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10 for 10: #7 Player Wins Above Replacement

Posted by Sean Forman on May 17, 2010

This post is the seventh in our series of ten new features for our tenth anniversary.

Sabermetricians have always been on the search for the best way to measure wins contributed by players. Baseball Prospectus has WARP, Bill James has win shares and now we are presenting Sean Smith's Wins Above Replacement or WAR data on the site.

Here are some sample pages:

--Career WAR leaders
--Albert Pujols, Ryan Howard, and Dwight Gooden year-by-year WAR data (just below their batting stats).
--2009 NL Batting Leaders with WAR top ten
--1980 AL Team and Player Value Register
--WAR Pitching Leaders from 2000-2009 via the Play Index Season Finder
--The top shortstops of the 1990's by WAR via the Play Index Season Finder
--Most runs atttibutable to all baserunning events 1961-1981
--Most 6.0 WAR seasons by a pitcher in their career
--2001 Mariners Player Values (scroll past the fielding data)

We will be incorporating this data throughout the site, and your suggestions and comments are as always welcome.

Rough Sketch of How We Do This

A couple of items of note about our WAR data. First, the Runs values listed are all versus average. We have implemented WAR data for position players for the 2010 season, and will do so very soon for the pitchers.

For Batters

--Rbat, batting runs are a linear weights formula utilizing custom weights depending on team runs scored and run scoring environment. For the current season this is adjusted batting runs.
--Rbsr, Baserunning events like stolen bases, advancing on passed balls, going first to third on a single. For 2010, this is currently just SB and CS data.
--Rroe gives a bonus or penalty depending on whether the player reached on error more often than average. Typically +/- 5 runs at the most. This is a relatively minor skill, but does in fact appear to be a skill. Not yet included for 2010.
--Rdp gives a bonus or penalty depending on whether the player grounds into more or fewer double plays than expected. Typically +/- 5 runs at the most. Not yet included for 2010.
--Rfield is the value in runs of all aspects of the player's fielding (fielding balls, outfield arms, turning the double play, controlling the running game).
--Rpos is the value in runs of playing a particular position. This is inversely proportional to the hitting ability of the average player at that position. 2009 values per 1,350 innings (150 games): Catcher 10 runs, Shortstop 7.5 runs, Second Base 3 runs, Third Base 2 runs, Center Field -2.5 runs, Right and Left Field -7.5 runs, First Base -10 runs, Designated Hitter -15 runs.
--Rrep is the value of an average player over a replacement player given the player's playing time. Replacement level is set at around a .320 team W-L percentage. AL's is 22 runs per 650 PA and NL's is 18 runs per 650 PA. A player's PA is the smaller of actual PA and 4PA/G*G in order to not overvalue leadoff hitters.
--RAR is the sum of all of the run components.
--WAR converts runs above replacement to wins above replacement. Runs per win is dependent on the run scoring environment the team played in. Currently using 10 runs/win for 2010 data. Will update this shortly.

For Pitchers.

--R pitcher's actual runs allowed
--Rrep runs allowed by a replacement level pitcher given this pitcher's defense, park, strength of opponents, and role (replacement level is different for starters and relievers). The number presented includes the defensive component, Rdef, already.
--Rdef runs above or below average for this pitcher's team defense. The team's overall defense weighted by the percent of balls in play allowed by this pitcher.
--aLI is the average leverage index this pitcher pitched in. To convert RAR to WAR, the pitcher's runs above replacement is weighted by the average of their leverage and 1.00 (due to bullpen chaining). Average leverage is 1.00. Above 1.00 includes high leverage and below 1.00 indicates lower leverage.
--RAR runs saved above replacement. This is not weighted by leverage yet.
--WAR RAR/(Runs per win), Runs per win varies with the run scoring environment of the pitcher and how that pitcher changes the environment. Typically around 10 runs per win.

A big thanks to Sean Smith for licensing this work to us and helping us get it updated during the season.

24 Responses to “10 for 10: #7 Player Wins Above Replacement”

  1. lar @ wezen-ball Says:

    Brilliant stuff. Great addition.

    And you're using Total WAR, too (batting plus pitching). The career WAR leaders have Ruth at 190, which is the sum of his 172 batting WAR and 18 pitching WAR. Nice work.

  2. Chris J. Says:

    Current glitch:

    Looking at the 1908 Pirates*, Rfield and Rbaser have the exact same definition. It looks like the Rbaser definition has been put up for Rfield as well. Don't know if this is true throughout the site, but I'm assuming so & am too lazy to do much of a check.

    * By which I mean when I put the cursor of the red font, and that little definitional box pops up. That's where Rfield and Rbaser are identical.

  3. Sean Forman Says:

    Chris, I have fixed that in the code. It will take awhile to get sitewide.

  4. Rich Says:

    Counting stats are bad....unless we're the ones who made them up!

    Not a big fan of WAR. Underrates Ted Williams tremendously. Serving his country = less of a ballplayer

  5. Charles Saeger Says:

    Will we be able to see the leaders in the components of WAR, like whom it rates as the best defensive center fielders or which pitchers were helped most by their fielders?

  6. Erik Says:

    Can we get WAR added to the pitching leader page, as with the batting page?

  7. Erik Says:

    Scratch that. I only checked 2010, which apparently doesn't have figures yet for pitchers.

  8. Sandlapper Spike Says:

    "Not a big fan of WAR. Underrates Ted Williams tremendously. Serving his country = less of a ballplayer"

    Kind of funny that a stat called WAR underrates a player because of his career in the service...

  9. Johnny Twisto Says:

    As we all know, Williams batted over .400 every year he was in the service, so you can just ignore WAR and use his batting average instead.

  10. Johnny Twisto Says:

    I would say the second decimal place on the leaders pages is unnecessary (57.4, instead of 57.40).

  11. Rich Says:

    "As we all know, Williams batted over .400 every year he was in the service, so you can just ignore WAR and use his batting average instead."

    Yep, notice I didn't say a thing about batting average, and he was also in the service for WWII during which he got 0 PA. You've really done a lot to convince WAR is meaningful though.

    Trust me, I love the newer stats, but ones like WAR where little more than things like "converts runs above replacement to wins above replacement" do little to suit me. Converts it how? Don't just tell me something is adjusted then don't explain how, and expect me to accept it.

    I'm not some avg/HR/RBI guy, but something like OPS+, while not more perfect, is a lot more clear as to how a player really compares to his contemporaries.

  12. Rich Says:

    while not *perfect

  13. Baseball-Reference Now Providing WAR Says:

    [...] hard to say that Baseball-Reference could get any more useful. But, Baseball-Reference just got even more useful. Sabermetricians have always been on the search for the best way to measure wins contributed by [...]

  14. masternachos Says:

    This isn't what this post is about, but I noticed you've added fielding stats in the 'Leaders' feature. I REALLY appreciate the 'Defensive games at' ones. Thank-you so much for that!
    Was that mentioned in another '10 for 10'? I'd check, but my connection here at home is SLOW.

  15. rWAR on Baseball Reference « Play a Hard Nine Says:

    [...] May 17, 2010 by erik Oh joy. Sean Smith’s WAR (Wins Above Replacement) is now at Baseball If you have play index, you can do all sorts of fun sorts. I’ll share a [...]

  16. Johnny Twisto Says:

    Rich, my point was only that discrediting a stat because it doesn't credit Williams for time he didn't play is ridiculous. One might as well say HR are meaningless. I mean Williams, one of the great power hitters of all time, isn't credited with a single HR during the time he was in the military! What a joke stat!

    Anyway, your reservations are understood, but I believe WAR is pretty open-source. If you have any questions about how it is calculated, I am sure people will try to answer them. If no one here knows the answers, post a question at and I'd guess the proprietor will answer you.

    As for converting runs into wins, it is based on the run environment. These days it is around 10 runs per win. (If you know the Pythagorean Theorem of run scoring, add or subtract 10 runs from a team's totals and see what happens to their expected record.)

    Finally, while I think the methodology behind WAR is pretty sound (as far as I understand it), I would never solely rely on it for ranking or evaluating players. And no one with any sense would say it proves Williams was less of a player for missing time. I mean, he didn't play those years, we don't need WAR to tell us that. It's up to each individual, and it depends what question they are trying to answer, how to credit Williams for that time.

  17. Nick Steiner Says:

    Awesome. Great job Sean and Sean.

  18. Baseball-Reference Blog » Blog Archive » WAR Data: Best Position Players Not In the Hall of Fame Says:

    [...] who are the best position players not to be inducted into the Baseball Hall of Fame? Using Baseball-Reference's new Wins Above Replacement data, we can attempt to answer that question. First, the players with the most total career value who [...]

  19. Mark Ahrens Says:

    Hank Greenberg's WAR stats were also impacted by service in WWII

  20. cubbies Says:

    can you add WAR data in the charts for MVPs and other awards? that would be really convenient (to see how acurate MVP voting is going with WAR)

  21. The Marlins’ Draft History: pre-1997 | Marlin Maniac | A Florida Marlins Blog Says:

    [...] you know that Baseball-Reference now has Rally’s WAR (rWAR) integrated everywhere on the site? Amazingly, that also includes its draft tool, something I [...]

  22. Dvd Avins Says:

    I second Cubbies' request.

  23. Baseball-Reference Blog » Blog Archive » WAR for Pitchers Updated Daily & WAR Leaders on Front Page Says:

    [...] are continuing to weave our Wins Above Replacement data throughout the site. Today, we started updating Pitcher WAR on a daily basis. Yes, Ubaldo [...]

  24. Sean Forman Says:


    It's on there. I've added it.