by Clifford Blau and John Eigenauer

Why do some players score a lot of runs while others lag far behind? The particular player who piqued an interest in this question was Red Rolfe. Looking at the single season leaders for runs scored, one finds the list dominated by power hitters like Ruth, Gehrig, Foxx, and Williams, as well as several nineteenth-century speedy leadoff-type hitters such as Billy Hamilton and Willie Keeler. Rolfe didn’t fit into either of these groups. Obviously, when a player hits a home run, he scores a run. Otherwise, he is largely dependent on his teammates to get across the plate. But players differ in their ability to score runs beyond the number of homers they hit. Let us examine the reasons for those differences, using Red Rolfe as the entry point.

Rolfe scored as many as 143 runs in a season, but it wasn’t because he was blasting a lot of home runs; his best season figure was 14, and he only hit 4 in 1937 when he scored those 143 runs. Was it due to his own ability, or was it simply the result of hitting in front of guys like Lou Gehrig and Joe DiMaggio on the Yankees? He had a pretty good on base average with a career figure of .360. But that was only .002 above the league average figure for his time. But one thing stands out: When Rolfe did reach base, he was much more likely to score than other players. Let’s call this frequency scoring efficiency, which is simply (runs scored minus home runs)/(times on base minus home runs). Rolfe’s career scoring efficiency was .474, while the league average figure in the same period was just .346. What accounts for this great disparity?

One possible explanation is baserunning. While Dan Fox has given examples of baserunning being accountable for up to an additional 20 runs per year, Rolfe’s superb scoring efficiency meant he scored as many as 46 extra runs in a season above an average player. Also, we don’t have complete base-running data from prior to the early 1950s, so we can’t directly determine how good a baserunner he was. Consequently, a different approach is needed to determine the extent to which Rolfe’s runs totals were due to his own ability versus his circumstances.

The most obvious circumstance from which Rolfe may have benefited was hitting in front of very powerful hitters such as Gehrig, DiMaggio, Gordon, and others. If his scoring efficiency is due to lineup factors, other players around him should have benefited as well. This is the case. For example, Frank Crosetti, who usually hit first while Rolfe batted second those years (1934-42) had a scoring efficiency those years (leaving out 1941 and 1942 when he wasn’t a regular) of .438, which was well above average, although less than Rolfe’s figure.

Could that difference be due to their batting order spots? To what extent does batting order position affect scoring efficiency? To determine the answer to those questions, a sample was gathered using the standard batting and base-stealing data by batting order position from both Major Leagues for the years 1957, 1960, 1963, 1966, 1969, and 1972. More recent years were not used due to the designated hitter rule making comparisons to earlier seasons difficult. From these data, two statistics were calculated, scoring efficiency and speed score, a statistic introduced by Bill James in his 1987 Baseball Abstract to measure how well players run. Two problems with using this were that scoring efficiency is one of the factors used in speed score, causing a lack of independence, and another factor is based on fielding, which couldn’t be used for league-wide data, so these two factors were excluded, making it less reliable.

These batting order data showed that scoring efficiency was highest for leadoff hitters and declined steadily to the number seven hitter, then rose for both the eighth and ninth hitters. Leadoff hitters scored 6.8 additional runs per 100 times on base (excluding home runs) compared to an average player while number seven hitters scored 5.5 fewer times than average per 100 times on base. In fact, only the first three hitters were above average. Thus, based on lineup position alone, we would expect Crosetti's scoring efficiency to be higher than Rolfe's. Speed scores followed a similar pattern.i Linear regressions were performed correlating scoring efficiency with speed score, the slugging average and OPS of the next one to four hitters in the lineup, and the number of times the player put himself in scoring position through extra base hits and steals. The factors that best explained scoring efficiency were speed score and the slugging average of the next three batters. Together they accounted for 96% of the variation in scoring efficiency. However, the correlation coefficient for those seasons between speed score and the slugging average of the next three hitters in the lineup was 0.83 because fast runners tend to hit at the top of the order, making it difficult to separate the importance of the player’s own skill (running) from his environment (how well his teammates hit). To deal with this and other issues, the season statistics for all players who reached base at least once were gathered, and the league totals as well.

These data were divided into two groups, the first 1876-1953, or the pre-Retrosheet era, and the second 1954-1993. For the latter group, we have available the number of times players reached base on errors, catcher’s interference, and unsuccessful fielder’s choices, making scoring efficiency more accurate. The league-wide data showed a changing relationship among the statistics. In the first group, scoring efficiency was most closely associated with fielding average, which by itself explained 89% of the annual variation in scoring efficiency. In the second group, however, the correlation between the two was a mere -.04. Whereas OPS could explain just 6% of the annual variation in scoring efficiency in the first group, it accounted for 80% in the second group. League scoring efficiency varied from a high of .537 in the 1876 National League to a low of .253 in the 1968 American League. Meanwhile, fielding average increased from a low of .866 in 1876 to .978 in the 1953 American League. In the second group, it had only improved to .981 by the end of the period. Obviously, after 1953 there was little variation in fielding average, and it was no longer important in explaining differences in runs scored. Likewise, the high rate of scoring efficiency in 1876 is clearly due in large part to better than one in eight plays resulting in an error. For the period 1920-1953, the so-called lively ball portion of group one, which includes Rolfe’s career, fielding average still explained 50% of the annual variation in scoring efficiency on a league-wide basis. One may conclude that the rate at which players reach base on errors was an important, albeit unknown, factor in individual scoring efficiency in this period.

The next step was to look at individual players. By subtracting the league average from each player’s scoring efficiency and multiplying the difference by the number of times each was on base, the number of runs above or below average each player scored (XR) was derived. The best and worst of each group are shown in the below table.







L. Brock




R. Henderson


A. Latham


W. Wilson


R. Ferrell




Spud Davis








From this we can see clearly that speed is a big factor. It is probably no surprise to find Ernie Lombardi at the bottom of the list, although the worst run scorer by this measure may have been Johnny Bassler, who in his seven years with the Tigers was -151. Willie Keeler might not have been anyone's prediction for the number one slot, but he had a fabulous run with the Orioles. In five seasons, he was 167 runs above average. With Brooklyn he was +90, and even in his declining seasons with the Yankees, he was still good for an additional 56 runs. Ty Cobb might have topped him if he had hit first or second rather than third and fourth. Red Rolfe was 226 runs above average for his nine year career. The best individual seasons belonged to Tom Brown (1891) at an amazing +60 and Tommy Leach (1909) with a +51 in group one, while Willie Wilson (1980) topped group two at +47 runs. Dan Fox estimated that Willie Wilson’s baserunning was worth 19 runs above average in 1980, which leaves 28 runs due to other factors. The worst seasons were turned in by Steve O'Neill (1922) with a -36 and Ken Singleton (1983) at -34. It is worth noting that as with most things in baseball, most players are below average, while the top players are further above the average than the worst are below it.

In order to try to separate the effects of speed and batting order position, we looked at some slow-to-average runners who hit either first or second in the order (slow tablesetters), as well as a few speedsters who hit eighth. For 43 seasons, the slow tablesetters (see appendix for details) averaged 6.7 XR. Thus, we should expect even slow hitters at the top of the order to score more often once they reach base than bottom of the order hitters. Looking at some of the individual players shows this further. Bobby Richardson had 74 XR in four seasons hitting either first or second for the Yankees. In the two previous seasons, when he hit eighth often, he had -3 XR. Thurman Munson had a +16 XR in 1971 hitting second; in the two surrounding seasons his total was -6. Eddie Mathews had 25 XR from 1954-1968; 15 of them came in the two seasons he usually hit second. When Carlton Fisk hit second for the White Sox in 1983-4, he had 13 XR; in the two surrounding seasons he was at -3. Dwight Evans had a career XR of +3, but it was +22 his two years as a number two hitter. Likewise, Brian Downing was at -57 for his career but +18 for his four seasons as a primary leadoff hitter. We can see the opposite effect looking at Ozzie Smith. In 1982 and 1984, he most often hit eighth, and in those two seasons he had a total XR of +2. In ten seasons batting second, he was +133. Frank Taveras shows a similar pattern; in 1974 he generally hit eighth and had 0 XR. Two years later he was usually hitting leadoff and had jumped to +22.

As another test, we compared Luis Aparicio and Nellie Fox for the years they hit first and second for the White Sox (1957 and 1959-61). Obviously they had two of the same three hitters following them, although the overall slugging average of the following three hitters was higher each year for Fox than for Aparicio. Aparicio’s scoring efficiency was better in each of the four seasons, ranging from .376 to .420 while Fox’s varied from .288 to .360. Thus we see that the faster Aparicio had a large advantage over Fox. This is analogous to the Crosetti/Rolfe situation, and suggests that Rolfe may have been quite speedy even though he didn’t steal many bases (or that Crosetti was slow).

Besides the factors already noted, luck also plays a large part. For players with at least 300 at bats in a season, the average number of runs scored in group one was 70, with a standard deviation of XR of 11.1. In group two, the average was 63.1 runs with a standard deviation of XR of 10.2. The largest season-to-season variation in XR was 59 runs by Blondie Purcell. He was at -27 runs in 1889 and +32 in 1890.

So we see that both lineup position and speed are important. What remains to be done, by someone with more statistical sophistication, is to systematically separate speed from the effect of lineup position.

It should be noted that the individual scores shown do not account for pinch-runners. This may make the slow runners’ XR figures worse than they should be if they were frequently replaced by pinch-runners. In fact, Willie McCovey was removed for a pinch-runner 332 times in his career, more than any other player in the Retrosheet era. This cost him perhaps 90 runs scored. This method could also be used to evaluate the effectiveness of pinch-runners such as Herb Washington. Scott Schleifstein in the Baseball Research Journal made the claim that Washington actually cost the A’s runs in 1974 with his low-percentage stealing. However, his scoring efficiency that year was .315 compared to the league average of .283, giving him an XR of +3. That said, the standard deviation of XR for his 92 times on base should be about five, so Washington may indeed have been a below-average runner.

Getting back to Red Rolfe, it appears that much of his high run totals were due to circumstance; teammate Frank Crosetti also scored at a well-above average rate. However, Rolfe had a little something extra. When Retrosheet makes play-by-play available for the years he played, we may be able to learn more about Rolfe’s baserunning skill.


The slow runners used were Wade Boggs (1983-86, 1988, 1989, and 1991), Al Dark (1954-59), Jim Davenport (1959), Brian Downing (1983, 1987, 1991, 1992), Dwight Evans (1982, 1984), Carlton Fisk (1983, 1984), Mike Hargrove (1977, 1978), Harvey Kuenn (1962, 1963), Whitey Lockman (1954), Eddie Mathews (1959, 1966), Thurman Munson (1971), Jody Reed (1991), Bobby Richardson (1961-64), Ken Singleton (1975), and Ed Yost (1954-60).


Dan Fox, “Will Raines Run into the Hall?”,, 1/6/2008.

Brandon Isleib, “Who Will Rid Me of This Pestilent McCovey?”,, 4/10/2007.

Bill James, The Bill James Baseball Abstract 1985 (New York: Ballantine Books, 1985), 174-177.

Scott Schleifstein, “Herb Washington’s Value to the 1974 A’s,” Baseball Research Journal 38 (2009): 82-87.

iCrosetti's speed score was 6.1 and Rolfe's was 5.9, calculated using all available factors for their years as regulars.

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