Glossary of Statistical Terms

 This Glossary contains definitions of the statistical terms and measures that may be unfamiliar to the average baseball fan or that represent what today might seem odd scoring practices. The Glossary will also be of value to the advanced fan who wishes to know more about the mathematical and theoretical foundations of certain statistics. "Adjusted"; means that the statistic to the immediate left of this mark has been normalized to league average and adjusted for home park factor. Stats that are normalized in this book are Batting Runs, Production, Batting Average, On Base Percentage, Slugging Average, Earned Run Average, and Pitcher Runs. ASSIST Although credited to pitchers on strikeouts in some of baseball's early years, not counted as such in this volume. ASSIST AVERAGE Assists divided by games played. Stat created by Philadelphia baseball writer Al Wright in 1875. AT-BATS Charged to batters on sacrifice hits, 1889-1893; on sacrifice-fly situations, 1931-1938 and 1940-1953; bases on balls, 1876, 1887. However, we did not count at-bats for bases on balls. AVERAGE AND OVER Early form of expressing averages for base hits, runs, and outs. The average of a batter with 23 hits in six games would be not 3.83 but 35 (an average of 3 with an overage, or remainder, of 5); borrowed from cricket. AVERAGE BASES ALLOWED A pitcher's total bases allowed, divided by his innings pitched--what might be termed Opponents' Slugging Average. Created by Alfred P. Berry in 1951. AVERAGE BATTING (PITCHING, FIELDING) SKILL The great philosophical as well as statistical puzzler: after one has normalized a player's performance to that of his league, how does one compare one season's league average with that of another far removed in time? Does a .266 batting average in the NL of 1902 mean the same thing as a .266 batting average in the AL of 1977? BASES ON BALLS Counted as outs for batters in 1876 and as hits for batters in 1887, but as neither throughout this book. Awarded for a varying number of errant pitches since 1876, from nine in that year to the current four (standardized in 1889). (After 1887, the batter was no longer allowed to specify strike zone as waist to shoulders or waist to shins.) BASES ON BALLS PERCENTAGE Batters' stat: most walks per 100 at-bats plus bases on balls. BASES ON BALLS PER GAME Game defined as nine innings; league- leading pitchers calculated on basis of lowest mark; computed as bases on balls times nine, divided by innings. BASE-OUT PERCENTAGE Barry Codell's stat for measuring complete offensive performance, in which the elements of the numerator represent bases gained while the events in the denominator represent outs produced (sacrifices and sacrifice flies appear in both because they achieve both--gaining a base for the team while costing it an out). The formula: ```Total Bases+Walks+HBP+Steals+Sacrifices+Sacrifice Flies --------------------------------------------------- At-bats-Hits+Caught Stealing+GIDP+Sac.+Sac.Flies``` (GIDP, in the equation above, stands for Grounded Into Double Play; HBP for Hit By Pitch.) BATTERS FACING PITCHER Unavailable before 1903 in the National League. The 1903 and 1908 data was not published and has been reconstructed. BFP was unavailable for the American League of 1901-1907. Excepting the NL of 1876-1888 and the AA of 1882 and 1884-1887, for which John Tattersall calculated BFP from box scores, earlier years in both leagues have had their BFP constructed from available data in this manner: subtract league base hits from league at-bats, divide by league innings pitched, multiply by the pitcher's innings, and add his hits allowed, walks, hit by pitch, and sacrifice hits, if available. Abbreviated as BFP. BATTER'S PARK FACTOR The Park Factor shown in the batters' section of the team statistics in the Annual Record, Player Register, and Home-Road Statistics. Above 100 means batters benefited from playing half their games in a good hitting park. Abbreviated as BPF or, in what are clearly batters' stats (as in the Player Register) simply as PF. See entry for Park Factor for the computation. BATTERY ERRORS In baseball's early years, wild pitches, passed balls, and hit batsmen were lumped together in the statistical summary of a game as battery errors and were charged against the fielding percentage of the pitcher or catcher. Such battery errors have been removed from individual and team stats for this book. BATTING AVERAGE Calculated as base hits divided by at-bats ever since its first appearance in print in 1874. In 1876 walks were counted as at-bats, and in 1887 they were counted as at-bats and as hits. For this book, batting averages are computed in uniform fashion throughout baseball history. Abbreviated in Part 2 of this volume as AVG, although it is also commonly abbreviated BA. BATTING RUNS The Linear Weights measure of runs contributed beyond those of a league-average batter or team, such league average defined as zero. The formula depends upon the run values for each offensive event that resulted from Pete Palmer's 1978 computer simulation of all major league games played since 1901. Run values change marginally with changing conditions of play (an out costs a team more in a hitters' year, such as 1930, than in a pitchers' year, such as 1908), and they differ slightly up and down the batting order (a homer is not worth as much to the leadoff hitter as it is to the fifth-place batter; a walk is worth more for the man batting second than for the man batting eighth); however, these differences have been averaged out historically in the figures below. Runs = (.47)1B + (.78)2B + (1.09)3B + (1.40)HR + (.33)(BB + HB) - (.25)(AB-H) - (.50)OOB (An out is considered to be a hitless at-bat and its value is set so that the sum of all events times their frequency is zero, thus establishing zero as the baseline, or norm, for performance.) Some events one might expect to see included in this formula but that do not appear are sacrifices, sacrifice hits, grounded into double plays, and reached on error. The last is not known for most years and in the official statistics is indistinguishable from outs on base (OOB). The sacrifice has values that essentially cancel one another, trading an out for an advanced base which, often as not, leaves the team in a situation with poorer run potential than it had before the sacrifice. The sacrifice fly has dubious run value because it is entirely dependent on a situation not under the batter's control: while a single or a walk or a hit by pitch always has potential run value, a long fly does not unless a man happens to be poised at third base. Last, the grounded into double play is to a far greater extent a function of one's place in the batting order than it is of poor speed or failure in the clutch, and thus it does not find a home in a formula applicable to all batters. It is no accident that Hank Aaron, who ran well for most of his long career and wasn't too shabby in the clutch, hit into more DPs than anyone else, nor that Roberto Clemente, Al Kaline, and Frank Robinson, who fit the same description, are also among the ten "worst" in this department. The Batting Runs formula can be condensed by eliminating the components for steals, caught stealing, and outs on base. Outs on base (calculated as Hits + Walks + Hit Batsman - Left on Base - Runs - Caught Stealing) is meaningful only for teams, not individuals. We eliminate steals from the formula in those years in which caught-stealing figures are not available, but the surviving data for the early years indicate that few of the men with high base-stealing totals exceeded the break-even point of 66.7 percent by a margin large enough to produce even one additional Batting Win. A further condensation that we have used for our historical data, as indicated in the formula above, involves setting the value of a single at .47 runs and each extra base at .31, making a double .78, a triple 1.09, and a homer 1.40. (This tends to even out the fluctuations in run values for base hits and extra bases over time: a double, for example, was in fact worth .82 runs from 1901-1920, .80 runs from 1941-1960, and .77 runs from 1961-1977.) Subtract the hits from the total bases and multiply the resulting extra bases by .31 and the hits by .47. This may introduce small variations from a more rigorous formula that includes differing run values for the differing periods or even for single years (generally amounting to a fraction of a run), but the calculation is much snappier for those without a computer. The Batting Runs formula may be long, even in its condensed form, but it calls for only addition, subtraction, and multiplication and thus is as simple as Slugging Average, whose incorrect weights (1, 2, 3, and 4) it revises and expands upon. Each event has a value and frequency, just as in Slugging Average, yet in Batting Runs outs are treated as offensive events with a run value of their own (albeit a negative one). Just as the run potential for a team in a given half-inning is boosted by a man reaching base, it is diminished by a man being retired; not only has he failed to brighten the situation on the bases but he has deprived his team of the services of a man further down the order who might have come up in this half-inning, either with men on base and/or with scores already in. The Batting Runs stat treats every offensive event in terms of its impact upon the team- -an average team, so that a man does not benefit in his individual record for having the good fortune to bat cleanup with the Red Sox or suffer for batting cleanup with the White Sox. The relationship of individual performance to team play is stated poorly or not at all in conventional baseball statistics. In Batting Runs it is crystal clear. Recognizing that some readers will wish to keep track of batting performance by compiling Batting Runs themselves over the course of a season and that they may be frustrated by the difficulty of separating out pitcher batting or of calculating the (At- Bats - Hits) factor for the league, we advise that using the fixed value of -.25 for outs will tend to work quite well if you wish to include pitcher batting performance, and a fixed value of - .27 will serve if you wish to exclude it. Actually, any fixed value will suffice in midseason; it's only when all the numbers are in and you care to compare this year's results with last year's (or, e.g., with those of the 1927 Yankees) that more precision is desirable. At that point the value of the out may be calculated by the more ambitious among you, but, ideally, the sporting press will provide accurate Batting Runs figures. (Who calculates ERA for himself?) Batting Runs are abbreviated as BR. BATTING WINS Adjusted Batting Runs divided by the number of runs required to create an additional win beyond average (see Runs Per Win). That average is defined as a team record of .500 because a league won-lost average must be .500, or as an individual record of zero because the value of the out for a given year is calculated to establish a baseline of zero. Abbreviated as BW. CALCULATED STAT One or more counting stats (see below) subjected to a mathematical process such as averaging. CHANCES ACCEPTED Putouts and assists, minus errors. CLUTCH HITTING INDEX Calculated for individuals, actual RBI over expected RBI, adjusted for league average and slot in batting order; 100 is a league- average performance. The spot in the batting order is figured as 5 - (9 X BFPGP - BFPGT) where BFPGP is the batters facing pitcher per game for the player, or plate appearances divided by games, and BFPGT is the batters facing pitcher per game of the entire team. Expected RBI are calculated as (.25 singles + .50 doubles + .75 triples + 1.75 homers) X LGAV X EXPSL where LGAV (league average) = league RBI divided by (.25 singles + .50 doubles + .75 triples + 1.75 homers), and EXPSL (expected RBI by slot number) = .88 for the leadoff batter, and for the remaining slots, descending to ninth, .90, .98, 1.08, 1.08, 1.04, 1.04, 1.04, and 1.02. Calculated for teams, Clutch Hitting Index is actual runs scored over Batting Runs. Abbreviated as CHI. CLUTCH PITCHING INDEX Expected runs allowed over actual runs allowed, with 100 being a league-average performance. Expected runs are figured on the basis of the pitcher's opposing at-bats, hits, walks, and hit batsmen (doubles and triples estimated at league average). Abbreviated as CPI. COUNTING STAT A raw figure that tells how many of an item have been accumulated, as opposed to a calculated or derived figure such as an average. DIFFERENTIAL The difference between a team's actual won-lost record and that predicted by the total of its Pitching Wins, Batting Wins, Fielding Wins, and Stolen Base Wins; this measure indicates the extent to which a team outperformed or underperformed its talent. Abbreviated as DIF. EARNED RUN AVERAGE Calculated as earned runs times nine, divided by innings pitched. For a few years after being introduced as an official stat in the National League in 1912 and the American League in 1913, runs aided by stolen bases were not counted as earned (see Chronology of Scoring Rules in Appendix 1, Rules and Scoring). For years before 1912, ERA has been constructed from raw data, but for some teams in some seasons, earned runs cannot be identified with perfect certainty. For those teams, we use the estimating procedure created by Information Concepts, Inc., of assigning to those runs whose earned/unearned status is unknown the percentage of earned runs to runs that characterize the team's known runs. In Total Baseball, we have created an Adjusted ERA by normalizing to the league average--which is done by dividing the league average ERA by the individual ERA--and then factoring in home park. EXPECTED WINS Calculated for the team based on its actual runs scored and allowed, not its predicted runs scored and allowed. A team that allows exactly as many runs as it scores is predicted to play .500 ball. The equation for expected wins is: ``` (Runs Scored - Runs Allowed) (Wins + Losses) -------------------------- + ------------------ Runs Per Win 2 ``` Abbreviated as W-EXP. FIELDING AVERAGE Defined as putouts and assists divided by the total of putouts, assists, and errors. The weakness of this stat is that it values a player with minimal range but good hands over another player who may accept many more chances but mishandle a few of these. Abbreviated as FA. See Range Factor, Total Chances. FIELDING RUNS The Linear Weights measure of runs saved beyond what a league-average player at that position might have saved, defined as zero; this stat is calculated to take account of the particular demands of the different positions. For second basemen, shortstops, and third basemen, the formula begins by calculating the league average for the position: ``` pos | .20 (PO + 2A - E + DP) league at position | AVG= | ----------------------------------------- | lg | PO league total - K league total | ``` where A = assists, PO =putouts, E = errors, DP = double plays, and K =strikeouts. Then we estimate the number of innings for each player at each position based upon each player's entire fielding record and his number of plate appearances. So, if the team played 1,500 innings and one player was calculated to have played 1,000 of those innings at a given position, his Fielding Runs (FR) would be calculated as: ```FR=.20(PO+2A-E+DP)player-avg.pos.lg X(PO - K) innings, player team team --------------- innings, team ``` Assists are doubly weighted because more fielding skill is generally required to get one than to record a putout. For catchers, the above formula is modified by removing strikeouts from their formulas and subtracting not only errors but also passed balls divided by two. Also incorporated in the catcher's Fielding Runs is one tenth of the adjusted Pitching Runs for the team, times the percentage of games behind the plate by that catcher. For pitchers, the above formula is modified to subtract individual pitcher strikeouts from the total number of potential outs (otherwise, exceptional strikeout pitchers like Nolan Ryan or Bob Feller would see their Fielding Runs artificially depressed). Also, pitchers' chances are weighted less than infielders' assists because a pitcher's style may produce fewer ground balls. Thus the formula for pitchers is .10(PO + 2A - E + DP), whereas for second basemen, shortstops, and third basemen it is .20(PO + 2A - E + DP). For first basemen, because putouts and double plays require so little skill in all but the odd case, these plays are eliminated, leaving only .20(2A E) in the numerator. For outfielders, the formula becomes .20(PO + 4A - E + 2DP). The weighting for assists is boosted here because a good outfielder can prevent runs through the threat of assists that are never made; for them, unlike infielders, the assist is essentially an elective play, like the stolen base. Outfielders' Fielding Runs were subject to some degree of error because outfielders sometimes switch fields within a game or season (Babe Ruth, for example, was positioned in the field that required the lesser range--right field in Yankee Stadium, left field in most road parks). Also, short distances to left-or right-field walls in some parks tend to depress putout totals. Since the third edition of Total Baseball, however, we have researched and obtained breakouts of all outfielders' games in left, center, and right fields. Center fielders now have higher ratings than they did in the first and second editions. Abbreviated as FR. FIELDING WINS Fielding Runs divided by the number of runs required to create an additional win beyond average. That average is defined as a team record of .500 because a league won-lost average must be .500. Abbreviated as FW. See Runs Per Win. GAMES BEHIND Figured by adding the difference in wins between a trailing team and the leader to the difference in losses, and dividing by two. Thus a team that is three games behind may trail by three in the win column and three in the loss column, or four and two, or any other combination of wins and losses totaling six. Abbreviated as GB. GAME-WINNING RUN BATTED IN Credited to the batter who drives in a run that gives his club a lead that it never relinquishes, no matter when that run is driven in nor what the final score is. Introduced in 1980 as an official stat and later disowned, the GWRBI is not recorded in this volume. GROUNDED INTO DOUBLE PLAY Kept officially since 1993 in the NL and 1939 in the AL (though the NL data of 1933-38 made no distinction between lined-into double plays and grounded-into double plays, and the AL data of 1939 was not published). This stat tends to be overvalued by the general public as an indicator of rally-killing ineptitude. Instead, it is largely a function of high totals of at-bats, which tend to be accumulated by the game's best players, not its worst. Abbreviated as GIDP. HANDS OUT The original 1840s scoring term for batters producing outs either at the plate or on the bases. On a force out, the runner retired on the bases would be charged with a hand out, not the batter. Also called Hands Lost, and abbreviated as HO or HL. HIT BY PITCH A batter struck by a pitched ball was not awarded first base until 1884 in the American Association and 1887 in the National League. Reconstruction of stats for batters and pitchers in the years 1897-1908 has been accomplished. Abbreviated as HBP. HITS Bases on balls originally counted as hits in 1887, but are recorded in this volume as neither hits nor at-bats. HOME RUN FACTOR A measure of the home runs hit in a given ballpark, with 100 representing the average home park and the highest figure above that representing the best home-run park. Computed in the same manner as Home Run Batter Rating (see above). Abbreviated as HRF. HOME RUN PERCENTAGE Home runs per 100 at-bats. HOME RUN PITCHER RATING A measure of a team's ability to prevent home runs, taking into account the Home Run Factor (see above) of the park and the team's not having to face its own batters. The average mark is represented as 100, and the lowest figure beneath that indicates the best. HOME RUNS When is a home run not a home run? Before 1920, not if it came with men on base in the ultimate inning and created a margin of victory greater than one run. A ruling of the Special Baseball Records Committee in 1969 reversed its earlier decision that had made home runs of 37 disputed final-inning, game-winning base hits. In accordance with the practice of the day, such a hit, even if it sailed out of the park, would be credited with only as many bases as necessary to plate the winning run. Thus Babe Ruth's "715th home run," hit on July 8, 1918, to win a game against Cleveland, remained a triple, and Jimmy Collins and Sherry Magee were each deprived of two home runs. INNINGS PITCHED Official baseball practice was, until 1982, to round off fractional innings for individuals to the next highest inning. Since then fractional innings have been kept for individuals and teams. In this volume fractional innings are supplied for all individuals and all teams in all years. Those men who took a turn on the mound but failed to retire a batter are credited with no innings pitched and, if they allowed a runner or runners to score, an ERA of infinity. INTENTIONAL BASES ON BALLS Recorded only since 1955. ISOLATED POWER Total bases minus hits, divided by at-bats; in other words, Slugging Average minus Batting Average. Appears to have been created by Allan Roth and Branch Rickey in the 1950s. LEAGUE-AVERAGE REPLACEMENT PLAYER That model player who performs at precisely the league average, creating a baseline against which to measure others. LEAGUE PERFORMANCE: Because the caliber of play in the Union Association of 1884 and the Federal League of 1914-15 was substantially below that of its rivals in those years, we have made an upward adjustment to overall league performance, thus lowering individual ratings or computed stats, while leaving unaffected the raw statistics of Organized Baseball. League at bats were reduced to 80 percent for the UA and 90 percent for the FL. We tested all players who appeared in at least 30 games for the UA in 1884 and 30 or more games in the NL or AA in the 1883-85 period. There were 31 players who played 2,182 games in the UA and had a Total Player Rating 2.6 wins higher per 112 games in the UA. There were 17 pitchers who pitched 3,678 innings in the UA with at least 30 innings in the UA and 30 innings in other leagues in the 1883-85 period). These pitchers had a Total Pitcher Index 0.8 wins higher in the UA per 112 innings. For the Federal League, there were 54 players with 30 games in the FL and at least 30 games in other leagues in the 1913-16 period. These players had 10,401 games in the FL and had a Total Player Rating 1.26 wins higher per 154 games. For pitchers, there were 39 with 30 or more innings in the FL and 30 innings in other leagues in the 1913-16 period). These pitchers had 13,872 innings and a Total Pitcher Index .49 wins higher in the FL per 154 innings. Actually, the calculations for the UA produced a .76 multiplier for on base percentage and slugging, which we have rounded to .80. The calculations for the FL produced a .90 multiplier for on base percentage and slugging, which we have incorporated. UA pitchers had an .875 multiplier for earned run average, which we have expressed as .80 for consistency with the batting figure. FL pitchers had a multiplier of .924, which we have rounded to .90. LINEAR WEIGHTS A system created by Pete Palmer to measure all the events on a ballfield in terms of runs. At the root of this system, as with other sabermetric figures such as Runs Created, is the knowledge that wins and losses are what the game of baseball is about, that wins and losses are proportional in some way to runs scored and runs allowed, and that runs in turn are proportional to the events that go into their making. NORMALIZING Restating a figure as a ratio by comparing it to the league average, or norm. ON BASE PERCENTAGE Created by Roth and Rickey in its current form--hits plus walks plus hit by pitch, divided by at-bats plus walks plus hit by pitch--in the early 1950s, although there were nineteenth-century forebears such as "Reached First Base." When OBP, as it is abbreviated, was adopted as an official stat in 1984, the denominator was expanded to include sacrifice flies. The effect is to penalize a batter in his on base percentage by giving him a plate appearance while at the same time crediting him in his batting average by deleting the plate appearance. In this book we calculate OBP without considering sacrifice flies, which in any event are calculable on a continuing basis only since 1954. ON BASE PLUS SLUGGING See Production. OPPONENTS' BATTING AVERAGE Hits allowed divided by at-bats allowed (or, if at-bats allowed is unknown, then at-bats equals hits plus inning times "K," where "K" is the league average of at-bats minus hits, all over innings). Abbreviated as OAV. OPPONENTS' ON BASE PERCENTAGE For years before 1908 in the American League and 1903 in the National League, the number of batters facing a pitcher has been constructed from the available raw data. We have subtracted league base hits from league at-bats, divided by league innings pitched, multiplied by the pitcher's innings, and added his hits and walks allowed and hit by pitch and sacrifices, if available. Abbreviated as OOB. OUTS Until 1883, included catching a ball on one bounce in foul ground. Not credited after three strikes in 1887, when the rule was "four strikes and yer out"--as it was, in fact, from 1871-1881, when batters commonly received "warning pitches" rather than called strikes. OUTS PER GAME The 1860s successor to Hands Out (see above), it joined with Runs Per Game to form the batting record before the rise of professional league play. PARK FACTOR Calculated separately for batters and pitchers. Above 100 signifies a park favorable to hitters; below 100 signifies a park favorable to pitchers. The computation of PF is admittedly daunting, and what follows is probably of interest to the merest handful of readers, but we feel obliged to state the mathematical underpinnings for those few who may care. We use a three-year average Park Factor for players and teams unless they change home parks. Then a two-year average is used, unless the park existed for only one year. Then a one-year mark is used. If a team started up in Year 1, played two years in the first park, one in the next, and three in the park after that and then stopped play, the average would be as follows (where Fn is the one-year park factor for year n): ``` Year 1 and 2 = (F1 + F2)/2 Year 4 = (F4 + F5)/2 Year 3 = F3 Year 5 = (F4 + F5 + F6)/3 Year 6 = (F5 + F6)/2``` Step 1. Find games, losses, and runs scored and allowed for each team at home and on the road. Take runs per game scored and allowed at home over runs per game scored and allowed on the road. This is the initial figure, but we must make two corrections to it. Step 2. The first correction is for innings pitched at home and on the road. This is a bit complicated, so the mathematically faint of heart may want to head back at this point. First, find the team's home winning percentage (wins at home over games at home). Do the same for road games. Calculate the Innings Pitched Corrector (IPC) shown below. If it is greater than 1, this means the innings pitched on the road are higher because the other team is batting more often in the last of the ninth. This rating is divided by the Innings Pitched Corrector, like so: ``` (18.5 -- Wins at home / Games at home) IPC = ----------------------------------- (18.5 -- Losses on road / Games on road)``` Note: 18.5 is the average number of half-innings per game if the home team always bats in the ninth. Step 3. Make corrections for the fact that the other road parks' total difference from the league average is offset by the park rating of the club that is being rated. Multiply rating by this Other Parks Corrector (OPC): ``` No. of teams OPC=---------------------------------- No. of teams - 1 + Run Factor, team``` (Note that this OPC differs from that presented earlier in The Hidden Game of Baseball, for in preparing the pre-1900 data for Total Baseball, we discovered that for some parks with extreme characteristics, like Chicago's Lake Front Park of 1884, which had a Home Run Factor of nearly 5, the earlier formula produced wrong results. For parks with factors of 1.5 or less, either formula works well.) Example. In 1982, Atlanta scored 388 runs and allowed 387 runs at home in 81 games, and scored 351 and allowed 315 on the road in 81 games. The initial factor is (775/81) / (666/81) = 1.164. The Braves' home record was 42-39, or .519, and their road record was 47-34, or .580. Thus the IPC = (18.5 - .519) / (18.5 - .420) = .995. The team rating is now 1.164/.995 = 1.170. The OPC = (12) / (12 - 1 + 1.170) = .986. The final runs-allowed rating is 1.170 X .986, or 1.154. We warned you it wouldn't be easy! The batter adjustment factor is composed of two parts, one the park factor and the other the fact that a batter does not have to face his own team's pitchers. The initial correction takes care of only the second factor. Start with the following (SF = Scoring Factor, previously determined [for Atlanta, 1.154], and SF1 = Scoring Factor of the other clubs [NT = number of teams]): ``` SF - 1 1 - ----- NT - 1``` Next is an iterative process in which the initial team pitching rating is assumed to be 1, and the following factors are employed: RHT, RAT= Runs per game scored at home (H) and away (A) by team, OHT, OAT= Runs per game allowed at home, away, by team RAL = Runs per game by both teams Now, with the Team Pitching Rating (TPR) = 1, we proceed to calculate Team Batting Rating (TBR): ``` |RAT RHT| | TPR-1| |--- + ---| |1+ -----| |SF1 SF | | NT- 1| TBR=------------------------------ RAL``` ``` |OAT OHT| | TBR-1| |--- + ---| |1+ -----| |SF1 SF | | NT- 1| TPR=------------------------------ RAL``` The last two steps are repeated three more times. The final Batting Corrector, or Batters' Park Factor (BPF) is ``` (SF + SF1) BPF=---------------- | | TPR-1 | | |2 X |1+ -----| | | | NT-1 | | ``` Similarly, the final Pitching Corrector, or Pitchers' Park Factor (PPF) is ``` (SF + SF1) PPF=---------------- | | TBR-1 | | |2 X |1+ -----| | | | NT-1 | | ``` Now an example, using the 1982 Atlanta Braves once again. ``` 388 351 RHT - --- - 4.79 RAT - --- - 4.33 81 81 ``` ``` 387 315 OHT - --- = 4.78 OAT - --- = 3.89 81 81 ``` ``` 7947 RAL = --- = 8.18 NT = 12 972 ``` ``` |1.154-1| SF = 1.154 SF1=1-|-------|=.986 | 11 | ``` ``` |4.33 4.79| | 1- 1| |--- + ----| |1+ --- | |.986 1.154| | 11 | TBR=---------------------------=1.044 8.18``` ``` |3.89 4.78| | 1.044- 1| |--- + ----| |1+ --------| |.986 1.154| | 11 | TBR=---------------------------=.993 8.18``` Repeating these steps gives a TBR of 1.04 and a TPR of .97. The Batters' Park Factor is ``` (1.170 + .986) BPF=----------------=1.07 | | 99-1 | | |2 X |1+ ----| | | | 11 | | ``` This is not a great deal removed from taking the original ratio, ``` 1.170 + 1 --------- , which is 1.08 2 ``` The Pitchers' Park Factor may be calculated in analogous fashion. To apply the Batters' Park Factor to Batting Runs, one must use this formula: ``` BR uncorr. BR = ------------------------------------------------------ corr. Runs (league) Runs (league) AB+BB+HBP ------------- - ---------- X (BPF - 1) X --------- AB+BB+HBP AB+BB+HBP (player or team) (league) (league) ``` For example, if a player produces 20 runs above average in 700 plate appearances with a Batters' Park Factor of 1.10, and the league average of runs produced per plate appearance is .11, this means that the player's uncorrected Batting Runs is 20 over the zero point of 700 X .11 (77 runs). In other words, 77 runs is the average run contribution expected of this batter were he playing in an average home park. But because his Batters' Park Factor is 1.10, which means his home park was 10 percent kinder to hitters (than the average), you would really expect an average run production of 1.1 X 77, or 85 runs. Thus the player whose uncorrected Batting Runs is 97 with a BF of 1.1 is only +10 runs rather than +20, and 10 is his Park Adjusted Batting Runs (in the Player Register, BR/A): 10 = 20/1.10 - .11 X (1.10 - 1) X 700. PERCENTAGE OF TEAM WINS A simple but deceiving measure of a good pitcher's contribution to a bad club; in this, it shares the virtues and flaws of Ted Oliver's Weighted Rating System and, to a lesser degree, our own Wins Above Team (both of which see). Steve Carlton had the highest single-season rating in this century when, in 1972, he went 27-10 for a Phillie club that won only 59 games. Yet his mark of 45.8 percent of his team's wins would not make the top 100 list of seasons since 1876, making this stat nearly useless for historical analysis. PITCHER DEFENSE Abbreviated as PD. See Fielding Runs. PITCHERS' PARK FACTOR The same as the Park Factor shown in the pitchers' section of the team statistics portion of the Annual Record and in the Pitcher Register; above 100 means a pitcher was hurt by playing half his games in a good hitting park. See Park Factor. PITCHER STRIKEOUTS Made tougher or easier by cyclically varying rules and conditions. For instance, foul tips did not count as strikes for many years, even when deliberate, as with bunts; fouls caught on a bounce were outs until 1883; the ball-strike count underwent much experimentation until settling at four balls and three strikes in 1889; not to mention the high-low strike zone, warning pitches, varying pitching distances, and restricted deliveries. It helps to know some history before rattling off stats to prove this or that, but normalizing a stat to its league helps, even with counting stats such as strikeouts. PITCHING RUNS The Linear Weights measure of runs saved beyond what a league-average pitcher or team might have saved, defined as zero. The math is simple: Pitching Runs = Innings Pitched X (League ERA/9) - Earned Runs Allowed. An alternate version is: Innings Pitched/9 X (League ERA - Individual ERA). Abbreviated as PR. PITCHING WINS Park Adjusted Pitching Runs divided by the number of runs required to create an additional win beyond average. That average is defined as a team record of .500 because a league won-lost average must be .500. Abbreviated as PW. See Pitching Runs, above, and Runs Per Win. PLAYER WIN AVERAGES The title of a 1970 book issued by the Mills brothers, Harlan and Eldon, as well as the name of their overall method of determining not only the what of baseball statistics but also the when, or clutch element. Computerizing complete play-by-play data for a full season for their book, they assigned "Win Points"--reflective of that event's potential impact on the team's prospects of victory--to every event on a baseball field. POSITIONAL ADJUSTMENT A key factor in the Total Player Rating that addresses the relative worth to a ball club of the defensive positions. A man who bats .270, hits 25 homers, and drives in 80 runs may be an average performer in left field, no matter how good his glove; but credit those batting stats to a shortstop or second baseman and you have a star, because the defensive demands of the position are so much greater. To balance the abundance of good-hitting outfielders or first basemen against the scarcity of such players at catcher or shortstop, we created a positional adjustment expressed in terms of the average batting skill needed to hold down a major league spot at that position. To determine the average defensive skill required of a position, simply subtract the average batting skill at that position from his Total Player Rating. This may seem strange at first glance, but it does put, for example, shortstops, first basemen, and left fielders on the same footing. The explanation that follows represents a change from previous editions, in which players were measured against only those who played their position in their league in that year. We have now redefined the positional adjustment as an average over both leagues for a three-year period centered on the measured year. This raised the ratings for Lou Gehrig and Jimmie Foxx by a win or two, as they are now compared with sixteen first basemen over three years (a total of forty-eight) rather than just eight. In the 1950-1970 period, AL outfielders averaged a few more Batting Runs per season than their counterparts in the NL. When both leagues were counted, NL players dropped a few Wins and AL players gained. Hank Aaron lost 4 Wins for this reason. In the years since 1977 the positional adjustment for, say a National League first baseman, will be in the context of the batting records of not merely twelve men, but twenty-six--times three, or seventy-eight--obviously, a much broader base of comparison. For each edition, the concluding season's positional adjustments are based on the average of that year and the preceding season. Let's say that last year all major league left fielders accounted for 198 batting runs. The positional adjustment, or factor for average defensive skill, for a left fielder who played in all 162 games would be 162 X 198/3,202 (which calculates to 10), where 3,202 is the number of games played in both leagues by all left fielders (or any other position, obviously). Thus a left fielder who played in all his team's games would have 10 runs subtracted from the sum of his Batting Runs, Stolen Base Runs, and Fielding Runs. If all major league shortstops last year accounted for 158 Batting Runs below average, the adjustment for a shortstop would be figured in the same way, multiplying his games played by -158/3,202, or -8 runs, meaning that 8 runs (minus a minus 8) would be added to his Total Player Rating. PRODUCTION On Base Percentage plus Slugging Average: a simple but elegant measure of batting prowess, in that the weaknesses of one-half of the formulation, On Base Percentage, are countered by the strengths of the other, Slugging Average, and vice versa. When PRO, as it is abbreviated, is adjusted for home park and normalized to league average to become PRO+, the calculation is modified slightly to create a baseline of 100 for a league-average performance. For PRO+, the calculation is ``` Player On Base Pct. Player Slugging Avg. -------------------- + -------------------- - 1 League On Base Pct. League Slugging Avg. ``` This produces a figure with a decimal point--an above-average figure, like 1.46, or a below-average figure, like 0.82. For ease of display, in this book we drop the decimal and express these as 146 and 82. PUTOUT AVERAGE Putouts divided by games played; a stat created by Philadelphia baseball writer Al Wright in 1875. QUALITY START A game started in which a pitcher lasts for six innings or more and allows three runs or less. RATIO Hits plus walks plus hit batsmen allowed per nine innings. Abbreviated as RAT. RBI OPPORTUNITIES An official American League stat for the first three weeks of 1918, until the league saw how much work it involved and scrapped it. Still a good idea, sort of, and the folks at the Elias Sports Bureau have tracked this type of "situational stat" since 1975. REACHED FIRST BASE A precursor of the On Base Percentage, this stat was introduced as an official National League measure in 1879, its one and only year of existence. It included times reached via hits, walks, and errors, but not hit by pitch because putting their bodies on the line did not yet, in 1879, send batters to first base. Trivia: the league leader in this stat's lone year of life was Paul Hines, with 193. RELATIVE BATTING AVERAGE Pioneered by David Shoebotham in a Baseball Research Journal article in 1976, this was the first traditional stat normalized to league average so as to permit cross-era comparison. Most folks who have employed this measure simply divide individual batting average by league batting average. Shoebotham's original computation was more precise: ``` player's hits ----------- player's AB RBA = --------------------------------------- league hits - player's hits --------------------------- league AB - player's AB``` In this manner a player's own performance would not be compared with itself. RELIEF POINTS Relief wins plus saves minus losses was the original formula used as the basis for the Rolaids Company's annual award to the top reliever in each league. Recently the formula has been changed to include a debit for blown saves. RELIEF RANKING Takes Relief Runs (which see), adjusts them for home park, then weights them by a factor (F in the formula below) reflecting the greater value of the innings pitched by a bullpen "closer." Relief Runs, which weights all innings identically, will tend to benefit long and middle relievers who are effective over many innings, while Relief Ranking--which was initially designed for those men who pitch less than three innings per game over a season or career--will tend to benefit relievers who may have fewer innings but who have more saves and decisions. The formula is ``` 9X(Wins+Losses+.25[Saves]) (Relief Runs)X F where the Factor = ------------------------ IP ``` The multiplier, or Factor, is usually around 1, but can get up to 1.5 or even 2 for some relievers, and can get down as low as 0.8 for some starters who have a lot of no-decision games. RELIEF RUNS Identical to Pitching Runs but confined to relief pitchers, defined as those who average less than three innings per appearance. Abbreviated as RR. See Relief Ranking. RUN BATTED IN Though widely regarded as a good measure of a batter's overall productivity and value to his team, the RBI is extremely situation-dependent, denying equal access to opportunity on the basis of a player's team, slot in the batting order, and particularly the men surrounding him in the batting order. RUN FACTOR A measure of the run scoring in a given ballpark compared to other ballparks, with 100 representing the average home park and the highest figure above that representing the best hitters' park. Abbreviated as RF, it is computed on the basis of comparing runs scored and allowed per inning at home and on the road. Innings are estimated from the number of games and games won, allowing for the home team not batting in the final inning of a game in which it leads. The resulting Run Factor is then compared to the league average. RUN RATING FOR BATTERS A measure of a team's run-scoring ability, taking into account the park's Run Factor (see above) and the team's batters not having to face its own pitchers, with 100 representing the average and the highest figure above that representing the best. Abbreviated as RB. RUN RATING FOR PITCHERS A measure of a team's run-prevention ability, taking into account the Run Factor (see above) and the team's pitchers not having to face its own batters, with 100 representing the average and the lowest figure beneath that representing the best. Abbreviated as RP. RUNS CREATED Bill James's formulation for run contribution from a variety of batting and baserunning events. Many different formulas are used, depending upon data available. In its basic expression, the formula is: ``` (Hits + Walks) (Total Bases) -------------------------- At-Bats + Walks ``` The essence of this formulation is that the ability to get on base and the ability to push baserunners around fairly describes offensive ability. James later refined the formula with a "stolen base version": ```(Hits+Walks-Caught Stealing)(Total Bases +.55 X Stolen Bases) ---------------------------------------------------------- At-Bats + Walks ``` Next came the "technical version": a longer formulation, presented below using the standard abbreviations for the various offensive events (the two elements multiplied in the numerator are referred to below as "A" and "B," and the denominator is referred to as "C"): ```(H+BB+HBP-CS-GIDP)(TB+.26[BB-IBB+HBP]+.52[SH+SF+SB]) ----------------------------------------------------- AB + BB + HBP + SH + SF ```From this technical version (Tech-1), James spun off 13 additional technical versions. "The reason that we have to do this," he wrote in The Bill James Historical Baseball Abstract, "is that the data set changes and evolves rapidly throughout the century, or at least up until about 1955, when the progress of evolution in statistical information came to a temporary halt (it stopped moving forward until Bill James and Pete Palmer came around, about twenty years later). In 1900 we have no data for how many times a player grounded into a double play, how many times he was hit by a pitch, how many of his walks might have been intentional, how many times he was caught stealing, or how many sacrifice flies he hit." Accordingly, James adjusted his Runs Created formula to fit the available data; some versions, such as Tech-3, cover as much as a decade in a given league, while others, such as Tech-4, are in force for only a single league season. In Total Baseball, we have computed Runs Created values for all players since 1876 using the version most applicable to the period, with the single exception of Tech-9, which James applied only to the American League of 1916 but which we use for 1914-1916 in the AL and 1915-1916 in the NL because we have discovered additional caught-stealing data. (For those players whose careers began before 1900, James used the Tech-11 formula "to estimate how many runs they had created," but appended a note saying that "these estimates were of indeterminate accuracy.") Here are the formulas for Runs Created (RC) technical versions 214 (Tech-1 was used for both leagues in 19551988): Tech-2 (1954) Factors A and C of Tech-1 remain the same, while Part B simply drops Intentional Bases on Balls. Tech-3 (AL 1940-1953; NL 1951-1953) Factor A remains the same, while SF is dropped from Factor C; Factor B changes to: 1.025 TB + .26(BB + HBP) + .52(SH + SB). Tech-4 (AL 1939) Factors A and C remain the same, while B becomes: TB + .26(BB + HBP) + .52(SH + SB). Tech-5 (AL 1931-1938) Factors B and C remain the same, while A becomes: .96(H + BB + HBP - CS). Tech-6 (AL 1920-1930; NL 1920-1925) Factors A and C remain the same, while B changes only in the value placed on the sacrifice hit and stolen base, which declines from .52 to .51. Tech-7 (NL 1926-1930) C remains the same, while A changes to: .93(H + BB + HBP), and B becomes: TB + .26(BB + HBP) + .46(SH). Tech-8 (AL 1913, 1917-1919; NL 1913-1914, 1917-1919) C remains the same, while A becomes: H + W + HBP - .02(AB), and B becomes: TB + .85(SH + SB). Tech-9 (AL 1914-1916; NL 1915-1916) B and C are the same, while A becomes: H + BB + HBP - CS. Tech-10 (AL, NL 1908-1912) A and C remain the same, while B becomes: 1.025(TB + SB) + .75(SH). Tech-11 (AL, NL 1900-1907) B and C remain the same, while A becomes: H + BB + HBP. Tech-12 (NL 1939-1950) A Factor: H + BB + HBP - GIDP B Factor: TB + .26(BB +HBP) + .52(SH) Tech-13 (NL 1933-1938) A and C remain the same as above, while B becomes: 1.025(TB) + .26(BB +HBP) + .52(SH) Tech-14 (NL 1931-1932) B and C remain the same, but A becomes: .95(H + BB + HBP). RUNS PER GAME With its mate Outs Per Game (which see), this was the precursor, in the 1860s, of the batting average; by the end of that decade it gave way to Hits Per Game. RUNS PER WIN Branch Rickey and Allan Roth first stated the proportional nature of runs and wins in their 1954 article in Life. Since then the point has been expanded upon by George Lindsey, Pete Palmer, Bill James, and every sabermetrician worth his salt: the point being that just as runs scored and allowed are the key to victory in a given game, so are they the key to success over the course of a season and the predictors of won-lost record with a surprising degree of precision. In 1982, Palmer wrote in The National Pastime, "My work showed that as a rough rule of thumb, each additional ten runs scored (or ten less runs allowed) produced one extra win. . . . However, breaking the teams into groups showed that high-scoring teams needed more runs to produce a win. This runs-per-win factor I determined to be ten times the square root of the average number of runs scored per inning by both teams. Thus in normal play, when 4.5 runs per game are scored by each club, each team scores .5 runs per inning--totaling one run, the square root of which is one, times ten." For Total Baseball, we have improved the Runs Per Win figure used in calculating the overall win figures in the Total Player Rating and the Total Pitcher Index. Rather than using 10 times the square root of the average number of runs scored per inning by both teams, we use adjusted runs per inning based on what the player or pitcher rating is. A hitter will increase the figure by adding in his rating over the number of games played, while a pitcher will have his rating subtracted. Say the average number of runs scored per inning is 1, as in the model above; then Runs Per Win = 10. Take a pitcher who allows 45 runs less than average in 25 games. This lowers the runs per game by 1.8, or runs per inning by .2, so the new Runs Per Win figure is 10 times the square root of the average number of runs scored per inning by both teams, minus the pitcher's rating. So we take from the one run per inning the .2 run saved by the pitcher, giving a result of 0.8. Ten times the square root of 0.8 is 8.9, so the pitcher gets 45/8.9, or 5.1, wins instead of 4.5. A hitter with plus 45 runs in 150 games, or .3 runs per game, contributes .03 runs per inning. His Runs Per Win is now 10 times the square root of the average number of runs scored per inning plus the batter's rating. So we add to the 1 run per inning the .03 runs added by the batter, giving a result of 10.1. Ten times the square root of 10.1 gives the batter 4.4 wins. (This method makes makes more of a difference in pitching because the runs are contributed over fewer games. With the same run contribution--45 beyond average--the pitcher gains 0.7 wins over the batter. This is because when the total number of runs scored is lowered, the value of each run is greater). RUNS PRODUCED Runs batted in plus runs scored minus home runs. SABERMETRICS Defined by Bill James, who coined the term in honor of the Society for American Baseball Research, as "the search for objective knowledge about baseball" and, earlier, as "the mathematical and statistical analysis of baseball records." SABR Pronounced "saber," this is the acronym for the Society for American Baseball Research, the organization that has, since its founding by Bob Davids in 1971, steadily advanced the state of baseball knowledge. SACRIFICE FLY First recognized as an event in 1908 but indistinguishable in the official records from sacrifice hits until 1954. There has been much flip-flopping since 1930 on whether to credit the sacrifice flier with an at-bat or an RBI or whether a fly ball that advances a runner to a base other than home plate also should exempt a man from an at-bat. SACRIFICE HITS Invented in the 1860s, recorded since 1889; sacrificer charged with an at-bat until 1894. Sabermetricians frown on the strategy because all the studies show that the trading of an out for a base advanced is a losing strategy--lowering the run expectations of the team that attempts it--in all but the most unusual of cases . . . even if the sacrifice "succeeds." SACRIFICE HITS ALLOWED Computed officially in the National League since 1913 but not published until 1916, and kept in the American League since 1921 but not published until 1922; what it signified about anything is unclear. SAVE Created by Jerome Holtzman of the Chicago Sun-Times, the save began to be reported by The Sporting News on a regular basis in 1960. The major leagues adopted the save in 1969, at which time it was credited to a reliever who finished a game that his team won. In 1973 the save was redefined so that a reliever had not only to finish the game but also to find the potential tying or winning run on base or at the plate, or, alternately, to pitch the final three innings of a victorious contest. In 1975 the rule was liberalized to include a reliever's appearance of one inning or more in which he protects a lead of three runs or less; or he enters the game with the tying or winning run on base, at bat, or on deck; or he pitches three innings to the game's conclusion. In this book, the 1969 definition is applied to all games before 1969; otherwise the rule in force at the time prevails. Abbreviated as SV. SHUTOUTS On an individual basis, credited only to pitchers of complete-game scoreless victories; former practice was to credit combined shutouts to the starting pitcher if he had pitched most of the way. Abbreviated as SH. SITUATIONAL STATISTICS How does a batter perform with the bases loaded? At night? On artificial turf? With no one on base? After the seventh inning when his team is tied or trails? The specialty of Baseball Workshop, Stats, Inc., and the Elias Sports Bureau. SLUGGING AVERAGE Total bases divided by at-bats; combines nicely with On Base Percentage to create Production (which see). Abbreviated as SLG. STARTER RUNS Identical to Pitching Runs (which see) but confined to starting pitchers, defined as those who average more than three innings per appearance. Abbreviated as SR. STOLEN BASE AVERAGE Stolen bases divided by attempts; its computation is dependent upon the availability of caught-stealing numbers. Abbreviated as SBA. STOLEN BASE RUNS For teams, the Linear Weights measure of runs contributed beyond what a league-average basestealing team might have gained, defined as zero; for individuals, Stolen Base Runs are calculated on the basis of the 66.7 percent success rate that sabermetric studies have shown to be the break-even point for producing runs beyond the average. Availability dependent upon caught stealing data as with Stolen Base Average. The formula is simple: .30(Stolen Bases) - .60(Caught Stealing). A man who steals two bases in three attempts is merely spinning his wheels in terms of value to his team, and even a man who succeeds at an 80 percent clip will have to steal a lot of bases--about 65--to create just one win beyond average. Abbreviated as SBR. STOLEN BASE WINS Stolen Base Runs divided by the number of runs required to create an additional win beyond average. Those runs are generally around around 10--historically in the range of 911. Abbreviated as SBW. See Runs Per Win. STOLEN BASES Recorded since 1886, but until 1898 steals are thought to have included a variety of daring baserunning exploits, such as going from first to third on a single or advancing an extra base on an out. Abbreviated as SB. STRIKEOUTS Varying rules concerning the strike zone, the foul strike, and the warning pitch--not to mention the fourth strike of 1887--all contribute to making the cross-era comparison of strikeout accomplishments a very sticky business. Abbreviated as SO. STRIKEOUT PERCENTAGE A batters' stat: fewest strikeouts per 100 at bats. TOTAL AVERAGE Tom Boswell's formulation for offensive contribution from a variety of batting and baserunning events; as with Runs Created, we have calculated Total Average to make use of the maximum available data in a given year. The concept of the numerator is bases gained, that of the denominator is outs made: ```(Total Bases + Steals + Walks + HBP - Caught Stealing) ----------------------------------------------------- (At-Bats - Hits + Caught Stealing + GIDP)``` Abbreviated as TA. See Base-Out Percentage. TOTAL BASEBALL RANKING The "MVP" of statistics, this ranks pitchers and position players by their total wins contributed in all their endeavors, revealing the most valuable performers in a given year. Abbreviated as TBR, it is not a computed stat but a sorting of players and pitchers by, respectively, the sum of their Total Batter Rating and Total Pitcher Index. TOTAL BASES AVERAGE Henry Chadwick's measure that divided total bases by games played; a forerunner of the Slugging Average. TOTAL BASES RUN A silly stat of one year's duration, 1880, this was sort of an RBI in reverse, from the runner's perspective. Also called "Bases Touched," it was nothing more than that and signified nothing about individual talent. Trivia: the National League's leader in 1880 was Abner Dalrymple, with 501 bases touched. TOTAL CHANCES Putouts plus assists plus errors; in other words, total chances offered, not total chances accepted. TOTAL PITCHER INDEX The sum of a pitcher's Pitching Runs-- expressed as Ranking Runs, employing the same formula used to compute Relief Ranking Runs-- Batting Runs (in the AL since 1973, zero), and Fielding Runs, all divided by the Runs Per Win factor for that year (generally around 10, historically in the 911 range); abbreviated as TPI. See Runs Per Win, Relief Ranking. TOTAL PLAYER RATING The sum of a player's Adjusted Batting Runs, Fielding Runs, and Base Stealing Runs, minus his positional adjustment, all divided by the Runs Per Win factor for that year (generally around 10, historically in the 911 range). See Runs Per Win. TRIPLE CROWN Long regarded as consisting of batting average, home runs, and RBI, but was not always so. In the early years of this century, newspapers spoke of Ty Cobb shooting for the "triple crown" of batting average, runs, and hits. WEIGHTED AVERAGE The next step in statistical sophistication after first, counting and, next, averaging. Chadwick's Total Bases Average was probably the first weighted average, in that it assigned values of 1 to a single, 2 to a double, 3 to a triple, and 4 to a home run. WEIGHTED RATING SYSTEM Ted Oliver's invention, promoted in a 1944 self-published booklet called Kings of the Mound. We have modified Oliver's pioneering effort to create Wins Above Team (see below), which entry presents a discussion of Oliver's effort. WIN POINTS See Player Win Averages. WINS ABOVE LEAGUE A pitcher's won-lost record restated by adding his Pitching Wins above the league average to the record that a league-average pitcher would have had with his number of decisions. Example: Tom Seaver has a hard-luck season, going only 1614 despite a 1.76 ERA and five Pitching Wins; applying the five wins to a league-average 1515 mark in the same 30 decisions results in a WAL of 20-10. WINS ABOVE TEAM How many wins a pitcher garnered beyond those expected of an average pitcher for that team. As the editors of this volume, in their earlier Hidden Game of Baseball, modified Ted Oliver's Weighted Rating System (see above), they now improve this statistic thanks to Bill Deane's corrective for its tendency to overvalue the contributions of good pitchers on awful teams. Oliver's Weighted Rating System for pitchers was motivated by the inadequacies of both the won-lost percentage and the ERA when it came to evaluating pitchers laboring for poor teams. The Oliver formula, ingenious if flawed, was: pitcher's won-lost percentage minus the team's won-lost percentage--after removing the pitcher's decisions from the team's record--then multiplying the difference by the pitcher's number of decisions. Here is an example of the Oliver method as applied to Bobby Castillo, who in 1982 pitched very well in going 13-11 for a very bad Minnesota club (60-102; without him, 47- 91): ``` |13 47 | |-- - --- | X 24 |24 138 | ``` ` or ` ` (.542 - .341) X 24 ` ` or ` ` .201 X 24 = 4.824 ` The figure of 4.824 would have been represented by Ted Oliver as "4,824 points"; he did not seem to recognize that had he retained the decimal point, his rating would have been expressed directly in wins. Thus the number of wins Castillo accounted for in his 24 decisions that an average Minnesota pitcher would not have gained was 4.8. Thanks to a key modification of our earlier formula for Wins Above Team, abbreviated as WAT, we now propose the following: calculate the pitcher's won-lost percentage and the team's winning percentage after his decisions have been set aside. If the pitcher's percentage is higher, then WAT is ``` |Pitcher pct. - Team pct.| Pitcher decisions X |------------------------| | 2 - 2 X Team pct. |``` If the pitcher's percentage is lower, then WAT is ``` |Pitcher pct. - Team pct.| Pitcher decisions X |------------------------| | 2 X Team pct. |``` WON-LOST PERCENTAGE Computed as wins over decisions.