The Process at First Base

July 28, 2020
  

First Basemen

Category

P

C

1B

2B

3B

SS

LF

CF

RF

Strikeouts

97%

3%

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Control

97%

3%

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HR Avoidance

100%

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Balks

100%

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Wild Pitches

70%

30%

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Passed Balls

35%

65%

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Stolen Bases All

40%

60%

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Outfield Assists

---

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30%

30%

40%

Pitcher Pickoffs

100%

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Catcher Pickoffs

---

100%

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Runners Caught Stealing

20%

80%

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Double Plays

16%

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10%

42%

12%

40%

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Error Avoidance

10%

10%

10%

15%

17%

22%

5%

6%

5%

Range

16%

---

10%

13%

10%

14%

11%

15%

11%

 

For first basemen, as you see above, we have three inputs into their defensive rating—from Double Plays, Range, and Fielding Percentage.  For first basemen, we are going to do something that we didn’t do or didn’t have to do at any other position.   First, we’re going to figure team totals at the position for Double Play Runs Saved and Range Runs Saved, add those two together, and then allocate them to individual fielders by one formula.  We do this, frankly, because defensive stats at catcher are so inarticulate, so. . . .difficult.   We’re doing the best we can with the data we have, but first base defensive stats do a poorer job of describing what the fielder has done than at any other position, so you wind with a radically different process. 

 

 

Formula 54:  1B-Tm-RS-DP  (First Basemen’s Runs Saved on Double Plays, team)

            This one is dead simple.  First basemen are assigned credit for 10% of the Double Play Runs Saved by their team.  It is done this way because:

1)     First basemen have to be given some credit for their role in this, and

2)     It is virtually impossible to determine, based on traditional fielding statistics, what the individual contribution of each first baseman is to double plays. 

 

Team Runs Saved on Double Plays were calculated much earlier in the series, as a result of Formula 16.  It was tagged as DP-RS-TM (Double Play Runs Saved, Team.)   I alerted the readers at that time to make a mental note of the number, because we would use it again.  The credit for first basemen is simply 10% of that number:

1B-Tm-RS-DP  = (DP – RS -TM) * .10

These were the Runs Saved by DP for these 15 teams, presented earlier:

 

YEAR

City

Team

Normalized DP

Runs Saved by DP

1960

Pittsburgh

Pirates

164.5

84.91

1964

New York

Mets

141.2

72.85

1968

Detroit

Tigers

162.5

83.87

1972

Texas

Rangers

131.5

67.84

1976

Cincinnati

Reds

171.3

88.40

1980

Seattle

Mariners

154.7

79.84

1984

Detroit

Tigers

174.7

90.17

1988

Baltimore

Orioles

153.4

79.14

1992

Toronto

Blue Jays

123.8

63.88

1996

Detroit

Tigers

104.2

53.77

2000

New York

Yankees

142.9

73.76

2004

Arizona

Diamondbacks

133.4

68.86

2008

Philadelphia

Phillies

147.7

76.22

2012

Houston

Astros

120.8

62.32

2016

Chicago

Cubs

143.6

74.11

 

Formula 55:  RS-1B-Range-Tm  (Runs Saved by First Basemen, Range, Team)

The manner in which all players including first basemen are credited with Runs Saved by range has already been explained in detail in formulas 26 to 31 and Formulas 36 to 38.   Formulas 26 to 29 created a stat called 1BQA, First Base Quasi-Assists.   Formulas 30 and 31 Translated 1BQA into 1B-En-Range, First Base Enhanced Range.   Formula 36 created a stat called Tm-Adj-Rg-Outs (Team Adjusted Range Outs.)  Formulas 37 and 38 created a value called Tm-RS-Range (Team Runs Saved by Range).  

First Base Runs Saved by Range is simply First Base Enhanced Range, divided by Team Adjusted Range Outs, times Team Runs Saved by Range, times .9. 

 

            RS-1B-Rg-Tm = 1B-En-Range / Tm-Adj-Rg-Outs  * TM-RS-Range * .90

That is, Formula 54 is Formula 31, divided by Formula 36, times Formula 38, times .90.  The "times .90" is in there because 10% of the Runs Saved by Range were diverted to give pitchers credit for a better-than-team-average batting average on balls in play (BABIP).     This chart summarizes the relevant data for the 15 teams in our study.  All of this data has been presented before; this chart merely brings the relevant material together into one:

YEAR

City

Team

P Ast

1B En R

2B En R

3B En R

SS En R

OF En Range

Team Range Plays

1960

Pittsburgh

Pirates

235

221

452

353

548

1362

2918

1964

New York

Mets

256

324

507

346

513

1397

3084

1968

Detroit

Tigers

192

405

366

317

460

1399

2878

1972

Texas

Rangers

221

348

380

290

462

1364

2812

1976

Cincinnati

Reds

169

336

361

304

631

1586

3092

1980

Seattle

Mariners

233

337

546

363

570

1536

3298

1984

Detroit

Tigers

170

412

495

210

475

1631

3089

1988

Baltimore

Orioles

157

355

486

326

474

1687

3171

1992

Toronto

Blue Jays

152

423

420

281

432

1614

3021

1996

Detroit

Tigers

196

330

468

366

474

1576

3118

2000

New York

Yankees

200

340

454

282

344

1590

2915

2004

Arizona

Diamondbacks

201

358

377

392

495

1310

2890

2008

Philadelphia

Phillies

196

369

465

307

483

1352

2921

2012

Houston

Astros

193

344

491

293

495

1322

2892

2016

Chicago

Cubs

200

414

345

322

441

1275

2761

 

And this chart gives the First Base Runs Saved by Range for each of the 15 teams:

YEAR

City

Team

Team Range Plays

Runs Saved By Range

1B Runs Saved by Range--Team

1960

Pittsburgh

Pirates

2917.9

134

10.15

1964

New York

Mets

3083.9

133

13.98

1968

Detroit

Tigers

2878.3

183

25.73

1976

Cincinnati

Reds

3091.8

141

15.73

1980

Seattle

Mariners

3298.3

145

13.66

1984

Detroit

Tigers

3089.4

134

17.79

1988

Baltimore

Orioles

3171

155

14.35

1992

Toronto

Blue Jays

3021.3

128

19.73

1996

Detroit

Tigers

3118.4

141

8.54

1996

Detroit

Tigers

3118.4

81

8.54

2000

New York

Yankees

2915

114

13.34

2004

Arizona

Diamondbacks

2890.3

102

12.66

2008

Philadelphia

Phillies

2921.1

112

14.10

2012

Houston

Astros

2892.5

86

10.23

2016

Chicago

Cubs

2760.6

148

22.13

 

 

 

 

Formula 56:  1B-Ind-Share (Individual First Baseman’s Share of Team Credits)

In Formula 57, we will add together the results of Formulas 54 and 55, First Base Runs Saved by Double Plays, Team and First Base Runs Saved by Range, Team.  Then we will split them between the Individual First Basemen on the team.   This formula, Formula 56, will be used to split them.  Formula 56 is:

1B-Ind-Share = (PO+2*Ast +DP – 7*Err) Ind-1B / (PO+2*Ast+DP – 7*Err)  Team-1B

            In other words, we add together a first baseman’s putouts, 2 times his assists, and his double plays, and subtract 7 times his errors.  We do that for all of the first basemen on the team, and each first baseman’s share of the team’s credits for double plays and for range depends on this formula.

            I know that people will argue with me about the decision to include Errors in the formula which is intended to represent Range and Double Play contribution, and.  . .go ahead and argue.   My goal is not to observe all of the proper and approved protocols of statistical attribution; my goal is to get the answers right.  I think that including errors in that formula gets us closer to the right evaluations of individual fielders than not including them.  So I’m doing it; when you do ratings, you can do them your way. 

 

 

Formula 57:  1B-Ind-1  (First Value for Individual First Basemen)

So the formula is:

1B-Ind-1 = [(1B-Tm-RS-DP) + (RS-1B-Range-Tm)] * (1B-Ind-Share)

 

We’ll outline the data for individual first basemen within our study after we explain how Fielding Percentages are dealt with. 

 

Formula 58:  Errors Avoided, First Base

The process for giving credit for errors avoided is the same at every position.  The process for pitchers was explained in this series under the headings Formula 20 through Formula 25.   The process for catchers was repeated briefly in Formula 53.   It is the same process here; you:

1)     Figure how many errors the player would have committed, if his error rate had been three times the league error rate at the position,

2)     Subtract the number of errors actually committed by the player,

3)     The result is errors avoided,

4)     Do the same for every player on the team,

5)     Find the team total,

6)     Find the player’s share of the team total,

7)     Apply that to the team’s total of Runs Saved by Error Avoidance, which was Formula 21 in this series.  

 
 

COMMENTS (6 Comments, most recent shown first)

DavidHNix
Ooops -- sorry, I misread the tables. Please delete my comment.
10:06 AM Jul 29th
 
DavidHNix
1960 Pirates? So Dick Stuart was the best defensive first baseman of our lifetimes?
10:04 AM Jul 29th
 
wovenstrap
The chart showing "1B Runs Saved by Range--Team" is missing the 1972 Texas Rangers and has the 1996 Detroit Tigers twice (with different data each time).
7:40 AM Jul 29th
 
voxpoptart
I continue to be fascinated by, and impressed with, your decision to work all the stages out of this new system in public, before you're sure if they will work.

The credit you award for Double Plays adds up to 120%. Is that my error of understanding, or a modest gaffe on your part, or something that's on purpose somehow?
3:26 PM Jul 28th
 
CharlesSaeger
@bjames: You should be reducing the value of the FiBupe (or whatever that acronym is for unassisted first baseman putouts; "FiBupe" sounds like a girl who gets a song named after her in the "Music Man") for this. It's clear from the data that first basemen do not start as many plays as third basemen since there are more right-handed batters than left, and don't get to many ground balls with a runner on first since the second baseman is in better position. Essentially, you're counting the 3/p and 3/fl plays in your first baseman numbers, while you (correctly) get rid of those for the other infield positions.

@evanecurb: I'm looking at the Philadelphia Inquirer for 9 June 1901 in another tab, and the box score for the Tigers/Athletics game from the day before lists "Missed grounder and fumble: Cross. Muffed fly ball: Barrett. Dropped thrown balls: Shaw and Buelow." They tried, but as Bill has pointed out many times, this stuff is a lot of work.
1:06 PM Jul 28th
 
evanecurb
A bold effort at a difficult problem. I wish the statisticians of old had recorded throwing errors vs. other misplays. That would have helped to show which first basemen were best at reducing throwing errors by infielders. We all know it's an important part of the position but we don't know whether a good first baseman saves one throwing error per week, one per month, or somewhere in between. I wonder if there's a way to get at this from a different angle. Bill's method is the first attempt I've seen to assign credit for this aspect. It's likely the best we have so far.
11:08 AM Jul 28th
 
 
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