12 November 2010

Tech Notes: Pitch Characteristics and the Strike Zone

This is a followup to my post on Beyond the Box Score and the ensuing discussion on the Inside the Book Blog. I ran a logistic regression on the variables listed below on a database comprised of all called pitches from 2009-2010, excluding pitches in which data was not made available in the PFX database. The data was pulled from Darrell Zimmerman's SQL-based PitchFX database.

This post isn't for the faint of heart or for those who aren't familiar with logistic regression, but feel free to chime in if you have a question or an idea.

11/17/10: Updated. Direction of rhb variable was the opposite of what it should be.
12/1/10: Updated. Zone Height and League variables added.
12/10/10: Updated. "Rulebook strike" variable replaced with "bad call" variable. Exhibition and Playoff dropped. Non-absolute spin deflection variables added. Normalized horizontal location added.
1/28/11: Added 2008 data. Added nibble, inside vs. outside during AB count and ratio variables.
2/28/11: Added nibble and swinging nibble during AB sums and rates.



Variable Key
call errant ball = -1; good call = 0; errant strike = 1
err_call Pitch FX reports as either errant ball or errant strike
ab_iz number of pitches thrown inside of zone from start of at bat through time of pitch
ab_oz number of pitches thrown outside of zone from start of at bat through time of pitch
ab_zone_avg (ab_iz - ab_oz) / (ab_iz + ab_oz)
nibble_sum sum of the distances between the pitch thrown and the nearest legal strike zone boundary over the course of an at bat (negative if in zone)
nibble_rate nibble_sum / pitches thrown during at bat
nibble_sum_2 nibble_sum excluding value of current pitch
nibble_rate_2 nibble_sum_2 / pitches thrown during AB
ab_swings_iz number of swings at pitches inside the zone from start of at bat through time of pitch
ab_swings_oz number of swings at pitches outside the zone from start of at bat through time of pitch
fishing_avg (ab_swings_iz - ab_swings_oz) / (ab_swings_iz + ab_swings_oz)
swing_nibble_sum nibble_sum on pitches at which batter swung
swing_nibble_rat swing_nibble_sum / pitches thrown during AB
px_rel px for rhb, px*(-1) for lhb
zone_height top of recorded zone - bottom of recorded zone
AL National League park = 0; American League Park = 1
home_ab top of inning = 0; bottom of inning = 1
rhp left-handed pitcher = 0; right-handed pitcher = 1
rhb left-handed batter = 0; right-handed batter = 1
inning_frac inning + 1/3 at time of pitch
game_pitches number of pitches thrown in game at time of pitch
outs outs at time of pitch
on_1b runner on first =1
on_2b runner on second = 1
on_3b runner on third = 1
base_out_re run value of the base-out state as calculated by Tom Tango
balls ball count
strikes strike count
ball_strike_re run value of the ball-strike count as calculated by Tom Tango
start_speed pitch velocity 50 ft. from plate
pfx_x horizontal spin deflection
abs_pfx_x absolute value of the horizontal spin deflection
rel_pfx_x pfx_x * -1 for lhb
pfx_z vertical spin deflection
abs_pfx_z absolute value of the vertical spin deflection
rel_pfx_z pfx_z / zone_height
fastball 0 = offspeed; 1 = fastball
_2008 dummy variable for 2008 data
_2009 dummy variable for 2009 data


Full Working Model


Ordered logistic  regression Number of obs = 1035300
LR chi2(39) = 245755.37
Prob > chi2 = 0
Log likelihood = -393866.76 Pseudo R2 = 0.2378
call Coef. Std. Err. z P>z [95% Conf . Interval]
err_call 1.749564 0.008076 216.64 0.000 1.733736 1.765393
ab_iz -0.2290493 0.0141553 -16.18 0.000 -0.2567931 -0.2013055
ab_oz 0.4674193 0.0140098 33.36 0.000 0.4399606 0.494878
ab_zone_avg -2.406632 0.0121693 -197.76 0.000 -2.430484 -2.382781
nibble_sum 1.768057 0.0251407 70.33 0.000 1.718782 1.817332
nibble_rate -5.674885 0.0413802 -137.14 0.000 -5.755988 -5.593781
nibble_sum_2 -2.062765 0.0334444 -61.68 0.000 -2.128315 -1.997215
nibble_rate_2 1.779836 0.0846936 21.01 0.000 1.613839 1.945832
ab_swings_iz 0.6667784 0.0206962 32.22 0.000 0.6262146 0.7073422
ab_swings_oz -0.8800139 0.0209484 -42.01 0.000 -0.9210719 -0.8389559
fishing_avg 0.282329 0.0212631 13.28 0.000 0.2406542 0.3240038
swing_nibbe_sum 1.288323 0.0562615 22.9 0.000 1.178053 1.398594
swing_nibble_rat 0.2369442 0.1694322 1.4 0.162 -0.0951368 0.5690252
px_rel -0.2251806 0.0033378 -67.46 0.000 -0.2317226 -0.2186386
zone_height -0.5829965 0.0251288 -23.2 0.000 -0.6322481 -0.533745
al -0.0749285 0.0061037 -12.28 0.000 -0.0868916 -0.0629654
home_ab -0.0292857 0.0064833 -4.52 0.000 -0.0419926 -0.0165787
rhp 0.100843 0.0086003 11.73 0.000 0.0839868 0.1176993
rhb -0.0019549 0.0069179 -0.28 0.777 -0.0155137 0.0116039
inning_frac 0.037721 0.0046694 8.08 0.000 0.028569 0.0468729
game_pitches -0.001278 0.0001384 -9.24 0.000 -0.0015492 -0.0010068
outs 0.0616862 0.0088531 6.97 0.000 0.0443345 0.0790379
on_1b 0.0065685 0.0099112 0.66 0.507 -0.0128571 0.0259941
on_2b 0.0741664 0.0143383 5.17 0.000 0.0460639 0.102269
on_3b 0.1005718 0.0191016 5.27 0.000 0.0631333 0.1380103
base_out_re -0.3720619 0.0266742 -13.95 0.000 -0.4243424 -0.3197813
balls -0.4756533 0.0172282 -27.61 0.000 -0.5094199 -0.4418868
strikes -0.1661571 0.0162886 -10.2 0.000 -0.1980822 -0.134232
ball_strike_re 2.644622 0.1795988 14.73 0.000 2.292615 2.996629
start_speed -0.0105325 0.0008558 -12.31 0.000 -0.0122098 -0.0088551
pfx_x 0.0080937 0.0006208 13.04 0.000 0.006877 0.0093103
abs_pfx_x -0.0105302 0.0009839 -10.7 0.000 -0.0124586 -0.0086019
rel_pfx_x -0.0028408 0.0005001 -5.68 0.000 -0.003821 -0.0018607
pfx_z 0.0162965 0.0058781 2.77 0.006 0.0047756 0.0278175
abs_pfx_z 0.0002681 0.0012321 0.22 0.828 -0.0021467 0.002683
rel_pfx_z -0.0243354 0.010239 -2.38 0.017 -0.0444034 -0.0042673
fastball 0.1865802 0.009905 18.84 0.000 0.1671668 0.2059936
_2008 -0.0752415 0.0077303 -9.73 0.000 -0.0903927 -0.0600904
_2009 -0.0600308 0.00754 -7.96
0.000
-0.074809 -0.0452526
/cut1 -5.184857 0.0863365 -5.354073 -5.015641
/cut2 1.98576 0.086003 1.817197 2.154323


Correlations


call err_call ab_iz ab_oz ab_zone_avg nibble_sum nibble_rate nibble_sum_2
call 1.0000
err_call 0.2145 1.0000
ab_iz -0.2412 -0.0155 1.0000
ab_oz 0.1420 -0.0507 0.0295 1.0000
ab_zone_avg -0.3239 0.0038 0.6382 -0.5220 1.0000
nibble_sum 0.1135 -0.0428 -0.4006 0.6483 -0.6193 1.0000
nibble_rate 0.1389 -0.0223 -0.4778 0.4242 -0.7819 0.8160 1.0000
nibble_sum_2 0.0364 0.0197 -0.3138 0.5159 -0.3306 0.7705 0.4339 1.0000
nibble_rate_2 0.0429 0.0262 -0.3410 0.4294 -0.3584 0.7020 0.4694 0.9256
ab_swings_iz -0.0262 -0.0470 0.6071 0.2799 0.1340 -0.0870 -0.0983 -0.2306
ab_swings_oz -0.0187 -0.0439 0.0840 0.5184 -0.1388 0.2934 0.1086 0.2636
fishing_avg -0.0089 -0.0093 0.4046 -0.1178 0.2126 -0.2493 -0.1599 -0.3441
swing_nibbe_sum 0.0138 0.0180 -0.4488 -0.0036 -0.1653 0.3144 0.1886 0.4470
swing_nibble_rat 0.0134 0.0155 -0.3668 0.0557 -0.1816 0.3105 0.2108 0.4371
px_rel -0.0869 -0.0393 0.0643 -0.0305 0.0657 -0.0733 -0.0773 -0.0452
zone_height -0.0415 0.0128 0.0350 -0.0411 0.0437 -0.0408 -0.0339 -0.0340
al -0.0094 0.0067 0.0044 -0.0034 0.0045 -0.0062 -0.0051 -0.0051
home_ab -0.0062 -0.0032 -0.0037 0.0054 -0.0056 0.0050 0.0039 0.0060
rhp 0.0117 0.0072 -0.0100 0.0075 -0.0107 0.0122 0.0106 0.0084
rhb -0.0473 -0.0411 0.0447 -0.0517 0.0626 -0.0756 -0.0701 -0.0563
inning_frac 0.0016 -0.0009 -0.0039 0.0108 -0.0144 0.0153 0.0188 0.0095
game_pitches -0.0029 -0.0028 0.0067 0.0339 -0.0198 0.0265 0.0238 0.0197
outs 0.0271 0.0167 0.0069 -0.0572 0.0311 -0.0474 -0.0306 -0.0389
on_1b 0.0003 0.0113 -0.0439 -0.0126 -0.0279 0.0142 0.0264 0.0162
on_2b -0.0021 0.0037 -0.0167 0.0365 -0.0323 0.0391 0.0323 0.0401
on_3b -0.0026 -0.0004 -0.0231 0.0277 -0.0329 0.0374 0.0335 0.0343
base_out_re -0.0212 -0.0069 -0.0412 0.0696 -0.0658 0.0791 0.0658 0.0713
balls 0.0135 -0.0023 0.3127 0.7697 -0.1706 0.4049 0.1706 0.4895
strikes -0.0491 -0.0819 0.5834 0.5478 0.0595 0.0959 -0.0410 -0.0933
ball_strike_re 0.0468 0.0606 -0.1791 0.2207 -0.1681 0.2564 0.1538 0.4767
start_speed 0.0116 0.0210 -0.0147 0.0431 -0.0319 0.0330 0.0254 0.0484
pfx_x -0.0102 -0.0148 0.0309 -0.0093 0.0273 -0.0275 -0.0293 -0.0272
abs_pfx_x -0.0069 0.0108 -0.0331 -0.0133 -0.0150 0.0131 0.0188 0.0262
rel_pfx_x 0.0162 0.0070 -0.0507 0.0287 -0.0585 0.0593 0.0645 0.0355
pfx_z 0.0180 0.0291 -0.0497 0.0179 -0.0386 0.0310 0.0288 0.0556
abs_pfx_z 0.0125 0.0318 -0.0174 -0.0079 -0.0040 -0.0067 -0.0040 0.0228
rel_pfx_z 0.0221 0.0278 -0.0536 0.0216 -0.0428 0.0349 0.0320 0.0591
fastball 0.0245 0.0362 -0.0392 0.0056 -0.0218 0.0184 0.0154 0.0536
_2008 -0.0077 0.0157 0.0056 -0.0026 0.0018 -0.0002 0.0011 -0.0033
_2009 -0.0003 -0.0028 -0.0020 0.0016 -0.0023 0.0006 0.0013 0.0016
nibble_rate_2 ab_swings_iz ab_swings_oz fishing_avg swing_nibbe_sum swing_nibble_rat px_rel zone_height
nibble_rate_2 1.0000
ab_swings_iz -0.2321 1.0000
ab_swings_oz 0.1784 0.1694 1.0000
fishing_avg -0.3275 0.6506 -0.5167 1.0000
swing_nibbe_sum 0.3873 -0.7267 0.2918 -0.7369 1.0000
swing_nibble_rat 0.4423 -0.6287 0.3016 -0.7552 0.9110 1.0000
px_rel -0.0468 0.0209 0.0144 0.0078 -0.0129 -0.0132 1.0000
zone_height -0.0313 0.0170 -0.0212 0.0268 -0.0356 -0.0349 0.0116 1.0000
al -0.0048 -0.0023 -0.0020 0.0001 0.0025 0.0024 -0.0257 -0.0487
home_ab 0.0059 -0.0038 -0.0011 -0.0017 0.0029 0.0032 0.0025 -0.0365
rhp 0.0081 0.0018 0.0064 -0.0036 0.0038 0.0037 -0.0175 -0.0169
rhb -0.0546 0.0064 -0.0040 0.0077 -0.0128 -0.0140 0.3276 0.0254
inning_frac 0.0112 0.0204 0.0196 0.0042 -0.0070 -0.0090 0.0020 -0.0028
game_pitches 0.0193 0.0307 0.0255 0.0081 -0.0132 -0.0129 -0.0014 -0.0096
outs -0.0338 0.0051 0.0161 -0.0043 0.0047 -0.0025 0.0139 0.0105
on_1b 0.0218 -0.0003 -0.0012 0.0019 -0.0005 -0.0048 -0.0330 0.0002
on_2b 0.0380 0.0156 0.0180 0.0007 -0.0034 -0.0029 -0.0080 0.0002
on_3b 0.0330 0.0122 0.0216 -0.0039 0.0023 0.0022 -0.0045 0.0007
base_out_re 0.0675 0.0122 0.0107 0.0019 -0.0043 -0.0008 -0.0293 -0.0055
balls 0.4353 0.2356 0.1694 0.0707 -0.1216 -0.0473 -0.0148 -0.0114
strikes -0.1896 0.5799 0.4865 0.1520 -0.2562 -0.2141 0.0365 -0.0105
ball_strike_re 0.4636 -0.2694 -0.2515 -0.0591 0.1031 0.1229 -0.0411 -0.0014
start_speed 0.0477 -0.0004 -0.0078 0.0037 -0.0052 -0.0022 -0.0121 -0.0084
pfx_x -0.0290 0.0203 0.0141 0.0073 -0.0110 -0.0103 0.1288 0.0059
abs_pfx_x 0.0301 -0.0443 -0.0341 -0.0141 0.0227 0.0215 -0.0452 -0.0028
rel_pfx_x 0.0377 -0.0132 -0.0051 -0.0073 0.0129 0.0123 -0.0619 -0.0250
pfx_z 0.0603 -0.0399 -0.0461 -0.0029 0.0089 0.0097 0.0271 0.0241
abs_pfx_z 0.0238 -0.0273 -0.0376 0.0026 0.0023 0.0017 0.0100 0.0248
rel_pfx_z 0.0635 -0.0418 -0.0441 -0.0058 0.0128 0.0134 0.0255 -0.0766
fastball 0.0553 -0.0388 -0.0418 -0.0043 0.0114 0.0116 -0.0371 0.0119
_2008 -0.0032 0.0095 0.0027 0.0064 -0.0059 -0.0053 0.0186 0.1381
_2009 0.0016 -0.0027 -0.0016 -0.0008 0.0016 0.0022 -0.0221 -0.0720
al home_ab rhp rhb inning_frac game_pitches outs on_1b
al 1.0000
home_ab 0.0029 1.0000
rhp -0.0209 -0.0034 1
rhb -0.0410 -0.0010 -0.1858 1.0000
inning_frac -0.0100 -0.0442 0.0622 -0.0017 1.0000
game_pitches -0.0023 0.0491 0.0631 -0.0047 0.9631 1.0000
outs -0.0042 -0.0076 0.0073 0.0166 0.0967 0.0389 1.0000
on_1b 0.0050 0.0084 -0.0081 0.0060 0.0259 0.0500 0.1653 1.0000
on_2b -0.0012 0.0057 -0.0023 0.0099 0.0249 0.0485 0.1549 0.2103
on_3b 0.0042 0.0106 0.0054 0.0068 0.0172 0.0370 0.1354 0.1816
base_out_re 0.0073 0.0154 -0.0053 -0.0011 -0.0356 0.0294 -0.4387 0.4070
balls 0.0004 0.0093 -0.0059 -0.0230 -0.0004 0.0251 -0.0779 -0.0180
strikes -0.0007 -0.0057 0.0070 -0.0039 0.0086 0.0197 0.0130 -0.0413
ball_strike_re 0.0002 0.0126 -0.0119 -0.0165 -0.0082 0.0060 -0.0868 0.0170
start_speed 0.0273 -0.0056 0.1308 -0.0211 0.0613 0.0644 0.0013 0.0294
pfx_x -0.0084 0.0010 -0.5606 0.1880 -0.0183 -0.0212 0.0125 -0.0055
abs_pfx_x 0.0342 0.0014 -0.0561 -0.0257 -0.0084 -0.0061 -0.0148 0.0128
rel_pfx_x 0.0221 -0.0057 -0.1291 -0.2229 -0.0395 -0.0388 -0.0195 0.0010
pfx_z 0.0259 -0.0039 -0.0250 0.0102 -0.0452 -0.0395 -0.0419 0.0094
abs_pfx_z 0.0373 -0.0034 -0.0533 0.0046 -0.0568 -0.0541 -0.0312 -0.0145
rel_pfx_z 0.0301 -0.0003 -0.0225 0.0065 -0.0449 -0.0385 -0.0430 0.0093
fastball 0.0094 -0.0062 0.0088 -0.0164 -0.0013 0.0038 -0.0319 0.0149
_2008 -0.0016 -0.0009 -0.0059 0.0080 0.0051 0.0016 -0.0004 0.0056
_2009 0.0042 0.0006 0.0100 -0.0206 -0.0027 0.0012 -0.0031 0.0019
on_2b on_3b base_out_re balls strikes ball_strike_re start_speed pfx_x
on_2b 1.0000
on_3b 0.2113 1.0000
base_out_re 0.5335 0.5358 1.0000
balls 0.0362 0.0208 0.0765 1.0000
strikes -0.0045 -0.0063 -0.0271 0.3063 1.0000
ball_strike_re 0.0353 0.0234 0.0944 0.6092 -0.5057 1.0000
start_speed 0.0049 0.0125 0.0195 0.0778 -0.0377 0.1061 1.0000
pfx_x 0.0078 0.0003 -0.0071 -0.0156 0.0323 -0.0396 -0.2981 1.0000
abs_pfx_x -0.0077 -0.0054 0.0096 0.0129 -0.0628 0.0604 0.1010 -0.1462
rel_pfx_x -0.0134 -0.0149 -0.0007 0.0145 -0.0254 0.0327 -0.0148 0.1326
pfx_z -0.0268 -0.0212 0.0064 0.0682 -0.0944 0.1413 0.6904 -0.1686
abs_pfx_z -0.0339 -0.0263 -0.0140 0.0350 -0.0633 0.0909 0.4190 -0.0635
rel_pfx_z -0.0267 -0.0213 0.0070 0.0688 -0.0937 0.1413 0.6865 -0.1692
fastball -0.0174 -0.0083 0.0128 0.0596 -0.0926 0.1379 0.7242 -0.2195
_2008 0.0057 0.0036 0.0063 0.0016 0.0031 -0.0012 -0.0210 0.0053
_2009 0.0002 0.0017 0.0034 0.0045 -0.0004 0.0043 0.0117 -0.0118
abs_pfx_x rel_pfx_x pfx_z abs_pfx_z rel_pfx_z fastball _2008 _2009
abs_pfx_x 1.0000
rel_pfx_x 0.1220 1.0000
pfx_z 0.0185 0.0469 1.0000
abs_pfx_z -0.0037 -0.0359 0.6803 1.0000
rel_pfx_z 0.0187 0.0507 0.9904 0.6716 1.0000
fastball 0.1258 -0.0458 0.6258 0.5321 0.6200 1.0000
_2008 0.0132 0.0017 0.0378 0.0316 0.0234 0.0642 1.0000
_2009 -0.0023 0.0032 0.0182 0.0281 0.0266 -0.0101 -0.5446 1.0000


Empty Counts Only


Ordered logistic  regression Number of obs = 371145
LR chi2(26) = 54209.03
Prob > chi2 = 0
Log likelihood = -175915.22 Pseudo R2 = 0.134
call Coef. Std. Err. z P>z [95% Conf. Interval]
err_call 2.0452 0.0128 159.56 0.000 2.0201 2.0703
nibble_x 0.4789 0.0124 38.70 0.000 0.4546 0.5032
nibble_z 0.9071 0.0115 78.75 0.000 0.8845 0.9297
px_rel -0.1847 0.0055 -33.74 0.000 -0.1955 -0.1740
zone_height -0.5588 0.0379 -14.76 0.000 -0.6330 -0.4846
AL -0.0471 0.0093 -5.05 0.000 -0.0653 -0.0288
home_ab -0.0241 0.0099 -2.45 0.014 -0.0435 -0.0048
rhp 0.0769 0.0133 5.80 0.000 0.0509 0.1029
rhb -0.0069 0.0107 -0.64 0.519 -0.0280 0.0141
inning_frac 0.0212 0.0069 3.05 0.002 0.0076 0.0348
game_pitches -0.0009 0.0002 -4.46 0.000 -0.0013 -0.0005
outs -0.0201 0.0134 -1.50 0.133 -0.0464 0.0062
on_1b -0.0007 0.0150 -0.05 0.960 -0.0301 0.0287
on_2b 0.0617 0.0218 2.83 0.005 0.0189 0.1044
on_3b 0.0979 0.0289 3.39 0.001 0.0413 0.1546
base_out_re -0.2875 0.0404 -7.12 0.000 -0.3666 -0.2084
start_speed -0.0108 0.0013 -8.28 0.000 -0.0133 -0.0082
pfx_x 0.0031 0.0010 3.21 0.001 0.0012 0.0050
abs_pfx_x -0.0089 0.0015 -5.83 0.000 -0.0118 -0.0059
rel_pfx_x -0.0001 0.0008 -0.11 0.914 -0.0016 0.0014
pfx_z -0.0139 0.0088 -1.57 0.116 -0.0311 0.0034
abs_pfx_z -0.0080 0.0019 -4.20 0.000 -0.0118 -0.0043
rel_pfx_z 0.0434 0.0154 2.82 0.005 0.0132 0.0736
fastball 0.1421 0.0151 9.43 0.000 0.1125 0.1716
_2008 -0.0784 0.0118 -6.64 0.000 -0.1015 -0.0552
_2009 -0.0627 0.0115 -5.45 0.000 -0.0853 -0.0402
/cut1 -4.8842 0.1286 -5.1361 -4.6322
/cut2 0.8861 0.1281 0.6351 1.1371


Correlations


call err_call nibble_x nibble_z px_rel zone_height AL home_ab
call 1.0000
err_call 0.2357 1.0000
nibble_x 0.1951 -0.0674 1.0000
nibble_z 0.2597 0.0904 0.6894 1.0000
px_rel -0.0975 -0.0442 -0.1235 -0.0637 1.0000
zone_height -0.0495 0.0075 -0.0257 -0.0428 0.0167 1.0000
AL -0.0056 0.0081 -0.0043 -0.0044 -0.0230 -0.0480 1.0000
home_ab -0.0065 -0.0033 0.0048 0.0009 0.0044 -0.0352 0.0019 1.0000
rhp 0.0179 0.0113 0.0119 0.0063 -0.0827 -0.0171 -0.0235 -0.0024
rhb -0.0552 -0.0513 -0.0734 -0.0521 0.3669 0.0249 -0.0333 -0.0003
inning_frac -0.0024 -0.0035 0.0293 0.0243 0.0025 -0.0056 -0.0091 -0.0453
game_pitches -0.0054 -0.0038 0.0327 0.0266 -0.0006 -0.0116 -0.0026 0.0466
outs 0.0084 0.0050 -0.0158 -0.0196 0.0187 0.0120 -0.0041 -0.0072
on_1b -0.0053 0.0065 0.0398 0.0220 -0.0196 -0.0038 0.0079 0.0082
on_2b -0.0067 -0.0005 0.0332 0.0198 -0.0011 -0.0001 -0.0008 0.0042
on_3b -0.0041 -0.0001 0.0360 0.0231 -0.0026 0.0019 0.0046 0.0099
base_out_re -0.0145 -0.0026 0.0622 0.0456 -0.0228 -0.0074 0.0082 0.0139
start_speed 0.0075 0.0148 0.0151 0.0015 -0.0189 -0.0149 0.0290 -0.0069
pfx_x -0.0213 -0.0203 -0.0311 -0.0169 0.1682 0.0103 -0.0077 0.0001
abs_pfx_x -0.0045 0.0105 0.0251 0.0008 -0.0506 -0.0059 0.0364 0.0007
rel_pfx_x 0.0248 0.0176 0.0717 0.0547 -0.0840 -0.0280 0.0220 -0.0043
pfx_z 0.0129 0.0208 0.0044 0.0045 0.0358 0.0153 0.0313 -0.0056
abs_pfx_z 0.0067 0.0197 -0.0161 -0.0026 0.0229 0.0197 0.0401 -0.0042
rel_pfx_z 0.0185 0.0201 0.0069 0.0085 0.0332 -0.0905 0.0358 -0.0021
fastball 0.0178 0.0257 0.0012 -0.0080 -0.0316 0.0047 0.0124 -0.0084
_2008 -0.0067 0.0214 0.0047 0.0014 0.0209 0.1320 0.0004 -0.0008
_2009 0.0003 -0.0052 0.0022 0.0036 -0.0270 -0.0647 0.0029 -0.0017
rhp rhb inning_frac game_pitches outs on_1b on_2b on_3b
rhp 1.0000
rhb -0.1819 1.0000
inning_frac 0.0637 -0.0021 1.0000
game_pitches 0.0648 -0.0055 0.9618 1.0000
outs 0.0050 0.0162 0.1004 0.0419 1.0000
on_1b -0.0048 0.0088 0.0305 0.0543 0.1747 1.0000
on_2b -0.0052 0.0109 0.0267 0.0492 0.1593 0.2184 1.0000
on_3b 0.0059 0.0071 0.0189 0.0382 0.1384 0.1872 0.2175 1.0000
base_out_re -0.0044 0.0007 -0.0359 0.0294 -0.4464 0.4086 0.5248 0.5275
start_speed 0.1344 -0.0160 0.0459 0.0499 -0.0047 0.0111 -0.0443 -0.0212
pfx_x -0.5806 0.1955 -0.0172 -0.0199 0.0171 -0.0020 0.0244 0.0090
abs_pfx_x -0.0628 -0.0337 -0.0110 -0.0089 -0.0150 0.0087 -0.0214 -0.0141
rel_pfx_x -0.1446 -0.2365 -0.0393 -0.0380 -0.0155 0.0015 -0.0111 -0.0148
pfx_z -0.0219 0.0118 -0.0736 -0.0668 -0.0577 -0.0219 -0.0804 -0.0609
abs_pfx_z -0.0506 -0.0027 -0.0841 -0.0802 -0.0455 -0.0450 -0.0765 -0.0576
rel_pfx_z -0.0193 0.0078 -0.0730 -0.0657 -0.0590 -0.0218 -0.0801 -0.0611
fastball 0.0199 -0.0217 -0.0249 -0.0186 -0.0500 -0.0186 -0.0752 -0.0500
_2008 -0.0054 0.0069 0.0017 -0.0020 0.0001 0.0039 0.0062 0.0052
_2009 0.0091 -0.0213 -0.0021 0.0019 -0.0022 0.0032 -0.0003 0.0014
base_out_re start_speed pfx_x abs_pfx_x rel_pfx_x pfx_z abs_pfx_z rel_pfx_z
base_out_re 1.0000
start_speed -0.0181 1.0000
pfx_x 0.0014 -0.3077 1.0000
abs_pfx_x -0.0005 0.1297 -0.1456 1.0000
rel_pfx_x -0.0018 -0.0026 0.1501 0.1341 1.0000
pfx_z -0.0351 0.6967 -0.1626 0.0153 0.0472 1.0000
abs_pfx_z -0.0473 0.4179 -0.0634 -0.0165 -0.0449 0.6937 1.0000
rel_pfx_z -0.0343 0.6925 -0.1633 0.0160 0.0512 0.9897 0.6849 1.0000
fastball -0.0303 0.7189 -0.2292 0.1395 -0.0479 0.6229 0.5227 0.6169
_2008 0.0062 -0.0267 0.0062 0.0144 0.0013 0.0304 0.0300 0.0160
_2009 0.0032 0.0152 -0.0125 -0.0022 0.0046 0.0225 0.0283 0.0304
fastball _2008 _2009
fastball 1.0000
_2008 0.0636 1.0000
_2009 -0.0055 -0.5406 1.0000

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