2007년 투수 Probabilistic Model of Range 순위

Pitcher	Team	InPlay 횟수	실제 아웃수	예상된 아웃수	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 횟수	실제 아웃수	예상된 아웃수	DER	예상된 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 횟수	실제 아웃수	예상된 아웃수	DER	예상된 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.

☞ 데이빗 핀토의 2007년 투수 PMR 순위입니다. 핀토의 수비스탯은 MGL의 UZR의 아이디어를 보다 구체적으로 실현했으며, 전 타구를 대상으로 측정을 했다는 점에서 더 신뢰도를 높일수 있었습니다.
I was basically repeating work done by Mitchel Lichtman which he named the Ultimate Zone Rating (UZR).

핀토는 다음의 6가지 요소를 바탕으로 수비수의 능력을 측정했습니다.

1. 공이 떨어진 지역
2. 타구의 유형 (플라이볼, 그라운드볼, 라인드라이브, 번트)
3. 타구의 강도 (슬로우, 미듐, 하드)
4. 경기장
5. 투수의 유형 (좌,우투수) 
6. 타자의 유형 (좌,우타자)