Working it through

July 21, 2020
  

 

OK, it will take us nine formulas to formalize all of that stuff that I just explained (yesterday.)  All nine formulas are pretty simple.  We will get to Runs Saved by Fielding Range in Formula 38. 

 

Formula 30:  Inf-Ast-Sum

 

            We need the SUM of the infield assists in order evaluate the assists number for each fielder.  What we will treat as the sum of the assists is:

            Inf-Ast-Sum = 1BQA + Ast(2b) + Ast(3b) + Ast(ss)

 

That is, the team’s First Base Quasi-Assists, plus the assists by all of the team’s second basemen, third basemen, and shortstops.

 

Formula 31:  1B-En-Range  (First Base Enhanced Range)

The first basemen’s enhanced range is twice the First Base Quasi-Assists, minus .20 * the Infield Assists Sum:

1B-En-Range = 2 * 1BQA – (.20 * Inf-Ast-Sum)

 

This refers to the team totals, not to any individual first baseman. 

 

 

Formula 32:  2B-En-Range  (Second Base Enhanced Range)

The second basemen’s Enhanced Range is figured in the same way, but with the standard for second basemen being 30%, rather than 20%: 

 

2B-En-Range = 2 * Ast(2b) – (.30 * Inf-Ast-Sum)

 

Formula 33:  3B-En-Range  (Third Base Enhanced Range)

The third basemen’s Enhanced Range is figured in the same way.

 

3B-En-Range = 2 * Ast(3b) – (.20 * Inf-Ast-Sum)

 

Formula 34:  SS-En-Range  (Shortstop Enhanced Range)

The shortstops’ Enhanced Range is figured in the same way.

 

SS-En-Range = 2 * Ast(ss) – (.30 * Inf-Ast-Sum)

 

The sum of the enhanced range for the four infielders is the same as the sum before they were enhanced, which was defined as Inf-Ast-Sum. 

 

 

Formula 35:  OF-En-Range  (Outfield Enhanced Range)

The outfield’s enhanced range is 1.14 times the putouts made by all of the team’s outfielders:

 

OF-En-Range = 1.14 * PO(of)

 

 

Formula 36:  Tm-Adj-Rg-Outs   (Team Adjusted Range Outs)

The team’s "Adjusted Outs" are the sum of the Infield Assists (Inf-Ast-Sum), the pitchers’ Assists, and the Outfield Enhanced Range:

Tm-Adj-Rg-Outs = Inf-Ast-Sum + Ast(p) + OF-En-Range

 

 

Formula 37:   Tm-H-Av  (Team Hits Prevented, or Avoided)

We assume that a completely incompetent defense would allow base hits on 36% (.360) of balls in play.  Any play made beyond that is a Hit Prevented (or Hit Avoided):

 

Tm-H-Av = (BFP – SO – BB – HBP – HR) * .360 – (H – HR)

 

 

Formula 38:  Tm-RS-Range  (Runs Saved by Range)

Each Hit Avoided on a ball in play is assumed to have a Run Prevention value of .373 Runs:

 

Tm-RS-Range = Tm-H-Av * .373

 

As mentioned before, 90% of this value will be assigned to fielders based on fielding stats.   The other 10% will be assigned directly to pitchers based on their Batting Average on Balls in Play (BABIP). 

 

Turning our attention now to the task of giving you the data for the 15 test teams that we are following, we will start with the range numbers for the four infield positions on each team

YEAR

City

Team

1B QA

2BA

3BA

SSA

Inf Range

OFPO

1960

Pittsburgh

Pirates

268

462

334

510

1574

973

1964

New York

Mets

331

507

342

510

1690

998

1968

Detroit

Tigers

357

415

313

462

1547

999

1972

Texas

Rangers

322

412

293

453

1480

974

1976

Cincinnati

Reds

331

425

315

560

1631

1133

1980

Seattle

Mariners

350

545

363

557

1815

1097

1984

Detroit

Tigers

365

486

264

476

1591

1165

1988

Baltimore

Orioles

341

489

327

483

1640

1205

1992

Toronto

Blue Jays

367

443

296

449

1555

1153

1996

Detroit

Tigers

329

480

347

483

1639

1126

2000

New York

Yankees

312

440

283

385

1420

1136

2004

Arizona

Diamondbacks

341

432

358

491

1622

936

2008

Philadelphia

Phillies

347

476

316

485

1624

966

2012

Houston

Astros

334

489

309

491

1623

944

2016

Chicago

Cubs

359

401

313

449

1522

911

 

And from that, we can move to Enhanced Range.  Enhanced Range gives us the Range Plays Made by each team (Team Adjusted Range Outs):

YEAR

City

Team

P Ast

1B En R

2B En R

3B En R

SS En R

OF En R

Team Range Plays

1960

Pittsburgh

Pirates

235

221

452

353

548

1362

3171

1964

New York

Mets

256

324

507

346

513

1397

3343

1968

Detroit

Tigers

192

405

366

317

460

1399

3138

1972

Texas

Rangers

221

348

380

290

462

1364

3065

1976

Cincinnati

Reds

169

336

361

304

631

1586

3386

1980

Seattle

Mariners

233

337

546

363

570

1536

3584

1984

Detroit

Tigers

170

412

495

210

475

1631

3392

1988

Baltimore

Orioles

157

355

486

326

474

1687

3484

1992

Toronto

Blue Jays

152

423

420

281

432

1614

3321

1996

Detroit

Tigers

196

330

468

366

474

1576

3411

2000

New York

Yankees

200

340

454

282

344

1590

3210

2004

Arizona

Diamondbacks

201

358

377

392

495

1310

3134

2008

Philadelphia

Phillies

196

369

465

307

483

1352

3172

2012

Houston

Astros

193

344

491

293

495

1322

3138

2016

Chicago

Cubs

200

414

345

322

441

1275

2997

 

As you seem, team Adjusted Range Outs is not highly variable from team to team, since each team makes 27 outs per game.   Range Outs go down when strikeouts go up; otherwise they don’t change very much.   What really matters is not the plays they DO make, but the plays that they DON’T make, the balls that fall in for hits.   We chart those by looking at the elements of Tm-H-Av (Team Hits Avoided), which was formula 37:

 

Tm-H-Av = (BFP – SO – BB – HBP – HR) * .360 – (H – HR)

 

YEAR

City

Team

H

HR

BFP

SO

BB

HBP

Hits Avoided

1960

Pittsburgh

Pirates

1363

105

5805

811

386

11

359

1964

New York

Mets

1511

130

6190

717

466

50

357

1968

Detroit

Tigers

1180

129

6043

1115

486

32

490

1972

Texas

Rangers

1258

92

5910

868

613

48

378

1976

Cincinnati

Reds

1436

100

6191

790

491

21

388

1980

Seattle

Mariners

1565

159

6330

703

540

27

358

1984

Detroit

Tigers

1358

130

6127

914

489

30

415

1988

Baltimore

Orioles

1506

153

6141

709

523

43

344

1992

Toronto

Blue Jays

1346

124

6108

954

541

45

378

1996

Detroit

Tigers

1699

241

6713

957

784

80

216

2000

New York

Yankees

1458

177

6256

1040

577

52

307

2004

Arizona

Diamondbacks

1480

197

6418

1153

668

75

274

2008

Philadelphia

Phillies

1444

160

6229

1081

533

57

299

2012

Houston

Astros

1493

173

6238

1170

540

48

231

2016

Chicago

Cubs

1125

163

5933

1441

495

63

396

 

 

            And, since each Hit Saved prevents .373 runs (Formula 38), we can now figure the Runs Saved by Range for each of these 15 teams:

 

YEAR

City

Team

Hits Avoided

Runs Saved By Range

1960

Pittsburgh

Pirates

359

134

1964

New York

Mets

357

133

1968

Detroit

Tigers

490

183

1972

Texas

Rangers

378

141

1976

Cincinnati

Reds

388

145

1980

Seattle

Mariners

358

134

1984

Detroit

Tigers

415

155

1988

Baltimore

Orioles

344

128

1992

Toronto

Blue Jays

378

141

1996

Detroit

Tigers

216

81

2000

New York

Yankees

307

114

2004

Arizona

Diamondbacks

274

102

2008

Philadelphia

Phillies

299

112

2012

Houston

Astros

231

86

2016

Chicago

Cubs

396

148

 

The number of Runs Prevented by Defensive Range is quite large compared to most other categories.  It is larger than any other category except strikeouts. 

 

 

Formula 39:  RS-Pit-Ast-P9  (Runs Saved-Pitcher’s Assists—9th pitcher’s value)

 

We are now ready to assign Runs Saved value to pitchers based on their defensive assists.  For any other position, we would have to make another adjustment, the adjustment of crediting each fielder with superior range (or limiting value based on limited range.  But since pitcher’s assist totals are not enhanced by range considerations, we can skip that step in their case.  In this formula, Ast(p) refers to the fielding assists by the individual pitcher, rather than by all of the team’s pitchers:

RS-Pit-Ast-P9 = Ast(p) / Tm-Adj-R-Outs * .9

 

Team Adjusted R Outs is the result of Formula 36. 

 

The only pitcher credited with saving 2.00 runs or more by his assists was Denny McLain in 1968, who was just over 2.00.   These are the updated standings for pitchers saving the most runs:

 

Year

Player

P1

P2

P3

P4

P5

P6

P7

P8

P9

Total

1968

Denny McLain

45

27

21

7

1

1

6

3

2

113

1960

Bob Friend

29

27

23

7

0

0

4

2

2

94

2004

Randy Johnson

47

20

18

4

2

0

0

1

1

93

1960

Vern Law

19

26

18

7

1

1

7

2

2

84

1984

Dan Petry

23

16

17

5

4

1

2

3

1

73

2008

Cole Hamels

32

18

12

5

1

1

2

1

1

72

1968

Earl Wilson

27

15

16

4

2

1

4

1

2

71

1968

Mickey Lolich

32

13

14

5

3

0

1

0

1

69

2016

Jon Lester

32

13

12

3

2

0

3

2

1

68

1992

Jack Morris

21

13

20

4

2

0

4

2

1

67

1984

Jack Morris

24

13

19

4

1

1

2

2

1

67

1976

Gary Nolan

18

25

13

4

1

0

2

1

1

66

1964

Jack Fisher

19

18

16

5

1

1

4

1

1

66

2016

Kyle Hendricks

27

13

14

3

2

1

2

3

1

66

2000

Andy Pettitte

20

11

17

5

2

1

7

1

1

65

 

We’ve got one category of Run Prevention left on the pitcher’s account.   When we get to the end of the pitchers, I’ll do a couple of things like outlining the records of the pitchers with the most runs saved, and looking at Runs Saved/Innings Pitched. 

Your reader comments on my last article in this series were good and helpful, and thank you all for your interest.  

 
 

COMMENTS (4 Comments, most recent shown first)

thoughtclaw
Indeed, McLain has had his problems and doesn't get around all that well anymore, but he is very much alive.
5:32 PM Jul 24th
 
vandorn
Be prepared for a visit from Denny and his associates for suggesting that he is dead.
11:28 AM Jul 24th
 
TheRicemanCometh
Good to see the late Denny McLain get some props. Guy was a helluva pitcher before everything fell apart on him, much of it not all self-inflicted.

I would hazard a guess that the greatest Runs Saved season by a pitcher will be Walter Johnson 1912. More IP and more Ks than his great 1913 season, and 150 more IP than Pedro in 2000.
12:17 AM Jul 22nd
 
evanecurb
The conclusion that team range results in mor runs avoided than anything other than strikeouts is logical. Nothing to add; I just think it’s always a good check when designing anything to make sure the results can be explained in a way that makes sense.
12:09 PM Jul 21st
 
 
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