Relative Batting Average: Landmarks of Sabermetrics, Part III

This 1976 article by David Shoebotham, whom I did not know then–but was amazed to bump into at this week’s SABR Analytics Conference in Mesa, Arizona–was a revelation to me. No one, to my knowledge, had ever taken this approach to cross-era comparison of baseball statistics. It may seem like common sense now, as many folks have compared single-season dominance in one year to that of another, across all batting, pitching, and fielding stats, but then that is the halmark of a truly great idea: It seems simple after someone else has come up with it. Think of David’s contribution as Baseball’s Theory of Relativity.

Chatting with David at the conference, I speculated that no one had ever attached his approach to batter walks, and that Roy Thomas, Phillies outfielder in the first decade of the last century, might well seem the Babe Ruth of his category once his totals were weighed against league average. David thought this was a possible outcome, but he would go back home and check it out. I suspect we have not heard the last from him or his revolutionary innovation.

Enough prologue. Here is where normalization to league average began. Read on, from SABR’s Baseball Research Journal of 1976.

Relative Batting Averages Print E-mail

By David Shoebotham

Who has the highest single season batting average in major league history? The modem fan would probably say that Rogers Hornsby’s .424 in 1924 is the highest. Old timers would point out that Hugh Duffy hit .438 in 1894. But the correct answer is Ty Cobb with .385 in 1910.

How can .385 be higher than .438? The answer is when it is compared to the average of the entire league for the year in question. This is the only way performances from different seasons and leagues can be compared. Thus a hitter’s relative batting average, which is the true measure of his ability to hit safely, is computed as follows:

As a further refinement (since it is unfair to compare a player to himself) the player’s own hits and ABs can be subtracted from the league totals, thus giving an average relative to the remainder of the league.

As an example, compare Bill Terry’s National League leading .401 in 1930 to Carl Yastrzemski’s American League leading .301 in 1968. At first glance the 100-point difference would make it appear that Yastrzemski’s average should not be mentioned in the same breath as Terry’s. But look at the calculations of relative averages:

The relative averages are almost identical, meaning that had the two performances occurred in the same season, the batting averages would have been within a few points of each other. The big difference, of course, is that in 1930 the National League had a combined average of .303, the highest of any major league in this century (and two points higher than Yastrzemski’s 1968 average), whereas in 1968 the American League had a combined average of .230, the lowest for any major league ever. (A relative average of 1.30 indicates that a player’s batting average was 30% higher than the remainder of his league.)

The following two graphs show league averages since 1900. It can be seen that the 1920s and ’30s, following the introduction of the lively ball, were fat times for hitters. Both leagues reached their recent lows in 1968, the “Year of the Pitcher.” Note that for the last three seasons the American League’s Designated Hitter rule has artificially raised the league’s average and thus lowered individual relative averages.

The table below shows the highest single season relative averages since 1900. The list is clearly dominated by Ty Cobb, who has 10 of the top 19 averages, including the highest of all: 1.594 in 1910. Interestingly, the second highest relative average is Nap Lajoie’s 1.592, also in 1910. That epic batting race, enlivened by the offer of a new car to the winner, resulted in a major scandal, the awarding of two automobiles, and incidentally the two highest relative averages of all time. Rogers Hornsby’s .424 produced the highest National League mark of 1.51, but this ranks only 14th on the list. (Duffy’s .438 reduces to a relative average of about 1.42.) Note that five of this century’s .400 averages do not qualify for this list.
Single Season Relative Average Greater Than 1.45

Lea.

Rel.

Rank

Player Year League AB

Hits

Avg.

Avg.

Avg.

1

Ty Cobb 1910 Amer.

509

196

0.385

0.242

1.594

2

Nap Lajoie 1910 Amer.

591

227

0.384

0.241

1.592

3

Nap Lajoie 1904 Amer.

554

211

0.381

0.243

1.570

4

Tris Speaker 1916 Amer.

546

211

0.386

0.247

1.570

5

Ty Cobb 1912 Amer.

553

227

0.410

0.263

1.560

6

Ty Cobb 1909 Amer.

573

216

0.377

0.242

1.560

7

Ty Cobb 1917 Amer.

588

225

0.383

0.246

1.560

8

Ty Cobb 1911 Amer.

591

248

0.420

0.271

1.550

9

Nap Lajoie 1901 Amer.

543

229

0.422

0.275

1.530

10

Ty Cobb 1913 Amer.

428

167

0.390

0.254

1.530

11

Ted Williams 1941 Amer.

456

185

0.406

0.265

1.530

12

Ted Williams 1957 Amer.

420

163

0.388

0.254

1.530

13

Ty Cobb 1918 Amer.

421

161

0.382

0.252

1.520

14

Rogers Hornsby 1924 Nat.

536

227

0.424

0.281

1.510

15

Joe Jackson 1911 Amer.

571

233

0.408

0.271

1.510

16

Joe Jackson 1912 Amer.

572

226

0.395

0.263

1.500

17

Ty Cobb 1916 Amer.

542

201

0.371

0.247

1.500

18

Ty Cobb 1915 Amer.

563

208

0.369

0.247

1.500

19

Ty Cobb 1914 Amer.

345

127

0.368

0.246

1.490

20

Honus Wagner 1908 Nat.

568

201

0.354

0.237

1.490

21

Cy Seymour 1905 Nat.

581

219

0.377

0.253

1.490

22

George Sisler 1922 Amer.

586

246

0.420

0.283

1.490

23

Joe Jackson 1913 Amer.

528

197

0.373

0.254

1.470

24

Tris Speaker 1912 Amer.

580

222

0.383

0.263

1.450

25

Stan Musial 1948 Nat.

611

230

0.376

0.259

1.450

26

George Stone 1906 Amer.

581

208

0.358

0.247

1.450

27

Joe Torre 1971 Nat.

634

230

0.363

0.251

1.450

28

George Sisler 1920 Amer.

631

257

0.407

0.282

1.450

29

Honus Wagner 1907 Nat.

515

180

0.350

0.242

1.450

With the modem preoccupation with home runs, high relative averages (not to mention high absolute averages) have become rare. The only relative average over 1.45 in recent years is Joe Torre’s 1971 mark.

For a look at other recent high marks, the next table shows the highest relative averages of the last 20 years. It is interesting to note that Rod Carew’s 1974 and 1975 marks would probably be well over 1.45 except for the Designated Hitter rule in the American League.

The final table shows the all-time leaders in career relative average. Not surprisingly, Ty Cobb tops the list with an average that is just a few hits short of 1.40. Close behind Cobb is Shoeless Joe Jackson, though the closeness of their averages is deceptive. Jackson’s career was abruptly terminated while he was still a star performer, and therefore he did not have the usual declining years at the end of his career that would have lowered his average. During the years that Jackson averaged 1.38, Cobb was averaging a fantastic 1.50.

It can be seen that despite the preponderance of pre-920 hitters in the single season leaders, the career list contains players from all periods since 1900, including four who are active. Rod Carew, who in 1975 moved past Ted Williams into third place, seems destined to be one of the all-time leaders in relative average. Whether all four active players will finish their careers among the leaders is an open question, but at least they show that hitting for high average is not altogether a lost art.

Highest Single Season Relative Averages During Last 20 Years (1956-1975)

Lea.

Rel.

Rank

Player Year League AB

Hits

Avg.

Avg.

Avg.

1

Ted Williams 1957 Amer.

420

163

.3S8

0.254

1.530

2

Joe Torre 1971 Nat.

634

230

0.363

0.251

1.450

3

Roberto Clemente 1967 Nat.

585

209

0.357

0.248

1.440

4

Mickey Mantle 1957 Amer.

474

173

0.365

0.254

1.440

5

Rico Carty 1970 Nat.

478

175

0.366

0.257

1.420

6

Norm Cash 1961 Amer.

535

193

0.361

0.255

1.420

7

Rod Carew 1974 Amer.

599

218

0.364

.257*

1.410

8

Harvey Kuenn 1959 Amer.

561

198

0.353

0.252

1.400

9

Rod Carew 1975 Amer.

535

192

0.359

.257*

1.400

10

Pete Rose 1969 Nat.

627

218

0.348

0.249

1.390

11

Carl Yastrzemski 1967 Amer.

579

189

0.326

0.235

1.390

12

Ralph Garr 1974 Nat.

606

214

0.353

0.254

1.390

13

Pete Rose 1968 Nat.

626

210

0.335

0.242

1.390

14

Roberto Clemente 1969 Nat.

507

175

0.345

0.250

1.380

15

Bill Madlock 1975 Nat.

514

182

0.354

0.256

1.380

16

Hank Aaron 1959 Nat.

629

223

0.355

0.259

1.370

17

Matty Alou 1968 Nat.

558

185

0.332

0.242

1.370

18

Tony Oliva 1971 Amer.

487

164

0.337

0.246

1.370

19

Roberto Clemente 1970 Nat.

412

145

0.352

0.257

1.370

20

Ralph Garr 1971 Nat.

639

219

0.343

0.251

1.370

*Designated Hitter rule in effect
Lifetime Relative Average Greater Than 1.20 (Over 4000 ABs)

Lea.

Rel.

Rank

Player Years AB

Hits

Avg.

Avg.

Avg.

1

Ty Cobb 1905-1928

11429

4191

0.367

0.263

1.390

2

Joe Jackson 1908-1920

4981

1774

0.356

0.258

1.380

3

Rod Carew 1967-1975*

4450

1458

0.328

0.247

1.330

4

Ted Williams 1939-1960

7706

2654

0.344

0.261

1.320

5

Nap Lajoie 1896-1916

9589

3251

0.339

0.258

1.310

6

Rogers Hornsby 1915-1937

8173

2930

0.358

0.275

1.300

7

Tris Speaker 1907-1928

10208

3515

0.344

0.266

1.290

8

Stan Musial 1941-1963

10972

3630

0.331

0.258

1.280

9

Honus Wagner 1897-1917

10427

3430

0.329

0.258

1.280

10

Eddie Collins 1906-1930

9949

3311

0.333

0.265

1.260

11

Rob.Clemente 1955-1972

9454

3000

0.317

0.254

1.250

12

Tony Oliva 1962-1975*

6178

1891

0.306

0.246

1.240

13

Pete Rose 1963-1975* 8221

2547

0.310

0.251

1.230

14

Harry Heilmann 1914-1932 7787

2660

0.342

0.278

1.230

15

Sam Crawford 1899-1917 9579

2964

0.309

0.252

1.230

16

George Sisler 1915-1930 8267

2812

0.340

0.278

1.230

17

Babe Ruth 1914-1935 8399

2873

0.342

0.279

1.230

18

Matty Alou 1960- 1974 5789

1777

0.307

0.252

1.220

19

Joe Medwick 1932-1948 7635

2471

0.324

0.266

1.210

20

Paul Waner 1926- 1944 9459

3152

0.333

0.275

1.210

21

Lou Gehrig 1923-1939 8001

2721

0.340

0.281

1.210

22

Bill Terry 1923-1936 6428

2193

0.341

0.282

1.210

23

Joe DiMaggio 1936-1951 6821

2214

0.325

0.269

1.210

24

Hank Aaron 1954-1975* 12093

3709

0.307

0.254

1.210

25

Jackie Robinson 1947- 1956 4877

1518

0.311

0.260

1.200

*Active player

3 Comments

Fascinating!

Well, well, well finally a stat that has some serious validity not the usual sabr gimmick stat. Now the thing that sticks out is the prevalance of one Roberto Clemente here! Now subtract the fact that his own pirate squad never had a hall of fame pitcher and imagine how much stronger his numbers would have been if he got to hit against his own pitching. Truth be told not that much better ’cause he was the most NATURALLY GIFTED hitter and his hitting against HOF pitchers is the highest of ALL TIME …only about 8 or 9 points less than his total avg. If we combine this with his BEST DEFENSIVE outfielder ever(stats or anecdotal) we have an individual that would be the best EVER…in other words what we saw first hand was indeed what Bowie Kuhn and others have said he gave the term COMPLETE a new meaning. Sabermetrics will say otherwise but we know that they have their own agenda and the truthful evaluation of Clemente doesn’t promote that agenda. In short Sabr has helped identify what’s wrong with baseball’s format, but they need to STAY OUT of the who’s BETTER who’s BEST pecking order business. Mel Ott better than Clemente? Really?

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