WAR Primer Volume 2 - Converting Position Player Runs to Wins
This post is part of a series that includes material originally written for The New York Yankees All-Time All-Stars but had to hit the cutting room floor prior to publication. For other posts in the series you can search for the label "Author's Cut" on this site.
In Volume 1 of this WAR Primer series we gave an overview of the run components that make up the base of the WAR and WAA calculations. Here we'll dig in deeper as to how those run totals are converted to wins.
As with the previous volume, if reading this leaves you wanting more, Baseball Reference's WAR Explainer is highly recommended.
It’s no secret that throughout baseball history, players at certain positions are expected to contribute more on offense than others. For instance, the average first baseman will usually bat cleanup and drive in lots of runs while the average shortstop will be a light hitter occupying the bottom third of a lineup. That being the case, there’s an inherent value in playing a difficult fielding position. A value that's been quantified by the smart people at Baseball Reference.
The result is a small bonus or penalty added to the runs total for each player depending on their position and scaled to the amount of innings they played. Catchers and shortstops receive the largest bonus while second baseman, third baseman and center fielders all get a smaller, but still positive bump. Corner outfielders and first basemen are penalized moderately whereas designated hitters incur the largest penalty of about 15 runs per season. After determining a player's positional adjustment, we’re ready to convert those runs to wins.
The simplest explanation of converting runs above average to WAA is that about 10 runs above average are equal to about 1 win above average, roughly. As a quick, back of the envelope calculation this works better than nothing, but the folks at Baseball Reference have gone through some painstaking detail to fine tune this and arrive at the best wins estimate possible. The key to it all is Pythagorean expectation, which calculates an expected winning percentage for teams using the number of runs they scored and allowed in a given season.
Using this method, a winning percentage can be calculated for each player each season. The runs scored value here would be the league average for team runs scored per game plus the per game averages of the player’s offensive run components (Rbat and Rbrdp). The runs allowed value is then the league average for team runs allowed per game plus the per game averages of the player's fielding run components (Rfield and Rpos).
After some fairly complex underlying calculations not worth getting into here, the upshot of this metric is that it tells us what the expected winning percentage would be of a team that includes that player and is otherwise filled with average players versus a team composed solely of perfectly average players. Since an average team, comprised of average players, would be expected to have a .500 winning percentage, a value above .500 for the player would indicate they are above average.
Once the player’s winning percentage is in hand, the calculation to arrive at WAA is a relatively simple one. First, subtract .500 from the player’s winning percentage to arrive at the marginal winning percentage above average that they were worth. Then simply multiply that marginal percentage by the number of games the player appeared in. The result is a single number that represents WAA.
A real life example may help. In 1985, the Yankees won 97 games and came tantalizingly close to a playoff berth, falling just two games short. For his contributions to the cause, Don Mattingly was named the American League MVP and he was a worthy candidate. Yet he had a more worthy teammate who put together arguably the best season of his Hall of Fame career. Just how good was Rickey Henderson in 1985?
Henderson was 47 runs above average with the bat, adding another 18 on the basepaths and 13 with his glove. When plugged into Baseball Reference's modified Pythagorean wins calculation, that yields a .556 personal winning percentage for Henderson. Translated to wins, he was a full 8.0 wins above average over his 143 games played. That is the highest single season total ever for a Yankee not named Babe Ruth, Lou Gehrig or Mickey Mantle.
The replacement level is officially defined at Baseball Reference by saying that a team full of replacement players would have a .294 winning percentage, or 48 wins over a 162 game season. Think of the New York Mets teams of the early 1960’s. Given that, they have calculated that the gap between average and replacement for a position player is about 20.5 runs per 600 plate appearances. That number is then scaled for the number of plate appearances a player actually made and adjusted for relative league strength (leagues were less competitive during World Wars I and II, for instance) and strike-shortened seasons. The resultant calculation is replacement runs, or Rrep.
From there, the WAR calculation is nearly identical to what is done for WAA. The only exception is adding in Rrep for the player along with the other offensive run components. Therefore, WAR will always be a bit higher than WAA for a player. Using the same Rickey Henderson example, his WAR was 9.9 in 1985, a mark that would have topped the major leagues in 2019.
Tune in for the next installment of the WAR primer series where we'll dig in to the pitching side of things.
In Volume 1 of this WAR Primer series we gave an overview of the run components that make up the base of the WAR and WAA calculations. Here we'll dig in deeper as to how those run totals are converted to wins.
As with the previous volume, if reading this leaves you wanting more, Baseball Reference's WAR Explainer is highly recommended.
WAA - Wins Above Average
Number of wins added by the player above that of an average player. In order to arrive at WAA, we start with the run components already described in Volume 1 and include one more not touched on yet. The last one is a positional adjustment known as Rpos.It’s no secret that throughout baseball history, players at certain positions are expected to contribute more on offense than others. For instance, the average first baseman will usually bat cleanup and drive in lots of runs while the average shortstop will be a light hitter occupying the bottom third of a lineup. That being the case, there’s an inherent value in playing a difficult fielding position. A value that's been quantified by the smart people at Baseball Reference.
The result is a small bonus or penalty added to the runs total for each player depending on their position and scaled to the amount of innings they played. Catchers and shortstops receive the largest bonus while second baseman, third baseman and center fielders all get a smaller, but still positive bump. Corner outfielders and first basemen are penalized moderately whereas designated hitters incur the largest penalty of about 15 runs per season. After determining a player's positional adjustment, we’re ready to convert those runs to wins.
The simplest explanation of converting runs above average to WAA is that about 10 runs above average are equal to about 1 win above average, roughly. As a quick, back of the envelope calculation this works better than nothing, but the folks at Baseball Reference have gone through some painstaking detail to fine tune this and arrive at the best wins estimate possible. The key to it all is Pythagorean expectation, which calculates an expected winning percentage for teams using the number of runs they scored and allowed in a given season.
Using this method, a winning percentage can be calculated for each player each season. The runs scored value here would be the league average for team runs scored per game plus the per game averages of the player’s offensive run components (Rbat and Rbrdp). The runs allowed value is then the league average for team runs allowed per game plus the per game averages of the player's fielding run components (Rfield and Rpos).
After some fairly complex underlying calculations not worth getting into here, the upshot of this metric is that it tells us what the expected winning percentage would be of a team that includes that player and is otherwise filled with average players versus a team composed solely of perfectly average players. Since an average team, comprised of average players, would be expected to have a .500 winning percentage, a value above .500 for the player would indicate they are above average.
Once the player’s winning percentage is in hand, the calculation to arrive at WAA is a relatively simple one. First, subtract .500 from the player’s winning percentage to arrive at the marginal winning percentage above average that they were worth. Then simply multiply that marginal percentage by the number of games the player appeared in. The result is a single number that represents WAA.
A real life example may help. In 1985, the Yankees won 97 games and came tantalizingly close to a playoff berth, falling just two games short. For his contributions to the cause, Don Mattingly was named the American League MVP and he was a worthy candidate. Yet he had a more worthy teammate who put together arguably the best season of his Hall of Fame career. Just how good was Rickey Henderson in 1985?
Henderson was 47 runs above average with the bat, adding another 18 on the basepaths and 13 with his glove. When plugged into Baseball Reference's modified Pythagorean wins calculation, that yields a .556 personal winning percentage for Henderson. Translated to wins, he was a full 8.0 wins above average over his 143 games played. That is the highest single season total ever for a Yankee not named Babe Ruth, Lou Gehrig or Mickey Mantle.
Rickey Henderson had a legendary, if underrated, season in 1985.
Rdikeman/Wikimedia Commons
WAR - Wins Above Replacement
A single number that represents the wins the player added to his team above what a replacement player would add. This is very similar in concept to WAA with the key difference being the concept of “replacement”. Rather than using an average player as the baseline for comparison, WAR uses a replacement player. It’s done this way because in real life average major league players can be difficult to acquire when one of your starters goes down. More often than not, a starter is replaced by a veteran well past his prime or a minor leaguer who is not quite good enough to play every day in the majors. Those players are well below average, and comparing a player to that baseline more accurately describes the player’s value compared to the alternative.The replacement level is officially defined at Baseball Reference by saying that a team full of replacement players would have a .294 winning percentage, or 48 wins over a 162 game season. Think of the New York Mets teams of the early 1960’s. Given that, they have calculated that the gap between average and replacement for a position player is about 20.5 runs per 600 plate appearances. That number is then scaled for the number of plate appearances a player actually made and adjusted for relative league strength (leagues were less competitive during World Wars I and II, for instance) and strike-shortened seasons. The resultant calculation is replacement runs, or Rrep.
From there, the WAR calculation is nearly identical to what is done for WAA. The only exception is adding in Rrep for the player along with the other offensive run components. Therefore, WAR will always be a bit higher than WAA for a player. Using the same Rickey Henderson example, his WAR was 9.9 in 1985, a mark that would have topped the major leagues in 2019.
Cody Bellinger, son of legendary Yankee Clay, led the majors with 9.0 WAR in 2019.
Johnmaxmena2/Wikimedia Commons
Tune in for the next installment of the WAR primer series where we'll dig in to the pitching side of things.
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