Throughout this book we introduce and define various statistical terms. There are also many terms not mentioned in this book that are relevant to baseball analysis. In an effort to consolidate all these concepts in one place, we’ve compiled this wide-ranging glossary.
Age-twenty-seven peak: In studying baseball players’ peak age, Bill James found that for players with significantly long careers, the most common peak age was twenty-seven. More broadly, the peak age range for players with long careers has been pegged at twenty-five to twenty-eight and twenty-five to twenty-nine by various researchers. Improved medical care, nutrition, and exercise regimens have helped the current generation of players—including future Hall-of-Famers Roger Clemens and Randy Johnson—perform at peak levels well into their thirties and early forties, leading to speculation that peak age may be older than it once was. To date, though, no study has conclusively refuted James’s findings, suggesting that the Rocket and the Big Unit remain outliers. (Chapter 7-3)
APR: Adjusted Pitching Runs. Measures the number of runs a pitcher prevented as compared to a league-average pitcher in a neutral park in the same number of innings. Derived from the pitching component of Linear Weights (Pitching Runs), APR includes an adjustment for ballpark and is based on all runs allowed, not just earned runs (see RA). The formula is APR = L × IP – R/PF, where L is the league average of runs per inning and PF is the park factor for the player’s home park. (Chapter 2-1)
ARP: Adjusted Runs Prevented. A measure of the number of runs a relief pitcher prevented as compared to an average pitcher, given the Base/Out state (the combination of outs and bases occupied) in which he entered and left each game, adjusted for league and park. Runners on base when a pitcher enters the game are called Inherited Runners. Runners on base when a pitcher exits the game are called Bequeathed Runners. (Chapter 2-2)
AVG/OBP/SLG: The holy trinity of batting stats, meant to convey a more accurate gauge of hitting ability than the traditional AVG/HR/RBI. AVG is the familiar batting average: hits per at-bat, not counting walks, hit by pitches, or sacrifices. OBP is on-base percentage: total number of times on base (hits plus walks plus hit by pitches) divided by the total of at-bats, walks, hit by pitches, and sacrifice flies (often called total plate appearances, although in fact sacrifice bunts and catcher’s interference are excluded). SLG is slugging average: total bases on hits (one for a single, two for a double, etc.) divided by at-bats. Together, the three provide an excellent snapshot of offensive prowess, combining the ability to get on base and to hit for power. (Chapter 1-1)
BABIP: Batting average on balls in play. A hitter’s average or pitcher’s average allowed on batted balls ending a plate appearance, excluding home runs. In the case of pitchers, BABIP for the most part is a function of luck and defense. The flip side of BABIP is Defensive Efficiency. (Chapters 2-1, 3-1, 3-2)
Base-Out Matrix: See Run Expectancy Table
Base-Out state: Also called Base-Out situation. For a given point during an inning, the combination of the number of outs and the bases occupied represents the “state” of the inning. This summary of the game situation is used to determine the expected number of runs that will score during the rest of the inning, to evaluate relief pitching effectiveness, and to help compute the expected win probability for the game. (Chapter 4-2)
Bequeathed Runs Prevented: Given the Base/Out state (the combination of outs and bases occupied) left by a pitcher exiting the game, the number of runs subsequent relievers allowed to score as compared to a park-adjusted league-average performance. A positive figure means the subsequent relievers kept more of the bequeathed runners from scoring than expected. A negative figure means more of the runners scored than expected. (Chapter 2-2)
BFP: Batters Faced Pitching, the total number of plate appearances against a given pitcher. Teams sometimes track BFP in addition to pitch counts to measure a pitcher’s workload and make decisions on leaving him in or lifting him based on those factors. (Chapter 2-3)
BRAA: Batting Runs Above Average, the difference between the Equivalent Runs that this player produced and the Equivalent Runs that an average player would have produced in the same number of outs. An “average player” by definition, has an Equivalent Average of .260. (Chapter 1-1)
BRAR: Batting Runs Above Replacement, the difference between the Equivalent Runs that this player produced and the Equivalent Runs that a replacement player would have produced in the same number of outs. A “replacement player” in EqA terms, has an Equivalent Average of .230; players who hit for a .230 EqA rarely remain in the major leagues for long unless they are seen as good defensive players. (Chapter 1-1)
Category I–V starts: Starting-pitcher outings are divided into five categories based on how many pitches were thrown and the associated risk of short-term decline in pitching performance. Derived from Baseball Prospectus’s Pitcher Abuse Points (PAP) research. (Chapter 2-3)
Category |
Pitch Range |
Risk of Short-Term Decline |
I |
0–100 |
smallest |
II |
101–109 |
minimal |
III |
110–121 |
moderate |
IV |
122–132 |
significant |
V |
133+ |
high |
CERA: Catcher ERA. Invented by Craig Wright for his book The Diamond Appraised, Catcher ERA is an attempt to measure a catcher’s defensive ability, in particular his ability to work with pitchers and call a good game. Subsequent studies suggest that catchers’ game-calling ability is nearly impossible to measure and that CERA isn’t a reliable stat. CERA = (Earned Runs while catching)/(Innings Caught) × 9. (Chapter 3-3)
Competitive balance: A somewhat nebulous term used to indicate the degree to which every team has a shot at competing for a postseason berth. Whether this means having a shot in a given year or being assured of a pennant race at least once every few years generally depends on who is making the argument. Commissioner Bud Selig has frequently argued for a drag on salaries (whether a salary cap, a luxury tax, or another mechanism) to provide more teams with “hope and faith” and improve competitive balance. This despite Major League Baseball’s producing nineteen different World Champions in the past twenty-six years, a record of parity unmatched by any other major professional sport. (Chapter 6-3)
Complete game percentage: The percentage of games completed by the starting pitcher, a number that has fallen drastically in recent times due to a variety of reasons including specialized relief roles, increased scoring, higher salaries, and the understanding that high pitch counts increase the risk of injury and ineffectiveness. In 2005, starters pitched complete games 3.9 percent of the time. In 1985, the percentage was 14.9 percent, in 1955 it was 30.3 percent, and a century ago it was 79.9 percent. (Chapter 2-3)
Correlation: A measure of how closely aligned two statistics are, on a scale of 1 to –1. A correlation of 1 means that the two move in lockstep (if statistic X goes up, so does statistic Y); –1 means they move in opposition (if X goes up, Y goes down); 0 means they bear no statistical relationship (X tells you nothing about what Y does, and vice versa).
Counting statistic/rate statistic: A counting statistic evaluates a player’s performance based on the total number of times he achieved a certain event. For example, home runs are a counting stat. A rate statistic looks at a player’s performance based on the rate at which he achieves a certain event. For example, batting average, which divides the number of hits a player produces by the number of at-bats he sees, is a rate stat. Both counting stats and rate stats can in some cases present a skewed view of a player’s achievements. A leadoff hitter, for instance, is more likely to accumulate 200 hits in a season than a cleanup hitter because he gets more chances at bat over the course of a season. On the other hand, a batter who hits .400 may seem like a superstar. But if he achieved that .400 average by collecting 4 hits in 10 at-bats, his feat is all but meaningless, since it’s skewed by a small sample size. (Chapter 1-1)
Defensive Efficiency: A thumbnail measure of the team’s defense that’s also the flip side of BABIP. Defensive Efficiency measures the percentage of balls in play (i.e., non-home-run batted balls ending a plate appearance) that a defense converts into outs. As is the case with all other statistics, Defensive Efficiency works best when adjusted to reflect the tendencies of the park in question. For instance, in Boston, balls that bang off the Green Monster thirty feet in the air count against the defense, even though such a ball is impossible to turn into an out. (Chapter 3-2)
Defensive Spectrum: An observation by Bill James that talent is unequally distributed across the range of defensive positions: The harder the position, the fewer players capable of handling it at a major league level. The spectrum runs 1B-LF-RF-3B-CF-2B-SS, with catchers something of a special case but toward the right end as well. As players age, they tend to drift leftward on the defensive spectrum, toward positions requiring less defensive skill; think of an outfielder moving to first base as he gets older and slows down. The result is a greater pool of talent available to play those left-of-spectrum positions, enabling teams to find better hitters to take those jobs. Shifts to the left happen frequently, sometimes in the low minor leagues just after a player is drafted. Shifts to the right rarely take place with any success; an exception would be Cal Ripken Jr. moving from third base to shortstop as a rookie. (Chapter 3-2)
DERA: Derived from Pitching Runs Above Average (PRAA), it is simply the ERA a pitcher would need to have that many PRAA in this many innings, given that an average pitcher has an EqERA of 4.50. Like PRAA, DERA has been adjusted for park effects, league offensive level, and the team’s fielding level. (Chapter 2-1)
DIPS: Stands for Defense-Independent Pitching Statistics. Developed by analyst Voros McCracken, DIPS attempts to isolate a pitcher’s performance from that of the fielders supporting him. To do this, DIPS focuses on the elements of the game most under the pitcher’s direct control: strikeouts, walks, hit batsmen, and home runs allowed. (Chapter 3-1)
DIPS ERA: An adjusted version of a pitcher’s traditional ERA in keeping with the tenets of Voros McCracken’s Defense-Independent Pitching Statistics. DIPS ERA differs from ERA in that the former uses as its components the elements of the game directly controlled by the pitcher (strikeouts, walks, hit batsmen, and home runs allowed). (Chapter 3-1)
DT: Davenport Translations, a process for converting a player’s statistical line from one league into a line of statistics for a different league without changing the underlying value of those statistics when it comes to wins and losses. Players’ statistics are a combination of their own skills and a background level of play that is unique to their league and park. DTs isolate the league and park effects from the stat line, allowing us to add the park and league effects we want—most often to give everybody the same effects and thus to project all players onto a common background. They are often used to compare players across eras (what would Ty Cobb hit if he played now?). They can also be used to convert minor league performances into an equally valuable major league line. In that context, they are conceptually similar to Bill James’s Major League Equivalencies, although the procedure itself is totally different. (Batting Practice, Chapter 7-2)
DW: Delta Wins, the difference between actual wins and expected wins based on a Pythagorean Formula that uses runs or run components (hits, walks, total bases, hit by pitches, stolen bases, etc.). A positive number indicates a team that has won more games than expected from its statistics.
EqA: Equivalent Average, a rate statistic designed to do two things: measure the offensive performance of a player and make the result easy to understand. EqA combines a player’s abilities to hit for average, hit for power, draw walks, get hit by pitches, and steal bases. It adjusts for the offensive level of the league and of the park; it can also adjust for the difficulty level of the league or for not facing your own team’s pitchers. It is basically Equivalent Runs per out, with some extra math included to make the answer look like a batting average. An average player in any league has, by definition, an EqA of .260 (unless league difficulty adjustments are made). The historical distribution between career EqAs and career batting averages is extremely close. Because of that, it is easy for even a casual fan to recognize the difference between a good EqA (.300), a really good EqA (.350), and a historically good EqA (.400) as well a really bad one (like Mario Mendoza’s career .191 EqA). (Chapter 1-1, others)
EqBR: Equivalent Base Runs. A player’s number of runs gained by baserunning (not including stolen bases) over league average, given his home park and the situations in which he ran the bases. The estimated number of runs gained is based on the Expected Runs Matrix (see Expected Runs) for the given season and the number of times the player took the extra base or was thrown out on the basepaths. (Chapter 4-1)
EqERA: Equivalent ERA, calibrated to an ideal major league where EqERA = 4.50. While a major league pitcher’s equivalent stats should not differ substantially from his actual numbers, a minor league pitcher’s equivalent stats undergo translation and may differ significantly. Equivalent stats are adjusted for park effects. (Chapters 2-1, 7-2)
EqR: Equivalent Runs, an estimate of how many runs a player produced for his team. EqR combines the abilities to hit for average, hit for power, draw walks, and steal bases—as well as playing time—into an estimate of runs added to an average team. When applied to teams throughout baseball history, EqR is a better estimator of how many runs they’ve scored than any other similar statistic (runs created, linear weights, etc.) we have tested. EqR is normally adjusted for park and league effects so that all players can be compared evenly (an EqR without those adjustments is called UEqR, for Unadjusted). A fan looking at EqR should think of them like runs or RBI; 100 in a season are a reasonable standard for excellence. (Chapter 1-1)
Expected Runs: The number of runs an average team will score in the remainder of the inning after a given number of outs and baserunners. For example, in 2005, with a man on first and no one out, teams scored an average of .90 runs in the rest of the inning. With a man on second and one out, they scored .69 runs. Expected Runs are extremely useful for testing the efficacy of 1-run strategies and analyzing the performance of relief pitchers. (Chapter 4-2)
Expected Wins: Like Expected Runs, Expected Wins show a team’s odds of winning the game given the inning, score, outs, and baserunners. Expected Wins are expressed as a percentage. For example, in 2005, visiting teams leading by 1 run in the top of the ninth inning won the game 87.6 percent of the time; if the game was tied, they won only 47.9 percent of the time. Expected Wins has many of the same practical applications as Expected Runs, but the Win Expectancy framework has largely replaced it in practical application. The primary reason for this is because some situations happen very infrequently in a season, and thus there is no Expected Wins number associated with that situation for a given season. In 2005, no visiting team ever loaded the bases with no one out while trailing by 1 run in the eighth inning; no home team faced a tie game in the ninth with a man on third and no one out. The absence of data points for these situations makes the theoretical Win Expectancy Framework a more robust tool for analyzing questions involving Expected Wins. (Chapter 4-2)
FRA: Fair Run Average, which measures a pitcher’s runs allowed per nine innings—adjusted to reflect the presence of inherited or bequeathed runners. (FRA also differs from the more traditional ERA in that it doesn’t unfairly distinguish between earned and unearned runs.) For instance, if a starter leaves the game with the bases loaded and no outs and the subsequent reliever manages to polish off the inning without allowing a run, then that starter’s “fair” runs allowed will exceed his actual runs allowed. After all, he deserved to give up more runs than he did in the frame, but thanks to the fine work of his bullpen, those three bequeathed runners didn’t score. (Chapters 2-1, 3-1)
FRAA: Fielding Runs Above Average, the number of runs a fielder has saved his team compared to an average player at the same position. Fielding Runs are determined through a complicated process that begins by separating the team’s defensive performance into pitching and fielding components. The team fielding is separated into catching, infield, and outfield portions; each of those is then split into separate positions; finally, each position is split into all of the players who played there during the season. At each step, the player’s defensive statistics are compared to standards defined by the league and modified by the team’s pitching (strikeouts, baserunners allowed, groundball/flyball ratios). The best player at any position in a given year is usually around 20 runs—typically a little higher for skill positions like shortstop and catcher and a little lower for first basemen and corner outfielders. (Chapter 3-2)
FRAR: Fielding Runs Above Replacement, similar to FRAA except that instead of being compared to an average player at his position, a player is compared to a replacement-level player at his position—roughly, the worst semiregular player in the league at that position. In general, the more important the position, the more runs the worst player costs you, so that FRAR works as a positional adjustment. In today’s game, an average shortstop or catcher is about 30 runs better than replacement level over the course of a season, while an average first baseman is only about 10 runs better (and a designated hitter, of course, is worth no runs, defensively). In the past, with fewer strikeouts and more balls in play, fielders had a higher share of total team pitching plus fielding; this is reflected in higher FRAR for players from other eras. (Chapter 3-2)
G/F: The ratio of groundballs to flyballs hit by a batter or produced by a pitcher. Depending on the data source, sometimes this ratio includes all batted balls or just balls converted into outs (many systems now strip out line drives and popouts as well). Either way, it’s a useful indicator for pitchers and one that correlates very well from year to year. Pitchers with a G/F ratio of 1.5 or greater are generally considered groundball pitchers. They tend to give up more base hits but fewer extra-base hits and home runs. Pitchers with G/F less than 1.5 are considered flyball pitchers. They tend to give up fewer base hits but more extra-base hits and home runs. Among pitchers who qualified for the ERA title in 2005 were Brandon Webb (4.58), Derek Lowe (3.69), and Jake Westbrook (3.61). The lowest G/F ratios were by John Patterson (0.90), Scott Elarton (0.90), and Chris Young (0.96). Among the ninety-two pitchers who qualified, the median G/F was 1.67. (Chapter 2-1)
Inherited runners: Baserunners still on base who are the responsibility of a previous pitcher when a relief pitcher comes into the game in the middle of an inning. We look at the percentage of inherited runners a relief pitcher allows to score in determining how well he’s pitched when brought into jams. Provides a useful measure of a relief pitcher’s value to the team. (Chapter 2-2)
ISO: Isolated Slugging, a measure used to evaluate a player’s pure power. It’s calculated by subtracting batting average from slugging average, i.e., SLG – AVG = ISO. Isolated Slugging is one of the most powerful predictors of a hitting prospect’s future success. (Chapter 1-1)
League adjustments: A fundamental principle of statistical analysis in baseball is that environment must be accounted for. Most often, this takes the form of park adjustments, but league context is also critical. Because of factors like rule changes, playing styles, training and nutrition breakthroughs, trends in park construction, and even equipment, different eras can affect run scoring in different ways. For instance, in 1968, when the strike zone stretched from the hitter’s shins to his shoulders, runs were hard to come by. But in, say, 1998, when the strike zone was much more compact and a number of hitter-friendly parks had been built, scoring levels were much, much higher. As a result, a run scored in one era may mean more or less than one scored in another era. (Batting Practice)
Leverage: Measures how important a given situation during a game is, relative to the start of the game. The start of the game is defined as a Leverage of 1.0. As the game progresses, the Leverage goes up and down, based on the inning, the number of outs, the runners on base, and the difference between the two teams’ runs scored thus far. More specifically, Leverage is the ratio between how much a single run scored changes the expected probability of winning in the current situation and how much a run would have changed the expected probability of winning at the very beginning of the game. For example, if a run scored in the seventh inning increases the probability of winning by 10 percent, while a run at the start of the game increases it by 5 percent, the Leverage of the situation in the seventh inning is 10 percent/5 percent = 2.00 Leverage. (Chapter 2-2)
Linear Weights: Created by Pete Palmer for Total Baseball, a system of estimating runs by assigning a weight to each event (via Batting Runs, Pitching Runs, and Fielding Runs) and adding up the sums. The total represents the number of runs contributed or saved beyond those of a league-average player or team.
Line drive percentage: The percentage of those batted balls ending a plate appearance that are classified as a line drive, as opposed to a groundball, a flyball, or a pop-up. Can be used as a predictor of future batting average gains or losses. (Chapter 8-2)
Log-5: A method introduced by Bill James in the 1981 Baseball Abstract to predict the probability of victory when two teams of a given winning percentage play against one another. The formula for Log-5 is as follows:
. . . where A is team A’s winning percentage, and B is team B’s winning percentage. The result of the formula indicates how often Team A should beat Team B. For example, if Team A wins 60 percent of its games and Team B wins 45 percent of its games, Team A should beat Team B 64.7 percent of the time. Researcher Tom Ruane has verified the log-5 method as an accurate predictor of team-versus-team matchups throughout baseball’s history. (Chapter 9-3)
Luck: The number of extra wins or losses a pitcher totaled compared to his expected record. That expected record, also known as a Support-Neutral Won-Lost record, is the mark a pitcher “should” have reached given his own performance and park-adjusted, league-average support from his offense and his bullpen. (Chapter 2-1)
Also, an element that helps explain the gap between actual performance and expected performance. In baseball the role of luck, or perhaps more accurately randomness, cannot be overstated. From a performance-analysis standpoint, it rears its head to varying degrees in the rates of hits on batted balls in play, in a team’s record in 1-run games, in the outcome of a short series, in the amount of offensive and bullpen support a pitcher gets, and in the season-to-season variations in player performance. All of these are generally the results of limited sample sizes, measured by imperfect tools. See also Delta Wins, DIPS, Regression to the mean, SNW. (Chapters 3-1, 5-3, 9-2)
Marginal cost: The additional cost occasioned by a certain move. For example, signing a $10 million a year player represents a marginal cost of $10 million, while trading a $7 million player for a $10 million one is a marginal cost of $3 million. Often compared with “marginal revenue,” which is how much more income is generated by a given move (from added ticket sales, a free-agent signing, a new stadium). (Chapter 5-2)
Marginal Wins/Marginal Dollars: A statistic first devised by the late Baseball Prospectus author Doug Pappas that measures efficiency in team spending. Marginal Wins are the number of wins above what a team making the major league minimum could reasonably accumulate (set by Pappas at 49); Marginal Dollars are how much actual payroll exceeds the minimum for a forty-man roster ($13 million in 2003). Dividing the two provides a number ranging from under $500,000 per added win (extremely efficient) to more than $4 million per added win (extremely inefficient). (Chapter 5-2)
Mendoza Line: A hypothetical line representing a .200 batting average. The term is named after weak-hitting shortstop Mario Mendoza, who played nine otherwise unremarkable seasons from 1974 to 1982 for three teams. The idea behind the term holds that if you can’t hit for a higher average than a popgun threat like Mendoza (though Mendoza’s lifetime batting average was actually .215), you don’t deserve a major league job. The concept has broader implications: It establishes a major league “replacement level,” the bare-minimum skill level that allows teams to make intelligent spending decisions based on how much a player contributes above that threshold. (Chapter 5-1)
MLEs: Major League Equivalencies, a system developed by Bill James for translating minor league performances into their major league equivalents by adjusting not only for scoring environment and park effects but also for the quality of competition. By correcting for these often-drastic distortions (such as the inflated hitting stats of the Pacific Coast League), past minor league performances become as useful for predicting future major league performances as past major league performances. Thus, it becomes possible to compare the production of a Triple-A player with that of a marginal major leaguer in considering personnel decisions. James held that in terms of using his sabermetric findings to help a baseball team, MLEs were the most important research he had ever done. (Chapter 7-2)
MLV: Marginal Lineup Value, a statistic measuring offensive production, expressed in runs above an average offensive player. Conceptually, MLV takes a theoretical team of nine average hitters, then replaces one of them with the player we want to measure, gives him the same percentage of the team’s total plate appearances as he had on his real team, and computes how many more (or fewer) runs the team would score as a result of the change. A positive MLV indicates that the player is above average. MLV can be negative, indicating the player is a below-average hitter. MLV is park-adjusted and calibrated to league average. Jason Giambi had a 41.0 MLV in 2005, meaning that his offense would have produced 41 more runs for an average team than a league-average hitter would have had in the same amount of playing time. (Chapter 1-1)
MLVr: Whereas MLV is a counting statistic like hits, home runs, or RBI, MLVr is a rate statistic like batting average or ERA. MLVr measures the rate of offensive production, expressed as runs per game. An MLVr of 0.000 is exactly league average (say, 4.50 runs per game). An MLVr of 0.100 means that an average team would score 0.1 more runs per game by replacing one of its hitters with this player (from 4.50 to 4.60 R/G). An MLVr of –0.050 means that an average team would score 0.05 R/G fewer with this player (from 4.50 to 4.45 R/G). (Chapter 1-1)
Normalization: As applied to baseball, the process of adjusting player statistics for a variety of contexts to allow better comparison without corrupting influences. For example, players compete in a variety of parks, leagues, and even historical eras that influence their performance. Normalization allows player performance from any league—minor leagues, foreign leagues, independent leagues—in any era to be compared to other players in different settings by removing extraneous factors and leveling the playing field. (Batting Practice)
NRA: Normalized Runs Allowed, used primarily in Davenport Translations to compare pitchers across different eras. Because some eras have vastly different averages—the 1960s were notoriously pitcher-friendly, while the late 1990s saw a massive increase in offense—pitchers with the same runs allowed (RA) in two different seasons may have different values to their teams. An RA of 4.00 in 2000 is very good; an RA of 4.00 in 1968 is very bad. NRA removes those differences and allows for an apples-to-apples comparison of pitchers from different eras. (Batting Practice)
Old player’s skills: Hitters who walk a lot and strike out a lot without showing meaningful speed on the bases and while playing a noncritical defensive position are said to have “old-player skills.” Players who show old-player skills early in their careers tend not to age well. In contrast, hitters who don’t strike out much and run the bases well tend to hold up better over time. (Chapters 7-2, 7-3)
1-run strategy: In-game decisions that attempt to exchange the possibility of a big inning for the increased probability of scoring a single run. The most popular of these strategies are stolen bases, sacrifice bunts, and intentional walks, typically employed late in close games when the value of a single run is nearly as valuable as that of many runs. (Chapter 4-2)
OPS or PRO: The sum of on-base percentage plus slugging average (a.k.a. Production from Total Baseball). While math purists cringe at the notion of adding what are in essence two fractions with different denominators (OBP is based on plate appearances, SLG on at-bats), OPS is a quick-and-dirty stat for gauging offensive productivity. It’s useful because it correlates better with run scoring than batting average, on-base percentage, or slugging average alone. However, OPS has its limitations. First, it assumes that OBP and SLG are of equal value while steamrolling the nuances preserved by keeping OBP and SLG separate. A hitter with a .350 OBP and a .350 SLG is very different from a hitter with a .250 OBP/.450 SLG; when considering how to build a lineup, those two players offer distinct pluses and minuses. OPS also ignores the context of ballpark effects and league scoring levels, both of which can greatly influence its two components. A .700 OPS in 1905 means something very different from a .700 OPS in 2005. The first limitation makes it more desirable to consider the trinity of AVG/OBP/SLG as a unit, with all of those nuances intact. The second limitation can be overcome by using a statistic such as Equivalent Average, which links the abilities to get on base and to advance runners with the run-scoring context. (Chapter 1-1)
OPS+ or PRO+: A comparison of a player’s OPS (on-base percentage plus slugging average) to the park-adjusted league average, providing a good deal more context than OPS itself. The formula is:
100 × [(Player OBP)/(Park-Adjusted League OBP) + (Player SLG)/ (Park-Adjusted League SLG) – 1]
An OPS+ of 100 is average. Thus, an OPS+ greater than 100 is better than league average; less than 100 is worse than league average. (Chapter 1-1)
PADE: Park-Adjusted Defensive Efficiency. Based on Defensive Efficiency, PADE measures team defense by determining the percentage of balls in play a defense converted into outs and adjusting for the team’s home park. For example, the Colorado Rockies face an inherent disadvantage in Defensive Efficiency because their park is so much larger than the league average. By adjusting for parks such as Coors Field, PADE shows how well each team’s defense would have performed in a league-average ballpark.
PAP: Pitcher Abuse Points, a measure developed by Baseball Prospectus to quantify starting pitcher usage and the risk of ineffectiveness and injury associated with overuse. PAP is computed for each game started as PAP = (# pitches – 100)3, if # pitches = more than 100, or 0 otherwise. (Chapter 2-3)
Park adjustments: Adjustments made to player statistics to reflect the playing environment. For example, a hitter slugging .500 in Coors Field, which drastically inflates run scoring, is showing less power than one slugging .475 in PETCO Park, which drastically deflates run scoring. Adjustments are made by comparing the numbers produced by a team and its opponents in home games versus what they produce in road games. Ideally, park adjustments will span at least three seasons so that a sizable data sample is used. (Batting Practice, Chapters 1-1, 8-2, others)
PECOTA: Short for Player Empirical Comparison and Optimization Test Algorithm (though the spelled-out version is not commonly used), a system used to forecast a player’s future performance based not only on his own past statistics but on the statistics of players similar to him. Age, position, and body type are all taken into account, along with the adjustment of the player’s statistics for ballpark, league, and quality of competition. Thus, a slow, slugging first baseman who walks a lot will be compared with the career progression of other slow, slugging first basemen who walked a lot, while a speedy center fielder will be compared to the progression of other speedy center fielders. PECOTA forecasts are expressed as a range of possible outcomes at the ninetieth, seventy-fifth, sixtieth, fiftieth, fortieth, twenty-fifth, and tenth percentiles, along with a weighted mean projection that accounts for the likelihood that performances in the lower percentiles will reduce his playing time. (Chapter 7-3)
PERA: A pitcher’s ERA as estimated from his peripheral statistics—including homers, walks, and strikeouts per 9 innings—adjusted for ballpark, league, and level of competition (abbreviated as EqHR9, EqBB9, EqK9). Because it’s not sensitive to the timing of batting events, PERA is less subject to luck than ERA and a better predictor of ERA going forward than actual ERA itself. PERA and its component peripherals are calibrated to an ideal league with an average PERA of 4.50. (Chapter 2-1)
Peripherals: The underlying pitching statistics that carry more predictive value (and thus offer more insight into a pitcher’s true ability) than other stats more readily embraced by the mainstream. Key peripherals include strikeout rate, walk rate, groundball-to-flyball ratio, and home-run rate. Studies of pitcher performance show that those peripheral stats allow teams to better gauge a pitcher’s future than won-lost record or even ERA. (Chapter 2-1)
Pitch counts: The number of pitches thrown by a pitcher in a game. The stat has gone from obscure to ubiquitous in the last decade, thanks to more advanced studies of pitcher usage and injuries. Studies of pitcher abuse—including those conducted by Baseball Prospectus—have shown that high-pitch-count starts can lead to future injuries and ineffectiveness for pitchers. Those findings remain controversial, though, given the multitude of variables associated with pitching performance and the numerous different types of pitchers. (Chapter 2-3)
Playoff Success Points (PSP): A measure designed by Nate Silver to indicate a team’s degree of success in the postseason in the era of divisional play. PSP assigns points to playoff teams as follows:
3 points for making the playoffs
3 points for winning the LDS
4 points for winning the LCS
4 points for winning the World Series
1 point for each postseason win
–1 point for each postseason loss
The highest possible PSP is 25, for a team that sweeps through all eleven postseason games, while the lowest is 0, for a team that is swept in the first round. (Chapter 9-3)
Plexiglas Principle: The tendency of players or teams to alternate seasons of improvement with those of decline. Bill James introduced this term in the 1982 Baseball Abstract by likening that proclivity to a piece of Plexiglas, which, once bent, tends to return to form. It’s really just a colorful, nonmathematical term for describing the concept of regression to the mean.
PMLV/PMLVr: Positional MLV (PMLV) is like MLV, except instead of comparing a batter to a league-average hitter, he is compared to an average hitter at the position he plays. First basemen are compared to an average first baseman; shortstops are compared to average-hitting shortstops. PMLVr is the rate statistic version, measuring the runs per game the batter produced above an average hitter at the same position. (Chapter 1-1)
PRAA: Pitching Runs Above Average, the number of runs that a pitcher saved his team compared to what an average pitcher would have allowed in the same number of innings. Pitchers are rated primarily by the number of runs (all runs, not just earned runs) they allow. We make adjustments for park effects and for league offensive level, just as we do for batting stats. However, pitchers also receive an adjustment for the quality of the fielders working behind them, who can have an enormous influence on the pitcher’s statistics (see FRAA and FRAR). Strikeout pitchers are somewhat less dependent on their defensive support than finesse pitchers, and this is also reflected in PRAA. (Chapter 2-1)
PRAR: Pitching Runs Above Replacement, like PRAA except that we compare a pitcher’s adjusted runs allowed to a replacement pitcher rather than an average pitcher. The level of a replacement pitcher has changed dramatically over time, increasing as the pitcher’s share of total defense (pitching plus fielding) has increased—as indicated by higher strikeout, walk, and home-run rates over time. The WARP system considers replacement-level defense—a replacement-level pitcher combined with a full set of replacement-level fielders—to be worth a little more than 3 runs a game. The pitcher’s share of those 3 or more runs has increased from about 15 percent in the 1800s to about 70 percent today. Thus, the RA of a replacement-level pitcher has risen from about 5.00 in the 1880s to about 6.75 today (on a scale where 4.50 = league average). (Chapter 2-1)
Pythagenport: The general name given to certain versions of the Pythagorean formula. Instead of using a fixed exponent, like “2” or “1.83,” Pythagenport versions use a variable exponent based on runs scored and allowed per game—the more runs, the higher the exponent. The first such formula, developed by Clay Davenport, used a logarithmic formula to estimate the exponent; later versions by other researchers, notably David Smyth and a blogger known as “Patriot,” developed simpler and better versions (sometimes called “Pythagenpat”). (pp. 308, 309)
Pythagorean Formula: Developed by Bill James around 1980, in answer to the question: Can you tell how many games a team will win, based on its runs scored and runs allowed? James found that there was a simple relationship between them, namely, that winning percentage was roughly equal to runs scored, squared, divided by the square of runs scored plus the square of runs allowed; writing it out reminded him of C2 = A2 + B2, the equation credited to the Greek mathematician Pythagoras describing the sides of a right triangle. James subsequently claimed that using an exponent of 1.83 in the formula worked better than 2; later researchers found that the formula could be adjusted for even more accuracy (see Pythagenport). (Chapter 8-1)
RA: Run Average, the number of runs (earned and unearned) allowed by a pitcher or team per 9 innings. Many measures of pitcher success focus on earned runs, but the arbitrary nature of official scoring and error attribution, the problems of reconstructing an inning to determine unearned runs, and the relatively small number of errors nowadays compared to a century ago (before gloves were used) make considering all runs allowed by a pitcher more desirable from a predictive standpoint. Pitchers good at preventing earned runs tend to be good at preventing unearned runs. (Chapters 2-1, 3-1)
RA: Runs allowed, the total number of runs allowed by a team (most often used as a component in calculating a team’s expected winning percentage via the Pythagorean formula); or the total number of runs, including unearned runs, allowed by a pitcher, to be used in calculating Run Average, which is useful for the reasons stated previously. (Chapters 2-1, 3-1)
RA+: A comparison of the number of runs per 9 innings (both earned and unearned) allowed by a particular pitcher to the performance of a league-average pitcher in the same ballpark. RA+ is calculated by taking the league RA (Run Average) per 9 innings, multiplying it by a park factor (which expresses the percentage by which a player’s home ballpark inflates or deflates scoring), dividing that by the pitcher’s RA, and multiplying the result by 100. An RA+ of 100 is league average, an RA+ of 110 is 10 percent better than league average, and an RA+ of 90 is 10 percent worse than league average.
RA+ is thus ideally suited to compare pitchers across contexts and eras. If we compare the relative quality of Bob Gibson’s 1968 (in which he posted an ERA of 1.12 and an RA of 1.45 in a league that averaged 3.43 runs per game) and Pedro Martinez’s 2000 (an ERA of 1.74 and an RA of 1.82 in a league that averaged 5.30 runs per game), we find that once the league context is taken into account, Martinez’s 293 RA+ (in fact the top single-season RA+ since 1890) is better than Gibson’s 236 (which ranks eighth). (Batting Practice, Chapter 2-1)
RBI Opportunities: The total number of runners on base during a player’s at-bats, as defined by Baseball Prospectus’s RBI Opportunities report at BaseballProspectus.com. The report also shows which bases those runners occupied. Different hitters will get different numbers of RBI Opportunities depending on multiple factors, including the on-base percentage of batters in front of them and total number of plate appearances. This can cause observers to label certain high-RBI hitters as “clutch,” when in fact they’re benefiting from greater opportunities. (Chapters 1-1, 1-2)
RCAA: Runs Created Above Average, an offensive statistic created by Lee Sinins that determines how many runs a hitter contributes relative to the league-average hitter.
Regression analysis: A statistical technique for estimating the value of one variable based on another. Visually, this can easily be represented on a scatterplot graph with the independent variable on one axis and the dependent variable on the other. Viewed this way, the relationship between the two variables often appears as a line or trend on the graph. Determining the relationship—or “line of best fit,” as it is sometimes called—involves the technique of Least Squares.
Regression to the mean: Baseball statistics are imperfect tools for measuring player performance. Given enough at-bats or innings pitched, the performance of a given player will reflect his actual skills. But the number of opportunities in a single season—to say nothing of a month, or a best-of-seven playoff series—generally isn’t enough for the performance and skill levels to converge perfectly. A good deal of randomness or luck comes into play, exaggerating the difference between players. Players whose performances tend toward the extremes—say, a batter hitting .450 or .150 for a couple of weeks, or a reliever allowing a 5.00 ERA one year and a 2.00 ERA the next—are almost always benefiting from a run of simple random luck (good or bad) beyond their inherent level of ability. Since randomness is, well, random, you don’t expect to see it continue, so the observed performance more likely will be closer to the player’s actual level than continue on a very lucky (or unlucky) streak. This statistical phenomenon, known as regression to the mean, has been observed in venues far beyond baseball stats. It’s the great equalizer, the reason streaks and slumps don’t last forever. (Chapter 9-2)
Replacement level: The expected level of performance a major league team will receive from one or more of the best available players who substitute for a suddenly unavailable starting player at the same position, who can be obtained with minimal expenditure of team resources. Measuring player value, the difference from replacement level, instead of the difference from average, more properly accounts for the value of durability and better reflects the distribution of talent that major league teams are able to draw from. (Chapter 5-1)
Baseball Prospectus uses the following formulas as replacement level, based on research presented in Baseball Prospectus 2002. For position players, replacement level is set at a percentage of the average production for the position, measured in runs per out.
Position |
Replacement Level % |
1B, DH |
75 |
2B, 3B, SS, OF |
80 |
Catcher |
85 |
Pitcher |
100 (applies to pitcher’s hitting only; see below) |
For pitchers, replacement-level Run Average (RA) is defined as:
Starting pitchers: RepLvlRA = 1.38 × LeagueRA - 0.66
Relief pitchers: RepLvlRA = 1.70 × LeagueRA - 2.27
R-squared: The common name for the “coefficient of determination,” a statistical measure that indicates the proportion of variance explained by a variable, expressed on a scale of zero to 1. (An R-squared of zero represents complete randomness, while 1 indicates a perfect determination.) In English, that means that when two variables are used in a regression, R-squared shows how much of the change in the second variable is a result of changes in the first. For example, batter strikeout rate and Isolated Slugging (ISO) usually have a high R-squared because players swinging for the fences have a propensity to strike out. Likewise, of the three major rate stats—AVG, OBP, and SLG—OBP has the highest R-squared when correlated to run scoring, meaning the team with the highest OBP will score the most runs more often than the team with the highest AVG or SLG. The high R-squared between OBP and team run scoring is one of the major reasons the Oakland Athletics determined that OBP was undervalued in the late 1990s, one of the main points of Michael Lewis’s best-selling book Moneyball.
Run environment: A term used to describe how park and league factors affect run-scoring levels. For example, Dodger Stadium in 1968 was much more hostile to hitters than Coors Field in 2000. (Chapter 8-2)
Run Expectancy Table (a.k.a. Base-Out Matrix State, a.k.a. Expected Run Matrix): A table showing the twenty-four combinations of outs and bases occupied and the number of runs a team can expect to score in the rest of that inning given that situation. For example, in 2005, teams in bases-loaded, no-out situations averaged 2.31 runs scored, while teams with two outs and nobody on averaged 0.11 runs. A Run Expectancy Table is often based on several seasons’ worth of data. It can be used to estimate the value of a given strategy, such as sacrificing a runner on second base over to third with nobody out. It’s important to remember that such outcomes are based on average hitters and pitchers and that different skill levels need to be taken into account as well. (Chapter 4-2)
Runs Created: A seminal modern offensive statistic created by Bill James, one of a number of statistics that attempts to account for multiple offensive events in one number. Its basic formula is OBP × TB, or (Hits + Walks) × total bases/plate appearances. More complicated forms include stolen bases, intentional walks, grounded into double plays, etc.
Sabermetrics: Popular name for advanced baseball statistical analysis, coined by Bill James after the acronym for the Society for Advanced Baseball Research (SABR, pronounced “saber”), where much of the early work was done. James defined the field simply as “the search for objective knowledge about baseball.”
SNL: Support-Neutral Loss(es), the expected number of losses a pitcher would accumulate given his performance plus park-adjusted, league-average offensive and bullpen support. (Chapter 2-1)
SNLVA: Support-Neutral Lineup-adjusted Value Added, the number of wins above average added by a pitcher’s performance, given league-average offensive and bullpen support and adjusted for the Marginal Lineup Value rate of each batter a pitcher faced. (Chapter 2-1)
SNLVAR: Support-Neutral Lineup-adjusted Value Added above Replacement, the number of wins above replacement level (as opposed to average) added by a pitcher’s performance, given league-average offensive and bullpen support and adjusted for the Marginal Lineup Value rate of each batter a pitcher faced. (Chapter 2-1)
SNVAR: Support-Neutral Value Above Replacement, the number of wins above replacement level added by a pitcher’s performance, given league-average offensive and bullpen support. (Chapter 2-1)
SNW: Support-Neutral Win(s), the expected number of wins a pitcher would accumulate given his performance plus park-adjusted, league-average offensive and bullpen support. The Support-Neutral stats, created by Baseball Prospectus author Michael Wolverton and updated by Keith Woolner, are a way to measure a starting pitcher’s performance in the familiar terms of wins and losses but without the distortions that make actual won-lost records extremely flawed. (Chapter 2-1)
Speed Score: One of five metrics used in the PECOTA projection system to identify players comparable to a given hitter. Speed Scores include five components: stolen-base percentage, stolen-base attempts as a percentage of times on first base, triples, double plays grounded into, and runs scored as a percentage of times on base. (Chapters 4-1, 7-3)
Statistical significance: An expression of the certainty that the result of an analysis is not random. Statistical significance is sometimes referred to as if there is a hard-and-fast level of significance, but in reality, significance is expressed in levels, or percentages. (It may also be referred to as the observed significance level, or p-value.) Results of statistical analysis can be significant at any percentage, allowing the certainty of the results of an analysis to be quantified. For example, if you wanted to determine the average walk rate in the National League, sampling a smaller number of players will yield an estimate of the overall league average. Depending on the number of players sampled, the statistical significance may be any number of values, expressing the certainty that the walk rates of the small group of players sampled matches the overall league average. As that sample size grows, the statistical significance of the result increases as well because you can be surer that the observed average is very close to the overall average. (Chapter 9-2)
Stress: A characterization of how much of a pitcher’s workload has been compressed into high pitch count outings. Higher stress ratings over the course of a career are associated with a higher likelihood of arm injuries. Stress = PAP/# pitches. (Chapter 2-3)
Support (bullpen): A cousin of run support, bullpen support measures the contributions relievers make in a given pitcher’s games. In addition to won-lost record, bullpen support can also skew a pitcher’s ERA. If a reliever replaces the starter with two outs and two on and gives up a 3-run homer to the worst hitter in baseball, the starter bears the brunt of that lousy performance by adding 2 earned runs to his ledger. (Chapters 2-1, 3-1)
Support (run): The number of runs a team scores when a given pitcher is on the mound. This can have a significant effect on a pitcher’s won-lost record that’s beyond his control. In 1987, Nolan Ryan led the league with a sparkling 2.76 ERA (and 270 strikeouts) for the Houston Astros but still finished with an ugly 8-16 record, thanks largely to poor run support. Meanwhile, Aaron Sele posted an 18-9 record in 1999, thanks to strong run support from the Texas Rangers—despite a 4.79 ERA that even after adjusting for his hitter-friendly home park was still just a tick better than average. Baseball Prospectus’s Support-Neutral statistics strip out run support to evaluate pitchers based on their own achievements rather than their teammates’. (Chapter 2-1)
Talent Pyramid: Baseball ability is not distributed equally. Rather, the distribution of talent is more like that of a pyramid. The largest number of players—say, those unable to make the jump from amateur baseball to the pros—form the base. Somewhere above that level are those capable of a replacement-level performance in the major leagues, a smaller subset of the remaining population. Above those are major league starters. Above that level are major league stars. The elite superstars of the game reside at the tip of the pyramid. If there are ten players currently playing who will wind up in the Hall of Fame, there may be one hundred capable of making an All-Star team, three hundred capable of holding down a regular job, one thousand who might appear in a major league game in a single year, and six thousand playing professional baseball. The pyramid helps to explain why the superstars make the salaries they do. Elite talent is truly scarce, whereas average to good players are comparatively plentiful and players worth the league minimum abound.
Three True Outcomes: Another term for strikeouts, walks, and home runs, Three True Outcomes are those events that occur independent of the defense. Three True Outcome hitters have often been underrated and underpaid, with teams underrating the value of walks and overrating the impact of a batter’s strikeout. Baseball Prospectus celebrates the Three True Outcomes by recognizing the hitter who had the highest percentage of his plate appearances result in a strikeout, walk, or home run. On the flip side, a pitcher who racks up a lot of strikeouts while yielding few walks and homers is said to possess good peripherals and is a candidate for future success. The term “Three True Outcomes” is derived from a tongue-in-cheek cult called the “Rob Deer Fan Club” whose eponymous slugger excelled at producing all three outcomes.
TINSTAAPP: A term coined by Baseball Prospectus founder Gary Huckabay that stands for “There Is No Such Thing As A Pitching Prospect.” TINSTAAPP is meant to be a warning to teams not to overinvest in young pitchers—especially high school pitchers—due to their high attrition rates. The term shouldn’t be taken absolutely literally, as some pitching prospects do beat the odds and become successful major leaguers. Inspired by TANSTAAFL, an acronym for “There Ain’t No Such Thing As A Free Lunch” from Robert Heinlein’s classic book The Moon Is a Harsh Mistress.
UZR: An individual defensive statistic developed by independent statistician Mitchel Lichtman, Ultimate Zone Rating uses a similar technique to Zone Rating but makes adjustments such as comparing players to the league-average fielder, then expresses its results in the number of runs each fielder saved his team. The results of UZR are very similar to FRAA, but whereas FRAA estimates the fielder’s total chances based on commonly available statistics, UZR does so with newly available play-by-play data.
Variance/standard deviation: Variance measures the dispersion of values around their average. If a set of values are widely scattered around the average, the variance will be high. If the values are close to the average, the value will be low. The standard deviation is simply the square root of the variance. For many kinds of statistical analyses in baseball, the standard deviation is a useful measure to include because it helps quantify the amount of statistical noise we would expect to see. Approximately two-thirds of all observed values will fall within plus or minus one standard deviation, and about 95 percent of all observed values will fall within two standard deviations of the mean due just to randomness and a limited sample size.
Suppose a player is a “true” .300 hitter, and thus has exactly a 30 percent chance of getting a hit in each at-bat. Over the course of 600 at-bats, we’d expect him to have 180 hits (the average, or mean, number). The standard deviation is 11.22 hits, meaning that about two seasons out of three, we’d expect him to have between 168.78 (180 – 11.22) and 191.22 hits (180 + 11.22), which corresponds to an observed batting average of between .281 and .319.
VORP: Value Over Replacement Player captures most aspects of a player’s value. It is like MLV, except instead of comparing a batter to a league-average hitter, he is compared to a replacement-level hitter at the position he plays. First basemen are compared to a replacement-level first baseman; shortstops are compared to replacement hitting shortstops. (Chapter 1-1, others)
VORPr: The rate statistic version of VORP, measuring the runs per game the batter produced above a replacement hitter at the same position. See MLV, Replacement Level, VORP. (Chapter 1-1)
WARP (WARP-1, WARP-2, WARP-3): Wins Above Replacement Player. WARP combines a player’s BRAR, PRAR, and FRAR into a single estimate of how many wins that player was worth to his team, compared to a replacement-level player. Note that the replacement-level player used in WARP is substantially worse than the replacement-level player used by other statistics, such as VORP. The traditional definition of replacement level considers the hitting level of an average defensive player, while the WARP replacement player is both a bad hitter and a bad fielder (and a bad pitcher, if he did that too). As a result, a team composed entirely of replacement-level players would be really, really bad, only winning about 25 games in a full season. The different flavors of WARP reflect different applications of the system. In WARP-1, players are compared only to the rest of their league. WARP-2 adds two adjustments: It uses a rating of the league’s quality of play to adjust all players in a league up or down, and it normalizes fielding totals across time. WARP-3 is exactly like WARP-2, except that it expands the rating to a 162-game schedule. This allows nineteenth-century stars, who played with short schedules and difficulty ratings stacked against them, to shine a little more brightly. (multiple chapters)
WinEx: Win-Expectancy framework, a theoretical framework introduced in Baseball Prospectus 2005. WinEx determines the probability that a team will win the game based on the overall offensive tendencies of the two teams involved, the number of outs, the inning, the score, and the runners on base. As opposed to observed win expectation (see Expected Wins), WinEx’s theoretical framework does not suffer small sample-size issues, allowing win expectations to be calculated for hypothetical situations and games that have not actually occurred yet and making it a more complete and intuitive measure of a team’s chances of winning a game. (Chapter 4-2)
Winning percentage: A team’s wins divided by its total games played (or, for pitchers, wins divided by total decisions). This is written as a decimal but is easily understood as a percentage: A team with a .600 winning percentage has won 60 percent of its games—excellent in baseball. (Chapter 8-3)
W-L record: For a team, the total number of wins and losses (won-lost) accumulated to date in a season. For a pitcher, the total number of wins and losses credited to that pitcher. (In either case, wins are always listed first, so that “20-10” indicates 20 wins and 10 losses.) Since the rules governing pitcher wins and losses can be somewhat arbitrary—the winning pitcher is the one who was in the game when his team took the lead for good, regardless of who pitched the most effectively—W-L record is considered by most sabermetricians to be a poor gauge of a pitcher’s actual performance level. (Chapter 2-1)
WX: Win expectation is the increase in the probability of a pitcher’s team going on to win the game given the game situation (inning, number of outs, runners on base, run differential) from when the pitcher entered the game until his exit, and how many runs the pitcher allowed to score, assuming that the pitcher’s team has a league average distribution of run scoring, and that all other pitchers on his team who follow are average. For example, Chad Orvella came into a game on July 22, 2005, with no outs in the sixth, a runner on first base, and a 2-run lead. He pitched two innings, stranding the runner, and allowing no additional runs to score. That performance increased Tampa Bay’s expected probability of winning from 73.0 to 90.8 percent. So Orvella is credited with 0.908 – 0.730 = 0.178 WX. (Chapter 2-2)
WXRL: Win expectation, adjusted for replacement level and lineup faced. WXRL is like WX but also adjusts the expected probability of winning during the pitcher’s appearances for how strong the opposing batters he faced have been during the season. It also compares the pitcher’s performance to how a replacement-level pitcher would have done in the same situation and number of innings. (Chapter 2-2)
ZR: Zone Rating, an individual defensive statistic developed by STATS, Inc., divides the field into zones. ZR assigns each player a specific part of the field—his “zone”—and determines the percentage of balls hit into that zone that he fielded. (Chapter 3-2)