Calculating Wins Above Replacement

Dave · February 6, 2008 at 2:50 pm · Filed Under Mariners 

If you’ve read the blog for a while, you’ve seen us refer to players as +/- so many wins. For instance, I’ll often call Adam Jones a “two win player” and Erik Bedard a “five win player” when talking about their 2008 value.

If you’ve ever wondered where those numbers come from, Tango has the post for you. In it, he breaks down the basics for calculating a player’s win values yourself. It’s actually easier than you might think, assuming math doesn’t make your head explode.

On a job application for running a major league franchise, this should be question #1. If you can’t grasp this concept, you don’t get to make decisions.

Comments

54 Responses to “Calculating Wins Above Replacement”

  1. Bender on February 6th, 2008 3:22 pm

    By that criteria, how much of the mariners staff would still be around?

    Also, thanks for all the great off-season content, you guys are keeping the rabid fan in me alive.

  2. crazyray7391 on February 6th, 2008 3:29 pm

    Can we forward that link to Bavasi?

  3. Graham on February 6th, 2008 3:45 pm

    I’m not sure I like everything being in terms of replacement. League average seems like it’s both far more intuitive and easier to work with mathematically.

    Oh well.

  4. tetrad on February 6th, 2008 3:51 pm

    I agree Bender; thanks to Dave and DMZ for great material and discussions. Remind me, how do we send them beer money?

    DMZ, mom really liked “Cheaters Guide to Baseball.”

  5. Dave on February 6th, 2008 3:52 pm

    The calculation starts with comparison to league average. You can just omit the replacement level calculation and this still works beautifully.

  6. JMHawkins on February 6th, 2008 3:56 pm

    I’m not sure I like everything being in terms of replacement. League average seems like it’s both far more intuitive and easier to work with mathematically

    I think the advantage of Replacement Level is that you can always find a replacement level player to fill a hole (that’s the definition). You can’t always find an average player. It has to do with being way, way, way to the right side of the bell curve.

  7. tangotiger on February 6th, 2008 4:00 pm

    Thanks for the link.

    Yes, you could simply start with average. Let’s say the average free agent player is worth 9.2MM a year. Each win around that is worth 4.4MM. So, a guy who is 1 win above average is 13.6MM (in full-time play). A guy 2 wins below average is 8.8MM less than average, or 0.4MM a year (i.e., league minimum).

    You see, it doesn’t really matter from where you start, since it all adds up anyway. An average player should get 9.2MM in full-time play. If he plays only half the time, he should get about half that right? Well, an average player (+2 wins above replacement in full time play), will be +1 wins above replacement in part-time play. Since each win is 4.4MM, you can see how it all works out pretty much the same.

  8. lailaihei on February 6th, 2008 4:01 pm

    So how many wins would a replacement level team get?

  9. Graham on February 6th, 2008 4:09 pm

    Yeah, I agree with the outcomes and understand the maths behind them. I was just wondering aloud on the use of replacement level vs. average and the merits of both.

    Seems to me that replacement starts from the financial side (i.e. paying every player league mins) and gets a bit fuzzier once we get into baseball, and working from average is the other way around. It’s all pretty interesting, I just worry that replacement level is a bit of an artificial construct.

  10. et_blankenship on February 6th, 2008 4:09 pm

    8

    20-25 wins.

  11. milendriel on February 6th, 2008 4:13 pm

    Wrong. The calculations are in the linked Tango post. A replacement level team would get 47.4 wins.

  12. Dave on February 6th, 2008 4:15 pm

    The concept of a vast supply of marginally productive players is vital to proper valuation. If we just dealt with league average, we’d have no concept of what an average player is worth. If we don’t know that he’s two wins better than what the league minimum player will provide, we won’t know whether that league average guy is worth hanging onto or not.

    There are times when using league average as the baseline is good enough, but we can’t abandon the replacement level concept, or we’ll lose out on a key ingredient of understanding how to price things correctly.

  13. terry on February 6th, 2008 4:17 pm

    League average seems like it’s both far more intuitive and easier to work with mathematically.

    Well it is pretty tough to argue that league average is set too low… Dave makes the point though. It’s pretty tough to freely get league average.

  14. et_blankenship on February 6th, 2008 4:17 pm

    11

    According to Baseball Prospectus: “It should be noted that a team which is at replacement level in all three of batting, pitching, and fielding will be an extraordinarily bad team, on the order of 20-25 wins in a 162-game season.”

  15. lailaihei on February 6th, 2008 4:18 pm

    So the 2003 Tigers were 4 runs under replacement level?

  16. Dave on February 6th, 2008 4:19 pm

    Baseball Prospectus is wildly wrong about replacement level. The concept of a player being both replacement level in hitting and fielding and actually getting any playing time in the majors is ridiculous. If you hit like Adam Everett and field like Raul Ibanez, you’re going to be in A-ball, not the big leagues.

  17. terry on February 6th, 2008 4:25 pm

    When valuating a player, I like to see his performance expressed against both baselines (replacement level and league average). Replacement level is helpful from the moola angle and league average is much more intuitive (for me) when comparing the potential advantage a player’s production might represent at least when quick and dirty is good enough.

    For instance, Adam Dunn is basically projected to be 15 runs above average offensively over 500 at-bats in ’08 (VORP=37)based upon averaging the big five projections for him. I’m very comfortable with the notion that his glove is worth -15 runs (probably -15 to -20). So Dunn has to basically OPS .910 this season to be equivalent to a league average left fielder.

    No pressure Adam…..

  18. et_blankenship on February 6th, 2008 4:26 pm

    16

    And just like that, my world is shattered. There is no god . . .

  19. terry on February 6th, 2008 4:27 pm

    I’m not sure that BP has a clue about defense on any level….

  20. Graham on February 6th, 2008 4:30 pm

    The concept of a vast supply of marginally productive players is vital to proper valuation.

    Yeah, but just because we know that the talent pool gets wider (and therefore cheaper) once we start looking at the lower ability levels doesn’t mean we should alter the maths to suit. Knowing the rough value of freely available players is, as you have said, massively important, but once you do have that value (-2 wins on average or whatever), I don’t see a compelling reason you would continue to use replacement level as a baseline.

    Anyway, I’m not going to push it – replacement level obviously works just was well as average. I was just going along with my desire to make the calculation more elegant.

  21. Dave on February 6th, 2008 4:37 pm

    Sure – you and I and Tango can probably use WAA instead of WAR and be fine. But the population at large still rejects the concept of replacement level – and this population includes the Mariners – and until that changes, we pobably need to keep that information in the equation on a general basis.

  22. galaxieboi on February 6th, 2008 4:44 pm

    not sure that BP has a clue about defense on any level….

    They were monkeying with a sorta +/- stat (like Dewan) a few days ago that showed a pretty close correlation to the more…respected metrics.

    I used to think the Davenport Translations were cool and then I came here and got eduacated. It’s nice because whereas BPro would like to use stats they develop, Dave and Derek just find what works best.

  23. hub on February 6th, 2008 4:52 pm

    I’m a big fan of ‘WAA’…but for selfish reasons (24-team DMB w/ no salaries). I’m not ‘math smart’ and have yet to find the right formula for transferring ‘league average’ from a 30-team format to a 24-team.

    A great big thanks goes out to Tango for introducing me to wOBA in his fabulous book (http://www.insidethebook.com). Especially the shortcut formula. It makes understanding the relationship between ‘performance’ and ‘wins’ a bit easier for my simple brain to understand. And if a moron like me can comprehend this concept, the M’s Front Office (filled with many smart folks) have no excuse.

  24. dlb on February 6th, 2008 4:54 pm

    I saw the optimal split in revenue spend on Hitters, SP and RP. Anyone know what the M’s breakdown as if we make the Bedard trade? My guess is we are way over on pitching, but that’s just a wild guess.

  25. Breadbaker on February 6th, 2008 5:07 pm

    I’ve always thought that the flaw in all these statistical evaluations of defense is this: there are going to be about 25.5 putouts in a game, no matter whether it’s the 2003 Mariners or the 1899 Cleveland Spiders. Although the outs will be spread out differently among different players, they will eventually come.

  26. Dave on February 6th, 2008 5:11 pm

    Nope – you’re missing strikeouts and you’re ignoring opportunities. If it takes 40 balls in play to get 20 putouts, that’s a hell of a lot different than if it takes 30 balls in play to get 20 putouts.

  27. marc w on February 6th, 2008 5:46 pm

    “Sure – you and I and Tango can probably use WAA instead of WAR and be fine. But the population at large still rejects the concept of replacement level – and this population includes the Mariners – and until that changes, we pobably need to keep that information in the equation on a general basis.”

    As far as I can see, this is the crux of the debate. Graham prefers WAA because it focuses the +/- on an area that ALL baseball fans ‘get’ (they may be a bit wrong in their assessment of league average, but they understand the concept).
    Lots of smart people STILL hold wildly divergent attitudes on what ‘replacement level’ means and, as we’ve just seen, how many games a replacement level team would win.

    I’m not disputing its importance as a concept that aids in analysis. I just think that, in talking w/more general fans, the concept of replacement level tends to start more arguments than it settles. People start quibbling about the baseline or a specific team’s prospects (replacement level for team A is waaay higher than for team B) and the conversation’s sidetracked.

  28. DMZ on February 6th, 2008 6:08 pm

    The problem I see with that though is it’s a lot harder to put together a .500 team than that acknowledges. A .300-.350 team is ridiculously easy. I could call some people together, form a front office, and put together a .300 team. If it wasn’t hard, the Royals and other franchises wouldn’t spend so long in funks. You have to be much smarter and luckier for every 10 wins you want above that.

    Replacement level acknowledges that.

    I am already thinking of how I’d put together a .300 team in one off-season, btw.

  29. tangotiger on February 6th, 2008 6:10 pm

    As Dave pointed out, I start with average. Everything I do revolves around wins above average (WAA). But, there is a second component: playing time. Moises Alou may be an above average player, but if he only plays half the time, then you are not going to pay him as if he were an average player playing 150 games. That’s the benefit of replacement level, to turn two dimension (performance and playing time) into one-dimension. Since you and I and the rest of the world is (eventually) evaluated in one-dimension (our salary), that’s the direct relationship between replacement level and wins.

    Furthermore, rather than saying an average nonpitcher get 8MM and the average starter with 180IP gets 10MM and the average reliever gets 2MM, I simply say that everyone above replacement gets 4.4MM.

    It all works out to the same thing. You can continue to work in average only, and ignore replacement level completely, and you will stick get the same numbers I do. But, you will soon find out that it’s alot more work to continue to work in the multi-dimensions, when you can simply accept the shortcut that replacement level allows you to work with.

    Plus, once confronted with replacement levels, you realize how close some guys are to simply being out of baseball.

  30. JMB on February 6th, 2008 6:33 pm

    WAR! Huuh. Good God y’all. What is it good for?

    Rating baseball players.

    Sing it again!

  31. Jeff Nye on February 6th, 2008 6:34 pm

    HE LIVES

  32. msb on February 6th, 2008 8:33 pm

    how’s Atlanta?!

  33. Bilbo on February 6th, 2008 8:40 pm

    On a job application for running a major league franchise, this should be question #1. If you can’t grasp this concept, you don’t get to make decisions.

    And if this is the only concept you grasp, you get to write a blog. ;-) This is a great article by Tango and I thank you for sharing it, but seriously Dave, stop pretending you know things the Mariners don’t.

  34. Dave on February 6th, 2008 8:42 pm

    Uhh, I do. Bavasi knows thousands of things that I don’t, and I know a few things that he doesn’t. You can call it humility if you want to deceive yourself, but if you really believe that the Mariners front office has all knowledge when it comes to baseball, then I’ll call it ignorance.

  35. Breadbaker on February 6th, 2008 8:45 pm

    26: But that doesn’t show up in the fielding statistics. Those are called “hits”.

  36. Dave on February 6th, 2008 8:47 pm

    You really don’t know how the fielding metrics work, do you?

  37. Jeff Nye on February 6th, 2008 8:52 pm

    From what I hear, Bavasi didn’t know about Willie’s affinity for ponies until this site broke the news.

    So, we’re up at least 2-0!

  38. coasty141 on February 6th, 2008 9:02 pm

    #33 Its comments like yours that make me just want to thank the guys the spend so much their time and effort on this site. So thank you DMZ, Dave, and others.

  39. Dave on February 6th, 2008 9:07 pm

    Don’t worry too much about Bilbo – if we went through the history of his comments on the site, he’s been wrong pretty much every single time he’s disagreed with us. He’s just projecting his lack of knowledge on others.

  40. thefin190 on February 6th, 2008 9:12 pm

    28 – Didn’t they try to do that in the movie “Major League”?

  41. coasty141 on February 6th, 2008 9:16 pm

    I’m getting OT but [deleted, ot]

  42. MKT on February 6th, 2008 9:23 pm

    27. I’m not disputing its importance as a concept that aids in analysis. I just think that, in talking w/more general fans, the concept of replacement level tends to start more arguments than it settles.

    Maybe so, but there was a time when the concept of on-base average caused arguments with people who preferred to look at batting average, and a time when RC, linear weights, OPS, etc. caused arguments with people who wanted to look at RBIs, etc.

    Dave states it very well in post 12. It’s the right way to look at roster construction questions.

    If you’ve taken Econ 101, remember when the instructor told you that the correct way to measure the cost of anything is to look at its opportunity cost? Whereas superficial measures such as sticker price or accounting cost lead to bad decision-making? It’s the same principle at work here: though it may be hard to measure exactly what the replacement level is, it’s the necessary starting point, because it enables us to calculate the opportunity cost of a player. (Replacement level = freely available talent, ie. no opportunity cost; talent above that level will have positive opportunity cost.)

  43. coasty141 on February 6th, 2008 9:32 pm

    From the bottom of Tango’s post
    The totals by position:
    563 wins nonpitchers
    346 wins starters
    100 wins relievers
    1009 wins total

    From this could I conclude the most important (valuable) player is an inexpensive position player who produces wins above replacement level? More so than a RP or SP for that matter?

  44. Dave on February 6th, 2008 9:44 pm

    Yep – position players are more valuable than pitchers. This is because position players get to affect both run scoring and run prevention. Their share of the game is bigger.

  45. coasty141 on February 6th, 2008 9:56 pm

    Can the wins by nonpitchers (the 563) be separated by offense and defense? Some thing like offense for a nonpitcher 400 wins and defense 163. And would it vary by position? SS defensive value should be greater than a 1B

  46. gwangung on February 6th, 2008 10:44 pm

    From this could I conclude the most important (valuable) player is an inexpensive position player who produces wins above replacement level? More so than a RP or SP for that matter?

    But..but…but..two Aces! Two Aces!

  47. Sidi on February 6th, 2008 11:41 pm

    Can the wins by nonpitchers (the 563) be separated by offense and defense? Some thing like offense for a nonpitcher 400 wins and defense 163. And would it vary by position? SS defensive value should be greater than a 1B

    I think you’d have to break it up into position. If you look at first base the contributions would be almost entirely offensively (unless you’re the Mariners). If you’re looking at left field it will be heavily somewhat (unless you’re the Mariners).

    Most stats that try to evaluate something like WARP or runs created do compare to a positional value, so it’s not just a general comparison.

  48. Sidi on February 6th, 2008 11:42 pm

    Ok, I lied when I clicked the button. I meant to say “left field it will be somewhat defensively.” Instead I got a edito, and it makes no sense.

  49. thefin190 on February 7th, 2008 12:48 am

    Dave, could you possibly calculate how many wins each Mariner this coming season will provide and add them up? That’d be interesting to see. I realize that spring training hasn’t started so we don’t know the full roster, but we have a pretty rough idea of who is going to be starting right?

  50. Evan on February 7th, 2008 9:56 am

    Seems to me that replacement starts from the financial side (i.e. paying every player league mins) and gets a bit fuzzier once we get into baseball, and working from average is the other way around. It’s all pretty interesting, I just worry that replacement level is a bit of an artificial construct.

    That’s exactly the position held by Lee Sinins, so you’re not completely out on a limb, here.

    I disagree because Replacement level makes more sense to me in terms of roster building, and both replacement level and average are functionally equivalent when comparing teams (though the use of average would mean everything would always add up to zero, making for easier error checking).

  51. Broadcast James on February 7th, 2008 10:37 am

    I’m having a really hard time grasping the argument for using average players as the baseline player over using the baseline player as the baseline…

    Bullet point one: How are you defining average? Mean? Median? Mode? I don’t see how any of those are of particular value. So what if all the batting averages equal out to .280, what does that have to do with the players that are actually available? I just think the entire concept of there being some non-mythical average players out there is flawed to begin with. (As a side note, if you’re using mode, replacement level might actually be the definition of an average ball player.)

    Bullet point two: Using the true baseline of talent makes intrinsic sense. In music theory it’s the bottom note of the triad that gives the chord it’s name, not some bizarre average. That’s just the way it works in nature, even tough it might seem counter intuitive at first.

    Bullet point three: If you’re going to be making business decisions you need your data to be practical. Replacement level players will always be a practical option, while, finding a “league average player (again, whatever that means)” might not be realistic.

    Maybe this just comes down to people looking at the world through different lenses, but again I just don’t get what the argument is here. Replacement level sets a realistic and authentic baseline… From a scientific perspective, that’s what you want.

    BTW: Can we figure out Wins Over “Dude of the Street” (WODotS) next? If we figure the average MLB team wins 81 games, and the dude off the street wins 1 due to a “Bad News Bears” type scenario, we can figure 80/25 is 3.2 wins per player… or 8 wins per starter (80/10)… So is Eric Bedard really only worth 13 wins over me?? :) I kid… most ridiculous analysis ever.

  52. smb on February 7th, 2008 10:55 am

    I think the best advantage is that it is geared toward payroll efficiency. This type of analysis is exactly why the A’s are able to consistently win more games than us without spending nearly as much money. What more proof of the value of these statistical constructs could be needed? If you compare the apparent analytical methodologies of two teams like the A’s and M’s, it’s like a freestyle swim race in which one competitor (M’s) is wearing lead socks. Either work the system to your advantage or get worked by it, right?

  53. gwangung on February 7th, 2008 11:03 am

    #51

    Gooooood points I like that.

    And to repeat some things….there are more replacement level players out there. Easier to get a hold of…AND you’re less likely to be distracted by the noise of individual players and easier to get a true picture.

  54. tangotiger on February 7th, 2008 1:21 pm

    The hard part of replacement level is deciding what that level is.

    The easy part of average is that we know exactly what that level is: 4.8 runs per game in the recent past.

    As I said, you can stick with average and ignore replacement completely. Consider that the average payroll is 90MM of which around 12MM is required minimum payroll, leaving you with 78MM to play with for an average team (.500). Presuming you allocate around 57% of your payroll to nonpitchers, that gives them 45MM to allocate for 9 full-time nonpitchers.

    That means the average player will get 5MM per 162 games played. Presume for the moment that each win (free agent, arbitration, pre-arb, on average) is worth $2.2MM per win. (Plus of course every player gets his 400K minimum.)

    So, this is what you get for a guy who plays 162 games:
    $7.6MM +1 win above average (WAA)
    $5.4MM +0 WAA
    $3.2MM -1 WAA
    $1.0MM -2 WAA
    $0.4MM -2.27 WAA

    And if he plays 81 games:
    $5.1MM +1 win above average per 81 games (WAA)
    $2.9MM +0 WAA
    $0.7MM -1 WAA
    $0.4MM -1.135 WAA

    So, roughly speaking, a guy who is an average player for 162 games is equal to a guy who is +1 wins above average over 81 games. How do you equate those two with 1 number, rather than necessitating carrying two numbers (his WAA, and his games played)?

    Well, if you add .014 wins per game to each player, this is what you get:
    First player: 0 wins above average + .014 * 162 = 2.27 wins
    Second player: 1 wins above average + .014 * 81 = 2.13

    As you can see, both roughly equal. If you multiply the above numbers by $2.2MM per win, and then add $400K, you get:
    2.27 * 2.2 + 0.400 = $5.4MM
    2.13 * 2.2 + 0.400 = $5.1MM

    And those are the numbers we got when we ONLY talked about average and never brought up replacement level.

    So, both sides can go ahead and do what they want to do: use only average or use only replacement. You end up at the exact same spot.

Leave a Reply

You must be logged in to post a comment.