Harry Jebsen wrote an article in the 1979 issue of the Society for American Baseball Research's "Baseball Research Journal" dealing with the 1888 Dallas Hams minor league team. The statistician in me was intrigued by one line in his article. Speaking of James "Tub" Welsh, Jebsen wrote "Coincidentally, he held a lifetime major league .261 average with 261 times at bat. I became curious how often it was that a major league player finished with a career batting average equal to his number of at bats. (note - Obviously we will be ignoring the fact that a batting average is a percentage and thus is less than one. Technically Welsh's average was one thousandth of his at bats total.)
First I decided to find out the number of at bats for which such an event was possible. Since batting averages range from .000 to 1.000, there are technically 1001 possible matches. Immediately we eliminate 0 as a possibility since a player with 0 at bats actually has no batting average due to the impossibility of dividing by 0. A player with 1 at bat would end up with an average of either .000 or 1.000 so there is no possible match there. The first successful occurrence was a batter who would have 3 hits in 55 at bats, producing a batting average of .055. Using MAPLE, a computer algebra system, I found that there are 508 different matches possible.
Obviously a number of these matches, though theoretically possible, are totally unrealistic. No batter will ever have 1000 hits in 1000 at bats for a batting average of 1.000. Or 998 hits in 999 at bats for an average of .999. Only 46 of the possible matches produce batting averages of .300 or less. Here are those cases:
# AVG AB H
1 .055 55 3
2 .063 63 4
3 .095 95 9
4 .100 100 10
5 .105 105 11
6 .114 114 13
7 .134 134 18
8 .138 138 19
9 .145 145 21
10 .155 155 24
11 .158 158 25
12 .161 161 26
13 .173 173 30
14 .176 176 31
15 .179 179 32
16 .187 187 35
17 .195 195 38
18 .200 200 40
19 .205 205 42
20 .210 210 44
21 .212 212 45
22 .217 217 47
23 .219 219 48
24 .226 226 51
25 .228 228 52
26 .230 230 53
27 .241 241 58
28 .243 243 59
29 .245 245 60
30 .247 247 61
31 .249 249 62
32 .251 251 63
33 .253 253 64
34 .255 255 65
35 .257 257 66
36 .259 259 67
37 .261 261 68
38 .270 270 73
39 .272 272 74
40 .274 274 75
41 .281 281 79
42 .283 283 80
43 .288 288 83
44 .290 290 84
45 .295 295 87
46 .300 300 90
We must keep in mind that only 10 of the 508 matches are actually exact matches. A player with 157 hits in 396 at bats would have an average of .39646464646... which is only equal to .396 after rounding off to the thousandths place. The following are the only ones where the match is exact.
# AVG. AB H
1 .100 100 10
2 .200 200 40
3 .300 300 90
4 .400 400 160
5 .500 500 250
6 .600 600 360
7 .700 700 490
8 .800 800 640
9 .900 900 810
10 1.000 1000 1000
I then went to www.majorleaguebaseball.com and used their sortable historical statistics feature to look for the players who actually achieved such a match. It is not surprising that most of the matches were at lower averages and that most of the matches were achieved by pitchers. After all, if a player were to achieve a batting average of .342 after his first 342 career at bats, it is highly probable his career would continue for a long time.
The first possible match provided the first actual match. John Dopson pitched for the Montreal Expos in 1985 and 1988, then for the Boston Red Sox from 1989 to 1993 and ended his career with the California Angels in 1994. In his two years in Montreal he was 3 for 55 for an average of .055. He never batted for the Red Sox or Angels.
No match has occurred at the next possible spot of 4 for 63. Dick Tidrow pitched for a number of teams from 1972 until 1984. Much of his time was spent in the American League so he ended his career with only 95 at bats, with 9 hits and thus a batting average of .095.
No player has ended his career with 100 at bats and a .100 average. Each of the next five possible matches has occurred, with one of them occurring twice. Jim Mooney (11-105, .105) pitched for the New York Giants and St. Louis Cardinals from 1931 - 1934. Clyde King (13-114, .114) pitched for the Brooklyn Dodgers and Cincinnati Reds during seven seasons between 1944 and 1953.
Pitcher Scott Elarton (18-134, .134) came to the Montreal Expos in 1998, moving to the Colorado Rockies in 2001. Elarton is still active, though not currently on any team's roster. If he catches on with someone, it is likely that the 2002 season will see him disqualify himself from this list.
The first non-pitcher on the list is John Tilley (19-138, .138) who played for the Cleveland Spiders in 1882 and the St. Paul Saints and Toledo Blue Stockings in 1884. Pitchers Yank Terry and Sam Kimber both finished with career totals of 21 hits in 145 at bats for an average of .145. Terry was with the Red Sox (1940, 1942-1945), Kimber was with the Brooklyn Atlantics (1884) and the Providence Grays (1885).
Only seven of the remaining possible matches have actually occurred. Crazy Schmit (26-161, .161) pitched for five teams during five seasons between 1890 and 1901. Ed Knouff (35-187, .187) pitched for five American Association teams from 1885-1889. Lev Shreve (38-195, .195) pitched for the Baltimore Orioles in 1887 and the Indianapolis Hoosiers from 1887-1889.
The rest of our list is made up of non-pitchers. Bud Sheely (44-210, .210) caught for the Chicago White Sox from 1951-1953. Harvey Russell (58-241, .241) caught for the Baltimore Terrapins of the Federal League in 1914 and 1915. Larry Raines (64-253, .253) was a utility man for the Cleveland Indians in 1957 and 1958. Last is the man who inspired this research, Tub Welsh (68-261, .261) who caught for the Toledo Maumees in 1890 and the Louisville Colonels in 1895.
As is often the case, playing with one statistical idea will bring up other interesting tidbits of statistical data. Fred Waterman (101-303, .333) played in the National Association (1871-1873, 1875). He has the most at bats in major league history while finishing with a batting average higher than his at bats total. Mike Moynahan (202-688, .294), who played for four teams in two leagues (1881-1882, 1883-1884) has the fewest at bats in a major league career that ended with more than 200 hits. Ichiro Suzuki (242-692, .350, through 2001) took over that distinction for a while in 2001 but finished the season with more at bats. Albert Pujols (201-610, .330, through 4/6/02) took that place in 2002, but, like Suzuki, lost it as his at bats passed Moynahan's.
Also by Fred Worth
» The Most Impressive Single-Season Home Run Records
» Major League Leaders Who Weren't: 1961's Unbalanced Schedule
» More submissions
Copyright © 2002 by Fred Worth. Posted May 20, 2002.
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