2005 Boston Red Sox
Baseball Player Won-Loss Records
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2005 Boston Red Sox*
Traditional Statistics and Splits (Retrosheet)
Boston Red Sox - Franchise Page

(Regular Season)

(2005 American 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
20.211.63.8
5.7
18.813.12.4
4.2
23.518.82.0
3.9
23.119.21.5
3.5
20.418.41.6
3.4
18.820.0-0.1
1.8
13.810.42.1
3.3
13.310.91.7
2.8
14.813.30.5
1.8
14.213.8-0.1
1.2
15.315.00.1
1.5
14.915.4-0.2
1.2
19.219.6-0.3
1.5
19.219.5-0.2
1.6
5.84.40.6
1.0
5.15.0-0.1
0.4
4.02.80.7
1.0
3.33.50.0
0.4
12.211.8-0.2
1.0
12.012.1-0.4
0.7
5.95.30.4
0.9
5.75.50.2
0.7
4.53.40.5
0.8
4.13.80.1
0.4
8.48.7-0.1
0.7
8.58.50.1
0.9
3.53.50.1
0.4
3.33.7-0.2
0.2
2.22.00.1
0.3
2.22.00.1
0.3
2.62.6-0.0
0.2
2.42.7-0.2
0.1
1.01.0-0.0
0.1
0.91.1-0.1
0.0
0.10.00.0
0.0
0.10.00.0
0.0
0.00.0-0.0
-0.0
0.00.0-0.0
-0.0
0.00.0-0.0
-0.0
0.00.0-0.0
-0.0
0.00.1-0.0
-0.0
0.00.1-0.0
-0.0
0.20.3-0.1
-0.0
0.20.4-0.1
-0.1
0.10.3-0.1
-0.0
0.20.2-0.0
-0.0
0.30.5-0.1
-0.1
0.30.5-0.1
-0.0
0.00.2-0.1
-0.1
0.00.2-0.1
-0.1
1.12.2-0.5
-0.4
1.12.1-0.5
-0.3
------ ------ ------ ------ ------ ------ ------ ------
SUB-TOTAL
179.1156.210.9
27.0
172.0163.33.8
19.8


Basic Player Won-Lost Records
Pitchers
(Sorted by pWORL)
Player pWins pLosses pWOPA pWORL eWins eLosses eWOPA eWORL
11.19.31.0
2.4
10.89.60.6
2.0
10.69.00.9
2.2
10.19.50.5
1.8
12.411.50.6
2.2
12.611.40.7
2.3
13.613.20.4
2.2
13.713.00.5
2.3
5.23.30.9
1.7
4.83.80.5
1.3
5.65.6-0.0
0.8
5.85.50.2
1.0
2.51.50.5
0.8
2.02.0-0.0
0.3
5.45.30.1
0.8
5.45.30.1
0.9
1.51.00.2
0.5
1.41.10.1
0.3
3.33.8-0.3
0.4
3.43.8-0.3
0.4
1.31.10.1
0.3
1.21.2-0.0
0.2
1.71.60.0
0.3
1.61.7-0.0
0.2
0.80.8-0.0
0.1
0.80.8-0.0
0.1
0.40.4-0.0
0.0
0.50.30.1
0.2
0.10.10.0
0.0
0.10.10.0
0.0
0.00.00.0
0.0
0.00.00.0
0.0
0.00.0-0.0
0.0
0.00.0-0.0
-0.0
0.00.0-0.0
-0.0
0.00.0-0.0
-0.0
0.10.1-0.0
-0.0
0.10.2-0.0
-0.0
0.00.0-0.0
-0.0
0.00.0-0.0
-0.0
0.10.2-0.0
-0.0
0.10.1-0.0
0.0
0.10.3-0.1
-0.1
0.20.2-0.0
-0.0
0.71.2-0.2
-0.1
0.91.0-0.1
0.1
0.20.5-0.1
-0.1
0.30.4-0.1
-0.0
0.00.5-0.3
-0.2
0.10.4-0.1
-0.1
1.12.4-0.7
-0.3
1.61.9-0.2
0.1
------ ------ ------ ------ ------ ------ ------ ------
SUB-TOTAL
77.972.82.8
14.1
77.373.42.3
13.6


pWins pLosses pWOPA pWORL eWins eLosses eWOPA eWORL
TEAM TOTALS
257.0229.013.8
41.1
249.3236.76.1
33.4


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.
16.411.1
0.597
0.50.8
0.380
0.00.0
0.000
0.20.3
0.414
14.810.6
0.584
0.70.7
0.511
0.00.0
0.000
5.76.7
0.461
11.512.2
0.484
1.30.6
0.683
0.00.0
0.000
5.36.3
0.454
10.88.9
0.550
0.70.7
0.519
0.00.0
0.000
1.31.2
0.522
8.77.8
0.528
0.61.0
0.369
0.00.0
0.000
4.54.6
0.494
10.710.5
0.504
0.60.9
0.379
0.00.0
0.000
4.04.2
0.487
12.911.6
0.526
1.40.8
0.650
0.00.0
0.000
4.56.6
0.403
3.53.4
0.507
0.10.3
0.318
0.00.0
0.000
0.80.7
0.545
2.52.5
0.499
0.10.2
0.362
0.00.0
0.000
0.30.3
0.489
8.98.7
0.505
0.70.6
0.505
0.00.0
0.000
2.52.7
0.479
3.83.8
0.503
0.50.2
0.656
0.00.0
0.000
1.71.8
0.492
2.72.7
0.501
0.30.1
0.710
0.00.0
0.000
1.51.4
0.512
5.25.4
0.490
0.50.4
0.534
0.00.0
0.000
3.33.1
0.513
2.12.3
0.477
0.10.1
0.450
0.00.0
0.000
1.21.4
0.465
1.61.4
0.548
0.10.1
0.470
0.00.0
0.000
0.50.5
0.503
1.81.9
0.491
0.10.1
0.628
0.00.0
0.000
0.91.1
0.436
0.70.7
0.491
0.00.1
0.219
0.00.0
0.000
0.10.2
0.435
0.10.0
0.749
0.10.0
0.783
0.00.0
0.000
0.10.0
0.761
0.00.0
0.000
0.00.0
0.000
0.00.0
0.000
0.00.0
0.805
0.00.0
0.000
0.00.0
0.000
0.00.0
0.000
0.0-0.0
1.025
0.10.1
0.461
0.00.0
0.517
0.00.0
0.000
0.00.1
0.397
0.20.2
0.425
0.00.0
0.539
0.00.0
0.000
0.00.2
0.141
0.30.4
0.432
0.00.0
0.552
0.00.0
0.000
0.10.2
0.386
0.20.3
0.421
0.10.0
0.552
0.00.0
0.000
0.10.2
0.337
0.00.3
0.084
0.00.0
0.105
0.00.0
0.000
0.00.0
0.169
0.71.3
0.359
0.10.1
0.324
0.00.0
0.000
0.40.8
0.342
------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------
SUB-TOTAL
120.4108.3
0.527
8.58.0
0.515
0.00.0
0.000
39.044.6
0.467


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.
0.00.1
0.325
0.00.0
0.117
10.19.2
0.523
0.20.2
0.535
0.20.2
0.542
0.00.0
0.149
9.58.9
0.517
0.10.3
0.283
0.00.0
0.000
0.00.0
0.000
10.89.8
0.525
0.20.3
0.363
0.10.2
0.411
0.00.0
0.335
11.811.3
0.510
0.20.2
0.489
0.00.0
0.000
0.00.0
0.000
4.43.3
0.575
0.10.3
0.223
0.00.0
0.000
0.00.0
0.000
5.24.9
0.512
0.10.1
0.530
0.00.0
0.000
0.00.0
0.000
1.91.9
0.495
0.00.0
0.714
0.10.0
0.747
0.00.0
0.156
4.94.8
0.507
0.10.2
0.388
0.00.0
0.000
0.00.0
0.000
1.91.5
0.549
0.10.1
0.590
0.00.0
0.000
0.00.0
0.000
2.52.9
0.468
0.00.0
0.495
0.00.0
0.000
0.00.0
0.000
1.11.2
0.485
0.00.0
0.748
0.00.0
0.000
0.00.0
0.000
2.93.0
0.494
0.00.0
0.630
0.00.0
0.000
0.00.0
0.000
1.41.5
0.481
0.00.0
0.861
0.00.0
0.000
0.00.0
0.000
0.80.5
0.638
0.00.0
0.501
0.00.0
0.000
0.00.0
0.000
0.60.5
0.527
0.00.0
0.353
0.00.0
0.000
0.00.0
0.000
0.00.0
0.821
0.00.0
0.000
0.00.0
0.000
0.00.0
0.000
0.10.1
0.267
0.00.0
0.000
0.00.0
0.000
0.00.0
0.000
0.10.3
0.311
0.00.0
0.904
0.00.0
0.000
0.00.0
0.000
0.40.8
0.317
0.00.0
0.615
0.00.0
0.000
0.00.0
0.000
0.00.0
0.398
0.00.0
0.000
0.00.0
0.000
0.00.0
0.000
0.30.4
0.475
0.00.0
0.958
0.00.0
0.000
0.00.0
0.000
0.20.2
0.404
0.00.0
0.000
0.00.0
0.000
0.00.0
0.000
2.42.6
0.483
0.00.1
0.336
0.00.0
0.000
0.00.0
0.000
0.40.6
0.402
0.00.0
0.758
0.00.0
0.000
0.00.0
0.000
0.10.4
0.252
0.00.0
0.875
0.00.0
0.000
0.00.0
0.000
2.02.4
0.447
0.10.0
0.831
------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------
SUB-TOTAL
0.40.5
0.479
0.00.1
0.159
75.873.1
0.509
1.31.8
0.435


Batting Baserunning Pitching Fielding
eWins eLoss Win Pct. eWins eLoss Win Pct. eWins eLoss Win Pct. eWins eLoss Win Pct.
TEAM TOTALS
120.9108.8
0.526
8.58.1
0.514
75.873.1
0.509
40.446.3
0.465


eWin, eLoss, eWOPA by Position
Catcher
Player eWins eLosses eWOPA
Jason Varitek12.710.61.5
Doug Mirabelli2.52.7-0.0
Kelly Shoppach0.00.3-0.1
Shawn Wooten0.00.0-0.0
------ ------ ------
TOTAL15.313.61.4
  
First Base
Player eWins eLosses eWOPA
Kevin Millar9.29.2-0.3
John Olerud4.34.1-0.0
David Ortiz1.41.10.1
Roberto Petagine0.70.8-0.0
Kevin Youkilis0.40.30.0
David McCarty0.20.00.1
------ ------ ------
TOTAL16.215.5-0.2
  
Second Base
Player eWins eLosses eWOPA
Mark Bellhorn8.88.80.1
Tony Graffanino6.05.80.2
Alex Cora2.62.7-0.0
Bill R. Mueller0.60.6-0.0
Ramon Vazquez0.10.4-0.1
Kevin Youkilis0.10.1-0.0
Alejandro Machado0.00.1-0.0
------ ------ ------
TOTAL18.118.30.1
  
Third Base
Player eWins eLosses eWOPA
Bill R. Mueller14.715.0-0.2
Kevin Youkilis1.71.40.2
Ramon Vazquez0.50.9-0.2
Alex Cora0.30.5-0.1
------ ------ ------
TOTAL17.217.8-0.3
  
Shortstop
Player eWins eLosses eWOPA
Edgar Renteria17.919.1-0.1
Ramon Vazquez0.50.8-0.1
Alex Cora0.50.6-0.0
Mark Bellhorn0.20.10.0
Alejandro Machado0.10.00.0
Hanley Ramirez0.00.0-0.0
------ ------ ------
TOTAL19.320.8-0.2
  
Left Field
Player eWins eLosses eWOPA
Manny Ramirez21.117.71.3
Kevin Millar1.41.7-0.2
Jay Payton0.60.50.0
Gabe Kapler0.10.1-0.0
Adam Stern0.00.1-0.0
Roberto Petagine0.00.1-0.0
Alejandro Machado0.00.0-0.0
Adam Hyzdu0.00.0-0.0
David McCarty0.00.00.0
------ ------ ------
TOTAL23.320.31.0
  
Center Field
Player eWins eLosses eWOPA
Johnny Damon18.718.9-0.2
Gabe Kapler1.10.90.1
Jay Payton1.00.80.1
Adam Hyzdu0.30.20.0
Adam Stern0.30.20.1
Alejandro Machado0.00.0-0.0
------ ------ ------
TOTAL21.421.10.1
  
Right Field
Player eWins eLosses eWOPA
Trot Nixon13.713.2-0.0
Jay Payton2.52.6-0.1
Gabe Kapler1.62.0-0.2
Kevin Millar1.31.10.0
Jose Cruz Jr.0.20.4-0.1
Adam Hyzdu0.10.2-0.1
Adam Stern0.10.2-0.1
Alejandro Machado0.00.0-0.0
------ ------ ------
TOTAL19.519.8-0.5
  
Designated Hitter
Player eWins eLosses eWOPA
David Ortiz15.711.02.0
Doug Mirabelli0.30.20.0
Manny Ramirez0.10.2-0.0
Johnny Damon0.00.1-0.0
------ ------ ------
TOTAL16.211.52.0
  
Pinch Hitter
Player eWins eLosses eWOPA
Jay Payton0.20.3-0.0
John Olerud0.20.3-0.0
Trot Nixon0.10.3-0.1
Doug Mirabelli0.20.10.0
Jason Varitek0.10.10.0
Kevin Millar0.10.10.0
Kevin Youkilis0.00.1-0.1
Bill R. Mueller0.10.1-0.0
Ramon Vazquez0.10.1-0.0
Roberto Petagine0.00.1-0.0
Gabe Kapler0.10.1-0.0
Edgar Renteria0.10.00.0
Manny Ramirez0.10.00.0
Alex Cora0.00.00.0
David Ortiz0.00.1-0.0
Kelly Shoppach0.00.1-0.0
David McCarty0.10.00.0
Johnny Damon0.00.00.0
Mark Bellhorn0.00.0-0.0
Adam Hyzdu0.00.0-0.0
Adam Stern0.00.0-0.0
Hanley Ramirez0.00.0-0.0
------ ------ ------
TOTAL1.52.1-0.2
  
Pinch Runner
Player eWins eLosses eWOPA
Adam Stern0.00.0-0.0
Jay Payton0.00.00.0
Kevin Youkilis0.00.0-0.0
Johnny Damon0.00.00.0
Ramon Vazquez0.00.0-0.0
Alejandro Machado0.00.0-0.0
David McCarty0.00.0-0.0
Adam Hyzdu0.00.0-0.0
Kelly Shoppach0.00.0-0.0
Trot Nixon0.00.0-0.0
Gabe Kapler0.00.0-0.0
Alex Cora0.00.0-0.0
------ ------ ------
TOTAL0.10.1-0.0
  
Pitcher Offense
Player eWins eLosses eWOPA
David Wells0.20.20.1
Tim Wakefield0.10.20.0
Wade Miller0.10.00.0
Matt Clement0.00.1-0.0
Bronson Arroyo0.00.0-0.0
------ ------ ------
TOTAL0.50.60.1
  
Starting Pitching
Player eWins eLosses eWOPA
Tim Wakefield12.011.50.3
Bronson Arroyo10.810.00.5
Matt Clement10.39.40.5
David Wells9.69.20.3
Wade Miller5.05.00.1
Curt Schilling3.83.60.1
Jonathan Papelbon0.91.0-0.0
Jeremi Gonzalez0.80.9-0.0
Lenny DiNardo0.30.20.0
John Halama0.20.3-0.0
------ ------ ------
TOTAL53.751.11.7
  
Relief Pitching
Player eWins eLosses eWOPA
Mike Timlin4.53.50.4
Keith Foulke2.62.9-0.2
John Halama2.22.4-0.1
Alan Embree2.02.5-0.2
Jeremi Gonzalez2.22.2-0.0
Mike Myers2.01.60.2
Curt Schilling1.51.40.0
Matt Mantei1.41.5-0.1
Chad Bradford1.21.2-0.0
Jonathan Papelbon1.00.90.0
Mike Remlinger0.40.8-0.2
Manny Delcarmen0.60.50.0
Blaine Neal0.40.6-0.1
Chad Harville0.40.4-0.0
Lenny DiNardo0.50.20.1
Cla Meredith0.20.4-0.1
Craig Hansen0.20.3-0.0
Abe Alvarez0.10.3-0.1
Bronson Arroyo0.20.10.0
Scott Cassidy0.10.1-0.0
W. Mike Stanton0.00.00.0
Matt Perisho0.00.0-0.0
------ ------ ------
TOTAL23.423.7-0.5


Team eWins over Positional Average by Position
PC1B2B3BSSLFCFRFOth
2005 Boston Red Sox1.31.4-0.20.1-0.3-0.21.00.1-0.51.8


pWin, pLoss, pWOPA by Position
Catcher
Player fWins fLosses eWOPA
Jason Varitek13.610.32.1
Doug Mirabelli3.32.50.5
Kelly Shoppach0.00.2-0.1
Shawn Wooten0.00.0-0.0
------ ------ ------
TOTAL16.913.02.5
  
First Base
Player fWins fLosses eWOPA
Kevin Millar9.89.00.1
John Olerud5.63.80.8
David Ortiz1.11.3-0.1
Roberto Petagine0.90.8-0.0
Kevin Youkilis0.50.5-0.0
David McCarty0.10.00.0
------ ------ ------
TOTAL18.015.40.7
  
Second Base
Player fWins fLosses eWOPA
Mark Bellhorn8.38.5-0.0
Tony Graffanino5.95.30.4
Alex Cora2.72.40.2
Bill R. Mueller0.50.5-0.0
Ramon Vazquez0.00.3-0.1
Kevin Youkilis0.10.10.0
Alejandro Machado0.00.0-0.0
------ ------ ------
TOTAL17.517.20.4
  
Third Base
Player fWins fLosses eWOPA
Bill R. Mueller14.714.30.2
Kevin Youkilis1.61.40.1
Ramon Vazquez0.51.0-0.3
Alex Cora0.30.5-0.1
------ ------ ------
TOTAL17.117.2-0.1
  
Shortstop
Player fWins fLosses eWOPA
Edgar Renteria20.418.41.5
Ramon Vazquez0.50.8-0.1
Alex Cora0.50.6-0.0
Mark Bellhorn0.10.1-0.0
Alejandro Machado0.00.00.0
Hanley Ramirez0.00.00.0
------ ------ ------
TOTAL21.419.91.4
  
Left Field
Player fWins fLosses eWOPA
Manny Ramirez23.318.42.0
Kevin Millar1.01.7-0.4
Jay Payton0.30.4-0.1
Gabe Kapler0.00.1-0.0
Roberto Petagine0.00.00.0
Adam Stern0.00.0-0.0
Adam Hyzdu0.00.0-0.0
Alejandro Machado0.00.0-0.0
David McCarty0.00.0-0.0
------ ------ ------
TOTAL24.620.61.6
  
Center Field
Player fWins fLosses eWOPA
Johnny Damon19.119.3-0.2
Jay Payton1.20.60.3
Gabe Kapler0.70.9-0.1
Adam Stern0.10.2-0.1
Adam Hyzdu0.10.1-0.0
Alejandro Machado0.00.0-0.0
------ ------ ------
TOTAL21.221.1-0.0
  
Right Field
Player fWins fLosses eWOPA
Trot Nixon14.513.00.5
Jay Payton2.72.20.2
Gabe Kapler1.81.60.1
Kevin Millar1.51.10.1
Jose Cruz Jr.0.20.3-0.1
Adam Stern0.10.2-0.0
Adam Hyzdu0.10.2-0.0
Alejandro Machado0.00.0-0.0
------ ------ ------
TOTAL20.918.60.7
  
Designated Hitter
Player fWins fLosses eWOPA
David Ortiz19.010.34.0
Doug Mirabelli0.70.20.2
Manny Ramirez0.10.2-0.1
Johnny Damon0.00.2-0.1
------ ------ ------
TOTAL19.810.94.0
  
Pinch Hitter
Player fWins fLosses eWOPA
John Olerud0.10.6-0.2
Trot Nixon0.20.3-0.0
Jay Payton0.20.20.0
Jason Varitek0.20.20.0
Bill R. Mueller0.10.1-0.0
Manny Ramirez0.20.10.0
Roberto Petagine0.10.2-0.0
Doug Mirabelli0.00.1-0.0
Edgar Renteria0.10.00.0
Ramon Vazquez0.10.00.0
Kevin Millar0.00.1-0.0
Johnny Damon0.10.00.0
Kevin Youkilis0.00.1-0.0
David Ortiz0.00.00.0
Gabe Kapler0.00.0-0.0
Mark Bellhorn0.00.0-0.0
Alex Cora0.00.0-0.0
Adam Hyzdu0.00.0-0.0
Kelly Shoppach0.00.0-0.0
David McCarty0.00.00.0
Adam Stern0.00.0-0.0
Hanley Ramirez0.00.0-0.0
------ ------ ------
TOTAL1.52.1-0.2
  
Pinch Runner
Player fWins fLosses eWOPA
Adam Stern0.10.1-0.0
Jay Payton0.00.00.0
Alejandro Machado0.00.00.0
Kevin Youkilis0.00.0-0.0
Johnny Damon0.00.00.0
David McCarty0.00.0-0.0
Trot Nixon0.00.0-0.0
Kelly Shoppach0.00.0-0.0
Ramon Vazquez0.00.0-0.0
Adam Hyzdu0.00.00.0
Alex Cora0.00.0-0.0
Gabe Kapler0.00.0-0.0
------ ------ ------
TOTAL0.10.10.0
  
Pitcher Offense
Player fWins fLosses eWOPA
Tim Wakefield0.30.40.1
David Wells0.20.20.1
Wade Miller0.00.1-0.0
Matt Clement0.00.1-0.0
Bronson Arroyo0.00.1-0.0
------ ------ ------
TOTAL0.50.90.1
  
Starting Pitching
Player fWins fLosses eWOPA
Tim Wakefield13.312.80.3
Bronson Arroyo12.411.20.7
Matt Clement11.19.21.0
David Wells10.48.80.9
Wade Miller5.35.20.1
Curt Schilling3.54.4-0.4
Jonathan Papelbon1.10.60.3
Jeremi Gonzalez0.80.9-0.0
Lenny DiNardo0.30.3-0.0
John Halama0.20.20.0
------ ------ ------
TOTAL58.453.52.8
  
Relief Pitching
Player fWins fLosses eWOPA
Mike Timlin5.23.30.9
Keith Foulke3.33.8-0.3
Alan Embree1.12.4-0.7
Curt Schilling2.11.30.4
Mike Myers1.51.00.2
Chad Bradford1.31.10.1
Jonathan Papelbon1.30.80.2
Jeremi Gonzalez0.90.80.1
Matt Mantei0.80.8-0.0
John Halama0.51.0-0.3
Blaine Neal0.20.5-0.1
Cla Meredith0.00.5-0.3
Craig Hansen0.10.3-0.1
Bronson Arroyo0.10.2-0.1
Chad Harville0.10.2-0.0
Lenny DiNardo0.10.10.0
Mike Remlinger0.10.1-0.0
Manny Delcarmen0.10.10.0
Matt Perisho0.00.0-0.0
Abe Alvarez0.00.0-0.0
W. Mike Stanton0.00.00.0
Scott Cassidy0.00.0-0.0
------ ------ ------
TOTAL19.018.5-0.0


Team pWins over Positional Average by Position
PC1B2B3BSSLFCFRFOth
2005 Boston Red Sox2.92.50.70.4-0.11.41.6-0.00.73.9


*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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