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Since the most recent upgrade to BB-Ref's WAR formulas and the introduction of WAA values to player records, I've been trying to break down the basic win-related components of WAR and WAA into some simple algebraic terms and equations. The upgrade has had some confusing results; for example, WAR for position players no longer simply equals offensive WAR plus defensive WAR, because oWAR and dWAR both now include the same positional adjustment. Also, on the site, abbreviations like WAR and WAA are used in both the Batter Value tables and the Pitcher Value tables for a player, which doesn't exactly reduce the confusion. So I'd also like to standardize the abbreviations to make them distinct from one another.
What is nice, however, is that BB-Ref now provides text files of WAR/WAA data for every team-season of every player's career. Here's the data for position players (http://www.baseball-reference.com/da..._daily_bat.txt), and here's the data for pitchers (http://www.baseball-reference.com/da...aily_pitch.txt). This data helpfully includes a few WAR/WAA components missing from the player pages. With that data, I was able to tease out all the basic win-related components I was looking for. I've expanded on the abbreviations used for these components on BB-Ref and added abbreviations to components not explicitly listed on the player pages or the text files. Below is a glossary of the terminology I use.
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Fundamental Components (these are the seven components of WAR and WAA which, when added together in different combinations, make up all the other components of WAR and WAA)
nrW = non-pitching replacement wins
This is the difference between WAR for position players and WAA for position players. It is explicitly listed in the position player text file as "WAR_rep." Including "WAR" in the abbreviation for this component is misleading, since it's the difference between WAR and WAA and is itself not any measure of WAR. Note that I use "non-pitching" to refer to position players -- this is because in the abbreviations, "p" stands for "pitching," so I needed a different letter ("n") to represent position players.
prW = pitching replacement wins
This is the difference between WAR for pitchers and WAA for pitchers. It is explicitly listed in the pitcher text file as "WAR_rep."
posW = positional adjustment wins
This is the aforementioned positional adjustment which is part of both oWAR and dWAR as listed on the player pages and position player text file. It is not explicitly listed anywhere, but can be found by adding oWAR and dWAR and then subtracting WAR for position players. I don't include "AA" or "AR" in the abbreviation because posW can be applied to either WAR or WAA.
levW = leverage adjustment wins
This is an adjustment applied to pitchers to account for the higher leverage situations faced by relievers when compared to starters. It appears in "Player Value--Pitchers" table on player pages as "WAAadj" and in the pitcher text file as "WAA_adj."
udWAA = unadjusted (for position) defensive wins above average [= udWAR = unadjusted (for position) defensive wins above replacement]
This is defensive WAA (= dWAR) minus the positional adjustment (posW). It is not explicitly listed anywhere. It is important to recognize that the positional adjustment can be separated out so as not to double-count it when adding offensive and defensive WAR or WAA. Defensive WAA is equal to defensive WAR (either adjusted for position or not) because the replacement fielder is considered an average fielder on BB-Ref.
uoWAA = unadjusted (for position) offensive wins above average
This is offensive WAA minus the positional adjustment (posW). It is not explicitly listed anywhere.
pWAA = pitching wins above average
This is pitching WAA without the leverage adjustment (levW). This component is explicitly listed in both the "Player Value--Pitchers" table on player pages (out to 1 decimal place) and in the pitcher text file (out to 4 decimal places) as "WAA."
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Derived Components (these are the remaining components of WAR and WAA which can be calculated by adding different combinations of the seven fundamental components)
dWAA = defensive wins above average [= dWAR = defensive wins above replacement]
dWAA = udWAA + posW [= dWAR = udWAR + posW]
This is defensive WAA (or WAR) adjusted for position. As mentioned earlier, defensive WAA is equal to defensive WAR because the replacement fielder is considered an average fielder on BB-Ref. This component is listed in the "Player Value--Batters" table on player pages as "dWAR" and in the position player text file as both "WAR_def" (out to 1 decimal place) and "WAA_def" (out to 2 decimal places).
oWAA = offensive wins above average
oWAA = uoWAA + posW
This is offensive WAA adjusted for position. It is explicitly listed in the position player text file as "WAA_off."
uoWAR = unadjusted (for position) offensive wins above replacement
uoWAR = uoWAA + nrW
This component is not explicitly listed anywhere. It is important to recognize that the positional adjustment can be separated out so as not to double-count it when adding offensive and defensive WAR or WAA.
oWAR = offensive wins above replacement
oWAR = uoWAA + posW + nrW
This is offensive WAR adjusted for position. This component is listed in the "Player Value--Batters" table on players pages as "oWAR" and in the position player text file as "WAR_off."
nWAA = non-pitching wins above average
nWAA = uoWAA + udWAA + posW
This is the combined WAA for position players, including both defense and offense. It can also be found by adding oWAA and dWAA and then subtracting the positional adjustment (posW). This component is listed in the "Player Value--Batters" table on player pages (out to 1 decimal place) and in the position player text file (out to 2 decimal places) as "WAA."
nWAR = non-pitching wins above replacement
nWAR = uoWAA + udWAA + posW + nrW
This is the combined WAR for position players, including both defense and offense. It can also be found by adding oWAR and dWAR and then subtracting the positional adjustment (posW). This component is listed in the "Player Value--Batters" table on player pages and in the position player text file as "WAR."
lpWAA = leveraged pitching wins above average
lpWAA = pWAA + levW
This is pitching WAA adjusted for leverage. It is not explicitly listed anywhere.
lpWAR = leveraged pitching wins above replacement
lpWAR = pWAA + levW + prW
This is pitching WAR adjusted for leverage. This component is listed in the "Player Value--Pitchers" table on player pages and in the position player text file as "WAR."
pWAR = pitching wins above replacement
pWAR = pWAA + prW
This component is not explicitly listed anywhere. Confusingly, the "WAR" given for pitchers is leveraged while the "WAA" given is unleveraged.
ltWAA = leveraged total wins above average
ltWAA = uoWAA + udWAA + posW + pWAA + levW
This is equivalent to WAA for position players (nWAA) plus leveraged WAA for pitchers (lpWAA). It is not explicitly listed anywhere.
ltWAR = leveraged total wins above replacement
ltWAR = uoWAA + udWAA + posW + nrW + pWAA + levW + prW
This is equivalent to WAR for position players (nWAR) plus leveraged WAR for pitchers (lpWAR). While it is not listed either on the player pages or in the text files, it does appear in the lists of career leaders and season leaders simply as "Wins Above Replacement."
tWAA = total wins above average (unleveraged)
tWAA = uoWAA + udWAA + posW + pWAA
This is equivalent to WAA for position players (nWAA) plus WAA for pitchers (pWAA). Though this component is not explicitly listed anywhere, it is the ultimate value to compare players based on their total contributions above average rather than above replacement (while not accounting for leverage).
tWAR = total wins above replacement (unleveraged)
tWAR = uoWAA + udWAA + posW + nrW + pWAA + prW
This is equivalent to WAR for position players (nWAR) plus WAR for pitchers (pWAR). Like tWAA, it's not listed anywhere, but it is the ultimate value to compare players based on their total contributions above replacement rather than above average (while not accounting for leverage).
~~~~~~
Here's a handy little chart that shows which fundamental components are included in each of the derived components:
~~~~~~
Attached is a zipped, comma-delimited text file which contains the career values for all the WAR/WAA components above for every player from 1871-2012.
So that's about it. I'm not sure if all this information would be more or less confusing to include on BB-Ref (though I think it'd be helpful), but you can let me know what you think. Questions, comments, and constructive criticism are welcome.
Since the most recent upgrade to BB-Ref's WAR formulas and the introduction of WAA values to player records, I've been trying to break down the basic win-related components of WAR and WAA into some simple algebraic terms and equations. The upgrade has had some confusing results; for example, WAR for position players no longer simply equals offensive WAR plus defensive WAR, because oWAR and dWAR both now include the same positional adjustment. Also, on the site, abbreviations like WAR and WAA are used in both the Batter Value tables and the Pitcher Value tables for a player, which doesn't exactly reduce the confusion. So I'd also like to standardize the abbreviations to make them distinct from one another.
What is nice, however, is that BB-Ref now provides text files of WAR/WAA data for every team-season of every player's career. Here's the data for position players (http://www.baseball-reference.com/da..._daily_bat.txt), and here's the data for pitchers (http://www.baseball-reference.com/da...aily_pitch.txt). This data helpfully includes a few WAR/WAA components missing from the player pages. With that data, I was able to tease out all the basic win-related components I was looking for. I've expanded on the abbreviations used for these components on BB-Ref and added abbreviations to components not explicitly listed on the player pages or the text files. Below is a glossary of the terminology I use.
~~~~~~
Fundamental Components (these are the seven components of WAR and WAA which, when added together in different combinations, make up all the other components of WAR and WAA)
nrW = non-pitching replacement wins
This is the difference between WAR for position players and WAA for position players. It is explicitly listed in the position player text file as "WAR_rep." Including "WAR" in the abbreviation for this component is misleading, since it's the difference between WAR and WAA and is itself not any measure of WAR. Note that I use "non-pitching" to refer to position players -- this is because in the abbreviations, "p" stands for "pitching," so I needed a different letter ("n") to represent position players.
prW = pitching replacement wins
This is the difference between WAR for pitchers and WAA for pitchers. It is explicitly listed in the pitcher text file as "WAR_rep."
posW = positional adjustment wins
This is the aforementioned positional adjustment which is part of both oWAR and dWAR as listed on the player pages and position player text file. It is not explicitly listed anywhere, but can be found by adding oWAR and dWAR and then subtracting WAR for position players. I don't include "AA" or "AR" in the abbreviation because posW can be applied to either WAR or WAA.
levW = leverage adjustment wins
This is an adjustment applied to pitchers to account for the higher leverage situations faced by relievers when compared to starters. It appears in "Player Value--Pitchers" table on player pages as "WAAadj" and in the pitcher text file as "WAA_adj."
udWAA = unadjusted (for position) defensive wins above average [= udWAR = unadjusted (for position) defensive wins above replacement]
This is defensive WAA (= dWAR) minus the positional adjustment (posW). It is not explicitly listed anywhere. It is important to recognize that the positional adjustment can be separated out so as not to double-count it when adding offensive and defensive WAR or WAA. Defensive WAA is equal to defensive WAR (either adjusted for position or not) because the replacement fielder is considered an average fielder on BB-Ref.
uoWAA = unadjusted (for position) offensive wins above average
This is offensive WAA minus the positional adjustment (posW). It is not explicitly listed anywhere.
pWAA = pitching wins above average
This is pitching WAA without the leverage adjustment (levW). This component is explicitly listed in both the "Player Value--Pitchers" table on player pages (out to 1 decimal place) and in the pitcher text file (out to 4 decimal places) as "WAA."
~~~~~~
Derived Components (these are the remaining components of WAR and WAA which can be calculated by adding different combinations of the seven fundamental components)
dWAA = defensive wins above average [= dWAR = defensive wins above replacement]
dWAA = udWAA + posW [= dWAR = udWAR + posW]
This is defensive WAA (or WAR) adjusted for position. As mentioned earlier, defensive WAA is equal to defensive WAR because the replacement fielder is considered an average fielder on BB-Ref. This component is listed in the "Player Value--Batters" table on player pages as "dWAR" and in the position player text file as both "WAR_def" (out to 1 decimal place) and "WAA_def" (out to 2 decimal places).
oWAA = offensive wins above average
oWAA = uoWAA + posW
This is offensive WAA adjusted for position. It is explicitly listed in the position player text file as "WAA_off."
uoWAR = unadjusted (for position) offensive wins above replacement
uoWAR = uoWAA + nrW
This component is not explicitly listed anywhere. It is important to recognize that the positional adjustment can be separated out so as not to double-count it when adding offensive and defensive WAR or WAA.
oWAR = offensive wins above replacement
oWAR = uoWAA + posW + nrW
This is offensive WAR adjusted for position. This component is listed in the "Player Value--Batters" table on players pages as "oWAR" and in the position player text file as "WAR_off."
nWAA = non-pitching wins above average
nWAA = uoWAA + udWAA + posW
This is the combined WAA for position players, including both defense and offense. It can also be found by adding oWAA and dWAA and then subtracting the positional adjustment (posW). This component is listed in the "Player Value--Batters" table on player pages (out to 1 decimal place) and in the position player text file (out to 2 decimal places) as "WAA."
nWAR = non-pitching wins above replacement
nWAR = uoWAA + udWAA + posW + nrW
This is the combined WAR for position players, including both defense and offense. It can also be found by adding oWAR and dWAR and then subtracting the positional adjustment (posW). This component is listed in the "Player Value--Batters" table on player pages and in the position player text file as "WAR."
lpWAA = leveraged pitching wins above average
lpWAA = pWAA + levW
This is pitching WAA adjusted for leverage. It is not explicitly listed anywhere.
lpWAR = leveraged pitching wins above replacement
lpWAR = pWAA + levW + prW
This is pitching WAR adjusted for leverage. This component is listed in the "Player Value--Pitchers" table on player pages and in the position player text file as "WAR."
pWAR = pitching wins above replacement
pWAR = pWAA + prW
This component is not explicitly listed anywhere. Confusingly, the "WAR" given for pitchers is leveraged while the "WAA" given is unleveraged.
ltWAA = leveraged total wins above average
ltWAA = uoWAA + udWAA + posW + pWAA + levW
This is equivalent to WAA for position players (nWAA) plus leveraged WAA for pitchers (lpWAA). It is not explicitly listed anywhere.
ltWAR = leveraged total wins above replacement
ltWAR = uoWAA + udWAA + posW + nrW + pWAA + levW + prW
This is equivalent to WAR for position players (nWAR) plus leveraged WAR for pitchers (lpWAR). While it is not listed either on the player pages or in the text files, it does appear in the lists of career leaders and season leaders simply as "Wins Above Replacement."
tWAA = total wins above average (unleveraged)
tWAA = uoWAA + udWAA + posW + pWAA
This is equivalent to WAA for position players (nWAA) plus WAA for pitchers (pWAA). Though this component is not explicitly listed anywhere, it is the ultimate value to compare players based on their total contributions above average rather than above replacement (while not accounting for leverage).
tWAR = total wins above replacement (unleveraged)
tWAR = uoWAA + udWAA + posW + nrW + pWAA + prW
This is equivalent to WAR for position players (nWAR) plus WAR for pitchers (pWAR). Like tWAA, it's not listed anywhere, but it is the ultimate value to compare players based on their total contributions above replacement rather than above average (while not accounting for leverage).
~~~~~~
Here's a handy little chart that shows which fundamental components are included in each of the derived components:
Code:
uoWAA udWAA posW nrW pWAA levW prW dWAA + + oWAA + + uoWAR + + oWAR + + + nWAA + + + nWAR + + + + lpWAA + + lpWAR + + + pWAR + + ltWAA + + + + + ltWAR + + + + + + + tWAA + + + + tWAR + + + + + +
Attached is a zipped, comma-delimited text file which contains the career values for all the WAR/WAA components above for every player from 1871-2012.
So that's about it. I'm not sure if all this information would be more or less confusing to include on BB-Ref (though I think it'd be helpful), but you can let me know what you think. Questions, comments, and constructive criticism are welcome.