March 16th, 2012

On Base Average for Players: Landmarks of Sabermetrics, Part II

This is the second of three pioneering statistical articles published in the years before Bill James coined the term sabermetrics, which has endured as an honor to the Society for American Baseball Research–and has brought me and 300 others to the first SABR Baseball Analytics Conferences in Mesa, Arizona. In 1984, Pete Palmer and I collaborated on The Hidden Game of Baseball, in which the now commonplace OPS (On Base Plus Slugging) made its debut. One component of that stat, Slugging Percentage, was developed in the 1860s but was not accepted by the National League as an official statistic until 1923 and the American until 1946. It  is hard today to imagine that when we wrote Hidden Game, On Base Average was not yet an official stat. Here is Pete’s landmark article on the OBA, from SABR’s Baseball Research Journal in 1973. Some of the tabular material (league leaders in lifetime OBA by position, through 1972) is not offered here as it has become largely outdated.
On Base Average for Players Print E-mail

By Pete Palmer

There are two main objectives for the hitter. The first is to not make an out and the second is to hit for distance. Long-ball hitting is normally measured by slugging average. Not making an out can be expressed in terms of on base average (OBA), where:

OBA    =  Hits    + Walks + Hit-by-Pitch

At Bats + Walks + Hit-by-Pitch

For example, if we were figuring out Frank Robinson’s career on base average, it would be compiled like this:  2641 hits + 1213 walks + 178 hit-by-pitch (4032), divided by 8810 at bats + 1213 walks + 178 HBP (10201). His OBA is .395, which happens to be the tops among active players, but does not compare very well with players of the past. Sacrifice hits are ignored in this calculation.

On base average can be quite different from batting average. Take for example Joe DiMaggio and Roy Cullenbine, once outfield teammates for the Yankees.  DiMag had a lifetime batting average of .325 and Cullenbine .276. But Roy was walked much more frequently than Joe and made fewer outs; he had an OBA of .404, compared to .398 for the Yankee Clipper.

In calculating OBA, the Macmillan Baseball Encyclopedia was used for hits, at bats, and bases on balls. Hit by pitch data are from official averages back to 1920 in the AL and 1917 in the NL. Figures back to 1909 have been compiled by Alex Haas from newspaper box scores.   Some data before then comes from Haas, John Tattersall, and Bob Davids.  Additional information is available in some of the old newspapers, but has not yet been compiled.  Players with incomplete totals are credited with HEP at the known rate from available data for those unknown appearances. When no data are to be obtained, league averages are used.  Before 1887, a batter was not awarded first base when hit by a pitch.

Who is the all-time leader in on base average [remember, this is as of 1973, when Barry Bonds was nine years old)? It is Ted Williams with a spectacular .483 mark. Not surprisingly, Babe Ruth is second with .474.  It is no secret that Williams and Ruth were both exceptionally good hitters as well as being among the most frequent walk receivers. It was not unusual for them to get on base 300 times a season. Ranking third is the all-time list is John McGraw, who was elected to the Hall of Fame as a manager, but was also a fine hitter. In addition, he was adept at getting on base from walks and HBP. He holds the all-time NL record for OBA both lifetime and season. Billy Hamilton, the stolen base king, and Lou Gehrig are next in line, followed by such big names as Rogers Hornsby, Ty Cobb, Jimmie Foxx and Tris Speaker. Rounding out the top ten is Ferris Fain, former first baseman of the A’s, who quietly attained a very high OBA to go with his two batting titles.

Some players who many fans might not think to be among the leaders in OBA are Max Bishop, second baseman of the A’s last super teams of 1929-31; Clarence “Cupid” Childs, Cleveland second sacker in the 1890s; Roy Thomas, Phils’ center fielder at the turn of the century; and Joe Cunningham, who played with the Cardinals and White Sox just a few years ago. On the other hand, some of the famous hitters of baseball are not included in the accompanying list of players with lifetime on base averages of .400 or better. Missing are such stars as Willie Keeler, Bill Terry, George Sisler, Nap Lajoie, Al Simmons, Hans Wagner, Cap Anson, Joe DiMaggio, and Roberto Clemente.

Since most of the players in the .400 list are either outfielders or first basemen, an additional table is shown that provides data on the top ten players at each position [tables npt offered here]. Many unheralded players are high in the OBA figures, such as Wally Schang, who played for many AL clubs in the teens and twenties, who is second among catchers, and Elmer Valo, another Connie Mack product, who ranks sixth in right field.

There are no active players with OBA’s of .400 or better, and only a few among the leaders by position. The level of OBA in the majors is presently quite low. This could be attributed to many factors, such as improved pitching (bigger and stronger pitchers throwing from the unchanged distance of 60 feet 6 inches, more use of relief pitchers, and the widespread use of the slider as an extra pitch), larger ball parks, and increased emphasis on hitting home runs. Those players with high OBA’s that are now active are shown below:

Frank Robinson 0.395 Harmon Killebrew 0.385
Carl Yastrzemski 0.389 Al Kaline 0.383
Willie Mays 0.388 Joe Morgan 0.383
Dick Allen 0.388 Henry Aaron 0.381
Willie McCovey 0.387 Norm Cash 0.379

It is interesting to note that if hit by pitch were not included in figuring OBA, Frank Robinson would rank only fourth.

In regard to season averages, Dick Allen led the majors in OBA in 1972 with a mark of .422. Joe Morgan was the NL leader with .419. The only others with .400 or better on base average were Carlos may at .408, and Billy Williams at .403.  These season averages are far, far below the top season averages of the past. The list of top season marks, which includes all instances of OBA of .500 or better, is dominated by another Williams named Ted, the all-time season leader, and by Ruth.

Ted Williams, 1941 .551 Babe Ruth, 1926 .516
John McGraw, 1899 .546 Mickey Mantle, 1954 .515
Babe Ruth, 1923 .545 Babe Ruth, 1924 .513
Babe Ruth, 1920 .530 Babe Ruth, 1921 .512
Ted Williams, 1957 .528 Rog. Hornsby, 1924 .508
Billy Hamilton, 1894 .521 Joe Kelley, 1894 .502
Ted Williams, 1946 .516 Hugh Duffy, 1894 .501

Ted Williams led the league in OBA every year he qualified except for his rookie season, and he had a higher OBA than the leader in three of his four seasons shortened by injury.  Those leading the league most often in OBA are:

AL                                                                   NL

Ted Williams               12                                 Rogers Hornsby          8

Babe Ruth                   10                                Stan Musial                 5

Ty Cobb                      6                                  Billy Hamilton            4

Lou Gehrig                  5                                  Richie Ashburn           4

Carl Yastrzemski         5                                  Mel Ott                       4

Honus Wagner            4

It is important to remember that OBA is only one component of hitting, and that slugging is equally valuable. Of course, the best long-ball hitters usually rank high in both departments because they are generally walked more frequently. One thing the OBA does is give percentage recognition to the player’s ability to get on via the walk and the HBP as well as the hit. He has saved his team an out and he is in a good position to score a run.


1000 games minimum – through 1972

Player Years




Ted Williams 1939-1960




39 0.483
Babe Ruth 1914-1935




42 0.474
John McGraw 1891-1906




105+ 0.462
Billy Hamilton 1888-1901




50* 0.452
Lou Gehrig 1923-1939




45 0.447
Rogers Hornsby 1915-1937




48 0.434
Ty Cobb 1905-1928




90 0.433
Jimmie Foxx 1926-1945




13 0.430
Tris Speaker 1907-1928




101 0.427
Ferris Fain 1947-1955




18 0.425
Eddie Collins 1906-1930




76 0.424
Joe Jackson 1908-1920




59 0.423
Max Bishop 1924-1935




31 0.423
Mickey Mantle 1951-1968




13 0.423
Mickey Cochrane 1925-1937




29 0.419
Stan Musial 1941-1963




53 0.418
DanBrouthers 1879-1904




32* 0.418
Jesse Burkett 1890-1905




63* 0.414
Clarence Childs 1890-1901




44* 0.414
Mel Ott 1926-1947




64 0.414
Rank Greenberg 1930-1947




16 0.412
Roy Thomas 1899-1911




42* 0.411
Charlie Keller 1939-1952




10 0.410
Harry Heilmann 1914-1932




40 0.410
Jackie Robinson 1947-1956




72 0.410
Eddie Stanky 1943-1953




34 0.410
Ed Delahanty 1888-1903




55* 0.409
Roy Cullenbine 1938-1947




11 0.408
Joe Cunningham 1954-1966




49 0.406
Riggs Stephenson 1921-1934




40 0.406
Arky Vaughan 1932-1948




46 0.406
Paul Waner 1926-1945




38 0.404
Chas. Gehringer 1924-1942




51 0.404
Joe Kelley 1891-1908




99+ 0.403
Lu Blue 1921-1933




43 0.402
Pete Browning 1882-1894




20* . 402
Denny Lyons 1885-1897




32* 0.401

+Hit by pitch estimated from partial career totals

*Hit by pitch estimated from league average

Average Batting Skill Through Major League History: Landmarks of Sabermetrics, Part I

Today still finds me in Arizona but at another conference, this one the premier edition of the SABR Analytics Conference in Mesa. Among the several compelling presentations on this first of a three-day event was Bill Squadron’s stunning presentation of the Bloomberg Analytics program, now adopted by twenty-four of MLB’s thirty clubs, which integrates pitch-by-pitch results with batted ball locations and coordinated video. To one who had a hand in the early days of sabermetrics, it was simply amazing.

Seated next to me was my old friend Richard D. Cramer, author of the first such program for an MLB club: the EDGE system created by Stats Inc. for the Oakland A’s in 1981. Dick is a man of manifold accomplishments, but for me it is hard to overestimate the brilliance and enduring influence of his article below, which he first published in SABR’s Baseball Research Journal in 1980. To celebrate SABR’s pioneering role, I offer it below as the first of three landmark essays that appeared in that publication.

It is today a commonplace wisdom that players of different eras may be compared by their relative dominance over league average performance. By this method Bill Terry’s .401 in 1930, when the NL batting average was .303, may be viewed as the same achievement as Carl Yastrzemski’s .301 in 1968, when the AL batted .230, in that each exceeded his league average by about 32 percent.

However, as Pete Palmer and I wrote in The Hidden Game of Baseball in 1984, “The trouble with this inference, reasonable though it is on its face, lies in a truth Einstein would appreciate: Everything is relative, including relativity. The National League batting average of .266 in 1902 does not mean the same thing as the American League BA of .266 in 1977, any more than Willie Keeler’s .336 in 1902 means the same thing as Lyman Bostock’s .336 in 1977: It does violence to common sense to suppose that, while athletes in every other sport today are measurably and vastly superior to those of fifty or seventy-five years ago, in baseball alone the quality of play has been stagnant or in decline. Keeler’s and Bostock’s Relative Batting Averages are identical, which signifies that each player exceeded his league’s performance to the same degree. But the question that is begged is ‘How do we measure average skill: What do the .266s of 1902 and 1977 mean?’”

Here, without further preamble, is Dick Cramer’s article:

Average Batting Skill Through Major League History

Is the American or the National a tougher league in which to hit .300? How well would Babe Ruth, Ty Cobb, or Cap Anson hit in 1980? What effect did World War II, league expansion, or racial integration have on the caliber of major league hitting? This article provides definitive answers to these types of questions.

The answers come from a universally accepted yardstick of batting competitiveness, comparing the performances of the same player in different seasons. For example, we all conclude that the National League is tougher than the International League because the averages of most batters drop upon promotion. Of course, factors other than the level of competition affect batting averages. Consider how low were the batting averages of the following future major leaguers in the 1971 Eastern League:

Lifetime BA,


1971 Eastern

majors (thru `79)

Bill Madlock



Mike Schmidt



Bob Boone



Andre Thornton



Bob Coluccio



Pepe Frias



Double A seems a bit tougher than the major leagues from these data because (1) this player sample is biased: most Eastern Leaguers don’t reach the majors, and I haven’t shown all the 1971 players who did, and (2) large and poorly lighted parks made the 1971 Eastern League tough for any hitter, as shown by its .234 league average. My study tries to avoid these pitfalls, minimizing bias by using all available data for each season-to-season comparison, and avoiding most “environmental factors” such as ball resilience or rule changes that affect players equally, by subtracting league averages before making a comparison. Of course, direct comparisons cannot be made for seasons more than 20 years apart; few played much in both periods, say, 1950 and 1970. But these seasons can be compared indirectly, by comparing 1950 to 1955 to 1960, etc., and adding the results.

Measures of batting performance are many. In the quest for a single accurate measure of overall batting effectiveness, I have developed the “batter’s win average” (BWA) as a “relative to league average” version of the Palmer/Cramer “batter’s run average” (BRA). (See Baseball Research Journal 1977, pp 74-9.) Its value rests on the finding that the scoring of major league teams is predicted from the BWA’s of its individual players with an error of ±21 runs (RMS difference) when all data are available (SB, CS, HBP, and GiDP as well as AB, H, TB, and BB) and about ±30 runs otherwise.

A property useful in visualizing the BWA in terms of conventional statistics is its roughly 1:1 equivalence with batting average, provided that differences among players arise only from singles. To make this point more clearly by an example, Fred Lynn’s +. 120 BWA led the majors in 1979. His value to the Red Sox was the same as that of a hitter who obtained walks, extra bases, and all other statistical oddments at the league average, but who hit enough extra singles to have an average .120 above the league, that is, a BA of .390. The difference between .390 and Lynn’s actual .333 is an expression mostly of his robust extra-base slugging.

The first stage in this study was a labor of love, using an HP67 calculator to obtain BWA’s for every non-pitcher season batting record having at least 20 BFP (batter facing pitcher) in major league history. The second stage was merely labor, typing all those BFP’s and BWA’s into a computer and checking the entries for accuracy by comparing player BFP sums with those in the Macmillan Encyclopedia. The final stage, performing all possible season-to-season comparisons player by player, took 90 minutes on a PDP10 computer. A season/season comparison involves the sum of the difference in BWA’s for every player appearing in the two seasons, weighted by his smaller number of BFP’s. Other weighting schemes tried seemed to add nothing to the results but complexity.

Any measurement is uncertain, and if this uncertainty is unknown the measure is almost useless. The subsequent treatment of these season/season comparisons is too involved for concise description, but it allowed five completely independent assessments of the level of batting skill in any given American or National League season, relative to their respective 1979 levels. The standard deviation of any set of five measurements from their mean was ±.007, ranging from .002 to .011. This implies that the “true” average batting skill in a season has a 2 in 3 chance of being within ±.007 of the value computed, and a 19 in 20 chance of being within ±.014, provided that errors in my values arise only from random factors, such as individual player streaks and slumps that don’t cancel. However, no study can be guaranteed free of “systematic error.” To cite an example of a systematic error that was identified and corrected: If a player’s career spans only two seasons, it is likely, irrespective of the level of competition, that his second season was worse than his first. (If he had improved, he was likely to have kept his job for at least a third season!) Another possible source of error which proved unimportant was the supposed tendency for batters to weaken with age (the actual tendency appears to be fewer hits but more walks). It appears that overall systematic error is less than 20 percent of the total differences in average levels. One check is that the 1972 to 1973 American League difference is attributable entirely to the calculable effect of excluding pitchers from batting, plus a general rising trend in American League skill in the 1970s.

Assessment of the relative strength of the major leagues, as might be expected, comes from players changing leagues. Results again were consistent and showed no dependence on the direction of the change. Results from the two eras of extensive interleague player movement, 1901 to 1905 and post-1960, agreed well also.

The results of my study are easiest to visualize from the graphical presentation [below]. (Because few readers will be familiar with the BWA units, I have not tabulated the individual numbers, but later convert them to relative BA’s and slugging percentages.) Theories on the whys and wherefores of changes in average batting skill I leave to others with greater personal and historical knowledge of the game. But the major trends are clear:

(1) The average level of batting skill has improved steadily and substantially since 1876. The .120-point difference implies that a batter with 1979-average skills would in 1876 have had the value of an otherwise 1876-average batter who hit enough extra singles for a .385 batting average.

(2) The American and National Leagues were closely matched in average batting strength for the first four decades (although not in number of superstars, the AL usually having many more). About  1938 the National League began to pull ahead of the American, reaching its peak superiority in the early ’60s. A resurgence during the ’70s makes the American League somewhat the tougher today, mainly because of the DH rule.

(3) The recent and also the earliest expansions had only slight and short-lived effects on batting competitiveness. However, the blip around 1900 shows the substantial effect on competition that changing the number of teams from 12 to 8 to 16 can have!

(4) World War II greatly affected competitiveness in 1944 and 1945.

Many baseball fans, myself included, like to imagine how a Ruth or a Wagner would do today. To help in these fantasies, I have compiled a table of batting average and slugging percentage corrections, based again on forcing differences in league batting skill overall into changes in the frequency of singles only. However, league batting averages and slugging percentages have been added back in, to reflect differences in playing conditions as well as in the competition. To convert a player’s record in year A to an equivalent performance in season B, one should first add to his year A batting and slugging averages the corrections tabulated for season A and then subtract the corrections shown for season B. The frequency of such other events as walks or stolen bases then can, optionally, be corrected for any difference in league frequencies between seasons A and B.

One interesting illustration might start with Honus Wagner’s great 1908 season (BWA=+. 145). What might Wagner have done in the 1979 American League, given a livelier ball but tougher competition?  The Table yields a batting average correction of – .059-(+.003)=- .062 and a slugging correction of – .020-(- .029)=+.009, which applied to Wagner’s 1908 stats gives a 1979 BA of .292 and SPct of .551. (In 600 ABs, he would have, say 30 HRs, 10 3BHs, 35 2BHs). Wagner’s stolen base crown and tenth place tie in walks translate directly to similar positions in the 1979 stats. That’s impressive batting production for any shortstop, and a “1979 Honus Wagner” would doubtless be an All-Star Game starter!

These results are fairly typical. Any 20th century superstar would be a star today. Indeed a young Babe Ruth or Ted Williams would out bat any of today’s stars. But of course, any of today’s stars–Parker, Schmidt, Rice, Carew–would before 1955 have been a legendary superstar. Perhaps they almost deserve their heroic salaries!

Facts are often hard on legends, and many may prefer to believe veterans belittling the technical competence of today’s baseball as compared, say, to pre-World War II. Indeed, “little things” may have been executed better by the average 1939 player. However, so great is the improvement in batting that if all other aspects of play were held constant, a lineup of average 1939 hitters would finish 20 to 30 games behind a lineup of average 1979 hitters, by scoring 200 to 300 fewer runs. This should hardly surprise an objective observer. Today’s players are certainly taller and heavier, are drawn from a larger population, especially more countries and races, are more carefully taught at all levels of play. If a host of new track and field Olympic records established every four years are any indication, they can run faster and farther. Why shouldn’t they hit a lot better?