## Clutch WAR: Measuring Value for What REALLY Happened

Wins Above Replacement (WAR) is a great stat. If I could make stats my children, I'd want WAR to be my first-born. WAR does it all, and lets us compare pitchers to catchers.

One of the few deficiencies (or benefits, depending on how you look at it) of WAR is that it's context-neutral: A home-run in the 3rd inning of a 10-0 game is as valuable as a walk-off homer in extra innings. How can we account for this? Enter WPA - Win Probability Added.

WPA is another fantastic stat, and it does one thing extremely well: It tells you exactly how much a player has added to a team's chance of winning with the bat. WPA factors in the base-runners, the inning of the game, and the score, and as such is great for telling a story. Unfortunately, the numerical value that WPA gives only factors in hitting and not fielding or position. We can, however, use some fairy dust (linear regression) to convert WPA to wRAA, which is WAR's measure of offensive value.*

*When doing this correlation, I noticed something very surprising. The relationship between wRAA and WPA appeared to be somewhat parabolic or exponential at the extremes (i.e., Barry Bonds and Pujols's WPAs are far, far better than would be expected). The only explanation I can think of is that better hitters are going to produce less WPA- at bats and more WPA+ at bats, so the increase compounds on itself.

This is a very convenient relationship because WPA and wRAA both compare to league average hitting. They give the relationship 11.4*WPA=wRAA, giving us a wRAA value we can plug right into the WAR formula.

Batting WPA WPA Batting Fielding Replacement Positional WAR Context WAR Clutch wins
Carl Crawford 20.9 2.19 24.8784 19.1 14.4 -4.4 5.1 5.4 0.3
Evan Longoria 21.7 1.7 19.312 4.1 15.3 1.6 4.4 4 -0.4
Ben Zobrist 10.1 -1.02 -11.5872 9.8 14.2 -3 3.2 0.9 -2.3
John Jaso 5.4 0.02 0.2272 -1 8.4 3.2 1.6 1.1 -0.5
Reid Brignac -1.1 0.48 5.4528 3 8.3 1.8 1.2 1.9 0.7
Sean Rodriguez -2.2 -0.3 -3.408 5 8.7 0.3 1.2 1.1 -0.1
Carlos Pena 6.7 0.11 1.2496 -1.4 14.1 -7.5 1.2 0.6 -0.6
B.J. Upton 0.5 -1.26 -14.3136 -3.9 12.7 1.4 1.1 -0.4 -1.5
Matt Joyce 4.8 1 11.36 0.9 3.3 -1.8 0.7 1.4 0.7
Jason Bartlett -6.6 -0.73 -8.2928 -4.3 11.4 3.5 0.4 0.2 -0.2
Kelly Shoppach -2.5 0.27 3.0672 -1 3.3 1.5 0.1 0.7 0.6
Willy Aybar -1.3 0.1 1.136 0.6 6.5 -4.7 0.1 0.4 0.3
Gabe Kapler -5.4 -0.52 -5.9072 0.1 4.3 -1.9 -0.3 -0.3 0

The rightmost column tells us how much additional "WAR" a player has when you account for context. A few random thoughts:

• Clutchiness: Yet another thing Carl Crawford is good at.
• I don't think I'll ever forget Kelly Shoppach's first at bat as a Ray. Coming in to pinch hit for Dioner Navarro in the bottom of a 9th inning opening day game with a man on first and no outs, he walloped a double that was inches from being a walkoff home run and went on to score the winning run. It was a truly majestic first at bat, and WPA agrees; it was worth 3.75 runs, about 5 times a normal double's value.
• Perhaps this is where much of the negative perception on BJ's hitting abilities comes from. He's been pretty unclutch so far this year.
• Ben Zobrist has pretty much re-defined unclutch this year in fact. His wOBA drops from .377 in low leverage situations to .244 in high leverage situations, thanks to a BABIP drop from .341 to .156.
• Reid Brignac's clutchitude is made even more impressive by how often those big hits come in pinch-hit situations. Pinch-hitting is not easy.
• Matt Joyce is a destroyer of worlds.

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