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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