0
0.754
0.00.0
0.000
0.00.0
0.000
0.10.2
0.319
0.00.0
0.000
0.00.0
0.870
0.00.0
0.058
2.62.6
0.497
0.10.0
0.768
0.00.0
0.000
0.00.0
0.000
0.20.2
0.496
0.00.0
0.579
0.00.0
0.000
0.00.0
0.000
0.20.3
0.374
0.00.0
0.278
0.00.0
0.000
0.00.0
0.000
1.10.6
0.640
0.00.0
0.798
0.00.0
0.000
0.00.0
0.000
0.70.5
0.562
0.00.0
0.484
0.00.0
0.000
0.00.0
0.000
0.00.0
0.165
0.00.0
0.000
0.10.3
0.193
0.00.0
0.223
2.12.4
0.456
0.10.1
0.425
0.00.1
0.117
0.00.0
0.000
2.21.8
0.553
0.00.1
0.305
0.00.0
0.000
0.00.0
0.000
1.41.7
0.465
0.20.3
0.394
------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------
SUB-TOTAL
4.07.6
0.346
0.10.3
0.329
80.973.6
0.523
2.52.3
0.520


Batting Baserunning Pitching Fielding
eWins eLoss Win Pct. eWins eLoss Win Pct. eWins eLoss Win Pct. eWins eLoss Win Pct.
TEAM TOTALS
115.9113.2
0.506
8.08.1
0.496
80.973.6
0.523
42.743.7
0.494


eWin, eLoss, eWOPA by Position
Catcher
Player eWins eLosses eWOPA
Travis d'Arnaud7.45.91.7
Kevin Plawecki5.45.9-0.3
Anthony Recker1.11.6-0.4
Johnny Monell0.60.9-0.3
------ ------ ------
TOTAL14.414.30.6
  
First Base
Player eWins eLosses eWOPA
Lucas Duda15.313.30.7
Daniel Murphy1.51.7-0.3
Mike Cuddyer1.41.5-0.3
Eric Campbell0.30.3-0.0
Kelly Johnson0.20.2-0.1
Anthony Recker0.00.1-0.1
------ ------ ------
TOTAL18.717.1-0.2
  
Second Base
Player eWins eLosses eWOPA
Daniel Murphy9.48.50.9
Wilmer Flores4.23.70.4
Dilson Herrera3.03.1-0.1
Kelly Johnson2.52.40.1
Ruben Tejada1.01.2-0.2
Juan Uribe0.60.9-0.3
Daniel Muno0.10.2-0.1
------ ------ ------
TOTAL20.719.90.8
  
Third Base
Player eWins eLosses eWOPA
Daniel Murphy4.75.0-0.4
David Wright4.74.6-0.1
Eric Campbell4.24.9-1.0
Juan Uribe2.82.20.5
Ruben Tejada2.31.90.4
Daniel Muno0.10.2-0.1
Kelly Johnson0.00.2-0.2
------ ------ ------
TOTAL18.819.0-0.8
  
Shortstop
Player eWins eLosses eWOPA
Wilmer Flores11.312.2-0.6
Ruben Tejada7.68.0-0.2
Kelly Johnson0.10.2-0.1
------ ------ ------
TOTAL19.020.3-0.9
  
Left Field
Player eWins eLosses eWOPA
Mike Cuddyer8.98.8-0.3
Michael Conforto5.44.30.9
Kirk Nieuwenhuis1.81.50.3
Yoenis Cespedes1.81.30.5
John Mayberry Jr.1.41.6-0.2
Darrell Ceciliani1.41.00.3
Eric Campbell0.40.5-0.1
Kelly Johnson0.10.1-0.0
Eric Young Jr.0.00.1-0.1
------ ------ ------
TOTAL21.219.01.3
  
Center Field
Player eWins eLosses eWOPA
Juan Lagares12.113.0-1.5
Yoenis Cespedes5.64.01.4
Kirk Nieuwenhuis1.11.2-0.2
Darrell Ceciliani0.50.6-0.1
Curtis Granderson0.40.4-0.0
------ ------ ------
TOTAL19.619.2-0.4
  
Right Field
Player eWins eLosses eWOPA
Curtis Granderson19.817.71.0
John Mayberry Jr.1.00.90.0
Mike Cuddyer0.70.50.1
Kirk Nieuwenhuis0.30.30.0
Kelly Johnson0.20.3-0.1
Juan Lagares0.20.10.1
Eric Young Jr.0.00.0-0.0
------ ------ ------
TOTAL22.219.81.1
  
Designated Hitter
Player eWins eLosses eWOPA
Mike Cuddyer0.30.3-0.0
Daniel Murphy0.20.10.1
Curtis Granderson0.10.1-0.0
Daniel Muno0.00.1-0.1
Juan Uribe0.00.1-0.1
Yoenis Cespedes0.00.1-0.0
------ ------ ------
TOTAL0.70.8-0.1
  
Pinch Hitter
Player eWins eLosses eWOPA
John Mayberry Jr.0.51.0-0.4
Mike Cuddyer0.50.50.0
Curtis Granderson0.60.30.4
Eric Campbell0.50.40.1
Kirk Nieuwenhuis0.30.4-0.1
Johnny Monell0.10.6-0.4
Kelly Johnson0.40.20.2
Darrell Ceciliani0.20.3-0.0
Juan Uribe0.30.20.1
Daniel Murphy0.10.3-0.2
Daniel Muno0.10.10.0
Travis d'Arnaud0.00.2-0.2
Juan Lagares0.10.10.1
Lucas Duda0.10.1-0.0
Ruben Tejada0.10.1-0.0
Wilmer Flores0.10.10.0
Michael Conforto0.10.00.0
Dilson Herrera0.00.1-0.0
Yoenis Cespedes0.00.1-0.1
Anthony Recker0.00.0-0.0
Eric Young Jr.0.00.1-0.0
Kevin Plawecki0.00.00.0
Jacob deGrom0.00.00.0
------ ------ ------
TOTAL4.25.2-0.4
  
Pinch Runner
Player eWins eLosses eWOPA
Eric Young Jr.0.10.10.0
Eric Campbell0.10.00.0
Juan Lagares0.00.0-0.0
Anthony Recker0.00.0-0.0
Kirk Nieuwenhuis0.00.0-0.0
------ ------ ------
TOTAL0.20.20.0
  
Pitcher Offense
Player eWins eLosses eWOPA
Jacob deGrom1.01.80.1
Matt Harvey0.61.7-0.1
Bartolo Colon0.61.5-0.1
Jonathon Niese0.81.10.3
Noah Syndergaard0.60.90.2
Steven Matz0.40.40.2
Dillon Gee0.10.3-0.1
Sean Gilmartin0.10.10.0
Logan Verrett0.00.1-0.0
Carlos Torres0.00.00.0
Rafael Montero0.00.0-0.0
Alexander Torres0.00.0-0.0
Erik Goeddel0.00.0-0.0
Tyler Clippard0.00.0-0.0
------ ------ ------
TOTAL4.17.90.4
  
Starting Pitching
Player eWins eLosses eWOPA
Bartolo Colon12.012.30.0
Jacob deGrom11.98.83.3
Jonathon Niese9.610.3-0.5
Matt Harvey10.08.41.8
Noah Syndergaard9.78.81.1
Dillon Gee2.22.4-0.2
Steven Matz2.22.00.2
Logan Verrett1.51.40.1
Sean Gilmartin0.40.40.0
Rafael Montero0.20.20.1
------ ------ ------
TOTAL59.755.05.9
  
Relief Pitching
Player eWins eLosses eWOPA
Jeurys Familia6.34.71.3
Hansel Robles2.82.7-0.0
Carlos Torres2.72.7-0.0
Tyler Clippard1.82.1-0.3
Bobby Parnell1.61.9-0.4
Sean Gilmartin1.91.30.5
Alexander Torres1.11.4-0.3
Addison Reed1.10.60.5
Erik Goeddel1.00.70.2
Logan Verrett0.70.50.2
Rafael Montero0.50.40.0
Buddy Carlyle0.40.40.0
Jerry Blevins0.60.20.4
Jenrry Mejia0.40.30.1
Eric O'Flaherty0.20.3-0.1
Jack Leathersich0.20.2-0.0
Tim Stauffer0.10.2-0.1
Dario Alvarez0.10.2-0.1
Jonathon Niese0.10.1-0.0
Bartolo Colon0.10.00.1
Dillon Gee0.00.0-0.0
Akeel Morris0.00.0-0.0
------ ------ ------
TOTAL23.621.01.8


Team eWins over Positional Average by Position
PC1B2B3BSSLFCFRFOth
2015 New York Mets8.10.6-0.20.8-0.8-0.91.3-0.41.1-0.6


pWin, pLoss, pWOPA by Position
Catcher
Player pWins pLosses pWOPA
Travis d'Arnaud8.25.13.3
Kevin Plawecki5.35.9-0.4
Anthony Recker1.11.6-0.5
Johnny Monell0.70.9-0.2
------ ------ ------
TOTAL15.313.52.3
  
First Base
Player pWins pLosses pWOPA
Lucas Duda15.912.81.9
Daniel Murphy1.91.30.5
Mike Cuddyer1.31.6-0.4
Eric Campbell0.20.4-0.2
Kelly Johnson0.20.2-0.0
Anthony Recker0.00.1-0.1
------ ------ ------
TOTAL19.516.31.6
  
Second Base
Player pWins pLosses pWOPA
Daniel Murphy9.88.11.7
Wilmer Flores4.33.60.8
Dilson Herrera2.83.3-0.5
Kelly Johnson2.92.00.9
Ruben Tejada1.01.1-0.0
Juan Uribe0.60.9-0.3
Daniel Muno0.10.2-0.1
------ ------ ------
TOTAL21.519.12.4
  
Third Base
Player pWins pLosses pWOPA
Daniel Murphy4.65.1-0.8
David Wright4.64.7-0.3
Eric Campbell3.95.2-1.4
Juan Uribe2.92.20.6
Ruben Tejada2.51.80.7
Daniel Muno0.10.2-0.2
Kelly Johnson0.00.2-0.2
------ ------ ------
TOTAL18.519.3-1.5
  
Shortstop
Player pWins pLosses pWOPA
Wilmer Flores11.412.2-0.5
Ruben Tejada7.58.1-0.5
Kelly Johnson0.10.1-0.0
------ ------ ------
TOTAL18.920.5-1.1
  
Left Field
Player pWins pLosses pWOPA
Mike Cuddyer8.69.0-0.8
Michael Conforto5.73.91.6
Kirk Nieuwenhuis2.01.20.7
Yoenis Cespedes1.61.50.1
John Mayberry Jr.1.31.7-0.5
Darrell Ceciliani1.31.10.1
Eric Campbell0.40.4-0.0
Kelly Johnson0.00.1-0.1
Eric Young Jr.0.00.1-0.0
------ ------ ------
TOTAL21.119.11.1
  
Center Field
Player pWins pLosses pWOPA
Juan Lagares12.612.5-0.5
Yoenis Cespedes6.13.52.4
Kirk Nieuwenhuis1.01.3-0.4
Darrell Ceciliani0.40.6-0.2
Curtis Granderson0.40.40.0
------ ------ ------
TOTAL20.418.31.3
  
Right Field
Player pWins pLosses pWOPA
Curtis Granderson20.217.21.9
John Mayberry Jr.1.00.90.1
Mike Cuddyer0.60.60.0
Kirk Nieuwenhuis0.30.3-0.0
Kelly Johnson0.30.3-0.0
Juan Lagares0.10.1-0.0
Eric Young Jr.0.10.00.0
------ ------ ------
TOTAL22.619.31.9
  
Designated Hitter
Player pWins pLosses pWOPA
Mike Cuddyer0.30.3-0.0
Daniel Murphy0.20.00.2
Curtis Granderson0.10.1-0.0
Daniel Muno0.00.1-0.1
Juan Uribe0.00.1-0.1
Yoenis Cespedes0.00.1-0.1
------ ------ ------
TOTAL0.70.8-0.2
  
Pinch Hitter
Player pWins pLosses pWOPA
John Mayberry Jr.0.41.1-0.5
Mike Cuddyer0.50.50.1
Curtis Granderson0.60.20.4
Eric Campbell0.70.20.5
Kirk Nieuwenhuis0.40.30.1
Johnny Monell0.20.5-0.3
Kelly Johnson0.50.10.3
Darrell Ceciliani0.30.3-0.0
Juan Uribe0.30.20.1
Daniel Murphy0.20.3-0.1
Daniel Muno0.20.10.1
Travis d'Arnaud0.00.2-0.2
Juan Lagares0.00.2-0.1
Lucas Duda0.00.2-0.1
Ruben Tejada0.00.1-0.1
Wilmer Flores0.00.1-0.1
Michael Conforto0.00.1-0.1
Dilson Herrera0.00.1-0.0
Yoenis Cespedes0.00.1-0.1
Anthony Recker0.00.0-0.0
Eric Young Jr.0.00.1-0.0
Kevin Plawecki0.00.0-0.0
Jacob deGrom0.00.00.0
------ ------ ------
TOTAL4.45.0-0.1
  
Pinch Runner
Player pWins pLosses pWOPA
Eric Young Jr.0.20.10.1
Eric Campbell0.00.1-0.0
Juan Lagares0.00.0-0.0
Anthony Recker0.00.00.0
Kirk Nieuwenhuis0.00.0-0.0
------ ------ ------
TOTAL0.20.20.1
  
Pitcher Offense
Player pWins pLosses pWOPA
Jacob deGrom1.11.60.3
Matt Harvey0.91.40.3
Bartolo Colon0.71.40.1
Jonathon Niese0.91.00.4
Noah Syndergaard0.60.80.2
Steven Matz0.60.20.5
Dillon Gee0.10.3-0.1
Sean Gilmartin0.10.10.0
Logan Verrett0.00.1-0.1
Carlos Torres0.00.00.0
Rafael Montero0.00.0-0.0
Alexander Torres0.00.0-0.0
Erik Goeddel0.00.0-0.0
Tyler Clippard0.00.0-0.0
------ ------ ------
TOTAL5.07.01.7
  
Starting Pitching
Player pWins pLosses pWOPA
Bartolo Colon11.812.5-0.5
Jacob deGrom12.28.54.0
Jonathon Niese9.510.3-0.6
Matt Harvey10.28.32.1
Noah Syndergaard9.88.71.2
Dillon Gee2.12.5-0.4
Steven Matz2.61.61.1
Logan Verrett1.21.6-0.3
Sean Gilmartin0.30.5-0.3
Rafael Montero0.20.20.0
------ ------ ------
TOTAL59.954.86.3
  
Relief Pitching
Player pWins pLosses pWOPA
Jeurys Familia7.04.02.8
Hansel Robles2.82.8-0.0
Carlos Torres2.52.9-0.5
Tyler Clippard2.01.90.0
Bobby Parnell1.32.2-0.9
Sean Gilmartin1.61.6-0.1
Alexander Torres1.41.10.3
Addison Reed0.81.0-0.2
Erik Goeddel0.90.80.1
Logan Verrett0.50.7-0.3
Rafael Montero0.40.5-0.1
Buddy Carlyle0.50.30.2
Jerry Blevins0.60.10.5
Jenrry Mejia0.50.10.4
Eric O'Flaherty0.20.3-0.0
Jack Leathersich0.20.2-0.0
Tim Stauffer0.20.20.0
Dario Alvarez0.20.10.0
Jonathon Niese0.10.10.0
Bartolo Colon0.10.00.1
Dillon Gee0.00.0-0.0
Akeel Morris0.00.0-0.0
------ ------ ------
TOTAL23.820.82.2


Team pWins over Positional Average by Position
PC1B2B3BSSLFCFRFOth
2015 New York Mets10.22.31.62.4-1.5-1.11.11.31.9-0.2


*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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