wRC and wRAA

Tonight we’ve completed the phasing out of Runs Created (RC) and Runs Created per 27 Outs (RC/27). In their place you will find two run stats based off wOBA, which is a sounder metric than the previously used Runs Created.

Big thanks to Tangotiger for both creating the stats and walking me through how to calculate them correctly!

wRC – This is total runs created based of wOBA. It is calculated as (((wOBA – lgwOBA) / wOBAScale) + (lgR/PA)) * PA

wRAA – This is the number of runs above average based off wOBA. It is calculated as (wOBA – lgwOBA) / wOBAScale * PA

wOBAScale is typically around 1.15, but changes slightly from year to year depending on the weights used in wOBA.

Also, the previously named BRAA has been renamed to RE24 to clarify that it is based off the 24 base/out states.

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David Appelman is the creator of FanGraphs.

42 Responses to “wRC and wRAA”

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  1. Rahul says:

    This is great, thanks. Can we expect something similar for pitchers using FIP? A Pitching Runs type of thing based on league Replacement/Average FIP?

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  2. dan says:

    So wRC is pretty much intended to be the same scale as traditional RC, or at least modeling the same thing. “If we take a player out of the lineup and don’t replace him with anybody, how many runs would the team lose?” Basically, I’m asking if it’s like traditional RC, or if it’s versus some baseline other than zero.

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  3. Rob says:

    This site keeps getting better…I really appreciate this. Thanks!

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  4. Josh says:

    Great news!

    These stats aren’t park adjusted, right?

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  5. Josh S says:

    I’ve been a long time reader, I’m trying to figure out the whole win system (I just bought the Book).

    So take Raul Ibanez … with wRAA last season he was 16.3 Runs above average which is about 1.6 wins? Take his defense which was -11 UZL/150 and he is more like a half a win upgrade?? There is another step I’m missing.. Or i’m entirely off base… Please help me out haha


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  6. Fett42 says:

    So if you made a wRAA/150 and added that to UZR/150, would that that give you total runs above average per ~season for a player?

    And then you would apply the positional and replacement adjustments to get the overall value of the player?

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  7. Alex JN says:

    Josh – those two steps leave you with him at 5 runs above average – then a positional adjustment is applied (-7.5 runs for a season) for the fact that he’s playing corner outfield, an easy defensive position. Add the replacement level baseline (20 runs or whatever) and you’re left with around a 1.8 WAR player or whatever.

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  8. Josh S says:

    Alex thanks a lot.

    I knew i forgot the replacement level adjustment and the positional one. Quick question though.

    If you are strictly looking for total runs above average you would just make the positional adjustment and not the replacement level one, right? The replacement level adjustment is only when one is looking for wins ,right ?

    If not, I’m not sure why the replacement level part is necessary and how it is applied. Who do you add 20 to, and who not, because in the end, it all would negate itself.

    Thanks again for the help.


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  9. TangoTiger says:

    Dan, Fett, Alex, the first Josh, and Rob: yes, you are all correct.

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  10. Josh S says:

    Is wRAA already scaled to the 150g?

    Sorry if I’m so annoyingly uninformed.

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  11. Fett42 says:

    Where can I find the positional / replacement run adjustments?

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  12. erik says:

    This is pretty fantastic stuff. Keep up the good work.

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  13. wRAA is currently not scaled to 150 games. You can find the replacement level adjustments here: http://www.insidethebook.com/ee/index.php/site/comments/complete_war_2008/

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  14. Rob says:

    This is a bit off-topic, but I’m having some trouble finding the correct formula for calculating a pitcher’s WAR. Does anyone know the correct replacement level modifiers for SP and RP? Also, I’ve seen some large discrepancies on what the league average ERA should be – resulting in more than a win difference depending on the formula. If anyone would be willing to run through this process using an example, I would greatly appreciate it.

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  15. Gary Velich says:

    I wish you could of kept up Runs Created and Runs Created per 27 outs. Those were my favorite stats. Isn’t there some way you could still list them? I enjoy tracking players Runs Created each year and keeping track of the ones getting 100 or more Runs Created- Technical version. Thanks.

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  16. Samg says:

    I know that RC tended to overvalue players with a high OBP and SLG, but, if on a good team, isn’t that a good thing? Conversely, I haven’t seen the effects on poor players, but wouldn’t it then tend to undervalue them?

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  17. Gary, we still have Runs Created it’s called wRC now and it’s a more accurate way to calculate Runs Created. Runs Created per 27 outs was a normalized version of the old Runs Created and you can use wOBA for those purposes.

    I’m sorry to say that I don’t think we’ll be bringing back the Bill James versions of RC and RC/27 since as Samg said they do overvalue players with a high OBP and SLG. And a player with a high OBP * TB on a poor team would also be overvalued.

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  18. Captain Crunch says:

    In the formula describing wRC, the term, PA, is used twice, but doesn’t it mean different things in each spot? In lgR/PA, it refers to league PA, and in the use at the end outside the brackets, it refers to player PA. Would it be clearer to use lgPA in the first term, and/or perhaps pPA at the end? I know this may seem nit-picky, but when I went through it the first time, I said to myself, wRC = wRAA + lgR, which is not correct.

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  19. Gary Velich says:

    Dear Fangraphs, I calculated Albert Pujols 2008 season wOBA and I come up with .431 and you have .458. Here are my calculations, He had 106 singles x .90 = 95.4, 44 doubles x 1.24 = 54.56, 37 homers x 1.95 = 72.15, 70 unintentional walks x .72 = 50.4, and 5 hit by pitcher x .75 = 3.75. I added them all up and got 276.26 and divided by his 641 plate appearances gives .431. You have him listed at .458. Could you please tell me what I am doing wrong? Also how do I put reach base on error in calculation? Where do I find this stat? It is weighted at .92. Thanks and I appreciate all your help.

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  20. Gary, you are using the standard weights for home runs, etc… There are two things we do different. First we adjust the weights by season to better reflect that particular season. This is done using the code found here: http://www.insidethebook.com/ee/index.php/site/comments/woba_year_by_year_calculations/

    Second we also include SB and CS. There’s nothing wrong with using the weights you are using to calculate wOBA for current years and you should multiply SB * 0.25 and CS by -0.50. If you do that your number should be pretty close to the one on FanGraphs.

    Also we don’t include RBOE because we just don’t have that stat. This is a harder one to find so I wouldn’t worry too much about it unless it becomes widely available.

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  21. Gary Velich says:

    Dear Mr. Appelman, I like the Bill James Runs Created and Runs Created per 27 outs stats better than the wOBA. In Bill James New Historical Baseball Abstract he says that if you take a teams hits + walks multiplied by Total Bases and divide by At-bats + walks which is the basic runs created formula . He says it is within 5 percent of the actual run total. I did several examples myself and he is correct. For example the 1970 Boston Red Sox scored 786 runs. I calculated the teams Basic runs created and got 789. That is a 99.6 correlation. I did several other teams from the past and they were within 5 percent of actual run total. I will continue to use Bill James Runs Created and RC/27 stat as I believe it is easier and better than wOBA. Thanks again for explaining your side.

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  22. Zach says:

    Gary, RC may be within 5% of every team’s run total, but so are all other run estimators. There are SEVERAL that are better at estimating team runs than RC (click on my name), and especially at the player level, where RC severely overrates the good players.

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  23. Gary Velich says:

    Zach, Runs Created is good enough for me. A team with nine of the same player is what Bill James is talking about. Not how a good player performs with different players. He means nine of the same player. We are just measuring the hitting of a certain player , and not different hypothetical teams.

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  24. Gary Velich says:

    Zach, Let me give you an example of what I mean. In 1972 Rod Carew had 170 hits, 43 walks, 203 total bases, 535 at-bats, 578 plate appearances (at-bats + walks), and he made 365 outs- At-bats minus hits. His basic Runs created is 74.81 and his RC/27 is 5.53. In 1972 Harmon Killebrew had 100 hits, 94 walks, 195 total bases, 433 at-bats, 527 plate appearances (at-bats plus walks), and he made 333 outs – At-bats minus hits. His basic Runs created is 71.78 and his RC/27 is 5.82. What I mean is a team with nine Harmon Killebrews will score 5.82 runs a game and a team of nine Rod Carews will score 5.53 runs a game. It shows that Harmon Killebrew was the better hitter than Rod Carew in 1972, despite Killebrew’s .231 batting average to Carew’s .318 average. I hope you understand what I am saying when nine of the same player. Thanks.

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  25. Gary, wOBA will show the same thing. That Killebrew was considerably better with a wOBA of .368 in 1972 than Carew with .339 in 1972. While I understand that RC and RC/27 may be adequate for your purposes, it doesn’t change the fact that they overvalue some individual players and as Zach pointed out, this is not the same as on a team level.

    Since wOBA, wRAA, and wRC does not have this flaw and it serves a similar purpose to RC and RC/27, there’s little reason to continue to display both on the site. Furthermore, I believe Bill James himself has admitted to issues with the “Basic” and “Technical” formulas and does not continue to use these versions of RC you’re referring to in his books.

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  26. Gary Velich says:

    Thank you for explaining Mr. Appelman. Yes I think I remembered Bill James said his formula had problems. He updated it and called it the 2002 version of the Runs Created Formula which is too complicated for me. I like his technical version of Runs Created the Best. As for Rod Carew and Harmon Killebrew in 1972, Killebrew was slightly better than Carew in RC/27. That goes to show people that batting average is not the best stat when evaluating hitters. Also, On-Base times Slugging is better than On-Base plus Slugging as a rate stat. I saw this on the internet. On-Base times Slugging is Runs Created per At-bat as you well know. I also saw a stat combining Batting average to OPS as a stat better than OPS. I saw this on Redlegstats.com. Let me know what you think of the batting average added to the OPS formula. I think they divided the total sum by three. An example would be .300 BA, .400 OBA, .500 SLG, total is 1.200 and divide by three gives .400 Absolute average as they call it. Check it out as it is very interesting.

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  27. Gary Velich says:

    I forgot to mention that I found another website that is probably the best stat yet. It is at http://www.basesproduced.com. It is made by play by play records. It also is very interesting. How would you rank this stat compared to weighted on-base average?

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  28. Gary Velich says:

    Also http://www.redlegstats.com is good. Click on Stats Blog for lots of stats etc.

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  29. Gary: The stat I believe you’re referring to on redlegstats.com, is disputed and argued against over wOBA (or linear weights) in a very long thread here: http://www.insidethebook.com/ee/index.php/site/comments/abso_lutely_not/#comments

    I’m not familiar with the work on basesproduced.com and can’t really say whether it is good or not, but you should know on FanGraphs there are metrics such as WPA, WPA/LI, or RE24 that do use play-by-play data to determine run/win values for various players based on who is on base, how that base runer is moved over, the score, the inning, the number of outs, etc… You can read about them more in the glossary and also by reading more about them in any of the resource links.


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  30. James Cohen says:

    I had a question about calculating the lgR/PA used in wRC. It seems to me that pitcher’s batting stats are included (given the way I got my calculations closest to the ones on this site was to include them), but shouldn’t they be excluded?

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  31. James: Pitchers are currently included when calculating the lgR/PA and I’ve been told by Tango that excluding them doesn’t make total sense. He’d be better able to inform you of the specifics.

    In reality, over 600 PA you’re looking at a total of 1.2 run difference since it’s like a .002 run difference per PA between excluding and including pitchers in the lgR/PA. Not much of a difference and it’s uniform so I don’t think it’s a particularly big deal either way.

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  32. Gary Velich says:

    Dear Mr. Appelman, I was looking at Jim Albert and Jay Bennett’s book titled Curve Ball this morning and in Chapter 6 on page 168 he says OPS dominates into the mid-1930′s. Total Average has the edge from then to the present day, TA has beenthe best estimator since 1991. And on page 170 he said TA, has a slight edge over OPS. And he then stated that a better model than OPS can be made by multiplying them together- OBA times SLG. And in the next paragraph he says BRA appears to be less effective than TA, but more effective than OPS. So, it seems that multiplying OBA and SLG produces a better model than adding the two values. Then on page 174 he says that Runs Created per game- Technical version he uses has the lowest average RMSE- (.136) from 1954-1999. He compared them to (BRA, DX, TA, and OPS). and on page 175 he says that from 1954 to 1999 RC/Game is a superior model to Total Average. So, that means that both the RC/Game stat, Total Average and BRA-OBA times SLG are better than OPS. I see that you have OPS on your fangraphs site. I am wondering if you could please still add the RC/27 stat with Runs Created and also the Total Average stat and BRA stat which are all better than OPS according to Jim Albert in his Curve Ball book. Could you list them in another section like you do for Standard stats and advanced stats and maybe another one called extended stats? I hope you could as I like your site alot Mr. Appelman. Thank you for considering my request.

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  33. Baltimoron says:


    Question about the plate appearances data are you using to calculate the projected wRC/wRAA calculations based on the Marcel and Bill James’ projections?

    For example, Marcel projects Brian Roberts to have 546 at bats/624 plate appearances, a .346 wOBA and a 7.6 wRAA.

    Bill James projects Brian Roberts will have 623 at bats (no PA projection), a .350 wOBA but only a 2.6 wRAA.

    Shouldn’t the wRAA for the Bill James projection be higher than the wRAA based on the Marcel projection, as James thinks Roberts will have a higher wOBA and also have more at bats than Marcel?


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    • Hmm…. well, I can tell you why it’s 2.6 and then I guess we can discuss if it should be 2.6, since I may not be dealing with lgwOBA correctly in the projections.

      Basically, the lgwOBA for the Bill James projections comes out to .346 instead of .328. That’s where the difference is, and since wRAA is runs above average, the average runs is considerably higher in the Bill James projection than it is the Marcel. Maybe I should be using the same baseline so we have an apples to apples comparison.

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  34. Baltimoron says:

    Hi David,

    I believe Bill James forecasts (or at least did) for a more limited set of players than other systems.

    If so, is averaging his forecasted players basically “selectively sampling” a group of above average players, so that it ends up excluding a lot of marginal, replacement type players whose predicted performance would otherwise pull down the average of forecasted players closer to actual league averages?

    I think that is what I gathered from this (http://tinyurl.com/3mb6ky) thread at The Book blog, which seemed to indicate Marcel only failed to forecast like 5% of plate appearances while with James, “10% of MLB PA were either unforecasted or unmapped.”

    I’m not sure if its correct but my sense too is that it might be helpful to use the same baseline for an apples to apples comparison.

    Thanks again for your great site.

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  35. Ben says:

    Do these numbers have factor in the home park? In other words, would 2 equally skilled players have the same wRC and wRAA if one played in Coors and the other in Petco?

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  36. Hey!
    I may be stupid (well I am but this individual effort may also be less than intelligent) but, what is the value for wOBAScale?
    I have been reading on all stats starting from linear weights on and from linear weights to WAR the only thing I’m missing is this value.

    Thank you preemptively for filling me in.


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  37. Ben says:

    Could you please explain the wOBA Scale calculation? I see that pacity0champs already asked, but no one anwered, so I’ll ask again. Thanks!

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  38. Ben says:

    Hi again,
    I know you don’t include Reached Base on Error in your calculation, but why is it included in Mr. Tango’s formula? Why should a batter get credit for the other team making a mistake? Thank you very much.

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  39. Rikki Gerhardt says:

    I think wOBAScale arithmetically translates to (League Runs / League Baserunners) / (League OBA).

    It is a factor to convert a wOBA point into a run.

    If we did the equation with OBA instead of wOBA and without the wOBAScale factor, we’d get Baserunners above average or Baserunners Created. If we then apply wOBA instead of OBA without the wOBAScale factor, we get Baserunners above average or Baserunners Created, adjusted for the advancement of other runners.

    The final step is the wOBAScale factor to convert from baserunners to runs. Or, the probability of one run scoring, given the state of the runner reaching base. (Hmm, this phrasing reeks of the hypergeometric distribution, but I hope that’s not what we need here.)

    I hope I got the arithmetics right…

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    • Rikki Gerhardt says:

      Anyway, I checked the book, I guess the 1.15 is the 15% in the book to get plain Markoved wOBA to the OBA scale, and only by coincidence for the major leagues the same as my calculations. My bad

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