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Around The Yankees Galaxy - 9/18/10 - Let's recalculate WAR

Jscape continued the conversation about the validity of WAR on Thursday night, and we all debated an interesting point:

Since CC Sabathia is able to pitch deep into games, he winds up keeping inferior middle relievers out of the game longer, or out of the game altogether. 

Fangraphs says CC has been worth 4.3 WAR in 2010, but they calculate this by comparing him to a replacement level pitcher who's thrown the same number of innings.  I don't know how much sense that makes, because if you give a replacement level pitcher 31 starts, how many innings do you think he'd pitch?  150? 160? 

CC has thrown 217 this season.   

If Albert Pujols went down with an injury tomorrow, the #3 spot in the Cardinals lineup would still come up about as often as it did before.  And most relief pitchers tend to be brought into a game based on the score, the inning, and the save rule, rather than how good they actually are.  

However, a starting pitcher can pitch many innings, or few innings, based on how good he is at preventing the other team from scoring and how economical he is with his pitches.   Some pitchers are significantly better at combining both of these traits than others, and so I tried to find a better way to caculate how much a CC Sabathia or a Roy Halladay is really worth, considering that there is no replacement player who's going to average 7 innings per start.

First, I calculated each individual pitcher's winning percentage based on Bill James' Pythagorean winning percentage formula (if you're not familiar, you can read up on it here). 

Let's use AJ Burnett as an example.  His FIP is 4.60 this season, and the average team is scoring 4.41 runs in 2010.  Based on that run differential, if you put him on the mound for 9 innings and give him average run support, you'd expect to win 47.9% of those games.  Then we compare this to pitcher with a replacement level FIP, which I calculate to be 5.19 in 2010, and do the same calculation  You'd win 41.9% of those games.

Burnett has pitched 168 1/3 innings over 29 starts, an average of 5.80.  How many innings would a replacement pitcher average?  Well, I really don't know.  I couldn't find an MLB average for IP per start to base an estimate on, so I used 5.0, which I think is a reasonable.  (If anybody knows where I can find the actual number, please let me know.)

So multiply Burnett's actual number of starts by his average of 5.80 IP per start and then divide that total by 9 (because there are nine innings in a game), and then finally multiply by his Pythag winning percentage to get a total of about 9.  Repeat this calculation using Burnett's actual number of starts but the replacement's average IP and Pythag winning percentage, and you get 6.75.   

So, considering that Burnett will not only allow fewer runs than a replacement pitcher, he's also likely to pitch more innings per start, he's probably worth about 2.2 more wins than a replacement pitcher, at least by this calculation.  By comparison, Fangraphs has him at 1.3 WAR.

I did this calculation for every pitcher who currently qualifies for the ERA title.  Their adjusted WAR is bolded in the right-hand column, next to their Fangraphs WAR.

Name G IP FIP IP/St Pythag W% WAR adjWAR
Roy Halladay 31 234.7 3.01 7.57 0.682 6.4 10.6
Cliff Lee 25 192.3 2.63 7.69 0.738 6.3 9.9
Felix Hernandez 31 225.7 3.01 7.28 0.682 5.9 9.9
Adam Wainwright 31 216.3 2.87 6.98 0.702 5.8 9.7
Josh Johnson 28 183.7 2.43 6.56 0.767 6.2 9.1
Francisco Liriano 28 178.3 2.36 6.37 0.777 6.3 8.9
Jered Weaver 31 204 3.05 6.58 0.676 5.4 8.1
Ubaldo Jimenez 29 196.3 3.03 6.77 0.679 5.7 8.1
Jon Lester 29 190 3.01 6.55 0.682 5.4 7.6
Justin Verlander 30 199.3 3.22 6.64 0.652 5.0 7.5
Brett Myers 30 205 3.36 6.83 0.633 4.3 7.4
CC Sabathia 31 217 3.56 7.00 0.605 4.3 7.4
Zack Greinke 30 203.3 3.36 6.78 0.633 4.8 7.3
Clayton Kershaw 30 192.3 3.19 6.41 0.656 4.3 7.0
Tim Lincecum 30 192.3 3.25 6.41 0.648 4.5 6.9
Matt Cain 30 204.3 3.54 6.81 0.608 4.0 6.8
Chris Carpenter 32 216 3.69 6.75 0.588 3.5 6.7
Johan Santana 29 199 3.55 6.86 0.607 3.7 6.7
Roy Oswalt 29 192.7 3.43 6.64 0.623 4.0 6.6
Mat Latos 27 166.7 3.02 6.17 0.681 3.6 6.3
David Price 28 186.7 3.46 6.67 0.619 3.9 6.3
Dan Haren 31 209 3.77 6.74 0.578 3.9 6.2
Yovani Gallardo 28 168 3.02 6.00 0.681 4.3 6.2
John Danks 29 192.7 3.59 6.64 0.601 4.1 6.1
Hiroki Kuroda 28 176 3.29 6.29 0.642 3.7 6.0
Name G IP FIP IP/St Pythag W% WAR adjWAR
Carl Pavano 30 210 3.93 7.00 0.557 3.2 6.0
Cole Hamels 30 194.7 3.62 6.49 0.597 3.8 5.9
Tim Hudson 30 203 3.81 6.77 0.573 3.2 5.9
Ricky Romero 29 191 3.64 6.59 0.595 3.7 5.9
Gavin Floyd 30 187.3 3.48 6.24 0.616 4.3 5.8
Anibal Sanchez 28 172 3.26 6.14 0.647 3.9 5.8
Chad Billingsley 28 172.3 3.27 6.15 0.645 3.7 5.8
Tommy Hanson 30 178 3.35 5.93 0.634 3.8 5.6
Wandy Rodriguez 29 176.7 3.45 6.09 0.620 3.5 5.4
C.J. Wilson 29 180 3.57 6.21 0.604 3.9 5.3
Colby Lewis 29 183 3.67 6.31 0.591 3.7 5.3
Livan Hernandez 30 194 3.87 6.47 0.565 3.0 5.2
Edwin Jackson 28 183.3 3.8 6.55 0.574 3.5 5.2
Max Scherzer 28 175 3.61 6.25 0.599 3.5 5.1
Jason Hammel 27 165.7 3.47 6.14 0.618 3.9 5.1
John Lackey 29 190 3.92 6.55 0.559 3.4 5.0
Clayton Richard 30 182.3 3.69 6.08 0.588 2.3 4.9
Ryan Dempster 30 193.7 3.98 6.46 0.551 3.1 4.9
R.A. Dickey 23 154.3 3.63 6.71 0.596 2.7 4.9
Jaime Garcia 28 163.3 3.43 5.83 0.623 3.2 4.8
Fausto Carmona 30 193.7 4.03 6.46 0.545 2.7 4.7
Shaun Marcum 28 176 3.79 6.29 0.575 3.1 4.7
Brandon Morrow 26 146.3 3.18 5.63 0.658 3.6 4.6
Gio Gonzalez 30 181.7 3.79 6.06 0.575 3.0 4.6
Doug Fister 25 152.7 3.51 6.11 0.612 3.0 4.6
Dallas Braden 26 166.7 3.81 6.41 0.573 2.7 4.5
Name G IP FIP IP/St Pythag W% WAR adjWAR
Mark Buehrle 30 192.3 4.08 6.41 0.539 3.1 4.5
Ervin Santana 30 201.3 4.34 6.71 0.508 2.2 4.4
Clay Buchholz 26 159.7 3.71 6.14 0.586 3.2 4.3
Mike Pelfrey 31 182.7 3.87 5.89 0.565 2.6 4.2
Jason Vargas 28 176.3 4.02 6.30 0.546 2.4 4.2
Johnny Cueto 28 171.3 3.96 6.12 0.554 2.8 4.0
Randy Wells 30 179.7 4.01 5.99 0.547 2.8 3.9
Trevor Cahill 27 177.7 4.29 6.58 0.514 1.9 3.9
Jeremy Guthrie 29 190 4.39 6.55 0.502 2.1 3.8
Ricky Nolasco 26 157.7 3.87 6.06 0.565 2.4 3.8
Derek Lowe 30 177 4.03 5.90 0.545 2.3 3.7
Justin Masterson 29 173 4.06 5.97 0.541 2.4 3.6
Brett Cecil 25 155 3.99 6.20 0.550 2.3 3.6
Jonathan Sanchez 31 176.7 3.96 5.70 0.554 2.6 3.6
James Shields 31 187 4.22 6.03 0.522 2.2 3.6
Barry Zito 31 186 4.27 6.00 0.516 2.0 3.4
Jake Westbrook 30 185.7 4.36 6.19 0.506 1.8 3.4
Scott Baker 27 160.3 4.02 5.94 0.546 2.3 3.4
Ian Kennedy 29 179 4.34 6.17 0.508 2.3 3.3
Jonathon Niese 27 161.3 4.12 5.98 0.534 1.9 3.3
Bronson Arroyo 30 197.7 4.74 6.59 0.464 1.5 3.2
Ted Lilly 27 171.7 4.49 6.36 0.491 1.6 3.1
Matt Garza 30 185.7 4.55 6.19 0.484 1.5 3.0
Joe Blanton 25 154.7 4.33 6.19 0.509 1.8 2.9
Jon Garland 30 180.7 4.48 6.02 0.492 0.6 2.9
Name G IP FIP IP/St Pythag W% WAR adjWAR
Phil Hughes 28 163 4.27 5.82 0.516 1.9 2.8
Kevin Slowey 27 146.3 3.98 5.42 0.551 2.1 2.7
Paul Maholm 30 171.3 4.4 5.71 0.501 1.5 2.6
Brian Matusz 29 157.7 4.21 5.44 0.523 2.0 2.4
Kyle Davies 28 161.7 4.5 5.77 0.490 1.7 2.3
Joe Saunders 30 183.3 4.83 6.11 0.455 1.2 2.3
A.J. Burnett 29 168.3 4.6 5.80 0.479 1.3 2.2
Jeremy Bonderman 27 157 4.58 5.81 0.481 1.4 2.1
Jeff Niemann 26 156.3 4.73 6.01 0.465 1.0 2.0
Kevin Millwood 28 171.7 4.91 6.13 0.447 0.9 2.0
Chris Volstad 27 153.3 4.57 5.68 0.482 1.1 1.9
Mitch Talbot 26 147.3 4.54 5.67 0.485 1.2 1.9
Randy Wolf 30 186.7 5.11 6.22 0.427 0.2 1.9
Rodrigo Lopez 30 184.3 5.15 6.14 0.423 0.8 1.7
Wade Davis 25 146.3 5.08 5.85 0.430 0.4 1.2
Brad Bergesen 27 152 5.11 5.63 0.427 0.5 0.9
Kyle Kendrick 30 163.3 5.11 5.44 0.427 0.5 0.8
David Bush 30 163 5.15 5.43 0.423 0.1 0.7
Javier Vazquez 28 148.7 5.35 5.31 0.405 -0.1 0.2

My methodology isn't perfect, but I do think it's headed in the right direction.  We already know that a starting pitcher who can pitch enough innings to qualify for the ERA title is worth a lot, because he's got to be very durable and at least half-decent when it comes to run prevention.  There simply are very, very few true "replacements" for somebody like that.   

So I don't know if Roy Halladay is really worth 10.6 more wins than a replacement, or if CC is worth 7.4 more, but I do know that there are only five pitchers who average 7 innings per start this season.  So they're probably worth more actual team wins than Fangraphs shows.