Systems to devise a single number that establishes a baseball player’s value to his team’s offense abound. While others had preceded him, Pete Palmer’s “Linear Weights” model, brought the concept to the general public in the sabermetric classic The Hidden Game of Baseball, by providing weights to various batter results to arrive at a departure of the player’s value from that of the average player. Bill James devised a set of formulas to calculate what he dubbed “Runs Created” and published them in various of his publications, most notably in his wonderful and influential Baseball Abstract series. The James equations were all some variation of the product of on base percentage and the traditional slugging percentage. More recently the sum of those two basic percentages, referred to as OPS, or as OPS+ when normalized to the league value, has come into common use.
The system presented here, while somewhat cumbersome to compute, can be useful for post hoc analysis of team offense, based on the contributions of its individual players.TOE (Total Offensive Efficiency) is an estimate of run contribution per plate appearance based on the various components of batter and baserunner outcomes. TOP (Total Offensive Production) is TOE accumulated over multiple plate appearances. Individual values of TOP, when added together within a team, yield the same value as TOP computed from team statistics. The results can easily be normalized so that effects such as length of season and offensive environment can be eliminated when doing year-to-year or player-to-player comparisons.
Stepwise linear regression was performed on the component offensive statistics of all major league teams during the period 1951-2005 to estimate team runs scored per plate appearance (TOE). Accumulated runs (TOP) are then estimated by multiplying TOE by plate appearances. RBI’s were not considered. All bases on balls were treated the same and when combined with hit batsmen created a new variable “free passes.” Sacrifice hits and flies were treated as ordinary outs and are counted as plate appearances. Separate equations were developed from the same data for seasons during which some components were not recorded.
A total of seven separate equations had to be developed to describe Major League baseball’s statistical history ( for anyone interested in detail, the full equations are presented in the Appendix). Singles, doubles, triples, homeruns and free passes are known for each season and all teams and players since 1876. Strikeouts, stolen bases, caught stealing, and “ground into double plays” are all absent during some seasons. Raw data were obtained from Sean Lahman’s baseball archive (www.baseball-archive.com) supplemented by additional unofficial data, primarily times caught stealing, published on their website by Retrosheet (www.retrosheet.org).
To enable comparisons of performance relative to the playing environment, computed results were scaled such that after the scaling each team had 6000 plate appearances and each league produced runs at a pace of .12 runs per plate appearance (.128 in the American League 1973-present). After scaling,(scaled pa=pa*6000/team pa for each player, scaled TOE=computed TOE*.12/league runs per plate appearance) the following hold within each season: (1) the ranking order of TOE order is maintained and (2) the ranking order of TOP may change, as batters in the more prolific lineups or on teams which may have played more games lose plate appearances relative to players on teams of lesser offense or on teams which played fewer games. Regular players who generally batted higher in the batting order are still credited with more plate appearances than teammates who usually were placed nearer the bottom of the order. The TOP and TOE references in this report refer to the scaled numbers..
Units of TOP are “runs (r)”. Units of TOE are “runs per plate appearance (r/pa)”. The term “APA” refers to the hypothetical number of plate appearances the batter would have on a 6000 plate appearance team. In general, 100 TOP indicates an all-star quality season. A TOP of 125 or more is a superb season and numbers in excess of 150 indicate a “hall of fame” quality, season-long performance. TOE’s of .150, .175, and .200 are indicative of similar qualities without reference to playing time. A relatively low TOE can be offset by cumulative contributions over time, especially for durable players who hit near the top of the batting order. Less durable players can demonstrate their offensive value by maintaining a high efficiency (TOE). TOE is very kind to players who minimize their outs (high on-base percentage) and maximize their hitting (high slugging percentage) without directly accessing those two dimensionally mismatched statistics.
2012 TOP Leaders – American League
2012 TOP Leaders – National League
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Career TOP and TOE are computed in the same manner as conventional statistics. It should be noted that while TOE computations for teams of the post-World War II era are generally accurate to with 5% of the team’s actual runs per plate appearance, that accuracy diminishes considerably as one retreats in time. The accuracy of the estimates tracks very closely with the number of errors committed (see the graph in Appendix), the implication being that runs which score as a result of errors distort the results when those errors are frequent. As a result, computed (unadjusted) values of TOE and TOP underestimate the number runs teams actually scored during the early years of the Major Leagues. Five leagues (National League, American League, 19th-century American Association, Players League of 1890, and the Federal League of 1914-1915) were used in compiling career records of TOP and TOE. All computations were scaled as described above to 6000 plate appearance teams in leagues that averaged .12 runs per plate appearance (.128 for American League since 1973).
According to TOP and TOE, the greatest individual offensive seasons in Major League history belong to Ty Cobb (TOP 192.7 runs in 1917) and Barry Bonds (TOE .301 runs per adj. pa in 2002). Overall Bonds led his league in TOP 10 times. Cobb, Babe Ruth, Ted Williams, and Mickey Mantle each produced 8 league titles. Cobb and Babe Ruth each won TOE “championships” 11 times. Rogers Hornsby recorded 10 such titles and Bonds, Williams, and Honus Wagner each captured 9 TOE titles.
While it is interesting to most readers to note all-time leaders in various statistical concoctions, it is my habit also to point out the bad with the good. Hence,it is worth noting that Dean Chance (played 1961-1971) compiled a TOP of -40 runs. Among players with at least 100 adjusted plate appearances, Ron Herbel (1963-1971) produced the low TOE of -.083. Among players with 2500 or more adjusted plate appearances,the low TOE belongs to the legendarily light-hitting deadball era catcher, Bill Bergen (1901-1911), with a career total of .019 runs.plate appearance (66 TOP in 3531 adjusted plate appearances).
Career TOP Leaders
TOE equations, where b1=singles, b2=doubles, b3=triples, hr=homeruns, so=strikeouts, fp=sum of walks and hit by pitch, sb=stolen bases, cs=caught stealing, gdp=ground into double play, pa=plate appearances, and bb=bases on balls (in the days before a hit batsman put a runner on base):
AL 1939-2012, NL 1950-2012 TOE=-.094+(.649*b1+.755*b2+1.112*b3+1.549*hr-.018*so+.459*fp+.139*sb-.172*cs-.457*gdp)/pa
NL 1933-1949 TOE=-.096+(.649*b1+.762*b2+1.128*b3+1.561*hr-.017*so+.462*fp+.091*sb-.457*gdp)/pa
NL 1915, 1919-1925 AL1914-1915, 1919-1938 TOE=-.097+(.610*b1+.717*b2 +1.262*b3+1.570*hr-.013*so+.440*fp+.208*sb-.173*cs)/pa
NL 1887-1902, 1910-1914, 1916-1918 AL 1901-1905, 1912-1913, 1916-1918 AA 1886-1891 PL 1890 FL 1914-1915 TOE=-.098+(.610*b1+.724*b2+1.272*b3+1.581*hr-.012*so+.444*fp+.16*sb)/pa
NL 1903-1909 AL 1906-1911 TOE=-.103+(.625*b1+.719*b2+1.292*b3+1.577*hr+
NL 1886 TOE=-.098+(.603*b1+.782*b2+1.202*b3+1.603*hr+ .438*bb+.152*sb)/pa
NL 1876-1885 AA 1882-1885 TOE=-.104+(.631*b1+.831*b2+1.237*b3+1.542*hr+
Time series of league-wide Errors per plate appearance, Runs per plate appearance, and error in TOE estimates for American and National Leagues