Wins Above Replacement (WAR) vs. Wins Above Average (WAA)

First, an introduction: I’m Adam Darowski and I’m a longtime fan (and occasional commenter) of HHS and its previous incarnations. If you’ve seen my name before, it was likely related to the Hall of wWAR work that I’ve done. I also contribute to Beyond the Box Score and Baseball Past and Present. This is my first post at HighHeatStats, though I already have another project in the works. Hi, everyone!

When Baseball-Reference updated their Wins Above Replacement (WAR) framework, they included Wins Above Average (WAA). Personally, I found this to be a tremendous addition. I had recently started calculating and visualizing Wins Above Average based on Rally’s original WAR spreadsheets. While B-R rendered all of my underlying data useless, they at least had the decency to save me from redoing all my work.

As I’ve started using WAA, I’ve had people ask me:

  • What’s the difference between WAR and WAA? and
  • Why haven’t we just been using WAA all along?

While both metrics are similar, they do serve very different purposes.

Why Replacement?

Perhaps the most difficult sabermetric concept to explain to uninitiated baseball fans (not even “casual”—just not objectively-focused) is that of the replacement player. Why in the world, they ask, would I compare a star to some AAA scrub?

Wins Above Replacement is useful for measuring the value of a player over the player freely available to replace him with. For the most part, every average player in baseball is employed by a big league club already. If you need to fill a hole on your roster, you either need to:

  1. Sign an expensive free agent (costs you monetary assets)
  2. Trade for a player (costs you other player assets) or
  3. Pick up a freely available player.

#3 is your replacement player. He’s the guy you can get for (essentially) nothing.

A good example of a replacement player is Mauro Gomez. Mauro Gomez is hitting over .300 and slugging over .600 for AAA Pawtucket so far this year. When Will Middlebrooks was conveniently hurt (immediately following the Kevin Youkilis trade), Gomez was recalled. The Red Sox didn’t trade for anyone—they grabbed a replacement player (not a prospect—someone that they pretty much got for free over the offseason). Gomez showed a bit power, hitting .300 with three doubles in nine games. But he also exposed why he’s a replacement player—his glove. DRS already rates his defense as four runs below average (in just nine games!). His Baseball-Reference WAR sits at –0.4. He’s a replacement player.

When WAA is Better

I do a lot of research related to the Hall of Fame. In my work, I’m not building rosters, I’m trying to figure out who the greatest players of all time were. For this reason, WAA might be a better metric for me to use than WAR. When considering someone for the Hall of Fame, do you say “Wow, he was so much better than the AAA players of his day?” or “Wow, he was so much better than everyone else?” I find WAA is a better way to measure how much a player was better than “everyone else”.

Why? WAR rewards you for just being there. WAA does not.

62% of WAR is Just Showing Up

For Pete Rose, it was.

Pete Rose was worth 76.7 WAR for his career. But he was also worth just 29.2 WAA. That’s a huge difference. Take Charlie Keller. He’s on the opposite end of the spectrum. Keller was worth 40.6 WAR, but 29.0 WAA. Yes, King Kong Keller’s WAA was about the same as Pete Rose’s.

What’s happening here? Rose played forever (15,890 PA). Keller didn’t (4,604 PA). WAR rewards you for playing time, as long as you’re better than a AAA player. WAA, meanwhile, will rip you apart if you’re below average.

Through age 35, Pete Rose was worth (in 10,001 PA), 70.1 WAR and 39.8 WAA. He had 2,762 hits at that point. You can see what I’m getting at here. From that point on, Rose collected 5,889 more PAs. He added a bit to his career WAR (just 6.6 WAR in ten years). However, he destroyed his WAA, coming in at –10.7.

At the same time, he collected his 3,000th hit, his 4,000th hit, and—most importantly—his 4,192nd (though the 4,190th turned out to really be the important one). So, while he was dismantling his WAA, he was building his legacy.

Therein lies the dilemma—showing up is still important, but the importance differs depending on the context). WAR rewards the ability to show up, WAA does not.

The Actual Difference Between the Two

The components of WAR are expressed in runs above or below average, not replacement. To calculate WAR, you need to make a replacement adjustment that is based on playing time. WAA simply eliminates that adjustment.

Here are Rose’s WAR components:

  • +368 runs for batting
  • +13 runs for baserunning
  • +5 runs for avoiding double plays
  • –54 runs for his defense
  • –91 runs for the positions he played

That’s a total of +241 runs above average. If you convert those runs to wins, you get 29.2 WAA.

If you add one more component, though:

  • +492 replacement runs, based on playing time

Rose then has a total of +733 runs above replacement. That converts to 76.7 WAR. Those 492 runs say “if a replacement player played as much as Rose, he would have been worth 492 runs below average“. Therefore, Rose is 241 runs above average, but a whopping 733 above replacement—mostly because of how long he played.

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Ed
Ed
8 years ago

Good information Adam! Would be nice if BR would update their leaderboards to include WAA.

http://www.baseball-reference.com/leaders/

Dr. Doom
Dr. Doom
8 years ago

So, Adam, I have a question. What would happen if you ran a complete “Hall of wWAA” and kept the same number of enshrinees? How much overlap would there be? Who would be out, and who would move in? I’m super curious about this, so if you have the time (and inclination), I’d love to see the work. Heck, you may have done it already, in which case you should link to wherever you posted it.

Dr. Doom
Dr. Doom
8 years ago
Reply to  Adam

A couple of things. First, if you simply added the two together, you’d already be double counting WAA – because WAR is just WAA plus Rrep. So that could make sense. I was just suggesting that for my own, selfish purposes, I’d like to see how much difference there is between the two, because I think that could be really interesting (I’ve got my eye on you, Eddie Murray!), but you’re probably right about a “compromise” method working out pretty well. I’m going to look at your Hall of wWAR stuff today and see if I can give any suggestions… Read more »

wlcmlc
wlcmlc
8 years ago
Reply to  Adam

Longevity is important considering most talks of a ball player making the HOF are if he can get to 500/600 HRS, 3000 hits or 300 wins.

Tubbs
8 years ago
Reply to  Adam Darowski

Craig Biggio’s passing of 3,000 hits also comes to mind & checking his WAA from ’02-’07 he’s -6.7 & wound up finishing his career at 29.1

Dan McCloskey
8 years ago
Reply to  Adam Darowski

I think combining them works well. If we used just WAA, then we’re basically penalizing Rose for sticking around when he was still useful. But, by combining them, the additional WAR is offset by the negative WAA.

Years of being “just useful” shouldn’t help a Hall of Fame case, but it shouldn’t hurt it either (as long as the rest of a player’s career are worthy, of course).

Richard Chester
Richard Chester
8 years ago
Reply to  Adam Darowski

After the 1961 season Early Wynn had 292 wins. He hung around for two more years to reach 300 and compiled an 8-17 record while doing so. He did have an excellent ERA in limited action in 1963.

Dr. Doom
Dr. Doom
8 years ago
Reply to  Adam Darowski

Adam (@18)- I would strongly disagree with this suggestion. You already have two provisions in the Hall of wWAR as it is which don’t penalize players, no matter how bad they get. Frankly, I would say that if a player is playing at less than average value, there’s no reason we shouldn’t subtract that. I mean, as you pointed out in the initial article, Rose and Keller were (for all intents and purposes) the same, relative to average. However, by doing wWAR>0, Rose would undoubtedly be much higher than Keller, simply by virtue of playing longer… but if you add… Read more »

Tmckelv
Tmckelv
8 years ago
Reply to  Adam Darowski

Adam @18, That was my immediate problem with WAA (the negative seasons) so I was thinking the WAA>0 also. I hate to bring something like this up in this forum, but I have to think that having a former star around the clubhouse is more useful than a young player (non-prospect) or journeyman that would put up the same stats for a given season. I would think the intangibles could somewhat cancel out the negative WAA. Similarly, I think that having a prospect at the major league level helps the player and team (future) more than a non-prospect/journeyman, so again… Read more »

John Autin
Editor
8 years ago
Reply to  Adam Darowski

I went on so long with my Rose comment that I didn’t see Adam’s idea @18 for counting only WAA>0. What about tweaking that to, “count only WAA>0 for age 40 and up”?

There’s no perfect solution for *not* penalizing milestone-chasing. Some such “hang-around” years happen before age 40, and also some players go beyond 40 *without* chasing milestones but are still below average. An age-40 cutoff would be a compromise.

Michael Sullivan
Michael Sullivan
8 years ago
Reply to  Adam Darowski

I agree with Dan M. I’m all for penalizing below replacement play in a HOF case, but penalizing WAR>0 but penalizing below average play seems foolish. Why should it hurt someone’s case that they played longer in a somewhat useful if diminished capacity?

kds
kds
8 years ago
Reply to  wlcmlc

Certainly the BBWA think those round numbers are very important. Lou Brock was a first ballot HOFer, with 42.8 brWAR and 8.4 WAA. Obviously the SB records helped, and the World Series and “fame”, but he is a poster boy of just a little above average accumulation. Let’s not forget how important getting to average is. For a team replacement level is about 50 wins. 94 wins should pretty well guarantee a playoff spot. Of 44 team WAR to get from replacement level to the playoffs 31 are to get to average, while 13 WAA (and often less) are needed… Read more »

no statistician but
no statistician but
8 years ago

How does wins above average compare with wins above team, a stat for pitchers Bill James referred to in one of his Historical Abstracts? He noted that, for pitchers with good teams, wins above team was a telling stat, whereas it didn’t necessarily reveal much with pitchers on poor teams. What about WAA for pitchers in this regard?

Dr. Doom
Dr. Doom
8 years ago
Reply to  Adam

I believe this is where you take the team winning% and multiply it by the number of decisions the pitcher had, then subtract that number from the number the pitcher actually won. For example, in 1972, the Phillies (yes, I’m going with the easiest/most famous example) won 37.8% of their games. Steve Carlton had 37 decisions. Thus, we would have expected 14 wins from Carlton. Instead, he won 27 – or 13 wins above team. I don’t recall ever reading about the difference between good and bad teams, though. Frankly, if it doesn’t work on that level, it seems pretty… Read more »

John Autin
Editor
8 years ago
Reply to  Dr. Doom

Doc, doesn’t WAT start with the combined W% of the team’s other pitchers, then apply that to the target pitcher’s decisions? The method’s weakness with bad teams was discussed somewhat in the Red Ruffing essay. James noted that Ruffing with the Yankees had a *better* W% than the team, but with the BoSox he had a *worse* W% than the team. BJ’s explanation was, basically, a good pitcher on a bad team gets worked too hard, gets matched against the best teams (back when rotations were more flexible), etc. I can see it as a small complementary method, but as… Read more »

no statistician but
no statistician but
8 years ago
Reply to  John Autin

JA: Just the essay I was going to reference when I had the time to reply. In rereading my original at #5 I don’t see that I was putting any stress on the validity or lack of it of WAT. What I’m interested in is whether WAA for pitchers addresses the point. Admittedly, the way starting pitchers are used now, being pulled after a certain number of pitches, etc,. and the sharing out of the final innings among specialists like the LOONY (or whatever it was discussed a couple of days ago) militate against deciding on a clear “winner,” but… Read more »

Dr. Doom
Dr. Doom
8 years ago
Reply to  John Autin

JA, you could be right about the “team w/o” thing. But you’re ABSOLUTELY right about it punishing the 90s Braveses of the world.

Michael Sullivan
Michael Sullivan
8 years ago
Reply to  John Autin

NSB@14: WAA is essentially the same as WAR in terms of measurement strengths and weaknesses. The only difference is the baseline for comparison. How pitching performance is measured is the same for WAA and WAR. I agree it’s not as clear a measure as for position players, but I still think it’s pretty good. Also, wins are the name of the game, but in my mind and a lot of other people’s, WAR is a far better measure of a pitcher’s contribution to team wins than pitcher W-L, not just for today’s players, but for all players. The pitcher cannot… Read more »

RJ
RJ
8 years ago

Thanks for this post Adam. For me WAA was always “that number that’s sort of like WAR that I don’t really understand”. No more!

Paul E
Paul E
8 years ago
Reply to  Adam Darowski

ADAM: ” ” When considering someone for the Hall of Fame, do you say “Wow, he was so much better than the AAA players of his day?” or “Wow, he was so much better than everyone else?” I find WAA is a better way to measure how much a player was better than “everyone else”.” ” That, in a nutshell, is the greatest argument in the world against WAR and for WAA. At the end of the season, the final MLB won-loss logs read something close to 1215-1215 or 81 – 81 on average. How the hell did the idea… Read more »

John Autin
Editor
8 years ago
Reply to  Paul E

@19, Paul E — Certainly we want our HOFers to rate far above average for their careers. But if you measure season by season only against the average (not replacement), and then compare certain careers head-to-head, you’ll get some weird conclusions. Imagine one guy who alternates 10 big WAA seasons with 10 purely average seasons, and another who has the same 10 big WAA seasons all in a row and then quits. Do you think those two have the same HOF credentials? Which team is likely to win more pennants? There *is* value in being average. Maybe we don’t want… Read more »

kds
kds
8 years ago
Reply to  Paul E

Paul, we use replacement level, and hence WAR because that is where we must start for studying economic/personnel issues. As Adam implies above you should be able to get replacement level players for minimum salary. This doesn’t mean that sub replacement level is worthless, you need to score/prevent enough runs to get to 48-50 wins, but there are enough players at that level that we don’t have to pay for those wins. This applies to trades, free agent signings, draft choices, etc. So WAR is necessary for many things, but other baselines, such as WAA can be more appropriate in… Read more »

Paul E
Paul E
8 years ago
Reply to  kds

kds: I understand completely. Unfortunately, as a baseball fan for the better part of 45+ years, I’ve never had too much interest in the Tommy Helms and Denny Doyles of the world. I have to believe you’ll agree with me when I say ”two drunks in a bar aren’t arguing whether Roger Metzger was the superior of Enzo Hernandez. It’s more likely DiMaggio versus Williams or Mantle versus Mays”. And that’s where WAA presents a better platform for the discussion – drunk or sober 🙂 But, certailnly WAR has its place and will probably gain more widespread use as even… Read more »

RJ
RJ
8 years ago
Reply to  Adam Darowski

Well I don’t understand the ins and outs of how WAR is calculated, but I ‘understand’ it, in that I can look at it quickly and make a passing evaluation of a player’s season/career. I couldn’t do that with WAA, as I didn’t have the same understanding of what good or bad numbers were, or how it was different to WAR. To be honest I’d never actually looked at it properly before 🙂

Dr. Doom
Dr. Doom
8 years ago

So, Adam, these are my thoughts about a new wWAR formula. First, as it stands now, the formula is: wWAR = WAR/162 + WAE + WAM + wWPA (Anyone who wants to know what these things mean, check out Adam’s AWESOME website – specifically, this page: http://darowski.com/hall-of-wwar/about/ ) Now, I have some critiques of that formula. First of all, my opinion would be to regress WAR/162 in some way (probably by giving WAR credit for the number of games played, and then credit for the rest of the season by giving the player a WAR rate that is halfway between… Read more »

Dr. Doom
Dr. Doom
8 years ago
Reply to  Adam Darowski

Do you think it would be necessary to pro-rate WAA, as well, making it WAA/162? Or do you feel it’s best to just have one of them pro-rated, and, if so, why WAR/162 and WAA, rather than WAA/162 and WAR? Just a thought.

Michael Sullivan
Michael Sullivan
8 years ago
Reply to  Adam Darowski

I don’t like your WAR/162 at all. It basically gives credit for games not played. Consider two players who’s WAR/PA is exactly the same, but one is injured often or platooned and averages only 75 games/year while the other averages 150 games. The second player’s WAR will be about double the first player’s, but their WAR/162 will be exactly the same. Surely the second player should get some extra credit for playing more games at the same level? I thought I remembered you using this hack only to give some WAE or WAM credit for players who killed it for… Read more »

Michael Sullivan
Michael Sullivan
8 years ago
Reply to  Adam Darowski

apologies, that makes much more sense.

John Autin
Editor
8 years ago

Welcome, Adam, and good piece! I would not dismiss WAA because of isolated individual results. But in Rose’s case, I think the final WAA number is a far worse assessment of his career value than WAR. Yes, Pete Rose hung on for several years at or below replacement level, and far below average. The question is how, or even whether, to integrate those years into his career snapshot. Two questions: — Ignoring all context, when should he have stopped playing? — Taking in all the circumstances, when can you imagine that a real person might have stopped playing? I’d say… Read more »

Doug
Editor
8 years ago
Reply to  John Autin

“But the -7.5 WAA he loses for his final 4 seasons only distorts a reasonable assessment of his career value.” Not sure I agree, John. Whatever the reasons for Rose playing in those years, the bottom line is he was a below average player. Whether the Reds did or didn’t have a better option is a different matter. The facts are that Rose played, and played at a below average level, and that’s what WAA is showing. If you think WAA is too harsh in the case of players like Rose, a statistic you might look at is to average… Read more »

John Autin
Editor
8 years ago
Reply to  Doug

“Whether the Reds did or didn’t have a better option is a different matter. The facts are that Rose played, and played at a below average level, and that’s what WAA is showing.” Yes, that’s what WAA is showing. But I can question whether it shows something meaningful. I think hang-around years should be treated differently than bad years in the middle of a career. To say it’s irrelevant whether the Reds had a better option ignores real-world factors in a player’s decision to keep going. Suppose that milestones were no factor for Pete, and he’s thinking about retiring after… Read more »

Doug
Editor
8 years ago
Reply to  John Autin

Your points are certainly plausible, and it isn’t anyone’s “fault” that Rose played after he was below average (most players do). The statistics, though, should measure objectively. And, that, I think is what WAR and WAA both try to do. Whether, the statistic alters our perception of a player is a function of our perception, not the statistic. 🙂 Your thought about an age component in WAR and WAA calculations seems, on the surface, to have some merit. Basically, tweak the metric up or down, based on how the player did relative to the replacement or average player of that… Read more »

John Autin
Editor
8 years ago
Reply to  Doug

“Whether, the statistic alters our perception of a player is a function of our perception, not the statistic.”

Good point, Doug.

Signing off — JA.

Michael Sullivan
Michael Sullivan
8 years ago
Reply to  Doug

well, it’s certainly true that WAA measures what it measures. But as soon as we start using it as a metric of a players career, we are making a case for it meaning more than simply a + b + c / d. When we are using metrics like WAR or WAA to make rough HoF cuts, we are implcitly assuming that they make a decent stand in for the value of a players career, and it is fair to consider their usefulness or shortcomings as a measure of player value. WAR makes sense to me as a rough cut… Read more »

RJ
RJ
8 years ago
Reply to  John Autin

There’s an analogous situation in Formula One right now. In his prime Michael Schumacher won seven world titles, two more than anyone else, and subsequently retired. But, now in his 40s, he has been tempted back into the sport and is driving at noway near the level of his peak. Should his so-so performance at the tail of his career detract from the fact that in his peak he was the most successful driver ever?

Sorry to mix sports, but I think its an interesting comparison.

Tubbs
8 years ago
Reply to  RJ

Awesome! “Schumi” makes it into a post on a baseball website! The closest I can think of a baseball player doing the same thing was Ryne Sandberg coming back in ’96 & ’97. I just don’t think Schumacher could turn down the chance to drive the Silver Arrows of Mercedes, though the team has failed to dominate like they did in the days of Caracciola/Rosemeyer & Fangio/Moss.

Dr. Doom
Dr. Doom
8 years ago
Reply to  Doug

True, Doug, but the question also has to be put in the context of Adam’s inquiry as to merit for the Hall of wWAR. This is why I’m not sure what to do with such seasons, either – because Adam doesn’t currently penalize for season BELOW MVP or Excellence levels… so it’s kind of hard to make him suddenly start penalizing for below average. Of course, he DOES penalize for being below replacement…

It’s a tough problem. Let’s just leave it at that.

Bradley Marinko
7 years ago

I imagined this was a seriously excellent blog post. I constantly like reading content pieces similar to this one. I should endure more of your respective posts.

Darien
7 years ago

More spammers should leave such hilariously backhanded compliments. Because: come on. That is brilliant.

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[…] Replacement, expressed on Baseball-Reference as Rrep and not searchable in the Play Index, fills the gap between replacement and average. […]

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[…] “But where are the third basemen of yesteryear?” Francois Villon might well have asked had he been (a) alive today; (b) able to speak English; and (c) modestly knowledgeable about baseball. Consider this: in 1973 three future Hall-of Fame third basement were active (Brooks Robinson, Mike Schmidt, and George Brett), though Brett was just getting his first cup of coffee. Several others (Ron Santo, Graig Nettles, Buddy Bell, Sal Bando, and Darrell Evans) who at least arguably belong in the Hall also played that year. According to Baseball Reference, third base was the most valuable non-pitching position in the… Read more »

Geoff Silver
Geoff Silver
3 years ago

62% of WAR is not “showing up.” It’s being good enough to play regularly in the Major Leagues. This is a critical distinction.