Statcast Search

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Baseball Savant’s search page allows you to query MLB’s Statcast database on a per-pitch, per-game, per-player, per-team, and per-season basis. Definitions for each Statcast metric may be found in the MLB Glossary.

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  • Pitch velocities from 2008-16 are via Pitch F/X, and adjusted to roughly out-of-hand release point. All velocities from 2017 and beyond are Statcast, which are reported out-of-hand.
  • For the limited subset of batted balls not tracked directly, estimates are included based on the process described here.
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Basic
Pitch Movement Averages
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Pitch Metric Averages
Hit Metric Averages
Fielder Positioning Averages
Pitch Metrics
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Hit Metrics
Expected Results
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Age
Lineup

Search Results

Rk. Player Pitches Total Pitch %      
1 Freese, David 48 118 40.7
Graphs
2 Jay, Jon 57 141 40.4
Graphs
3 Hernández, Marco 40 107 37.4
Graphs
4 Arraez, Luis 110 300 36.7
Graphs
5 Dickerson, Corey 76 207 36.7
Graphs
6 Díaz, Elias 91 251 36.3
Graphs
7 Duffy, Matt 42 119 35.3
Graphs
8 González, Erik 38 109 34.9
Graphs
9 Tauchman, Mike 66 190 34.7
Graphs
10 Garcia, Greg 79 231 34.2
Graphs
11 Slater, Austin 37 109 33.9
Graphs
12 Pence, Hunter 74 219 33.8
Graphs
13 LeMahieu, DJ 174 517 33.7
Graphs
14 Desmond, Ian 110 327 33.6
Graphs
15 Smith, Kevan 52 155 33.5
Graphs
16 Gallagher, Cam 33 100 33.0
Graphs
17 Lugo, Dawel 72 218 33.0
Graphs
18 Sánchez, Yolmer 128 389 32.9
Graphs
19 Kiner-Falefa, Isiah 51 155 32.9
Graphs
20 Cabrera, Miguel 128 390 32.8
Graphs
21 DeShields, Delino 87 267 32.6
Graphs
22 Cain, Lorenzo 149 460 32.4
Graphs
23 Duggar, Steven 60 186 32.3
Graphs
24 Taylor, Chris 83 258 32.2
Graphs
25 Adrianza, Ehire 54 168 32.1
Graphs
26 Mazara, Nomar 105 327 32.1
Graphs
27 García, Leury 145 452 32.1
Graphs
28 Gamel, Ben 67 209 32.1
Graphs
29 Cooper, Garrett 87 273 31.9
Graphs
30 Sandoval, Pablo 67 210 31.9
Graphs
31 Reyes, Victor 68 214 31.8
Graphs
32 Ohtani, Shohei 88 278 31.7
Graphs
33 Eaton, Adam 149 472 31.6
Graphs
34 Senzel, Nick 87 275 31.6
Graphs
35 Alfaro, Jorge 88 279 31.5
Graphs
36 Pérez, Roberto 86 273 31.5
Graphs
37 Urías, Luis 50 159 31.4
Graphs
38 Peraza, José 100 320 31.3
Graphs
39 Russell, Addison 50 160 31.3
Graphs
40 Guzmán, Ronald 54 173 31.2
Graphs
41 Miller, Brad 34 109 31.2
Graphs
42 Posey, Buster 104 336 31.0
Graphs
43 Demeritte, Travis 33 108 30.6
Graphs
44 Smith, Mallex 114 372 30.6
Graphs
45 McCann, James 92 303 30.4
Graphs
46 Caratini, Victor 57 188 30.3
Graphs
47 Lagares, Juan 56 186 30.1
Graphs
48 Lopez, Nicky 99 332 29.8
Graphs
49 Grossman, Robbie 100 336 29.8
Graphs
50 Rojas, Miguel 127 427 29.7
Graphs
51 Hernández, César 153 516 29.7
Graphs
52 Robertson, Daniel 44 148 29.7
Graphs
53 Castro, Harold 81 274 29.6
Graphs
54 Anderson, Tim 115 391 29.4
Graphs
55 Muñoz, Yairo 40 136 29.4
Graphs
56 Freeman, Mike 37 126 29.4
Graphs
57 Nola, Austin 52 177 29.4
Graphs
58 Bichette, Bo 43 147 29.3
Graphs
59 Frazier, Adam 142 484 29.3
Graphs
60 Anderson, Brian 102 348 29.3
Graphs
61 Greiner, Grayson 41 140 29.3
Graphs
62 Dean, Austin 39 133 29.3
Graphs
63 Vázquez, Christian 113 387 29.2
Graphs
64 Markakis, Nick 105 361 29.1
Graphs
65 Marisnick, Jake 58 200 29.0
Graphs
66 Moore, Dylan 45 155 29.0
Graphs
67 Inciarte, Ender 46 159 28.9
Graphs
68 Camargo, Johan 55 190 28.9
Graphs
69 Almora Jr., Albert 82 284 28.9
Graphs
70 Grisham, Trent 32 111 28.8
Graphs
71 Berti, Jon 53 184 28.8
Graphs
72 Strange-Gordon, Dee 98 341 28.7
Graphs
73 Martínez, José 73 254 28.7
Graphs
74 d'Arnaud, Travis 78 272 28.7
Graphs
75 Cervelli, Francisco 29 101 28.7
Graphs
76 Goins, Ryan 29 101 28.7
Graphs
77 Solano, Donovan 48 168 28.6
Graphs
78 Puig, Yasiel 122 426 28.6
Graphs
79 Wieters, Matt 35 123 28.5
Graphs
80 Dahl, David 77 271 28.4
Graphs
81 Happ, Ian 29 102 28.4
Graphs
82 Moustakas, Mike 121 427 28.3
Graphs
83 Tilson, Charlie 30 106 28.3
Graphs
84 Descalso, Daniel 32 113 28.3
Graphs
85 Bauers, Jake 73 260 28.1
Graphs
86 Wolters, Tony 84 299 28.1
Graphs
87 McMahon, Ryan 90 322 28.0
Graphs
88 Nido, Tomás 28 100 28.0
Graphs
89 Nimmo, Brandon 37 132 28.0
Graphs
90 Prado, Martín 58 207 28.0
Graphs
91 Schwarber, Kyle 106 379 28.0
Graphs
92 Merrifield, Whit 156 559 27.9
Graphs
93 Báez, Javier 105 377 27.9
Graphs
94 Newman, Kevin 121 434 27.9
Graphs
95 Lowe, Nathaniel 29 104 27.9
Graphs
96 Canó, Robinson 90 324 27.8
Graphs
97 Acuña Jr., Ronald 122 439 27.8
Graphs
98 Casali, Curt 42 151 27.8
Graphs
99 Seager, Corey 110 395 27.8
Graphs
100 Smith, Dominic 37 133 27.8
Graphs
101 Hosmer, Eric 128 461 27.8
Graphs
102 Castro, Jason 42 151 27.8
Graphs
103 Story, Trevor 116 417 27.8
Graphs
104 Correa, Carlos 58 209 27.8
Graphs
105 Long Jr., Shed 31 112 27.7
Graphs
106 León, Sandy 36 130 27.7
Graphs
107 Narváez, Omar 94 339 27.7
Graphs
108 Sogard, Eric 94 339 27.7
Graphs
109 Díaz, Yandy 69 250 27.6
Graphs
110 Tapia, Raimel 90 326 27.6
Graphs
111 Granderson, Curtis 61 221 27.6
Graphs
112 Machado, Manny 127 462 27.5
Graphs
113 Mathis, Jeff 39 142 27.5
Graphs
114 Hiura, Keston 57 208 27.4
Graphs
115 Hamilton, Billy 64 234 27.4
Graphs
116 Freeman, Freddie 129 472 27.3
Graphs
117 Bruce, Jay 63 231 27.3
Graphs
118 Contreras, Willson 71 260 27.3
Graphs
119 Judge, Aaron 65 238 27.3
Graphs
120 Díaz, Isan 33 121 27.3
Graphs
121 Murphy, Daniel 100 368 27.2
Graphs
122 Barnes, Austin 43 158 27.2
Graphs
123 Romine, Austin 49 180 27.2
Graphs
124 Joyce, Matt 42 155 27.1
Graphs
125 Dickerson, Alex 36 133 27.1
Graphs
126 Vargas, Ildemaro 48 178 27.0
Graphs
127 Hampson, Garrett 58 215 27.0
Graphs
128 Galvis, Freddy 112 415 27.0
Graphs
129 Zimmerman, Ryan 36 134 26.9
Graphs
130 Villar, Jonathan 127 472 26.9
Graphs
131 Castellanos, Nick 128 475 26.9
Graphs
132 Crawford, J.P. 72 268 26.9
Graphs
133 Smith Jr., Dwight 75 280 26.8
Graphs
134 Rosario, Amed 133 497 26.8
Graphs
135 Osuna, José 58 217 26.7
Graphs
136 Devers, Rafael 142 531 26.7
Graphs
137 Parra, Gerardo 58 218 26.6
Graphs
138 Travis, Sam 29 109 26.6
Graphs
139 Reynolds, Bryan 99 373 26.5
Graphs
140 Martinez, J.D. 117 442 26.5
Graphs
141 Mancini, Trey 123 464 26.5
Graphs
142 Andrus, Elvis 136 514 26.5
Graphs
143 Pinder, Chad 68 257 26.5
Graphs
144 Rengifo, Luis 71 268 26.5
Graphs
145 Núñez, Renato 106 402 26.4
Graphs
146 Naquin, Tyler 56 212 26.4
Graphs
147 Haseley, Adam 43 163 26.4
Graphs
148 Panik, Joe 105 397 26.4
Graphs
149 Soto, Juan 110 416 26.4
Graphs
150 Ervin, Phillip 46 175 26.3
Graphs
151 Wendle, Joey 51 194 26.3
Graphs
152 Gurriel Jr., Lourdes 61 232 26.3
Graphs
153 Polanco, Jorge 138 524 26.3
Graphs
154 Adames, Willy 100 382 26.2
Graphs
155 Benintendi, Andrew 107 409 26.2
Graphs
156 Reyes, Pablo 28 107 26.2
Graphs
157 Broxton, Keon 27 103 26.2
Graphs
158 Segura, Jean 133 507 26.2
Graphs
159 Brantley, Michael 134 513 26.1
Graphs
160 Goodrum, Niko 75 287 26.1
Graphs
161 Turner, Justin 103 396 26.0
Graphs
162 Santana, Domingo 75 289 26.0
Graphs
163 Kendrick, Howie 75 290 25.9
Graphs
164 Conforto, Michael 105 405 25.9
Graphs
165 La Stella, Tommy 68 264 25.8
Graphs
166 Abreu, José 127 492 25.8
Graphs
167 Aguilar, Jesús 62 240 25.8
Graphs
168 Swanson, Dansby 94 365 25.8
Graphs
169 Ramírez, Harold 85 331 25.7
Graphs
170 Bell, Josh 107 416 25.7
Graphs
171 Cabrera, Melky 87 338 25.7
Graphs
172 Holt, Brock 53 206 25.7
Graphs
173 Vogelbach, Daniel 81 315 25.7
Graphs
174 Maybin, Cameron 43 167 25.7
Graphs
175 Walker, Neil 67 261 25.7
Graphs
176 Martin, Richie 53 206 25.7
Graphs
177 Yastrzemski, Mike 69 268 25.7
Graphs
178 Hechavarría, Adeiny 40 156 25.6
Graphs
179 Riley, Austin 43 168 25.6
Graphs
180 Reddick, Josh 114 445 25.6
Graphs
181 Cordell, Ryan 40 156 25.6
Graphs
182 Cruz, Nelson 83 326 25.5
Graphs
183 Barnhart, Tucker 60 235 25.5
Graphs
184 Owings, Chris 26 102 25.5
Graphs
185 Blackmon, Charlie 122 481 25.4
Graphs
186 Pham, Tommy 113 445 25.4
Graphs
187 Alvarez, Yordan 56 221 25.3
Graphs
188 Gordon, Alex 117 463 25.3
Graphs
189 Belt, Brandon 102 403 25.3
Graphs
190 Heredia, Guillermo 37 147 25.2
Graphs
191 Difo, Wilmer 26 103 25.2
Graphs
192 Votto, Joey 102 405 25.2
Graphs
193 Dixon, Brandon 65 259 25.1
Graphs
194 Donaldson, Josh 99 396 25.0
Graphs
195 Dozier, Hunter 95 380 25.0
Graphs
196 Santana, Danny 82 328 25.0
Graphs
197 Stallings, Jacob 38 152 25.0
Graphs
198 Molina, Yadier 91 366 24.9
Graphs
199 Hernández, Enrique 80 321 24.9
Graphs
200 Moncada, Yoán 90 361 24.9
Graphs
201 Reyes, Franmil 86 345 24.9
Graphs
202 Turner, Trea 102 410 24.9
Graphs
203 Ahmed, Nick 113 456 24.8
Graphs
204 Goldschmidt, Paul 107 434 24.7
Graphs
205 Mercado, Óscar 90 365 24.7
Graphs
206 Engel, Adam 37 150 24.7
Graphs
207 Frazier, Clint 39 158 24.7
Graphs
208 Arcia, Orlando 97 393 24.7
Graphs
209 Dietrich, Derek 44 178 24.7
Graphs
210 Carpenter, Matt 72 293 24.6
Graphs
211 Wong, Kolten 100 406 24.6
Graphs
212 Realmuto, J.T. 104 423 24.6
Graphs
213 Robles, Victor 102 417 24.5
Graphs
214 Piscotty, Stephen 68 277 24.5
Graphs
215 Rondón, José 26 106 24.5
Graphs
216 Fletcher, David 131 534 24.5
Graphs
217 Díaz, Aledmys 46 188 24.5
Graphs
218 Winker, Jesse 68 278 24.5
Graphs
219 Kipnis, Jason 93 381 24.4
Graphs
220 Rendon, Anthony 114 468 24.4
Graphs
221 Vogt, Stephen 47 193 24.4
Graphs
222 Dyson, Jarrod 77 317 24.3
Graphs
223 Davis, Khris 82 337 24.3
Graphs
224 Hicks, Aaron 37 152 24.3
Graphs
225 Choo, Shin-Soo 97 399 24.3
Graphs
226 Peralta, David 72 296 24.3
Graphs
227 Urshela, Gio 87 359 24.2
Graphs
228 Edman, Tommy 64 265 24.2
Graphs
229 Chirinos, Robinson 60 248 24.2
Graphs
230 Naylor, Josh 46 190 24.2
Graphs
231 White, Tyler 40 165 24.2
Graphs
232 Cron, C.J. 85 353 24.1
Graphs
233 Bote, David 51 212 24.1
Graphs
234 Ramos, Wilson 98 407 24.1
Graphs
235 Bogaerts, Xander 120 498 24.1
Graphs
236 Springer, George 89 370 24.1
Graphs
237 Healy, Ryon 32 133 24.1
Graphs
238 Semien, Marcus 134 556 24.1
Graphs
239 Iglesias, Jose 105 437 24.0
Graphs
240 Fowler, Dexter 84 350 24.0
Graphs
241 Marte, Starling 108 451 23.9
Graphs
242 Choi, Ji Man 74 309 23.9
Graphs
243 Chapman, Matt 105 439 23.9
Graphs
244 Piña, Manny 26 109 23.9
Graphs
245 Seager, Kyle 74 309 23.9
Graphs
246 Braun, Ryan 85 357 23.8
Graphs
247 Torres, Gleyber 101 424 23.8
Graphs
248 O'Hearn, Ryan 55 231 23.8
Graphs
249 Jones, JaCoby 49 206 23.8
Graphs
250 Flowers, Tyler 40 168 23.8
Graphs
251 Tatis Jr., Fernando 54 227 23.8
Graphs
252 Santander, Anthony 71 298 23.8
Graphs
253 Jiménez, Eloy 80 336 23.8
Graphs
254 Alberto, Hanser 114 480 23.8
Graphs
255 Wilkerson, Stevie 53 224 23.7
Graphs
256 Trout, Mike 84 354 23.7
Graphs
257 Verdugo, Alex 71 300 23.7
Graphs
258 Astudillo, Willians 44 186 23.7
Graphs
259 Walker, Christian 89 375 23.7
Graphs
260 Pérez, Hernán 40 169 23.7
Graphs
261 Martin, Leonys 38 161 23.6
Graphs
262 Kemp, Tony 48 203 23.6
Graphs
263 Chavis, Michael 52 220 23.6
Graphs
264 Bradley Jr., Jackie 81 344 23.5
Graphs
265 Gomes, Yan 54 231 23.4
Graphs
266 Mejía, Francisco 40 171 23.4
Graphs
267 McNeil, Jeff 102 436 23.4
Graphs
268 Morales, Kendrys 34 145 23.4
Graphs
269 Plawecki, Kevin 30 128 23.4
Graphs
270 Cave, Jake 30 128 23.4
Graphs
271 Yelich, Christian 87 374 23.3
Graphs
272 Harper, Bryce 93 399 23.3
Graphs
273 Rizzo, Anthony 100 429 23.3
Graphs
274 Beckham, Tim 47 202 23.3
Graphs
275 Bryant, Kris 93 400 23.3
Graphs
276 Franco, Maikel 77 331 23.3
Graphs
277 Crawford, Brandon 90 387 23.3
Graphs
278 Lucroy, Jonathan 57 245 23.3
Graphs
279 Moran, Colin 82 353 23.2
Graphs
280 Farmer, Kyle 29 125 23.2
Graphs
281 Brinson, Lewis 36 155 23.2
Graphs
282 Davis, J.D. 73 315 23.2
Graphs
283 Núñez, Eduardo 33 143 23.1
Graphs
284 Grandal, Yasmani 87 379 23.0
Graphs
285 Garver, Mitch 52 226 23.0
Graphs
286 Goodwin, Brian 66 288 22.9
Graphs
287 Gonzalez, Marwin 75 328 22.9
Graphs
288 García, Avisaíl 84 367 22.9
Graphs
289 Locastro, Tim 39 170 22.9
Graphs
290 Muncy, Max 78 342 22.8
Graphs
291 Forsythe, Logan 50 219 22.8
Graphs
292 Shaw, Travis 32 141 22.7
Graphs
293 Pillar, Kevin 120 529 22.7
Graphs
294 Arenado, Nolan 113 503 22.5
Graphs
295 Jones, Adam 87 387 22.5
Graphs
296 Betts, Mookie 113 505 22.4
Graphs
297 Allen, Greg 41 183 22.4
Graphs
298 Guerrero Jr., Vladimir 84 375 22.4
Graphs
299 Bellinger, Cody 102 455 22.4
Graphs
300 Longoria, Evan 77 346 22.3
Graphs
301 Hernández, Teoscar 59 265 22.3
Graphs
302 Kiermaier, Kevin 77 345 22.3
Graphs
303 Gurriel, Yuli 112 505 22.2
Graphs
304 Soler, Jorge 92 415 22.2
Graphs
305 Lindor, Francisco 112 507 22.1
Graphs
306 Flores, Wilmer 52 235 22.1
Graphs
307 Zunino, Mike 37 168 22.0
Graphs
308 Profar, Jurickson 85 387 22.0
Graphs
309 Myers, Wil 59 269 21.9
Graphs
310 Jansen, Danny 59 270 21.9
Graphs
311 Laureano, Ramón 70 320 21.9
Graphs
312 Heyward, Jason 89 406 21.9
Graphs
313 Aquino, Aristides 32 147 21.8
Graphs
314 Castro, Starlin 116 534 21.7
Graphs
315 Encarnación, Edwin 69 318 21.7
Graphs
316 Kingery, Scott 68 314 21.7
Graphs
317 Cabrera, Asdrúbal 76 351 21.7
Graphs
318 Lowe, Brandon 40 184 21.7
Graphs
319 Marte, Ketel 105 485 21.6
Graphs
320 Kelly, Carson 51 236 21.6
Graphs
321 Ruiz, Rio 61 285 21.4
Graphs
322 Alonso, Yonder 48 224 21.4
Graphs
323 Beaty, Matt 46 216 21.3
Graphs
324 Stewart, Christin 58 272 21.3
Graphs
325 Davis, Chris 36 171 21.1
Graphs
326 Cuthbert, Cheslor 51 242 21.1
Graphs
327 Canha, Mark 64 305 21.0
Graphs
328 Sánchez, Gary 57 272 21.0
Graphs
329 Bader, Harrison 49 233 21.0
Graphs
330 Haniger, Mitch 35 167 21.0
Graphs
331 Ford, Mike 24 115 20.9
Graphs
332 Mondesi, Adalberto 61 292 20.9
Graphs
333 Lamb, Jake 28 134 20.9
Graphs
334 Phegley, Josh 54 258 20.9
Graphs
335 Castillo, Welington 33 158 20.9
Graphs
336 Ramírez, José 86 414 20.8
Graphs
337 Sisco, Chance 22 106 20.8
Graphs
338 Suárez, Eugenio 81 392 20.7
Graphs
339 McCutchen, Andrew 34 164 20.7
Graphs
340 Beckham, Gordon 32 155 20.6
Graphs
341 Albies, Ozzie 109 532 20.5
Graphs
342 Drury, Brandon 63 308 20.5
Graphs
343 Grichuk, Randal 87 425 20.5
Graphs
344 Thames, Eric 53 258 20.5
Graphs
345 Hicks, John 43 211 20.4
Graphs
346 Hoskins, Rhys 82 403 20.3
Graphs
347 Escobar, Eduardo 105 516 20.3
Graphs
348 Meadows, Austin 81 399 20.3
Graphs
349 Rosario, Eddie 97 482 20.1
Graphs
350 Mercer, Jordy 40 199 20.1
Graphs
351 Murphy, Tom 35 174 20.1
Graphs
352 Luplow, Jordan 33 165 20.0
Graphs
353 Bour, Justin 20 100 20.0
Graphs
354 Dozier, Brian 62 312 19.9
Graphs
355 Upton, Justin 29 146 19.9
Graphs
356 Martin, Russell 30 151 19.9
Graphs
357 Moreland, Mitch 45 226 19.9
Graphs
358 Voit, Luke 57 288 19.8
Graphs
359 DeJong, Paul 86 440 19.5
Graphs
360 Tellez, Rowdy 50 257 19.5
Graphs
361 Margot, Manuel 61 313 19.5
Graphs
362 Adams, Matt 38 196 19.4
Graphs
363 Calhoun, Kole 76 392 19.4
Graphs
364 Buxton, Byron 40 206 19.4
Graphs
365 Gardner, Brett 75 386 19.4
Graphs
366 Candelario, Jeimer 46 237 19.4
Graphs
367 Polanco, Gregory 20 104 19.2
Graphs
368 McKinney, Billy 35 182 19.2
Graphs
369 Kepler, Max 82 429 19.1
Graphs
370 Ozuna, Marcell 71 372 19.1
Graphs
371 Starling, Bubba 25 131 19.1
Graphs
372 VanMeter, Josh 33 173 19.1
Graphs
373 Kinsler, Ian 39 205 19.0
Graphs
374 Schoop, Jonathan 60 318 18.9
Graphs
375 Alonso, Pete 79 417 18.9
Graphs
376 Santana, Carlos 88 467 18.8
Graphs
377 Odor, Rougned 65 346 18.8
Graphs
378 Gallo, Joey 24 129 18.6
Graphs
379 Pujols, Albert 80 431 18.6
Graphs
380 Pederson, Joc 63 341 18.5
Graphs
381 Tucker, Cole 20 108 18.5
Graphs
382 Pollock, AJ 44 238 18.5
Graphs
383 France, Ty 25 136 18.4
Graphs
384 Gregorius, Didi 50 273 18.3
Graphs
385 Altuve, Jose 77 422 18.2
Graphs
386 Olson, Matt 63 346 18.2
Graphs
387 Hedges, Austin 37 206 18.0
Graphs
388 Bregman, Alex 86 479 18.0
Graphs
389 Zobrist, Ben 23 128 18.0
Graphs
390 Simmons, Andrelton 65 361 18.0
Graphs
391 McCann, Brian 41 230 17.8
Graphs
392 Smoak, Justin 55 309 17.8
Graphs
393 Frazier, Todd 60 341 17.6
Graphs
394 Calhoun, Willie 45 258 17.4
Graphs
395 Biggio, Cavan 40 233 17.2
Graphs
396 Harrison, Josh 19 112 17.0
Graphs
397 Rickard, Joey 20 118 16.9
Graphs
398 Maldonado, Martín 42 250 16.8
Graphs
399 Severino, Pedro 39 235 16.6
Graphs
400 Stewart, DJ 16 101 15.8
Graphs
401 Smith, Will 19 121 15.7
Graphs
402 Rodríguez, Ronny 31 199 15.6
Graphs
403 Suzuki, Kurt 38 247 15.4
Graphs
404 Sanó, Miguel 33 222 14.9
Graphs
405 Renfroe, Hunter 39 292 13.4
Graphs
406 Kang, Jung Ho 14 113 12.4
Graphs