Prof Pepper's Assistant

Fastball vs Change-up, featuring Johan Santana

2009-07-04T08:20:00.002-04:00

Here is my latest effort at THT.
Master of Fooling featuring Johan Santana and his feared change-up... and a few nice 3D charts.

Pitching to pitchers

2009-06-19T11:34:00.002-04:00

I had look on how pitchers throw to... pitchers. At THT, as usual.

The best locations for each pitch

2009-06-05T14:22:00.004-04:00

A followup to my first article at The Hardball Times.
This time both horizontal and vertical locations are taken into account (but not together yet).

Meanwhile, in case you missed it, the previous article generated a lot of discussion at The Book Blog.

"Weighted" shift

2009-05-23T05:16:00.002-04:00

My third article at The Hardball Times deals with defensive alignment too.
Some of the issues that arose from my first post here are taken into account.
There is already some discussion going on at The Book's Blog.

On the shift again

2009-05-10T04:35:00.002-04:00

Here's my second article at THT.
I'm looking at defensive alignment one more time. This time I try to see if moving slightly according to the pitch selection may help the fielders.

Painting the corners... at THT!

2009-04-24T16:05:00.000-04:00

My plan was to analyze the table I posted a couple of weeks ago: I still would like to figure who are the pitchers that induce swings on balls way off the zone.

I changed plans because I got the call by The Hardball Times.
Here you can find my first article for them.
I should be writing there every other Thursday.

Please come back here now and then, maybe I will add something here too.

The year of The Bird

2009-04-18T07:36:00.002-04:00

I like doing statistical analysis and producing charts, so this is my tribute to Mark Fidrych.

Click on the chart to have it zoomed.
A red cross (plus day of the week) is placed on games started by The Bird. Information on attendance is not available for a couple of his starts at the end of the season.
Thanks a lot to Retrosheet for providing the data.

Foolers - The other side of the coin

2009-04-13T04:30:00.004-04:00

This will be a post consisting of three tables and very little commentary.

In my next to last post I looked at batters swinging at really bad pitches. Here I will present the numbers for the pitchers.

Here are the ten pitchers with the highest percentage of swings induced on balls way out of the zone (probability of being called strike lower than 10%).

LAST	FIRST	n	swung	pct
Johnson	Josh	309	162	52%
Volstad	Chris	334	160	48%
Hampton	Mike	338	150	44%
Balester	Collin	329	138	42%
Nippert	Dustin	300	124	41%
Liriano	Francisco	314	128	41%
Davies	Kyle	506	197	39%
Lackey	John	556	209	38%
Baker	Scott	575	216	38%
Sabathia	C.C.	880	329	37%

And here are the bottom ten.

LAST	FIRST	n	swung	pct
Gorzelanny	Tom	444	74	17%
McGowan	Dustin	385	60	16%
Penny	Brad	376	57	15%
Miller	Andrew	451	64	14%
Chacon	Shawn	389	53	14%
Eaton	Adam	440	55	12%
Wang	Chien-Ming	343	41	12%
Glavine	Tom	372	44	12%
Bedard	Erik	304	31	10%
Dumatrait	Phil	362	31	9%

I have to look carefully at the tables yet.
At first glance I haven't been able to spot any pattern in the rankings, but here I give you the full table (2008 pitchers with at least 300 bad pitches thrown), in case you can find anything quicker than me.

LAST	FIRST	n	swung	pct
Johnson	Josh	309	162	52%
Volstad	Chris	334	160	48%
Hampton	Mike	338	150	44%
Balester	Collin	329	138	42%
Nippert	Dustin	300	124	41%
Liriano	Francisco	314	128	41%
Davies	Kyle	506	197	39%
Lackey	John	556	209	38%
Baker	Scott	575	216	38%
Sabathia	C.C.	880	329	37%
Street	Huston	363	135	37%
Kazmir	Scott	743	276	37%
Sowers	Jeremy	447	162	36%
Miner	Zach	583	206	35%
Halladay	Roy	798	281	35%
Campillo	Jorge	674	237	35%
Webb	Brandon	815	286	35%
Correia	Kevin	481	168	35%
Martinez	Pedro	502	174	35%
Rusch	Glendon	302	104	34%
Garza	Matt	814	278	34%
Morton	Charlie	329	112	34%
Wellemeyer	Todd	738	251	34%
Shields	James	730	248	34%
Lidge	Brad	393	133	34%
Kuroda	Hiroki	751	254	34%
Harden	Rich	620	209	34%
Liz	Radhames	348	117	34%
Perez	Odalis	692	232	34%
Buehrle	Mark	815	273	33%
Moehler	Brian	463	155	33%
Baek	Cha Seung	506	169	33%
Fogg	Josh	366	122	33%
Hamels	Cole	759	251	33%
Perkins	Glen	403	133	33%
Slowey	Kevin	449	148	33%
Dempster	Ryan	816	267	33%
Sonnanstine	Andy	575	188	33%
Lester	Jon	784	256	33%
Perez	Oliver	810	264	33%
Kershaw	Clayton	415	135	33%
Nolasco	Ricky	637	207	32%
Madson	Ryan	317	103	32%
Young	Chris	406	131	32%
de la Rosa	Jorge	575	184	32%
Lincecum	Tim	791	253	32%
Oswalt	Roy	626	200	32%
Pineiro	Joel	456	145	32%
Broxton	Jonathan	302	96	32%
Haren	Dan	746	237	32%
Hernandez	Felix	656	208	32%
Galarraga	Armando	696	220	32%
Peavy	Jake	792	250	32%
Santana	Johan	720	226	31%
Marcum	Shaun	615	193	31%
McClellan	Kyle	306	96	31%
Blackburn	Nick	552	173	31%
Santana	Ervin	812	254	31%
Greinke	Zack	716	222	31%
Ramirez	Ramon	313	97	31%
Beckett	Josh	619	191	31%
Moyer	Jamie	869	266	31%
Durbin	Chad	407	124	30%
Bergmann	Jason	572	174	30%
Maddux	Greg	503	153	30%
Billingsley	Chad	880	267	30%
Danks	John	612	185	30%
Matsuzaka	Daisuke	748	226	30%
Lowe	Derek	950	287	30%
Johnson	Randy	649	196	30%
Pettitte	Andy	792	239	30%
Wolf	Randy	803	242	30%
Franklin	Ryan	342	103	30%
Sheets	Ben	646	194	30%
Byrd	Paul	483	145	30%
Maholm	Paul	644	193	30%
Olsen	Scott	596	178	30%
Vazquez	Javier	757	226	30%
Garland	Jon	717	213	30%
Carmona	Fausto	465	138	30%
Cain	Matt	738	219	30%
Looper	Braden	803	238	30%
Bonser	Boof	413	122	30%
Masterson	Justin	404	119	29%
Lee	Cliff	520	153	29%
Burnett	A.J.	915	269	29%
Pelfrey	Mike	837	246	29%
Jurrjens	Jair	827	243	29%
Rowland-Smith	Ryan	409	120	29%
Cueto	Johnny	805	236	29%
Jackson	Edwin	739	216	29%
Parra	Manny	625	182	29%
Floyd	Gavin	798	232	29%
Park	Chan Ho	394	114	29%
Lannan	John	730	211	29%
Lilly	Ted	564	163	29%
Robertson	Nate	583	168	29%
Olson	Garrett	552	159	29%
Wainwright	Adam	462	133	29%
Grilli	Jason	351	101	29%
Litsch	Jesse	602	173	29%
Affeldt	Jeremy	348	100	29%
Chamberlain	Joba	470	135	29%
Harang	Aaron	670	192	29%
Cormier	Lance	311	89	29%
Marquis	Jason	664	190	29%
Dickey	R.A.	406	116	29%
Davis	Doug	649	185	29%
Rodriguez	Wandy	509	145	28%
Saunders	Joe	720	205	28%
Gallagher	Sean	528	150	28%
Bush	Dave	695	197	28%
Backe	Brandon	682	193	28%
Weathers	David	364	103	28%
Sampson	Chris	354	100	28%
Jimenez	Ubaldo	812	229	28%
Snell	Ian	649	183	28%
Cordero	Francisco	401	113	28%
Rasner	Darrell	401	113	28%
Howell	J.P.	396	111	28%
Mussina	Mike	655	183	28%
Villanueva	Carlos	445	124	28%
Delcarmen	Manny	316	88	28%
Ponson	Sidney	504	140	28%
Lohse	Kyle	749	208	28%
Zambrano	Carlos	729	202	28%
Green	Sean	307	85	28%
Weaver	Jered	695	192	28%
Heilman	Aaron	375	103	27%
Smith	Greg	883	242	27%
Verlander	Justin	831	227	27%
Bannister	Brian	719	196	27%
Bell	Heath	305	83	27%
Hammel	Jason	324	88	27%
Banks	Josh	321	87	27%
Blanton	Joe	838	226	27%
Myers	Brett	802	216	27%
Volquez	Edinson	844	227	27%
Zito	Barry	819	220	27%
Rogers	Kenny	686	184	27%
Romero	J.C.	358	96	27%
Duke	Zach	567	152	27%
Lincoln	Mike	342	91	27%
Guthrie	Jeremy	654	174	27%
Gaudin	Chad	340	90	26%
Arroyo	Bronson	811	214	26%
Sarfate	Dennis	430	113	26%
Redding	Tim	709	186	26%
Suppan	Jeff	744	193	26%
Millwood	Kevin	541	140	26%
Guerrier	Matt	369	95	26%
Hanrahan	Joel	402	103	26%
Burres	Brian	523	134	26%
Meche	Gil	855	217	25%
Bass	Brian	332	84	25%
Torres	Salomon	329	83	25%
Cook	Aaron	580	146	25%
Wright	Jamey	330	83	25%
Yates	Tyler	327	82	25%
Grabow	John	329	82	25%
Hochevar	Luke	514	128	25%
Cabrera	Daniel	754	186	25%
Feldman	Scott	532	130	24%
Padilla	Vicente	621	150	24%
Sanchez	Jonathan	647	156	24%
Buchholz	Clay	307	74	24%
Silva	Carlos	561	135	24%
Duchscherer	Justin	488	117	24%
Kendrick	Kyle	627	150	24%
Marmol	Carlos	368	88	24%
Reyes	Jo-Jo	470	112	24%
Rupe	Josh	389	92	24%
Hernandez	Livan	747	175	23%
Francis	Jeff	631	147	23%
Rivera	Saul	391	91	23%
Hendrickson	Mark	482	111	23%
Washburn	Jarrod	666	153	23%
Wakefield	Tim	565	129	23%
Maine	John	597	133	22%
Eveland	Dana	686	146	21%
Batista	Miguel	530	111	21%
Ledezma	Wilfredo	309	64	21%
McClung	Seth	433	87	20%
Bennett	Jeff	404	79	20%
Hudson	Tim	569	111	20%
Gregg	Kevin	352	67	19%
Owings	Micah	405	72	18%
Pinto	Renyel	312	55	18%
Laffey	Aaron	358	62	17%
Bonderman	Jeremy	334	57	17%
Contreras	Jose	468	78	17%
Gorzelanny	Tom	444	74	17%
McGowan	Dustin	385	60	16%
Penny	Brad	376	57	15%
Miller	Andrew	451	64	14%
Chacon	Shawn	389	53	14%
Eaton	Adam	440	55	12%
Wang	Chien-Ming	343	41	12%
Glavine	Tom	372	44	12%
Bedard	Erik	304	31	10%
Dumatrait	Phil	362	31	9%

Hitting where the ball is pitched

2009-04-06T15:00:00.000-04:00

I play amateur baseball. I'm a second baseman with no power who makes a lot of contact. Since I rarely hit a ball past the outfielders, I always try to hit 'em where they ain't, to spray the balls to all the field, to hit it where it's pitched... pull the inside pitch, place the outside one in the opposite field.

Big leaguers have power.
Some of them are known to pull every ball, others seem to place the ball according to where it is pitched.
During the next paragraphs we will look at this issue.

I looked for a number to quantify the amount to which a hitter responds to the location of a pitch.

Here's what I've done.

Using gameday hit locations I calculated the trajectory of every batted ball, varying from -45° (down the LF line) to 45° (down the RF line); then I rescaled the trajectory value to have it varying from -1 to 1 (this made life easier for me in the following calculations).

Note: actually the trajectory of some hits, e.g. the groundballs that leave the infield inside the bag then roll in foul territory, exceeds the -45°/+45° boundary, but I coded those hits like having a trajectory of (-)45°.

Then, from PitchF/x, I took the horizontal coordinate of the pitches resulting in balls in play. Again I rescaled the values to have them bounded from -1 (inside for a RHB) to +1.

Note: I did not assign the value 1 to the outermost ball (for a RHB) in my dataset, because I had some severe outliers; I rescaled to one the 95th percentile coordinate. Same thing for -1 and LHBs.

With this couple of values for every ball in play I have all I need to get a value for hitting 'em where they're pitched.
I just need to calculate, for all the hitters, the correlation between the trajectory values and the location values: high correlation (near 1) means the hitter has a tendency to pull inside pitches and hit outside pitches the other way; zero correlation means that where the ball is put into play by the hitter is absolutely unrelated to where the pitch was located; inverse correlation (near -1) would mean the hitter hits... inside-out and outside-in.

Here are the top ten and bottom ten lists. I reported the correlation coefficient (rho) and the 95% confidence interval (lcl = lower confidence limit, hcl = higher confidence limit).
At the end of the post I'll give you a table containing all the players with at least 200 balls in play in 2008.

Top ten

LAST	FIRST	rho	lcl	hcl
Mientkiewicz	Doug	0.42	0.31	0.52
Byrd	Marlon	0.42	0.32	0.50
Morneau	Justin	0.41	0.33	0.48
Dobbs	Greg	0.40	0.27	0.51
Roberts	Brian	0.40	0.32	0.47
Payton	Jay	0.39	0.29	0.49
Fukudome	Kosuke	0.39	0.30	0.47
Johjima	Kenji	0.39	0.30	0.48
DeJesus	David	0.38	0.30	0.46
Lopez	Jose	0.38	0.31	0.45

Bottom ten

LAST	FIRST	rho	lcl	hcl
Willingham	Josh	0.08	-0.04	0.20
Kendrick	Howie	0.08	-0.04	0.19
Martinez	Victor	0.07	-0.07	0.20
Rodriguez	Alex	0.06	-0.04	0.16
Beltran	Carlos	0.05	-0.03	0.14
Hall	Bill	0.05	-0.06	0.17
Aybar	Willy	0.04	-0.07	0.15
Berroa	Angel	0.04	-0.11	0.18
Rollins	Jimmy	0.01	-0.08	0.09
Hawpe	Brad	0.00	-0.10	0.11

OK, nobody hits the "wrong way".

I wondered if hitting the ball the "right way" improves the outcome of the batted ball.
A first (expected) answer is positive, since no player in the Majors hits inside-out and outside-in.
But I wanted some more.

I divided the batted balls in four quadrants, according to the sign of the trajectory and of the location values. Thus a pitch thrown outside to a RHB (location value approaching 1) hit to right field (trajectory value approaching 1) is in the first quadrant; similarly a ball with negative location value and positive trajectory value is in the second quadrant, negative-negative is in the third and positive-negative is the fourth.
Actually I removed a bunch of batted balls and put them in a fifth box; they are the balls with either the location or the trajectory value between -0.2 and 0.2.

Here are the average run values for balls in play by quadrant (quadrant numbers in the corners in roman).

As we would expect in the hypothesis that hitting the ball where it's pitched has a positive effect, we see higher values for the first and third quadrant: those are the boxes representing outside pitches hit the other way and inside pitches pulled by RHBs, respectively (those boxes also contain, respectively, pulled inside pitches and "pushed" outside pitches by LHBs).
Let's split RHBs and LHBs.

RHBs

LHBs

Accordingly to common sense we get higher values in the third quadrant for RHBs and in the first quadrant for LHBs: those are their pull quadrants for inside pitches.
The relative differences among quadrants also make some sense: the inside pitch pulled by the LHB can be snatched by one of the right infielders and converted into an out; for a RHB, the shortstop (or third baseman) making a diving catch on a hard roller still has a lot to do to get the out - opposite reasoning goes for opposite field batted balls on outside pitches (and thus the higher gap between 1st and 3rd quadrant for RHBs).

There's still something that might be polluting my numbers. Maybe in the first and third quadrants there are a lot of balls hit by players who are pull hitters who wait for the inside pitch. So we probably have some bias: in those two quandrants we simply have many balls hit by the best batters.

I redid the calculations.
For every batted ball I subtracted, from the outcome run value, the hitter's (the one who put the ball in play) average run value on batted balls. Now the values in the quadrants should be "cleaner".

RHBs

LHBs

Again we see the effects described before.

I don't think there's anything groundbreaking in this post. I just wanted to quantify a couple of things that are quite known.

Note: I haven't considered the vertical coordinate of the pitch location at all. I acknowledge this can be an issue.

Here is the full table I promised before.

LAST	FIRST	rho	lcl	hcl
Mientkiewicz	Doug	0.42	0.31	0.52
Byrd	Marlon	0.42	0.32	0.50
Morneau	Justin	0.41	0.33	0.48
Dobbs	Greg	0.40	0.27	0.51
Roberts	Brian	0.40	0.32	0.47
Payton	Jay	0.39	0.29	0.49
Fukudome	Kosuke	0.39	0.30	0.47
Johjima	Kenji	0.39	0.30	0.48
DeJesus	David	0.38	0.30	0.46
Lopez	Jose	0.38	0.31	0.45
Polanco	Placido	0.38	0.30	0.45
Blanco	Gregor	0.38	0.28	0.47
Dellucci	David	0.37	0.26	0.48
Matsui	Kazuo	0.37	0.27	0.46
Scutaro	Marco	0.37	0.28	0.45
Gutierrez	Franklin	0.37	0.26	0.46
Torrealba	Yorvit	0.36	0.23	0.48
Cairo	Miguel	0.36	0.23	0.48
Helton	Todd	0.36	0.24	0.47
Jackson	Conor	0.36	0.28	0.44
Ordonez	Magglio	0.36	0.28	0.44
Nady	Xavier	0.36	0.27	0.44
Lee	Carlos	0.36	0.27	0.44
Belliard	Ronnie	0.36	0.24	0.47
Reed	Jeremy	0.36	0.24	0.46
Lowrie	Jed	0.36	0.23	0.47
Infante	Omar	0.36	0.25	0.45
Hairston	Scott	0.36	0.24	0.46
Burriss	Emmanuel	0.35	0.23	0.47
Butler	Billy	0.35	0.26	0.44
Anderson	Garret	0.35	0.27	0.43
Hernandez	Ramon	0.35	0.26	0.43
Miles	Aaron	0.34	0.24	0.43
Gerut	Jody	0.34	0.23	0.44
Pedroia	Dustin	0.34	0.27	0.41
Kinsler	Ian	0.34	0.25	0.42
Catalanotto	Frank	0.34	0.21	0.45
Cabrera	Melky	0.33	0.23	0.42
Pujols	Albert	0.33	0.24	0.41
Bradley	Milton	0.33	0.22	0.43
Braun	Ryan	0.33	0.24	0.40
Barajas	Rod	0.32	0.21	0.42
Grudzielanek	Mark	0.32	0.21	0.42
Castillo	Luis	0.32	0.20	0.43
Eckstein	David	0.32	0.21	0.42
Weeks	Rickie	0.32	0.22	0.41
Lamb	Mike	0.32	0.19	0.44
Cabrera	Orlando	0.32	0.24	0.39
Iwamura	Akinori	0.31	0.23	0.39
Kapler	Gabe	0.31	0.18	0.44
Lopez	Felipe	0.31	0.22	0.40
Inglett	Joe	0.31	0.20	0.41
Youkilis	Kevin	0.31	0.23	0.39
Callaspo	Alberto	0.31	0.18	0.43
Kubel	Jason	0.31	0.21	0.40
Floyd	Cliff	0.31	0.18	0.43
Hill	Aaron	0.31	0.16	0.44
Molina	Yadier	0.31	0.22	0.39
Wilson	Jack	0.31	0.19	0.41
Reyes	Jose	0.31	0.23	0.38
Ortiz	David	0.31	0.21	0.40
Loretta	Mark	0.31	0.18	0.42
German	Esteban	0.30	0.17	0.43
Francoeur	Jeff	0.30	0.22	0.38
Young	Michael	0.30	0.22	0.38
Zimmerman	Ryan	0.30	0.20	0.40
Tejada	Miguel	0.30	0.22	0.38
Crosby	Bobby	0.30	0.21	0.38
Gonzalez	Edgar	0.30	0.18	0.41
Counsell	Craig	0.30	0.17	0.42
Hinske	Eric	0.30	0.18	0.40
Drew	J.D.	0.30	0.19	0.40
Vizquel	Omar	0.30	0.18	0.41
Rivas	Luis	0.30	0.15	0.43
Theriot	Ryan	0.29	0.21	0.37
Furcal	Rafael	0.29	0.14	0.43
Matsui	Hideki	0.29	0.18	0.40
Lind	Adam	0.29	0.18	0.40
Berkman	Lance	0.29	0.20	0.37
Brown	Emil	0.29	0.19	0.39
Navarro	Dioner	0.29	0.20	0.38
Dye	Jermaine	0.29	0.21	0.37
Suzuki	Ichiro	0.29	0.22	0.36
Martin	Russell	0.29	0.20	0.37
Bautista	Jose	0.29	0.18	0.39
Schumaker	Skip	0.29	0.20	0.37
DeWitt	Blake	0.29	0.18	0.39
Dunn	Adam	0.29	0.19	0.38
Byrnes	Eric	0.29	0.14	0.43
Hardy	J.J.	0.29	0.20	0.37
Spilborghs	Ryan	0.29	0.15	0.41
Taveras	Willy	0.29	0.19	0.37
Sheffield	Gary	0.29	0.18	0.38
Buck	John	0.28	0.17	0.39
Izturis	Maicer	0.28	0.17	0.39
Sanchez	Freddy	0.28	0.20	0.36
Izturis	Cesar	0.28	0.19	0.37
Beltre	Adrian	0.28	0.19	0.36
Boone	Aaron	0.28	0.13	0.42
Schneider	Brian	0.28	0.17	0.39
Hairston	Jerry	0.28	0.15	0.40
Wigginton	Ty	0.28	0.17	0.38
Fontenot	Mike	0.28	0.14	0.40
Inge	Brandon	0.28	0.16	0.39
Ibanez	Raul	0.28	0.19	0.36
McLouth	Nate	0.28	0.19	0.36
Glaus	Troy	0.27	0.18	0.36
Ross	Cody	0.27	0.17	0.37
Aurilia	Rich	0.27	0.17	0.37
Coste	Chris	0.27	0.15	0.39
Tulowitzki	Troy	0.27	0.17	0.37
Rios	Alex	0.27	0.19	0.35
Stairs	Matt	0.27	0.14	0.39
Casilla	Alexi	0.27	0.17	0.37
Damon	Johnny	0.27	0.18	0.35
Zaun	Gregg	0.27	0.13	0.40
Michaels	Jason	0.27	0.13	0.39
Ellsbury	Jacoby	0.27	0.18	0.35
Suzuki	Kurt	0.27	0.18	0.35
Sweeney	Ryan	0.27	0.16	0.37
Lewis	Fred	0.27	0.16	0.36
Kotchman	Casey	0.26	0.18	0.35
McCann	Brian	0.26	0.17	0.35
Gross	Gabe	0.26	0.15	0.37
Markakis	Nick	0.26	0.18	0.35
Lee	Derrek	0.26	0.18	0.34
Huff	Aubrey	0.26	0.18	0.34
Bay	Jason	0.26	0.17	0.35
LaRoche	Adam	0.26	0.16	0.36
Ellis	Mark	0.26	0.16	0.36
Blake	Casey	0.26	0.17	0.35
Erstad	Darin	0.26	0.14	0.37
Burrell	Pat	0.26	0.17	0.35
Bartlett	Jason	0.26	0.17	0.35
Ethier	Andre	0.26	0.17	0.34
Hamilton	Josh	0.26	0.17	0.34
Atkins	Garrett	0.26	0.17	0.34
Guillen	Carlos	0.26	0.15	0.35
Murphy	David	0.25	0.15	0.35
Snyder	Chris	0.25	0.12	0.37
Molina	Jose	0.25	0.12	0.37
Loney	James	0.25	0.17	0.33
Bako	Paul	0.25	0.12	0.38
Barton	Daric	0.25	0.15	0.35
Lowell	Mike	0.25	0.15	0.35
Chavez	Endy	0.25	0.13	0.36
Edmonds	Jim	0.25	0.13	0.36
Blalock	Hank	0.25	0.11	0.38
Betancourt	Yuniesky	0.25	0.16	0.33
Longoria	Evan	0.25	0.15	0.34
Cabrera	Miguel	0.25	0.16	0.33
Giambi	Jason	0.25	0.14	0.34
Crawford	Carl	0.25	0.15	0.33
Gload	Ross	0.24	0.14	0.34
Shoppach	Kelly	0.24	0.11	0.37
Fielder	Prince	0.24	0.15	0.33
Carroll	Jamey	0.24	0.13	0.35
Barmes	Clint	0.24	0.14	0.35
Phillips	Brandon	0.24	0.15	0.33
Sizemore	Grady	0.24	0.16	0.32
Amezaga	Alfredo	0.24	0.12	0.35
Pierre	Juan	0.24	0.14	0.33
Keppinger	Jeff	0.24	0.14	0.32
Konerko	Paul	0.24	0.13	0.33
Abreu	Bobby	0.24	0.15	0.32
Guerrero	Vladimir	0.24	0.15	0.32
Escobar	Yunel	0.23	0.14	0.32
Kent	Jeff	0.23	0.14	0.33
Hunter	Torii	0.23	0.14	0.32
Thomas	Frank	0.23	0.09	0.37
Young	Delmon	0.23	0.14	0.32
Bourn	Michael	0.23	0.13	0.33
Cust	Jack	0.23	0.12	0.34
Kennedy	Adam	0.23	0.12	0.34
DeRosa	Mark	0.23	0.13	0.32
Jones	Chipper	0.23	0.13	0.32
Ramirez	Manny	0.23	0.14	0.31
Iannetta	Chris	0.23	0.10	0.35
Matthews	Gary	0.23	0.12	0.33
Soto	Geovany	0.22	0.12	0.32
Kouzmanoff	Kevin	0.22	0.13	0.31
Pena	Tony	0.22	0.08	0.36
Bowker	John	0.22	0.10	0.34
Mathis	Jeff	0.22	0.08	0.35
Renteria	Edgar	0.22	0.12	0.31
Punto	Nick	0.22	0.10	0.33
Garko	Ryan	0.22	0.12	0.31
Moss	Brandon	0.22	0.06	0.36
Rivera	Juan	0.22	0.09	0.34
Hudson	Orlando	0.22	0.11	0.32
Aviles	Mike	0.22	0.11	0.31
Patterson	Corey	0.22	0.10	0.32
Utley	Chase	0.21	0.13	0.29
Rodriguez	Luis O.	0.21	0.07	0.35
Pierzynski	A.J.	0.21	0.12	0.30
Gathright	Joey	0.21	0.09	0.33
Giles	Brian	0.21	0.12	0.30
Granderson	Curtis	0.21	0.12	0.30
Molina	Bengie	0.21	0.12	0.29
Buscher	Brian	0.21	0.06	0.35
Werth	Jayson	0.21	0.10	0.31
Milledge	Lastings	0.21	0.11	0.30
Jenkins	Geoff	0.21	0.08	0.33
Easley	Damion	0.21	0.09	0.32
Lugo	Julio	0.20	0.07	0.34
Cano	Robinson	0.20	0.12	0.29
Sexson	Richie	0.20	0.06	0.34
Rolen	Scott	0.20	0.10	0.31
Holliday	Matt	0.20	0.11	0.29
Wells	Vernon	0.20	0.10	0.30
Iguchi	Tadahito	0.20	0.07	0.32
Kearns	Austin	0.20	0.08	0.32
Guillen	Jose	0.20	0.11	0.29
Wright	David	0.20	0.11	0.28
Cantu	Jorge	0.20	0.12	0.28
Harris	Brendan	0.20	0.09	0.30
Gomez	Carlos	0.20	0.11	0.29
Prado	Martin	0.20	0.06	0.33
Howard	Ryan	0.20	0.10	0.29
Figgins	Chone	0.20	0.10	0.29
Feliz	Pedro	0.20	0.10	0.29
Tracy	Chad	0.20	0.06	0.32
Baker	Jeff	0.19	0.06	0.32
Ruiz	Carlos	0.19	0.09	0.30
Gonzalez	Luis	0.19	0.08	0.30
Hermida	Jeremy	0.19	0.09	0.29
Guzman	Cristian	0.19	0.11	0.28
Ramirez	Aramis	0.19	0.10	0.28
Reynolds	Mark	0.19	0.09	0.30
Olivo	Miguel	0.19	0.06	0.32
Young	Chris	0.19	0.10	0.28
Crede	Joe	0.19	0.07	0.30
Drew	Stephen	0.19	0.10	0.27
Cuddyer	Michael	0.19	0.05	0.32
Delgado	Carlos	0.19	0.10	0.28
Johnson	Kelly	0.19	0.10	0.28
Rodriguez	Ivan	0.19	0.08	0.29
Laird	Gerald	0.19	0.07	0.30
Francisco	Ben	0.19	0.08	0.29
Vazquez	Ramon	0.19	0.06	0.31
Gonzalez	Carlos	0.18	0.05	0.31
Overbay	Lyle	0.18	0.09	0.28
Winn	Randy	0.18	0.10	0.27
Johnson	Reed	0.18	0.06	0.30
Davis	Rajai	0.18	0.03	0.32
Gordon	Alex	0.18	0.08	0.28
Velez	Eugenio	0.18	0.05	0.30
Millar	Kevin	0.18	0.08	0.27
Hart	Corey	0.18	0.09	0.26
Cabrera	Asdrubal	0.17	0.06	0.29
Duncan	Chris	0.17	0.02	0.32
Greene	Khalil	0.17	0.06	0.29
Jacobs	Mike	0.17	0.07	0.27
Swisher	Nick	0.17	0.07	0.27
Jeter	Derek	0.17	0.09	0.26
Kendall	Jason	0.17	0.08	0.26
Scott	Luke	0.17	0.07	0.27
Span	Denard	0.17	0.05	0.28
Vidro	Jose	0.17	0.05	0.28
Castillo	Jose	0.17	0.06	0.27
Mauer	Joe	0.17	0.08	0.25
Crisp	Coco	0.16	0.05	0.27
Teahen	Mark	0.16	0.07	0.25
Cedeno	Ronny	0.16	0.01	0.31
Gonzalez	Adrian	0.16	0.07	0.25
Encarnacion	Edwin	0.16	0.06	0.26
Stewart	Shannon	0.16	-0.01	0.32
Rowand	Aaron	0.16	0.06	0.25
Upton	B.J.	0.16	0.06	0.25
Thames	Marcus	0.16	0.02	0.28
Flores	Jesus	0.16	0.02	0.28
Thome	Jim	0.16	0.05	0.26
Victorino	Shane	0.16	0.07	0.24
Varitek	Jason	0.15	0.05	0.26
Jones	Adam	0.15	0.05	0.25
Kemp	Matt	0.15	0.06	0.24
Griffey Jr.	Ken	0.15	0.05	0.25
Durham	Ray	0.15	0.04	0.26
Helms	Wes	0.15	0.00	0.29
Doumit	Ryan	0.15	0.04	0.25
Cameron	Mike	0.15	0.03	0.26
Peralta	Jhonny	0.15	0.06	0.23
Tatis	Fernando	0.15	0.01	0.28
Bruntlett	Eric	0.14	-0.00	0.29
Soriano	Alfonso	0.14	0.04	0.25
Hannahan	Jack	0.14	0.03	0.25
Kotsay	Mark	0.14	0.04	0.24
Ramirez	Alexei	0.14	0.04	0.23
Aybar	Erick	0.13	0.02	0.24
Headley	Chase	0.13	-0.00	0.26
Ramirez	Hanley	0.13	0.04	0.22
Harris	Willie	0.13	0.01	0.24
Ludwick	Ryan	0.13	0.03	0.23
Dukes	Elijah	0.13	-0.01	0.26
Blum	Geoff	0.13	0.00	0.24
Quentin	Carlos	0.12	0.02	0.22
Wilkerson	Brad	0.12	-0.02	0.26
Pence	Hunter	0.12	0.03	0.21
Ankiel	Rick	0.12	0.01	0.23
Church	Ryan	0.12	-0.01	0.25
Davis	Chris	0.12	-0.03	0.26
Choo	Shin-Soo	0.11	-0.02	0.24
Bruce	Jay	0.11	-0.00	0.22
Pena	Carlos	0.11	0.00	0.21
Ausmus	Brad	0.11	-0.05	0.26
Teixeira	Mark	0.10	0.01	0.19
Uggla	Dan	0.10	-0.00	0.21
Mora	Melvin	0.10	0.01	0.20
Uribe	Juan	0.10	-0.02	0.22
Ojeda	Augie	0.10	-0.04	0.24
Votto	Joey	0.10	0.00	0.19
Upton	Justin	0.10	-0.04	0.23
Balentien	Wladimir	0.09	-0.07	0.24
Marte	Andy	0.09	-0.06	0.23
Willingham	Josh	0.08	-0.04	0.20
Kendrick	Howie	0.08	-0.04	0.19
Martinez	Victor	0.07	-0.07	0.20
Rodriguez	Alex	0.06	-0.04	0.16
Beltran	Carlos	0.05	-0.03	0.14
Hall	Bill	0.05	-0.06	0.17
Aybar	Willy	0.04	-0.07	0.15
Berroa	Angel	0.04	-0.11	0.18
Rollins	Jimmy	0.01	-0.08	0.09
Hawpe	Brad	0.00	-0.10	0.11

Bad ball swingers

2009-04-01T07:57:00.005-04:00

As the new season is ready to roll, I take some time to give away the 2008 Vladimir Guerrero Award.
Using Pitchf/x data I looked at the players who swing frequently at bad pitches, and I tried to figure if they hurt themselves by trying to hit everything.

Initially I planned to look at all swings occurred on a pitch that was a ball according to the rulebook strike zone; then I decided to do things differently.
Using spatial smoothing I calculated the probability of a pitch to be called strike, given it's location. A previous study I run on my Italian website, and other researches by other authors at THT and elsewhere, had showed that batter handedness influences umpire decisions more than pitcher handedness, so I calculated different probabilities for RHB and LHB.

A couple of charts will summarize this part.

I decided to classify a pitch as a "bad ball" when its probability to be called strike is lower than 10% (the cutoff value is purely subjective, and I'd welcome suggestions for a different choice).

Here are the top ten bad ball swingers:

LAST	FIRST	swing_pct
Soriano	Alfonso	43%
Barmes	Clint	42%
Headley	Chase	41%
Span	Denard	41%
Ramirez	Alexei	41%
Aviles	Mike	40%
Stewart	Ian	40%
Gomez	Carlos	39%
Uribe	Juan	38%
Lowrie	Jed	38%

No Vlad on the list? I must have done something wrong!... No, he's the eleventh, just out of the table, at 37%.
I compared my full list with the one at FanGraphs and while they don't coincide, they are quite similar. Anyway they don't have to coincide, since FG charts outside zone swing %, while I'm charting "really outside zone swing %".

Here's the bottom of the list.

LAST	FIRST	swing_pct
Matthews	Gary	19%
Dellucci	David	19%
Lewis	Fred	19%
Murphy	David	18%
Crede	Joe	18%
Matsui	Hideki	16%
Sexson	Richie	16%
Upton	Justin	16%
Castillo	Luis	10%
Helton	Todd	5%

For this work I selected players who have seen at least 300 bad pitches. I don't know if this choice caused some players who don't swing at bad pitches to be left out.

Next thing I investigated is run value for swings on bad balls.
Many players are notorious bad ball swingers, but they are also feared because they can do a lot of damage even when they chase pitches in the dirt.
In the following table I summed up the run values obtained by hitters when they swung at a bad pitch.

LAST	FIRST	swing_run_value
Sheffield	Gary	9.37
Garko	Ryan	7.28
Stewart	Ian	5.86
Mauer	Joe	4.99
Glaus	Troy	4.87
Ortiz	David	4.24
Cust	Jack	4.02
Kubel	Jason	3.95
Huff	Aubrey	3.74
Hinske	Eric	2.55

But what if all those pitches were let go by?
I calculated the net run value for bad pitches, which you will find in the next table, as following:
- if the batter didn't swing, assign the run value of the pitch (likely the run value of a ball; but if the ump called it a strike, then the run value of a strike);
- if the batter swung, assign the run value of the event minus the expected run value of the pitch had the batter not swung (that is something like 90+% * run value of a ball + 10-% * run value of a strike).

LAST	FIRST	net_run_value
Sheffield	Gary	1.85
Stewart	Ian	-1.77
Glaus	Troy	-2.34
Hinske	Eric	-2.76
Cust	Jack	-3.08
Murphy	David	-3.39
Mauer	Joe	-3.84
Kubel	Jason	-3.85
Helton	Todd	-3.97
Bourn	Michael	-4.31

As we see from the table, Gary Sheffield is the only player in MLB to have a positive value for his bad pitch swinging (at 29% his swinging percentage on bad pitches is middle-of-the-pack). Jose Reyes, the worst in this ranking, has lost 32 runs by swinging at balls way out of the zone.
Players like Ryan Howard and Vladimir Guerrero can have a gross production of more than 11 runs when swinging at bad balls, but when you look at what they would have produced had they let those pitches go by you get a net loss of nearly 30 runs.

I think I made you wander too long in the dark by giving just a few top-ten tables. Here's a spreadsheet with all the players that made my cut of 300 bad pitches seen.

Another one bites the clutch

2009-03-26T15:49:00.005-04:00

A lot of words have been spent on clutch hitting and by many people smarter than me.
Anyway I would like to share some work I did a few years ago on my Italian website. That work has gone through some imporant refinement before giving birth to this post.

At the time I wrote the Italian article, the wonderful FanGraphs didn't have the Clutch stat yet, thus I was looking for some way to measure if (and possibly how much) a particular season by a particular player was clutch.
(Those were the times when A-Rod won the MVP award and many Sox fans - and Yankee haters - cried that Big Papi was more deserving due to his clutch performance).

The following was my line of thinking.

1. Using average Run Values for batting events, I can assign a value to each plate appearence of a particular player. This value measures the outcome of the at bat without taking into account the importance (leverage... more on that in few moments) of the situation.

2. And I have Leverage, that is a number that measures the importance of the moment without looking at the outcome of the AB.

Suppose there's a player who is the clutchiest guy on the face of earth. He may have whatever batting line, but he will get the greatest production (HRs) in the highest leverage situations and the least production (Ks) in the lowest leverage situations.
Take all the at bats of this player, put the run values in a spreadsheet column, then put the corresponding leverage index in the next column.
Sort your spreadsheet for the run value column; now sort for the leverage column. Nothing changes for this particular guy.

Obviously such a player doesn't exsist, but I can use correlation between run values and leverage index to look at a player clutchiness.
If a player has a correlation of zero, then he achieved his best and worst results randomly across the leverage spectrum; the closer to one the more he has been clutch, the closer to minus one the more he has been a choker.
But how closer to 1 (or -1) can a player go in a season (or a career)?

This leads to the first enhancement I have made over my original article. Since at bat run values can only assume a limited set of values, correlation between RV and LI can not be exactly one even for the hypothetical super clutch player. Thus, when I show confidence intervals for the correlation, they have been calculated using bootstraping techniques.

The other improvement has to do with the way Leverage is calculated. At that time I used something like Keith Woolner's formula (Baseball Prospectus 2005), now it's something more like Tango's and Elan Fuld's (he uses the acronym PIOGO for his index, and his work can be found here).

Note: I realize that Tango's numbers for LI are now widely used and I would like to perform my analyses using his values, but I had a table with my own values that was already formatted as I needed. I checked some of my values with the corresponding ones on Tango's website and I didn't find big discrepancies (save for the fact that he chooses to put LI = 1 at the average leveraged situation, while I put LI = 1 at the beginning of the game).

There's a third refinement, that occurred when I was ready to post (thus forcing me to redo all you read from now on).

Run Values are centered at 0 and are additive: a natural scale is the right thing to use.

Leverage Index is a ratio, centered at one; a LI of 0.5 and a LI of 2 are conceptually equidistant from a LI of 1: we need a logarithmic transformation to get the right behaviour from the numbers (e.g. log(1)=0; log(0.5)=-0.69; log(2)=0.69).

Well, let's look at some players.

Fangraphs has Pujols in 2006 as one of the best recent seasons for clutch hitting performance (Clutch = 3.25). Correlation between his RVs and the LI at which he compiled them is 0.05, with a 95% confidence interval of -0.02 - 0.13.

Such a "clutch" season might have been occurred by chance, since the confidence interval contains zero.

Here's Big Papi in 2005, the clutch season par antonomasia (FanGraphs has it at a 3.31 Clutch score).

Correlation: 0.02 (95% confidence interval: -0.06 - 0.09).
We can make a couple of observations on these numbers. Even a very clutch season likely won't result in a correlation significantly different from zero (i.e. the 95% confidence interval doesn't have the value zero in between), and should we find one we'd have to look at - at least - the 2nd decimal value.

And now, A-Rod (A-Choke?) 2008 (-3.16 by FanGraphs metric).

Correlation: -0.09 (95% confidence interval: -0.18 - 0.004).

It seems that it's really difficult to get a value significantly different from zero. Here we must note one important thing: to get a high value of correlation, a player should overperform in high leverage situations AND underperform in low leverage situations. Thus players like Pujols or Ortiz who always perform near the excellence level can't possibly overachieve in high leverage situations - I believe that a correlation significantly different from zero (albeit we have to look at the second or third decimal point) on the positive side is noteworthy nonetheless; it's no surprise that we have found a significant (though minuscule) effect on the negative side for a very good hitter like Rodriguez.

In Weaver on Strategy, the Earl of Baltimore talked about Eddie Murray as a guy who always produced when the game was on the line, but tanked a bit in lopsided games. Let's have a look at his run value / leverage index correlation values.

Year - Correlation (95% Confidence Interval)
1977 - 0.004 (-0.09 - 0.07)
1978 - 0.06 (-0.003 - 0.12)
1979 - 0.02 (-0.06 - 0.08)
1980 - 0.04 (-0.03 - 0.11)
1981 - -0.07 (-0.19 - 0.01)
1982 - 0.01 (-0.09 - 0.09)
1983 - -0.05 (-0.14 - 0.02)
1984 - 0.07 (0.01 - 0.14)
1985 - 0.10 (0.03 - 0.16)
1986 - 0.01 (-0.08 - 0.09)
1987 - 0 (-0.08 - 0.06)
1988 - 0 (-0.08 - 0.07)
1989 - 0.01 (-0.07 - 0.08)
1990 - 0.08 (0.01 - 0.14)
1991 - 0.06 (-0.01 - 0.13)
1992 - 0.01 (-0.08 - 0.10)
1993 - -0.02 (-0.10 - 0.04)
1994 - 0.04 (-0.06 - 0.12)
1995 - -0.03 (-0.13 - 0.05)
1996 - -0.003 (-0.08 - 0.06)
1997 - 0.05 (-0.07 - 0.16)

There are a few seasons in which Eddie beat the zero, only one of them under Weaver (1985 - and the book came out one year earlier).
I reapeat. When we find an effect, it is very small (so small we can doubt it really is an effect). Anyway, this player that was perceived to be clutch by one of his managers never had a choke season (defined as one for which the entire 95% CI is under zero).

The next natural step is to look at correlation values for a career.

Since I reported every season for Eddie Murray, here's his career clutch line:

Correlation: 0.02 (95% confidence interval: 0 - 0.03).

Here are the other players I mentioned so far.

Albert Pujols: Correlation: 0.02 (95% confidence interval: -0.01 - 0.04).

David Ortiz: Correlation: 0.03 (95% confidence interval: 0.004 - 0.05).

Alex Rodriguez: Correlation: -0.002 (95% confidence interval: -0.02 - 0.02).

Since we are looking at a very small effect, it's easier to find something statistically significant (if there is any effect) when looking at a career - i.e. at more observations.

I'm tempted to write a few more lines of code in order to calculate correlation values with confidence intervals for every player in the Retrosheet era (for every single season, and for entire careers). Maybe I will do that. Would it be useful, and for what purpose? Sure you can't say that Ortiz's career values are better than Murray's: the respective confidence intervals overlap a lot; thus it won't be helpful to single out the clutchiest player ever.

I'm curious to see if there are any players that beat the zero correlation year in and year out (I doubt) or players that both shows clutch and choke seasons.

Toward valuing a hit kept in the infield

2009-03-19T13:00:00.000-04:00

Sunday night I was playing with my newly populated Retrosheet Database (thanks a lot Colin Wyers!) and watching Japan vs Cuba.

As I finished calculating run values for various events, Johjima was on second with one out; Iwamura hit a groundball that looked headed to centerfield. Instead second baseman Yulieski Gourriel made a diving grab, turned his body and tried to get the runner at first. Akinori was safe, but the play by Gourriel prevented Johjima from scoring (he would undoubtely have, had the ball gone through).

Fielding metrics that compare outs made vs expected outs treat such a play as a failure for the infielder; maybe Gourriel wouldn't be charged with a great negative contribution, since the ball was in a zone where not many outs are expected to be made. Anyway I believe the Cuban second baseman might deserve more than a mild negative score on that play.

Using data from the last five years, I calculated that a single that goes to the outfield has a run value of 0.477, while a single that stays in the infield is worth 0.409 runs.

Those are values averaged across all the possible base/outs situation. In the specific enviroment in which the play occurred the difference would be between 0.681 and 0.482.

Let's stick with the average values for singles. This implies that infielders tries with same effort to keep the ball in the infield when the bases are empty (can we consider this to be true?).

Let's assume that the ball hit by Iwamura, on average, goes to the outfield 80% of the times, ends as an infield hit 15% of the times and is converted in an out the remainig 5% of the times (numbers entirely made up on the spot). The expected run value is 0.8 x 0.477 + 0.15 x 0.409 + 0.05 x (-0.288) = 0.429 (-0.288 is the value for the out I got from the 2004-08 data).

Gourriel kept the ball in the infield, for a run value of 0.409, thus we should credit him for preventing 0.02 runs.

I haven't read the second edition of the Fielding Bible, but I suspect that the plus/minus system doesn't properly value a play like this.

I'm pretty sure that David Pinto's PMR (that I prefer to +/-) doesn't deal with this either (PMR is outs made vs expected outs).

It's been a long time since I've read MGL's work on UZR at Baseball Primer, so I don't remember if UZR addresses similar events.

I don't know if factoring this kind of play into a fielder's evaluation has a significant impact on his contribution, but I believe it's worth to investigate into the matter.

Note: the percentages I made up have been chosen by design to give a positive value for Gourriel's play. If we delve into real data and find real probabilities, infield singles will give the fielder negative contribution most of the time (less negative than outfield singles, anyway).

Arm 2.0

2009-03-11T18:30:00.000-04:00

A few years ago I did some work on right fielders arm on my Italian website. I won't go into details of that work because it was very similar to what John Walsh did at THT. Actually my first article and his first article saw the light on the very same day.
Conceptually our works were very similar: they used the run expectancy matrix and compared the run prevented (allowed) by an outfielder with his arm compared to league average.
The main difference between our analyses was that I focused my research on a very limited subset of actions. I just considered singles fielded by right fielders with a man on first and second base empty. This choice, while leaving out a lot of opportunities in which an outfielder arm is tested, was intended to compare the RFs on equal opportunities - I supposed that singles to right are very similar one another (i.e. they are all fielded in a small area of the field), while that's not true of doubles (that may go into the gap or down the line) or fly outs (that can be made close to the infield or against the wall).
All the work was done using Retrosheet data.

Enter Gameday data.
In the following lines I'll try to see if my assumption - that singles to right are created (nearly) equal (relative to "arm testing") - is true, and if outfielders' arm evaluation need to (and can) be corrected using batted ball location data.

Again, I take every base/out situation (in my restricted example it's just 0-1-2 outs and man on 1st / men on 1st and 3rd), and calculate the runs prevented (allowed) by an average arm right fielder on a single.
This time I add the location information. Ideally I want to have the average run value at every possible location where a right fielder can collect a single.
Obviously there can't be enough observations to have every single point on the field covered, thus I used loess smoothing.
Very quickly on loess smoothing: you estimate the (run-)value of every point on the field using the run values of points in the neighborhood which have observations - nearer points have more weight on the estimation.

The chart above shows how much the expected run value of a single with a man on first is increased (lighter blue) or decreased (darker blue) due to where the ball is collected by the right fielder.
It makes quite sense. Maybe I was expecting something like the following (the more the distance from home plate - and from third - the more likely the runners will advance extra bases):

But looking back at the previous chart, I think I can give a reasonable explanation to the increasing run value of the areas close to the infield: while the throwing distance is short when you field a ball in those zones, it's likely that you had to run many more yards to get there - and the runners were circling the bases in the meantime.

OK, so for every outfielder I adjust his expected run value according to where he fielded the singles batted at him.
Here's a table containing both unadjusted and adjusted arm run values for the right fielders with at least 30 chances (singles fielded with man on first and second base open) in 2008.

	N	arm	adj_arm	adjustment
Abreu Bobby	64	0.52	0.70	0.18
Church Ryan	40	0.10	0.39	0.29
Drew J.D.	46	1.12	0.47	-0.65
Dye Jermaine	51	-0.05	-0.22	-0.17
Ethier Andre	42	-0.42	-0.43	-0.02
Francoeur Jeff	43	-0.51	-0.56	-0.05
Fukudome Kosuke	45	-0.87	-0.90	-0.03
Giles Brian	53	1.23	1.24	0.00
Griffey Jr. Ken	31	0.29	0.25	-0.05
Gross Gabe	35	-1.01	-1.00	0.01
Guerrero Vladimir	32	0.85	0.79	-0.06
Guillen Jose	31	-0.68	-0.53	0.15
Gutierrez Franklin	50	-1.28	-1.59	-0.31
Hart Corey	53	0.66	-0.40	-1.06
Hawpe Brad	62	-0.02	-0.31	-0.29
Hermida Jeremy	60	-0.76	-0.74	0.02
Kearns Austin	34	-0.39	-0.52	-0.14
Ludwick Ryan	48	-0.52	-0.59	-0.06
Markakis Nick	60	0.53	0.35	-0.18
Nady Xavier	38	-0.06	-0.32	-0.26
Ordonez Magglio	63	0.95	0.88	-0.07
Pence Hunter	52	-2.30	-2.35	-0.05
Span Denard	32	-0.14	-0.01	0.12
Suzuki Ichiro	32	-1.67	-1.68	-0.00
Teahen Mark	33	1.81	1.68	-0.13
Upton Justin	43	1.59	1.59	-0.01
Winn Randy	43	1.40	0.99	-0.42

In many cases the adjustment is quite small, but there are some exceptions.
J.D. Drew, for example, sees a significant improvement when taking into account the batted ball locations: as we see in the following graph he fielded a couple of singles very far away from home.

Corey Hart has even more balls collected in unusual (for a single) places.

Maybe the adjustment I applied using loess smoothing is way to big, since a couple of outlying observations can change a lot in the valuing of a fielder. Anyway, I think the work I've done outlines that some correction is due when evaluating outfielders' arms. It's possible that the couple of "long singles" against Drew are the product of some unusual event (the batter slipping while rounding first, or not running because of an injury, or whatever else); without looking at batted ball location data, we assume that those hits are just like any other single and that JD has an average chance of holding the runner at second or gunning him at third. Obviously, that's not the case and, if we don't trust in the adjustments I proposed, we should at least consider dropping the two outliers.

As I did three years ago using Retrosheet data, I considered a limited subset of plays that test an outfielder's arm. The subset was intended to consist of very similar batted balls, but we ended seeing at least some unusual observations. If we want to have a complete evaluation of the arms, I'm sure the locations will have a higher impact: as I said at the beginning of this post, doubles go in the gap or down the line, flies are caught calling off an infielder or against the wall, and this makes a huge difference in the chances an outfielder has on holding/killing the runner(s).

PS: as I was writing this, Pete Jensen published his normalization of Gameday coordinates at THT. While applying his correction would certainly affect the values of RF arms, I believe that what I wrote in the final paragraphs holds.

MoneyBasketBall

2009-03-07T05:31:00.005-05:00

I believe I'm in good company, among stats oriented baseball fans, having read Michael Lewis' article on Shane Battier on February 13th.

Michael tells a fascinating story, but numbers don't appear in his writing (and I think they shouldn't). So I was curios and I did some checking, thanks to data provided at basketballvalue.com.

It's a quick and dirty work, but I think it's worth a look.

The following table shows how the Lakers perform with Kobe on the court, with Kobe off the court and with Kobe on the court against Battier and the Rockets (data from the full 2007/08 season).

Lakers production

	pts/min	off reb / min	def reb / min	poss/min	pts/poss
with Bryant	2.29	0.27	0.74	2.01	1.14
w/o Bryant	2.08	0.29	0.70	1.94	1.07
with Briant vs. Battier	1.79	0.32	0.70	1.90	0.94

Lakers scoring drops by 0.2 points per minnute when Kobe is sitting on the bench. Their possessions per minute drop to some extent too: this can be something done intentionally by the team (their best player is off the court, so they slow down the game pace to minimize the effect of the absence).
Something else may be going on, too: difficult shots that a superstar player can take (and make) are not taken by other players, thus needing a longer time for the team to find a shoting opportunity.

The slower pace when Bryant is off the court is not enterily responsible of the drop in points, as the points per possessions also go down a bit; the fact that LA grabs more rebounds under the opponents board when their star is out is likely due to worse shoting percentage.

When Battier is playing against the Lakers, and Bryant is on the court, LA sees a substantial drop, performing even worse than in other games with Bryant sitting on the bench (LA offensive rebounds rise, perhaps due to lower shoting percentages).

I add another comparison table.

Here is Lakers with Bryant vs Rockets with Battier compared to Lakers with Bryant vs Rockets without Battier.

Lakers (with Bryant) production VS Rockets

	pts/min	off reb / min	def reb / min	poss/min	pts/poss
w/o Battier	2.02	0.26	0.74	1.97	1.03
with Battier	1.79	0.32	0.70	1.90	0.94

We see that LA (with Kobe playing) scores less against Houston (compared to what they do against the league), but Battier's presence on the court is what seems to bring Lakers offense down most.

Since basketball has a lot more interaction between players than baseball, we can't conclude that Lakers scoring less when Shane is playing is entirely Shane's responsibility. Maybe Battier is always playing together with a very good defenseman and they get benched together.

I only looked at scoring (with a quick glance at rebounding) because those were the data readily available at basketballvalue.com; there's another wonderful source of basketball play-by-play data (basketballgeek.com), where one can look deeper at the issues I presented.

Predictability - A baseline for future analyses

2009-03-06T12:24:00.002-05:00

Here are the most and least predictable pitchers... in theory.
What do I mean?
I set the conditions in my previous posts (I - II).
Every MLB pitchers I considered has his repertoire and his mix combination.

The Minimum Level of Predictability of a pitcher is the percentage of correct guesses that can be made on his selection... if he chooses his pitches without being at all influenced by the situation (opponent, score, outs, inning, men on, etc.)

High Theoretical Predictability

pitcher	MLP	repertoire
Tim Wakefield	99.7%	KN-FB-CB
Grant Balfour	86.2%	FB-SL-CH-CB
Jonathan Papelbon	78.7%	FB-SL-CH-SF
Neal Cotts	76.7%	FB-SL-CH-CB
Matt Thornton	76.4%	FB-SL-CT-CH
Brad Ziegler	75.2%	FB-CB-SL-CH
Dennis Sarfate	69.7%	FB-CB-SL
David Riske	69.5%	FB-CH-SL
Joe Beimel	69.4%	FB-CB-CH-SL
Daniel Cabrera	68.9%	FB-SL-CH-CB

Low Theoretical Predictability

pitcher	MLP	repertoire
Andy Sonnanstine	24.1%	FB-CT-CB-SL-CH
R.A. Dickey	24.2%	KN-FB-CB-CH-SL-SF
Jorge Campillo	26.9%	FB-SL-CH-CB-CT
Shaun Marcum	27.0%	FB-SL-CH-CB-CT-SF
Bronson Arroyo	27.2%	FB-CB-CH-SL-CT
Carlos Villanueva	27.2%	FB-SL-CH-CB
Mike Mussina	28.1%	FB-CB-SL-CH-SF
Doug Davis	28.7%	CT-FB-CB-CH-SL
Lance Cormier	29.2%	CB-SL-FB-CT-CH
Jered Weaver	29.7%	FB-CH-SL-CT-CB

Some observations
The pitch repertoire is what comes out from MLBAM Gameday (not necessarily correct)

I showed the top-10 and bottom-10 because lot of people like to see ranking tables, but I think in this case they don't make a lot of sense. Anyway a quick look at them can't be harmful.

First of all, my dataset has Wakefield throwing nearly 100% knuckleballs (thus yelding the highest predictability value); I don't know if either I did something wrong in importing pitchf/x data or MLBAM classification algorithm marks every offering by Tim as a knuckler - anyway Fangraphs (BIS data) has his split at 81% KN, 13% FB, 6% CB, and ESPN Insider at 82% KN, 13% FB, 5% CB (using these sources I would get 67.7% and 69.2% predictability value, respectively).

Wakefield leads to another point: knuckleballs have a very high degree of variability, so knowing that the pitch coming at you is called knuckleball, won't tell you anything about the path the ball will travel.

You can make a similar case for Mariano's cutter (Mo's out of the top ten list): it's not really a single pitch, because he varies the position of his fingers to obtain different cuts.

Analyzing how much Wakefield or Rivera are predictable on their selection is pretty useless, as it is for guys like Ballfour who throw (nearly) nothing but fastballs: hitters already know what is gonna come at them - Ballfour, Wakefield and Mo don't live on surprising opponents.

Further analyses on this subject can be more useful if done on pitchers with, say, three very distinguishable pitches (e.g. Fastball, Slider, Changeup) none thrown more than 3/4 of the time, and that's what I'll try to do in the future.

Now you might ask what's all this effort in getting theoretical predictabilities for.

I'd like to look at individual pitchers' predictabilities using advanced statistical techniques, such as multinomial logistic regression: I would like to build models to help me predict what a pitcher will throw on a specifical situation (i.e. against a right hander, late in a close game, with a runner on first, nobody out and following a slider); but I needed to set a minimum usefulness for the models... if I build model performs worse than the Minimum Level of Predictability, then it is useless.
On the other side, if a model for a pitcher significantly outperforms the Minimum Level of Predictability, then maybe the pitcher is falling into patterns, and this fact could be exploited by the opposition.

As I said, I'll tackle the models in the future.

Predictability (Play Ball!)

2009-03-03T03:39:00.004-05:00

I found the answer to the predictability question in last post with basic probability.
In such a hypothetical situation, what the pitcher is going to throw and what the hitter thinks is coming at him are independent events.

Thus we have four scenarios (the following example is for Pitcher B - the one who throws 90% Fastball, 10% slider).

Pitcher B is going to throw a fastball (probability = 90%, or P(PF) = .9) and Hitter C is looking for a fastball (P(HF) = .9): the probability of this scenario is P(PF) * P(HF) = .9 * .9 = .81;
Pitcher B is going to throw a fastball (P(PF) = .9) and Hitter C is looking for a slider (P(HS) = .1): the probability of this scenario is P(PF) * P(HS) = .9 * .1 = .09;
Pitcher B is going to throw a slider (P(PS) = .1) and Hitter C is looking for a fastball (P(HF) = .9): the probability of this scenario is P(PS) * P(HF) = .1 * .9 = .09;
Pitcher B is going to throw a slider (P(PS) = .1) and Hitter C is looking for a slider (P(HS) = .1): the probability of this scenario is P(PS) * P(HS) = .1 * .1 = .01;

The probability of a correct guess is the sum of the probabilities for first and last scenarios, i.e. 0.82.

You can be more general and calculate the Minimum Level of Predictability given any number of pitch types a pitcher has in his toolbox, any way he mixes them, and the information the hitter has on him (that might not be accurate).
It's as simple as:

Prob pitcher throws fastball * Prob hitter looks for fastball
+ Prob pitcher throws slider * Prob hitter looks for slider
+ Prob pitcher throws curve * Prob hitter looks for curve
+ and so on...

Obviously the Minimum Level of Predictability is lower for pitchers who

have more pitches in their repertoire
and use them in equal proportions.

Here are some combinations coming out of my mind as examples:

# pitches in repertoire	selection percentages	MLP
2	50-50	50%
2	90-10	82%
3	90-5-5	81.5%
3	50-30-20	38%
3	34-33-33	33%
4	50-30-15-5	36.5%
4	90-5-3-2	81.4%
4	25-25-25-25	25%

I think it's too much for theory (well, not so fast... look at the note below). Next time I'll write some real pitcher names.

Note
If you think that Pitcher P is never going to change his mixing (90% FB, 10% SL), the guessing hitter will have more success if he always guesses Fastball (he'll be correct 90% of the times instead of 82%).
Obviously, in such a case, after some time the pitcher will stop throwing fastballs to that hitter at all; then the hitter will adjust and look only for sliders. After some back and forth adjustments the couple will reach an equilibrium. Ideally that would be at 50-50, since it's the most unpredictable combo; but the pitcher, as we said in our example, might not have equal confidence in both pitches and/or one pitch might be more stressful for his body; thus he will reach a different equilibrium (90-10 in our example).

Predictability (cerimonial first pitch)

2009-03-02T08:23:00.001-05:00

Can we measure how much a pitcher is predictable in choosing the type of pitch he will deliver?
Today I will introduce the Minimum Level of Predictability.

Let's say Pitcher A has two pitches in his arsenal, e.g a fastball and a slider. He is so confident on both pitches that he delivers fastball 50% of the time and slider the other 50%. Suppose also he is perfectly random in his selection: no matter the count, the on base situation, the score, the hitter, the last pitch he has thrown - every delivery is just like a coin toss.

Pitcher B has a fastball and a slider too, but he chooses the hard one 90% of the time. Though his predilection toward the fastball is huge, he doesn't care the situation either: whatever is happening (or has just happened) on the field, his selection will be absolutely random (though heavily unbalanced).

Now we have Hitter C, who is an extreme guess hitter. Every time he's going to face a pitch he spins a roulette in his head to decide what pitch to look for. He is not entirely devote to Lady Luck: he talks a lot with the advanced scouts and takes notes.
The scouts have told him that Pitcher A throws fastball-slider in a 50-50 proportion and Pitcher B throws the same combination but with a 90-10 ratio.
He sets up his mental roulette accordingly.

How many times will he correctly guess offerings from Pitcher A and from Pitcher B?
Short answer: 50% correct against Pitcher A, 82% correct against Pitcher B.
Long answer: ...will see you tomorrow night!

Before moving on

2009-02-25T08:15:00.001-05:00

I'm happy with my debut in the blogosphere.
I got some feedback and - most importantly - critics and suggestions.
I'd like to thank those of you who spread the news about the new kid on the block.

I will use this post to sum up what has emerged from the comments here and at Tango's blog.

1. What my analysis shows is the best (or at least a very good) alignment for maximizing the proportions of batted balls that are caught by the seven fielders. That's not the whole picture about defense.
The first baseman has to take care of the assists by the other infielders so he's not completely free to take a position on the field; my model doesn't account for this.

2. Not all batted balls are created equal. An up-the-middle groundball usually produces a single, while a grounder down either foul line is more likely to produce an extra-base hit. My analysis treats all the batted balls the same way.
Batted balls should be weighted according to the likelihood of them becoming a single, a double and so on. Anyway such a weighting would improve a theoretical defense alignment without considering the game situation: sometimes you have to concede the single and guard the lines, in other situations a hit is all the opponent needs to win the game so you don't care about giving up a single or a double (obviously, in such a case, you wouldn't dream of leaving the left side of the infield unguarded).
On the same subject I'd like to reiterate that we have no available information on the speed of the batted balls: even if the third basemen had as much range as the shortstops, we should probably expect them to cover less ground, because balls get at them more quickly. I think that is just a matter of having the data, because cluster analysis can cope with more than two dimensions.

3. Not all hitters are created equal. A second baseman throwing from short right can easily beat the big men running to first; the specific batter I considered can move faster than Big Papi, Howard & co.
Utley's speed also makes him a bigger threat on the basepaths, should he decide to lay down a bunt to the left side.

4. Not all fielders are created equal. Defensemen have different ranges, some move better on one side, some can't run backward, and so on. Obviously they should choose their position according to their strenghts and weaknesses too.

With my first couple of posts I intended to scratch a surface, and I'm really happy that people read them with interest. I never thought that a team can look at the graphs I posted and place his fielders in the very same spots. I'm not even sure that a team can learn anything new from such charts: a few readers of my posts weren't aware about the pull tendency of Chase Utley, but the Rays were playing him shifted four months ago (actually it was their weird alignment that made me delve on the issue).

Anyway, a quick look at one of those chart, won't hurt.

A few side notes: to draw the basepaths on my charts I used the coordinates suggested by Adler in Baseball Hacks; though they are pretty close, Mike Fast provided more accurate values on Tango's blog, and Peter Jensen is expected to publish normalized values at THT, since the coordinate system varies from park to park.

Refining the shift

2009-02-23T11:40:00.000-05:00

I worked some more on the subject of last post.
First of all, as I said at the end of that post, I rerun the cluster analysis after having removed the short grounders from my data set.
Here's the resulting chart.

No more fielders behind the rubber... I like it.

Then I tried to do things separately for infielders and outfielders. In this way I have more confidence in constraining the clusters to having equal sizes. This makes sense especially for the outfielders.

Here is a first chart for infielders: I run a model for four players.

I'm sorry for the questionable choice of colors, but I haven't fully grasped how the customizations of plots works for the package I'm using (Mclust for R, for those interested).

And here are the outfielders (three for the moment).

Then I tried to move one player from the infield to the outfield. Following are the charts for three infielders and four outfielders, respectively.

Summing up.
Playing Utley shifted is the right thing to do. You don't need anybody playing near the third base bag. Putting a fielder in short right makes sense too: the statistical analysis puts him there to catch short flies, but (as managers who employ the shift know) he is mainly valuable for handling the grounders not collected by the infielders on that side.
When data on batted ball velocity are available, a new dimension will be added to the cluster analysis: balls along the lines that get quicker to the infielders would be treated appropriately, thus producing clusters of different sizes (in the spatial dimensions considered here) for third basemen and first basemen.

Chase-ing the FieldF/x

2009-02-22T04:07:00.008-05:00

In the first inning of the last World Series the Rays fielders played Chase Utley extremely shifted, the way teams defend against guys like Big Papi, Giambi, or Howard. Chase tried to get advantage of the alignment by laying down a bunt, but it rolled out of the third base line; then he decided to ignore the opponents placement and hit a ball that no shift can take care of.

I hadn't watched many Phillies games during the regular season (living in Europe I'm usually exposed to the Cubbies... unless my boss accepts me sleeping on my desk in the morning), so I didn't know whether it is common place for teams to defend shifted against Utley. From what I heard during the telecast, Rays alignment was pretty unusual for that guy.

Using data both from Gameday and Retrosheet, I tried to figure an optimal positioning against Chase.
Here's what I've done.

First I plotted the locations of every Utley's batted ball, using coordinates from Gameday.

I plotted grounders in red. All the GBs you see in the outfield have gone through the infield and - theoretically - could have been caught by a well positioned infielder (or one that happened to be where the ball was hit). That's why people working at Project Scoresheet used to record, for groundball hits, the place where the ball left the infield, instead of that where the ball was collected in the outfield (you can see this good habit in the Retrosheet files of the '80s). As we see that's not the case with Gameday stringers.

I corrected for this. I dusted off a couple of geometry books and projected every groundball that went to the outfield to the place it left the infield.

Here's the new graph.

Finally I added some random noise because the groundball hits (those that went through) were plotted one over the other and wasn't easy to distinguish (or count) them.
Here's something easier to read.

"You can observe a lot just by watching". In this case, just watching you can see where batted balls tend to cluster.

Cluster analysis is a statistical tool that can help our eyes in this task.
I hoped that, with the help of cluster analysis, I could more or less identify where to place seven fielders against Chase Utley (pitcher and catcher are not so free to move around the field).

I must admit I didn't expect to be so lucky, and I don't expect to be when I perform similar analyses on other batters.
It turned out that I forgot to put a costraint on the number of clusters I wanted to find, but the algorithm I used chose exactly seven as the optimal result. Should that happen to every following analysis I do, that would be a scientific demonstration that nine players on the field is the perfect number for baseball.

Here's a chart showing the defensive alignment cluster analysis suggests for Utley. You put a player in the middle of each circle and he's responsible of every ball in that circle (or in the neighborhood, just look at the colors).

Weren't for that third baseman (I suppose) just behind the pitcher mound, the result would have looked too good to be true - I would have understood every one accusing me of making up the data.

It looks like the Rays alignment made sense. I'm curious about the midway (between infield and outfield) position where the second baseman usually plays in this kind of shift: the clustering algorithm places a player there to take care of short flies, while managers put the man there to tackle hard grounders too.

This analysis doesn't take into account the range a player can realistically cover. This causes the player behind the pitcher mound having to take care of all the infield grass; besides you have to believe that, however well positioned, you can't count on your pair on the right scooping every groundball.

I didn't expect running a simple cluster analysis (well, that's not so simple, to be honest) and finding results that make so much baseball sense.

Maybe if I remove from the data set the very short grounders (those that become infield hits or that are catcher/pitcher responsibility), I can even get that third baseman off the pitching mound!

Play ball!

2009-02-20T14:11:00.001-05:00

A few of the guys I spent some time with at the Pitchf/x Summit last May in San Francisco, Prof Alan Nathan among others, spurred me to write articles in English.
It's been a very long time since then, but now I'm willing to give it a try.
Stay tuned.