Hitting where the ball is pitched

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).

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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°.

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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.

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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.

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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.

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

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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