Value over replacement player
Encyclopedia
In baseball
, value over replacement player (or VORP) is a statistic popularized by Keith Woolner
that demonstrates how much a hitter contributes offensively or how much a pitcher contributes to his team in comparison to a fictitious "replacement player," who is an average fielder at his position and a below average hitter. A replacement player performs at "replacement level," which is the level of performance an average team can expect when trying to replace a player at minimal cost, also known as "freely available talent."
VORP's usefulness is in the fact that it measures contribution at the margin (as in marginal utility
). Other statistics compare players to the league average, which is good for cross-era analysis (example: 90 runs created
in 1915 are much better than 90 RC in 1996, because runs were more scarce in 1915). However, league-average comparisons break down when considering a player's total, composite contribution to a team. Baseball is a zero-sum game; in other words, one team can only win if another loses. A team wins by scoring more runs than its opponent.
It follows, then, that a contribution of any runs helps a team toward a win, no matter how small the contribution. However, the Major Leagues are highly competitive, and talent distribution in baseball does not resemble the traditional "bell curve" of a normal distribution; rather, the majority of players fall within the category of "below-average" or worse. (Since only the most talented baseball players make the Major Leagues, if all Americans' baseball talent was distributed on a bell curve then the Major Leagues would only see the uppermost edge of it, resulting in a "right-skewed" distribution.) Therefore, the so-called "average player" does not have a value of zero, like in Pete Palmer
's Total Player Rating, but instead is a valued commodity. One alternative is to rank players using "counting stats" -- simply their gross totals—but this is unacceptable as well, since it is likely that the contribution a marginal player makes, even if it does help a team win one game, is not enough to justify his presence in the Majors. This is where the concept of the replacement level enters the picture.
VORP is a cumulative stat or counting stat, not a projected stat. For example, if Bob Jones has a VORP of +25 runs after 81 games, he has contributed 25 more runs of offense to his team than the theoretical replacement player would have, over 81 games. As Bob Jones continues to play the rest of the season, his VORP will increase or decrease, depending upon his performance, and settle at a final figure, e.g., +50 runs, at the end of the season.
' runs created
, Pete Palmer
's linear weights, BaseRuns, etc. Baseball Prospectus
author Keith Woolner
uses Clay Davenport's
Equivalent Runs
in the calculation of VORP. Armed with runs and outs (for the player and that player's league), one can finally calculate VORP.
Critics of VORP take issue with where the formula's arbitrary "replacement level" is set. Many equations and methods exist for finding the replacement level, but most will set the level somewhere around 80% of the league average, in terms of runs per out. There are two exceptions to this, though: catcher
s, who shoulder a larger defensive responsibility than any other player in the lineup (and are therefore more scarce), have a replacement level at 75% of the league average. At the other end of the defensive spectrum
, first basemen
and designated hitter
s must produce at a level above 85% of the average to be considered better than "replacement level," since defense is not a big consideration at either position (it is not a consideration at all for the DH).
Therefore, to calculate VORP one must multiply the league's average runs per out by the player's total outs; this provides the number of runs an average player would have produced given that certain number of outs to work with. Now multiply that number (of runs) by .8, or whatever percentage of average the replacement level is designated to be; the result is the number of runs you could expect a "replacement player" to put up with that number of outs. Simply subtract the replacement's runs created from the player's actual runs created, and the result is VORP.
This is not the final adjustment, however: while the replacement's run total will be park-neutral (by definition, because replacement numbers are derived from league averages), the player's raw numbers won't be. Before calculating the VORP, the individual player stats must be normalized via park factors
to eliminate the distortions that can be created by each ballpark, especially extreme parks like Coors Field
in Denver (where the thin high-altitude air allows baseballs to travel farther than at sea level
, although the humidor has significantly decreased the runs scored in Coors Field, to the extent that Denver is no longer considered a pure hitter's haven) and Petco Park
in San Diego
(where the heavier sea air couples with distant fences to suppress run-scoring). After the final adjustment, the resultant VORP may be used to estimate how "valuable" the player in question is by providing a good picture of that player's marginal utility
.
), determine how many runs a theoretical "replacement" would have given up in that playing time (at the most basic level, the replacement level is equal to 1 plus the league's average runs per game), and subtract from that number the amount actually allowed by the pitcher to arrive at VORP. As an aside, Run Average is used as a measure of pitcher quality rather than Earned Run Average
. ERA is heavily dependent on the concept of the error
, which most sabermetricians have tried to shy away from because it is a scorer's opinion; also, we are trying to determine VORP in units of runs, so a calculation that uses earned runs is not of very much use to us in this instance.
The "old" definition of pitching VORP, as alluded to above, was simply:
However, further research indicated that starting pitchers and relief pitchers have different replacement thresholds, as it is easier to put up a low RAvg in relief than as a starter. Armed with that knowledge, Baseball Prospectus
2002 published the current formula for determining the replacement level for pitchers:
Therefore, the current formula for VORP is:
As was the case with hitters, run average should be normalized for park effects before VORP is calculated. Pitcher VORP is on the same scale as that of hitters.
Baseball
Baseball is a bat-and-ball sport played between two teams of nine players each. The aim is to score runs by hitting a thrown ball with a bat and touching a series of four bases arranged at the corners of a ninety-foot diamond...
, value over replacement player (or VORP) is a statistic popularized by Keith Woolner
Keith Woolner
Keith Woolner is an author for Baseball Prospectus and is the creator of the runs-based statistic VORP or Value Over Replacement Player. VORP is acknowledged by the sabermetrics community as one of the key concepts in the analysis of a player's performance and market valuation.-Education and early...
that demonstrates how much a hitter contributes offensively or how much a pitcher contributes to his team in comparison to a fictitious "replacement player," who is an average fielder at his position and a below average hitter. A replacement player performs at "replacement level," which is the level of performance an average team can expect when trying to replace a player at minimal cost, also known as "freely available talent."
VORP's usefulness is in the fact that it measures contribution at the margin (as in marginal utility
Marginal utility
In economics, the marginal utility of a good or service is the utility gained from an increase in the consumption of that good or service...
). Other statistics compare players to the league average, which is good for cross-era analysis (example: 90 runs created
Runs created
Runs created is a baseball statistic invented by Bill James to estimate the number of runs a hitter contributes to his team.-Purpose:James explains in his book, The Bill James Historical Baseball Abstract, why he believes runs created is an essential thing to measure:With regard to an offensive...
in 1915 are much better than 90 RC in 1996, because runs were more scarce in 1915). However, league-average comparisons break down when considering a player's total, composite contribution to a team. Baseball is a zero-sum game; in other words, one team can only win if another loses. A team wins by scoring more runs than its opponent.
It follows, then, that a contribution of any runs helps a team toward a win, no matter how small the contribution. However, the Major Leagues are highly competitive, and talent distribution in baseball does not resemble the traditional "bell curve" of a normal distribution; rather, the majority of players fall within the category of "below-average" or worse. (Since only the most talented baseball players make the Major Leagues, if all Americans' baseball talent was distributed on a bell curve then the Major Leagues would only see the uppermost edge of it, resulting in a "right-skewed" distribution.) Therefore, the so-called "average player" does not have a value of zero, like in Pete Palmer
Pete Palmer
Pete Palmer is a major contributor to the applied mathematical field referred to as sabermetrics. Along with the Bill James Baseball Abstracts, Palmer's book The Hidden Game of Baseball is often referred to as providing the foundation upon which the field of sabermetrics was built.Palmer began his...
's Total Player Rating, but instead is a valued commodity. One alternative is to rank players using "counting stats" -- simply their gross totals—but this is unacceptable as well, since it is likely that the contribution a marginal player makes, even if it does help a team win one game, is not enough to justify his presence in the Majors. This is where the concept of the replacement level enters the picture.
VORP is a cumulative stat or counting stat, not a projected stat. For example, if Bob Jones has a VORP of +25 runs after 81 games, he has contributed 25 more runs of offense to his team than the theoretical replacement player would have, over 81 games. As Bob Jones continues to play the rest of the season, his VORP will increase or decrease, depending upon his performance, and settle at a final figure, e.g., +50 runs, at the end of the season.
VORP for Hitters
The currency of baseball is the out. There is a finite number of outs that a team can make in one game, and it is almost always 27 (or 3 outs/inning * 9 innings/game). A player consumes these outs to create runs, and at the simplest level, runs and outs are the only truly meaningful stats in baseball. Outs are calculated by simply taking at-bats and subtracting hits, then adding in various outs that don't count toward at-bats: sacrifice hits, sacrifice flies, caught stealing, and grounded into double-play. Runs may be estimated by one of many run-approximation methods: Bill JamesBill James
George William “Bill” James is a baseball writer, historian, and statistician whose work has been widely influential. Since 1977, James has written more than two dozen books devoted to baseball history and statistics...
' runs created
Runs created
Runs created is a baseball statistic invented by Bill James to estimate the number of runs a hitter contributes to his team.-Purpose:James explains in his book, The Bill James Historical Baseball Abstract, why he believes runs created is an essential thing to measure:With regard to an offensive...
, Pete Palmer
Pete Palmer
Pete Palmer is a major contributor to the applied mathematical field referred to as sabermetrics. Along with the Bill James Baseball Abstracts, Palmer's book The Hidden Game of Baseball is often referred to as providing the foundation upon which the field of sabermetrics was built.Palmer began his...
's linear weights, BaseRuns, etc. Baseball Prospectus
Baseball Prospectus
Baseball Prospectus is an organization that publishes a website, BaseballProspectus.com, devoted to the sabermetric analysis of baseball. BP has a staff of regular columnists and provides advanced statistics as well player and team performance projections on the site...
author Keith Woolner
Keith Woolner
Keith Woolner is an author for Baseball Prospectus and is the creator of the runs-based statistic VORP or Value Over Replacement Player. VORP is acknowledged by the sabermetrics community as one of the key concepts in the analysis of a player's performance and market valuation.-Education and early...
uses Clay Davenport's
Clay Davenport
Clay Davenport, a native of Hampton Roads, Virginia, now living in Baltimore, Maryland, is a baseball sabermetrician who co-founded Baseball Prospectus in 1996. He co-edited several of the Baseball Prospectus annual volumes and is a writer for BaseballProspectus.com...
Equivalent Runs
EQA
EQA may refer to:*Equivalent average , a baseball metric*European Quality Award*External quality assessment...
in the calculation of VORP. Armed with runs and outs (for the player and that player's league), one can finally calculate VORP.
Critics of VORP take issue with where the formula's arbitrary "replacement level" is set. Many equations and methods exist for finding the replacement level, but most will set the level somewhere around 80% of the league average, in terms of runs per out. There are two exceptions to this, though: catcher
Catcher
Catcher is a position for a baseball or softball player. When a batter takes his turn to hit, the catcher crouches behind home plate, in front of the umpire, and receives the ball from the pitcher. This is a catcher's primary duty, but he is also called upon to master many other skills in order to...
s, who shoulder a larger defensive responsibility than any other player in the lineup (and are therefore more scarce), have a replacement level at 75% of the league average. At the other end of the defensive spectrum
Defensive spectrum
In Sabermetrics, the defensive spectrum is the graphical representation of the positions on a baseball field, arranged from top to bottom .-Arrangement:The defensive spectrum looks like this:#Designated hitter...
, first basemen
First baseman
First base, or 1B, is the first of four stations on a baseball diamond which must be touched in succession by a baserunner in order to score a run for that player's team...
and designated hitter
Designated hitter
In baseball, the designated hitter rule is the common name for Major League Baseball Rule 6.10, an official position adopted by the American League in 1973 that allows teams to designate a player, known as the designated hitter , to bat in place of the pitcher each time he would otherwise come to...
s must produce at a level above 85% of the average to be considered better than "replacement level," since defense is not a big consideration at either position (it is not a consideration at all for the DH).
Therefore, to calculate VORP one must multiply the league's average runs per out by the player's total outs; this provides the number of runs an average player would have produced given that certain number of outs to work with. Now multiply that number (of runs) by .8, or whatever percentage of average the replacement level is designated to be; the result is the number of runs you could expect a "replacement player" to put up with that number of outs. Simply subtract the replacement's runs created from the player's actual runs created, and the result is VORP.
This is not the final adjustment, however: while the replacement's run total will be park-neutral (by definition, because replacement numbers are derived from league averages), the player's raw numbers won't be. Before calculating the VORP, the individual player stats must be normalized via park factors
Batting Park Factor
Batting Park Factor, also simply called Park Factor or BPF, is a baseball statistic that indicates the difference between runs scored in a team's home and road games. Most commonly used as a metric in the sabermetric community, it has found more general usage in recent years...
to eliminate the distortions that can be created by each ballpark, especially extreme parks like Coors Field
Coors Field
Coors Field, located in Denver, Colorado, is the home field of Major League Baseball's Colorado Rockies. It is named for the Coors Brewing Company of Golden, Colorado, which purchased the naming rights to the park prior to its completion in 1995...
in Denver (where the thin high-altitude air allows baseballs to travel farther than at sea level
Sea level
Mean sea level is a measure of the average height of the ocean's surface ; used as a standard in reckoning land elevation...
, although the humidor has significantly decreased the runs scored in Coors Field, to the extent that Denver is no longer considered a pure hitter's haven) and Petco Park
PETCO Park
Petco Park is an open-air ballpark in downtown San Diego, California, USA. It opened in 2004, replacing Qualcomm Stadium as the home park of Major League Baseball's San Diego Padres. Before then, the Padres shared Qualcomm Stadium with the NFL's San Diego Chargers...
in San Diego
San Diego, California
San Diego is the eighth-largest city in the United States and second-largest city in California. The city is located on the coast of the Pacific Ocean in Southern California, immediately adjacent to the Mexican border. The birthplace of California, San Diego is known for its mild year-round...
(where the heavier sea air couples with distant fences to suppress run-scoring). After the final adjustment, the resultant VORP may be used to estimate how "valuable" the player in question is by providing a good picture of that player's marginal utility
Marginal utility
In economics, the marginal utility of a good or service is the utility gained from an increase in the consumption of that good or service...
.
VORP for Pitchers
VORP can also be calculated for pitchers, as a measurement of the number of runs he has prevented from scoring that a replacement-level pitcher would have allowed. The concept is essentially the same as it was for hitters: using the player's playing time (in a pitcher's case, his innings pitchedInnings pitched
In baseball, innings pitched are the number of innings a pitcher has completed, measured by the number of batters and baserunners that are put out while the pitcher on the pitching mound in a game. Three outs made is equal to one inning pitched. One out counts as one-third of an inning, and two...
), determine how many runs a theoretical "replacement" would have given up in that playing time (at the most basic level, the replacement level is equal to 1 plus the league's average runs per game), and subtract from that number the amount actually allowed by the pitcher to arrive at VORP. As an aside, Run Average is used as a measure of pitcher quality rather than Earned Run Average
Earned run average
In baseball statistics, earned run average is the mean of earned runs given up by a pitcher per nine innings pitched. It is determined by dividing the number of earned runs allowed by the number of innings pitched and multiplying by nine...
. ERA is heavily dependent on the concept of the error
Error (baseball)
In baseball statistics, an error is the act, in the judgment of the official scorer, of a fielder misplaying a ball in a manner that allows a batter or baserunner to reach one or more additional bases, when such an advance would have been prevented given ordinary effort by the fielder.The term ...
, which most sabermetricians have tried to shy away from because it is a scorer's opinion; also, we are trying to determine VORP in units of runs, so a calculation that uses earned runs is not of very much use to us in this instance.
The "old" definition of pitching VORP, as alluded to above, was simply:
- VORP = (((League Runs/Game + 1) - RAvg)/9)*Innings Pitched
However, further research indicated that starting pitchers and relief pitchers have different replacement thresholds, as it is easier to put up a low RAvg in relief than as a starter. Armed with that knowledge, Baseball Prospectus
Baseball Prospectus
Baseball Prospectus is an organization that publishes a website, BaseballProspectus.com, devoted to the sabermetric analysis of baseball. BP has a staff of regular columnists and provides advanced statistics as well player and team performance projections on the site...
2002 published the current formula for determining the replacement level for pitchers:
- For starting pitchers, Repl. Level = 1.37 * League RA - 0.66
- For relief pitchers, Repl. Level = 1.70 * League RA - 2.27
Therefore, the current formula for VORP is:
- VORP = ((Repl. Level - RAvg)/9)*Innings Pitched
As was the case with hitters, run average should be normalized for park effects before VORP is calculated. Pitcher VORP is on the same scale as that of hitters.