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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55 Comments on "Wins Above Replacement (WAR) vs. Wins Above Average (WAA)"

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Ed
Guest

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

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

Dr. Doom
Guest

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.

no statistician but
Guest

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?

RJ
Guest

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!

Dr. Doom
Guest
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 »
John Autin
Editor
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
“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
“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
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

“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
Guest
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
Guest

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
Guest

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
Guest

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
Guest

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
Guest

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

trackback

[…] 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
Guest

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

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