November 05, 2007
Probabilistic Model of Range, Defense Behind Pitchers
One thing PMR can measure is the luck of pitchers by looking at the predicted DER and actual DER behind them. The following table rates pitchers with at least 300 balls in play against them:
Probabilistic Model of Range, Defense Behind Pitchers, 2007. Visit Smoothed Distance Model. 2007 Data Only
Pitcher | Team | In Play | Actual Outs | Predicted Outs | DER | Predicted DER | Ratio |
Chien-Ming Wang | NYY | 643 | 448 | 414.94 | 0.697 | 0.645 | 107.97 |
Jeremy Guthrie | Bal | 527 | 375 | 356.60 | 0.712 | 0.677 | 105.16 |
Dustin McGowan | Tor | 484 | 346 | 330.21 | 0.715 | 0.682 | 104.78 |
Sean Marshall | ChC | 330 | 231 | 221.12 | 0.700 | 0.670 | 104.47 |
Roger Clemens | NYY | 307 | 215 | 205.94 | 0.700 | 0.671 | 104.40 |
Brian Bannister | KC | 540 | 393 | 376.52 | 0.728 | 0.697 | 104.38 |
Jarrod Washburn | Sea | 627 | 440 | 422.32 | 0.702 | 0.674 | 104.19 |
Mike Bacsik | Was | 414 | 291 | 279.42 | 0.703 | 0.675 | 104.14 |
Tom Glavine | NYM | 674 | 474 | 455.80 | 0.703 | 0.676 | 103.99 |
Jason Hirsh | Col | 340 | 252 | 242.53 | 0.741 | 0.713 | 103.91 |
Ted Lilly | ChC | 586 | 427 | 411.59 | 0.729 | 0.702 | 103.74 |
Braden Looper | StL | 581 | 416 | 401.23 | 0.716 | 0.691 | 103.68 |
Chris Sampson | Hou | 414 | 292 | 281.66 | 0.705 | 0.680 | 103.67 |
Cole Hamels | Phi | 495 | 348 | 336.00 | 0.703 | 0.679 | 103.57 |
Brad Penny | LAD | 643 | 450 | 435.62 | 0.700 | 0.677 | 103.30 |
Dontrelle Willis | Fla | 667 | 442 | 428.96 | 0.663 | 0.643 | 103.04 |
Yovani Gallardo | Mil | 318 | 216 | 209.67 | 0.679 | 0.659 | 103.02 |
Jesse Litsch | Tor | 371 | 259 | 251.51 | 0.698 | 0.678 | 102.98 |
Jason Bergmann | Was | 332 | 248 | 241.02 | 0.747 | 0.726 | 102.90 |
Anthony Reyes | StL | 332 | 236 | 229.52 | 0.711 | 0.691 | 102.82 |
Curt Schilling | Bos | 485 | 338 | 328.75 | 0.697 | 0.678 | 102.82 |
Chuck James | Atl | 484 | 352 | 342.43 | 0.727 | 0.707 | 102.80 |
Nate Robertson | Det | 573 | 389 | 378.44 | 0.679 | 0.660 | 102.79 |
Aaron Cook | Col | 572 | 401 | 390.44 | 0.701 | 0.683 | 102.70 |
Tim Lincecum | SF | 389 | 277 | 269.87 | 0.712 | 0.694 | 102.64 |
Jon Garland | CWS | 705 | 493 | 480.70 | 0.699 | 0.682 | 102.56 |
Steve Trachsel | Bal | 491 | 351 | 342.47 | 0.715 | 0.697 | 102.49 |
Daisuke Matsuzaka | Bos | 555 | 384 | 375.16 | 0.692 | 0.676 | 102.36 |
Noah Lowry | SF | 502 | 349 | 340.97 | 0.695 | 0.679 | 102.35 |
Tim Hudson | Atl | 722 | 504 | 492.65 | 0.698 | 0.682 | 102.30 |
C.C. Sabathia | Cle | 701 | 476 | 465.40 | 0.679 | 0.664 | 102.28 |
Chad Durbin | Det | 417 | 304 | 297.37 | 0.729 | 0.713 | 102.23 |
Carlos Zambrano | ChC | 610 | 439 | 429.45 | 0.720 | 0.704 | 102.22 |
Micah Owings | Ari | 461 | 332 | 324.88 | 0.720 | 0.705 | 102.19 |
James Shields | TB | 615 | 435 | 425.93 | 0.707 | 0.693 | 102.13 |
Erik Bedard | Bal | 431 | 306 | 299.70 | 0.710 | 0.695 | 102.10 |
Jake Westbrook | Cle | 481 | 329 | 322.43 | 0.684 | 0.670 | 102.04 |
John Lackey | LAA | 668 | 459 | 450.14 | 0.687 | 0.674 | 101.97 |
Oliver Perez | NYM | 483 | 341 | 334.57 | 0.706 | 0.693 | 101.92 |
Justin Verlander | Det | 577 | 407 | 399.34 | 0.705 | 0.692 | 101.92 |
Barry Zito | SF | 608 | 441 | 432.73 | 0.725 | 0.712 | 101.91 |
Roy Halladay | Tor | 722 | 497 | 488.79 | 0.688 | 0.677 | 101.68 |
Jason Marquis | ChC | 626 | 440 | 432.86 | 0.703 | 0.691 | 101.65 |
Zack Greinke | KC | 350 | 239 | 235.18 | 0.683 | 0.672 | 101.63 |
Buddy Carlyle | Atl | 335 | 229 | 225.46 | 0.684 | 0.673 | 101.57 |
A.J. Burnett | Tor | 414 | 301 | 296.47 | 0.727 | 0.716 | 101.53 |
Johan Santana | Min | 555 | 394 | 388.14 | 0.710 | 0.699 | 101.51 |
Jake Peavy | SD | 571 | 409 | 403.20 | 0.716 | 0.706 | 101.44 |
Kyle Kendrick | Phi | 401 | 284 | 280.03 | 0.708 | 0.698 | 101.42 |
Greg Maddux | SD | 681 | 466 | 459.63 | 0.684 | 0.675 | 101.39 |
Tim Wakefield | Bos | 600 | 425 | 419.24 | 0.708 | 0.699 | 101.37 |
Fausto Carmona | Cle | 654 | 463 | 456.92 | 0.708 | 0.699 | 101.33 |
Kelvim Escobar | LAA | 572 | 387 | 382.00 | 0.677 | 0.668 | 101.31 |
Joe Blanton | Oak | 750 | 520 | 513.28 | 0.693 | 0.684 | 101.31 |
Rich Hill | ChC | 527 | 378 | 373.19 | 0.717 | 0.708 | 101.29 |
Odalis Perez | KC | 494 | 325 | 320.93 | 0.658 | 0.650 | 101.27 |
Matt Morris | SF | 473 | 315 | 311.16 | 0.666 | 0.658 | 101.23 |
Carlos Silva | Min | 699 | 485 | 479.14 | 0.694 | 0.685 | 101.22 |
Adam Eaton | Phi | 525 | 356 | 351.83 | 0.678 | 0.670 | 101.19 |
Felix Hernandez | Sea | 567 | 372 | 367.73 | 0.656 | 0.649 | 101.16 |
Wandy Rodriguez | Hou | 536 | 366 | 361.86 | 0.683 | 0.675 | 101.14 |
Vicente Padilla | Tex | 407 | 270 | 266.96 | 0.663 | 0.656 | 101.14 |
Aaron Harang | Cin | 642 | 451 | 446.11 | 0.702 | 0.695 | 101.10 |
Livan Hernandez | Ari | 704 | 488 | 482.76 | 0.693 | 0.686 | 101.08 |
Orlando Hernandez | NYM | 388 | 299 | 295.82 | 0.771 | 0.762 | 101.08 |
Jamie Moyer | Phi | 633 | 432 | 427.41 | 0.682 | 0.675 | 101.08 |
Ian Snell | Pit | 606 | 413 | 408.93 | 0.682 | 0.675 | 101.00 |
Andy Pettitte | NYY | 690 | 457 | 452.68 | 0.662 | 0.656 | 100.96 |
Tom Gorzelanny | Pit | 642 | 439 | 435.75 | 0.684 | 0.679 | 100.75 |
Matt Albers | Hou | 362 | 247 | 245.52 | 0.682 | 0.678 | 100.60 |
Lenny DiNardo | Oak | 430 | 302 | 300.28 | 0.702 | 0.698 | 100.57 |
John Danks | CWS | 427 | 289 | 287.39 | 0.677 | 0.673 | 100.56 |
Mark Hendrickson | LAD | 395 | 262 | 260.58 | 0.663 | 0.660 | 100.55 |
Jorge Sosa | NYM | 361 | 256 | 254.94 | 0.709 | 0.706 | 100.42 |
Brandon Webb | Ari | 692 | 480 | 478.35 | 0.694 | 0.691 | 100.34 |
Carlos Villanueva | Mil | 318 | 229 | 228.36 | 0.720 | 0.718 | 100.28 |
John Maine | NYM | 527 | 377 | 376.07 | 0.715 | 0.714 | 100.25 |
Justin Germano | SD | 426 | 302 | 301.31 | 0.709 | 0.707 | 100.23 |
Chad Billingsley | LAD | 400 | 279 | 278.70 | 0.697 | 0.697 | 100.11 |
Ben Sheets | Mil | 431 | 307 | 306.74 | 0.712 | 0.712 | 100.09 |
Roy Oswalt | Hou | 675 | 456 | 456.10 | 0.676 | 0.676 | 99.98 |
Jered Weaver | LAA | 514 | 348 | 348.13 | 0.677 | 0.677 | 99.96 |
Mike Mussina | NYY | 512 | 335 | 335.31 | 0.654 | 0.655 | 99.91 |
Josh Beckett | Bos | 566 | 385 | 385.40 | 0.680 | 0.681 | 99.90 |
Matt Chico | Was | 548 | 380 | 380.44 | 0.693 | 0.694 | 99.88 |
Matt Belisle | Cin | 570 | 378 | 378.52 | 0.663 | 0.664 | 99.86 |
Shaun Marcum | Tor | 456 | 329 | 329.69 | 0.721 | 0.723 | 99.79 |
Jeff Weaver | Sea | 511 | 340 | 340.84 | 0.665 | 0.667 | 99.75 |
Derek Lowe | LAD | 604 | 412 | 413.67 | 0.682 | 0.685 | 99.60 |
Kameron Loe | Tex | 464 | 305 | 306.28 | 0.657 | 0.660 | 99.58 |
Joe Saunders | LAA | 358 | 235 | 236.04 | 0.656 | 0.659 | 99.56 |
Brad Thompson | StL | 451 | 307 | 308.45 | 0.681 | 0.684 | 99.53 |
Josh Fogg | Col | 556 | 381 | 383.08 | 0.685 | 0.689 | 99.46 |
Horacio Ramirez | Sea | 361 | 231 | 232.31 | 0.640 | 0.644 | 99.44 |
Jeff Francis | Col | 662 | 447 | 449.57 | 0.675 | 0.679 | 99.43 |
Miguel Batista | Sea | 615 | 415 | 417.51 | 0.675 | 0.679 | 99.40 |
Paul Byrd | Cle | 686 | 465 | 467.91 | 0.678 | 0.682 | 99.38 |
Gil Meche | KC | 663 | 459 | 462.21 | 0.692 | 0.697 | 99.31 |
Claudio Vargas | Mil | 419 | 281 | 283.02 | 0.671 | 0.675 | 99.29 |
Mark Buehrle | CWS | 648 | 455 | 458.82 | 0.702 | 0.708 | 99.17 |
Boof Bonser | Min | 539 | 359 | 362.02 | 0.666 | 0.672 | 99.17 |
Javier Vazquez | CWS | 583 | 409 | 412.68 | 0.702 | 0.708 | 99.11 |
Edwin Jackson | TB | 516 | 333 | 336.02 | 0.645 | 0.651 | 99.10 |
Bartolo Colon | LAA | 328 | 205 | 206.87 | 0.625 | 0.631 | 99.09 |
Tony Armas Jr. | Pit | 305 | 208 | 209.93 | 0.682 | 0.688 | 99.08 |
Jorge de la Rosa | KC | 431 | 285 | 287.91 | 0.661 | 0.668 | 98.99 |
Jason Jennings | Hou | 319 | 214 | 216.25 | 0.671 | 0.678 | 98.96 |
Edgar Gonzalez | Ari | 324 | 228 | 230.41 | 0.704 | 0.711 | 98.96 |
Chris Young | SD | 448 | 336 | 339.55 | 0.750 | 0.758 | 98.96 |
Julian Tavarez | Bos | 455 | 307 | 310.39 | 0.675 | 0.682 | 98.91 |
Woody Williams | Hou | 632 | 443 | 448.01 | 0.701 | 0.709 | 98.88 |
Daniel Cabrera | Bal | 608 | 415 | 419.74 | 0.683 | 0.690 | 98.87 |
Bronson Arroyo | Cin | 661 | 449 | 454.60 | 0.679 | 0.688 | 98.77 |
Kyle Lohse | Cin | 426 | 293 | 296.71 | 0.688 | 0.697 | 98.75 |
Cliff Lee | Cle | 317 | 216 | 218.74 | 0.681 | 0.690 | 98.75 |
Paul Maholm | Pit | 583 | 391 | 396.00 | 0.671 | 0.679 | 98.74 |
Chad Gaudin | Oak | 603 | 413 | 418.34 | 0.685 | 0.694 | 98.72 |
Ervin Santana | LAA | 457 | 302 | 306.05 | 0.661 | 0.670 | 98.68 |
Doug Davis | Ari | 597 | 400 | 405.62 | 0.670 | 0.679 | 98.61 |
Sergio Mitre | Fla | 522 | 343 | 347.92 | 0.657 | 0.667 | 98.59 |
Adam Wainwright | StL | 654 | 441 | 447.57 | 0.674 | 0.684 | 98.53 |
Byung-Hyun Kim | Fla | 316 | 212 | 215.40 | 0.671 | 0.682 | 98.42 |
Ramon Ortiz | Min | 324 | 217 | 220.56 | 0.670 | 0.681 | 98.39 |
Kevin Correia | SF | 306 | 217 | 220.82 | 0.709 | 0.722 | 98.27 |
Kevin Millwood | Tex | 571 | 364 | 370.63 | 0.637 | 0.649 | 98.21 |
Jeremy Bonderman | Det | 533 | 354 | 360.70 | 0.664 | 0.677 | 98.14 |
Scott Baker | Min | 454 | 302 | 308.06 | 0.665 | 0.679 | 98.03 |
Dan Haren | Oak | 661 | 457 | 466.27 | 0.691 | 0.705 | 98.01 |
Randy Wolf | LAD | 309 | 205 | 209.32 | 0.663 | 0.677 | 97.93 |
Jeff Suppan | Mil | 708 | 472 | 482.96 | 0.667 | 0.682 | 97.73 |
Josh Towers | Tor | 347 | 229 | 234.38 | 0.660 | 0.675 | 97.71 |
Matt Cain | SF | 571 | 409 | 419.20 | 0.716 | 0.734 | 97.57 |
John Smoltz | Atl | 586 | 400 | 410.60 | 0.683 | 0.701 | 97.42 |
Brandon McCarthy | Tex | 340 | 232 | 238.54 | 0.682 | 0.702 | 97.26 |
Taylor Buchholz | Col | 305 | 207 | 212.87 | 0.679 | 0.698 | 97.24 |
Andy Sonnanstine | TB | 408 | 272 | 280.02 | 0.667 | 0.686 | 97.13 |
Brian Burres | Bal | 378 | 249 | 256.88 | 0.659 | 0.680 | 96.93 |
Brett Tomko | LAD | 339 | 219 | 226.04 | 0.646 | 0.667 | 96.89 |
Joe Kennedy | Oak | 346 | 242 | 250.10 | 0.699 | 0.723 | 96.76 |
Scott Kazmir | TB | 534 | 346 | 358.19 | 0.648 | 0.671 | 96.60 |
Chris Capuano | Mil | 456 | 297 | 307.78 | 0.651 | 0.675 | 96.50 |
Robinson Tejeda | Tex | 302 | 204 | 212.16 | 0.675 | 0.703 | 96.16 |
David Wells | SD | 416 | 271 | 282.44 | 0.651 | 0.679 | 95.95 |
David Bush | Mil | 594 | 395 | 412.87 | 0.665 | 0.695 | 95.67 |
Zach Duke | Pit | 399 | 246 | 258.54 | 0.617 | 0.648 | 95.15 |
Jose Contreras | CWS | 647 | 420 | 441.74 | 0.649 | 0.683 | 95.08 |
Kip Wells | StL | 522 | 342 | 360.50 | 0.655 | 0.691 | 94.87 |
Scott Olsen | Fla | 578 | 366 | 387.16 | 0.633 | 0.670 | 94.53 |
Chien-Ming Wang comes out on top by far, not surprising given the Yankees overall defensive rating. What bothers me about Wang, however, is the low level of his predicted DER. You would think that someone who gets a lot of ground balls would be somewhat higher. The following chart breaks down Wang by ball in play type:
CM Wang by Batted Ball Type, 2007
Batted Ball Type | In Play | Actual Outs | Predicted Outs | DER | Predicted DER | Ratio |
Fly | 112 | 101 | 98.85 | 0.902 | 0.883 | 102.18 |
Liner | 92 | 29 | 16.14 | 0.315 | 0.175 | 179.66 |
Grounder | 377 | 291 | 269.40 | 0.772 | 0.715 | 108.02 |
Bunt Grounder | 6 | 4 | 4.20 | 0.667 | 0.700 | 95.24 |
Bunt Fly | 1 | 1 | 1.00 | 1.000 | 1.000 | 100.00 |
Fliner (Fly) | 29 | 13 | 14.12 | 0.448 | 0.487 | 92.09 |
Fliner (Liner) | 26 | 9 | 11.23 | 0.346 | 0.432 | 80.12 |
Notice that the defense behind Wang caught a lot more line drives than predicted. Line drives tend to fall for hits, so by adding thirteen extra outs with liners, the Yankees really helped Wang. So Chien-Ming got a bit lucky that way. The grounders, however, is where the defense really shined. They picked up about twenty one more outs than expected on ground balls. How did they do that? The Yankees made a lot of plays on low probability vectors:
Wang Ground Balls by Vector, 2007
Vector | In Play | Actual Outs | Predicted Outs | DER | Predicted DER | Ratio |
28 | 8 | 6 | 7.02 | 0.750 | 0.877 | 85.52 |
29 | 17 | 13 | 12.05 | 0.765 | 0.709 | 107.90 |
30 | 29 | 21 | 17.57 | 0.724 | 0.606 | 119.49 |
31 | 28 | 27 | 24.76 | 0.964 | 0.884 | 109.04 |
32 | 19 | 18 | 18.43 | 0.947 | 0.970 | 97.66 |
33 | 32 | 29 | 26.75 | 0.906 | 0.836 | 108.40 |
34 | 17 | 12 | 9.48 | 0.706 | 0.558 | 126.59 |
35 | 11 | 9 | 7.38 | 0.818 | 0.671 | 121.97 |
36 | 23 | 14 | 13.01 | 0.609 | 0.566 | 107.58 |
37 | 22 | 12 | 13.66 | 0.545 | 0.621 | 87.82 |
38 | 27 | 24 | 23.07 | 0.889 | 0.854 | 104.04 |
39 | 31 | 30 | 25.58 | 0.968 | 0.825 | 117.26 |
40 | 22 | 19 | 17.41 | 0.864 | 0.792 | 109.11 |
41 | 34 | 24 | 17.12 | 0.706 | 0.504 | 140.19 |
42 | 27 | 17 | 19.83 | 0.630 | 0.734 | 85.73 |
43 | 11 | 9 | 9.71 | 0.818 | 0.883 | 92.67 |
44 | 10 | 5 | 4.56 | 0.500 | 0.456 | 109.71 |
The vectors go from a low of 28 at the third base line to a high of 44 at the first base line. By looking at the Predicted DER column, you can see where the holes are in the infield. Vector 30 represents the hole between third and short, vectors 34-37 the area around second base where ground balls go into centerfield, and vector 41, the hole between first and second. Note that Wang does well in the holes, as if the defense were shifted a bit toward first base. Both the line drive and ground ball data make me wonder if someone was doing a very good job of positioning the Yankees fielders. I don't know who was in charge of that, but in the case of Wang, they did a very good job.
That brings up a point I haven't made in a while. Range is probably a poor word for the ability measured here. Range implies that the fielder can move a long way to get a ball. But sometimes anticipating where the ball gets hit is just as important. So the ability to move and the ability to position are two factors in what the model means by range.
On the other end of the spectrum, Matt Cain not only received no run support, he didn't get much defensive support either. And the defense behind Kazmir was just ridiculous. Here's a pitcher who keeps balls in play to a minimum, and his defense can't turn the few hit to them into outs.
I'll start on individual positions tomorrow.
David,
you only show 17 vectors in the ground ball chart for Wang (and 368 balls in play, vs 377 listed in the batted ball type chart). I think you're missing a vector.
Good stuff. I love looking at this stuff in such fine detail.
David-
You often hear baseball commentators, especially former players, talk about how much the defense prefers to play behind a pitcher who works quickly because it keeps them on thier toes, more into the game, etc. I suppose the same could be said for a pitcher who doesn't walk many batters, which implies that there is less time between the batted balls.
Is there anything in this data that would either support or refute that claim?
I note that Justin Verlander ranks much higher than Jeremy Bonderman. Verlander works extremely quickly, Bonderman not so much so, at least by my observation.
(as an aside, we hear so many pronouncements by analysts, many of which sound right, many of which don't. I always enjoy seeing folks like you put those pronouncements to the test.)
It would be cool if "average time between pitches" was available. We could look at walks or strike %, as somebody like Daniel Cabrera is going to keep his fielders waiting regardless of whether he works fast or not, but if fielders look worse behind him it could be just that he's pitching behind and letting the hitters get into good hitting counts.
As a general rule, GB pitchers get more outs on GB than FB pitchers do. This is actually built into MGL's UZR model.
And, it's easy to see why. The extra 30 outs that Wang is getting is not necessarily due to the Yanks fielders, but by Wang himself.
I'm not sure how David is calculating the "predicted DER" here. It sounds like he's using the knowledge of Wang's handedness, but not his GB tendency. It might mean that "predicted DER" is based on both the fielders and Wang himself, so I'm not sure what the data is supposed to tell us.
where do you get these vectors to make these stats? is there any way i can get the vector data?
Contact BIS, and give them a few hundred (thousand?) dollars with a promise that it's for personal-use only.
STATS will want thousands for sure.