Taro points out, "WAR also underrates relievers slightly.  Yes, Position players and SPs are far more valuable, but elite relievers pitch in much more leveraged situations."

This leveraging can amount to a factor of about 1.5, in my opinion. 

For non-closer, #1 setup relievers brought in to put out fires, it might be more than that.  You are not going to see me using WAR to evaluate trades for franchise relievers.

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Per WAR, Mariano Rivera has averaged 2.2 WAR the last eight years -- so he's as valuable as an exactly league-average outfielder, right?   Two wins above replacement level = league average?

Think you could have gotten Rivera from the Yankees for a 2-win outfielder?  How about for a 3-win outfielder?  No way.  The Yankees would have looked you right in the eye and said, Rivera is worth 50-100% more than his WAR indicate.

And they've paid him accordingly.  In 2008, they gave him $15m per -- appropriate for 3-4 wins, not two.

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=== Z Axis Dept. ===

The 2001 Mariners ran Arthur Rhodes, Jeff Nelson and Kazuhiro Sasaki out there -- those guys running 10k rates, saving 25 runs or so and getting credit for about 2.5 WAR apiece.   The reality is that those three relievers shaped ballgames -- about 116 of them.

I've got nothing about RC/27 and its derivatives, EqA, wOBA, xFIP* and WAR.  Here's my post defending its integrity despite its high values for FA's this offseason.   But bases-per-out does not capture (among other things) the timing of bases gained and lost.   If bases are the X axis, outs the y axis, then timing is the Z axis.

The fundamental rules of baseball allow for managers to change pitchers at a time of his choosing.  If the manager can -- at will -- change to Papelbon, Rivera, or Brandon League* -- the timing of that move warps the routine x-y axis metrics.

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And there's a domino effect.  If you know that KRod is staying out of the game unless needed .... but that if you get two guys on, he'll come in and embarrass you anyway ... that affects you even when he doesn't come in.

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The Pythagorean Theorem, by the way, is another manifestation of the Z axis that is invisible to WAR-type metrics.

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=== W Axis ===

There's a W axis.  X and Y are mostly captured by WAR.  Play a game of Strat-O, with in-game managerial decisions, and you've captured much of the Z axis.

If baseball were played by machines, you'd be done.  But it's played by human beings rather than video algorithms, and that's the W axis.  Humans play with hangovers and injuries.  They come in visualizing the positive, or they don't.

Humans get kicked in the gut with two straight Eddie Guardado blown saves, and they play lousier the third day.  That's the W axis.

Relievers are important -- the more so if your only closer is David Aardsma.

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What causes a player to have an UP year or a DOWN year?  This is another example of the human factor, the Z axis.  These aren't Strat-O cards.

When other players around them are playing well -- when they have Rhodes, Nellie and Daimajin waiting to seal a victory -- it's easier for some other player to visualize success, and to play well himself.

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=== Can You Win Your Next Pennant With This Player, Dept. ===

Step away from the slide rule and ask yourself something:  are Jon Papelbon and Mariano Rivera key parts of their championship teams?   There probably isn't a Yankee who wouldn't tell you that Rivera has been one of the 3 or 4 most important parts of the 1996-2009 Yankees.  Many Yankees would surely tell you that Rivera -- meandering along at his 2.2 WAR -- has been THE most important part of many Yankee teams.

Would all those Yankees be wrong, or is there something about baseball that WAR is not capturing here?

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I love Brandon Morrow, and wanted to see the 17-6, 2.89 season :- ) or else see him go out in a deal for AGone.

But if you think Brandon League is a 1 WAR commodity, watch a ballgame sometime.  ;- )  If you're going to slap a WAR figure on League, use the number 3.  That's conservative.

Cheers,

Dr D