December 31, 2001

If Pedro Plunked You, He Probably Meant It
by Steve Lombardi

A recent exchange with a fellow baseball fan left me thinking about the possibility of statistically measuring (to some extent) "intent" with respect to pitchers throwing at batters.  For a handle, I immediately began thinking of Brushback Average, or BBA.

The obvious place to start was Hit By Pitch (HBP) totals - - relative to Batters Faced (BF).  However, BF statistics were not kept for parts of the early 1900s.  Therefore, if one were to pursue this approach, and intended on utilizing a HBP/BF ratio, an "estimation of batters faced" (herein "eBF") would have to suffice.  To this end, the formula eBF equals (Innings Pitched*2.82)+Hits+Walks was used - - enabling pitchers with incomplete official BF totals (such as Pink Hawley, Win Mercer, Cy Seymour, Nixey Callahan, Ed Doheny, Wiley Piatt, Clark Griffith, et al) to be included in the study.

But, a ratio of HBP/eBF only illustrates the estimated percentage of the number of batters faced whom were hit by a pitch.  Still, the matter of "intent" needed to be factored into the process.

"Command" ratio (Strikeouts per Walks Allowed) quickly came to mind as means to address this need.  As a measure of a pitcher's ability to throw strikes over balls, it can also be used as in indication of a pitcher's ability to place his pitches.

Therefore, in this examination, HBP/eBF will be factored by Command - - making this interim tool appear as [{HBP/eBF}*{K/BB}].  

The label interim is applied due to some tweaking which was applied to the final tally.  In order to provide a more user friendly appearance to these results, something more along the lines of a "batting-average-ish" number, a multiplier of ten was used.  Thus, yielding the final equation of:

BBA = [{HBP/eBF}*{K/BB}]*10

This in hand, Brushback Average (BBA) was calculated for all pitchers with 1,500+ career innings pitched (IP) - - during the years 1900 through 2001.  What follows are the top twenty, in terms of BBA, for those captured within the aforementioned IP parameter:

Rate Rank HBP Rank PITCHER HBP IP H BB SO eBF HBP/eBF Command BBA
1 T95 Pedro Martinez 75 1692.67 1262 467 1981 6502.33 0.0115 4.24 0.489
13 13 Randy Johnson 125 2748 2113 1160 3412 11022.36 0.0113 2.94 0.334
14 T7 Don Drysdale 154 3432 3084 855 2486 13617.24 0.0113 2.91 0.329
17 4 Jim Bunning 160 3759.33 3433 1000 2855 15034.31 0.0106 2.86 0.304
21 T57 Pedro Astacio 89 1742.67 1798 572 1366 7284.33 0.0122 2.39 0.292
23 T42 Jesse Tannehill 97 1940 1886 323 739 7679.80 0.0126 2.29 0.289
25 T18 Kevin Brown 119 2776 2588 768 2021 11184.32 0.0106 2.63 0.280
26 T25 Rube Waddell 108 2868.33 2374 783 2267 11245.69 0.0096 2.90 0.278
38 T10 Roger Clemens 129 3886.67 3306 1258 3717 15524.41 0.0083 2.95 0.246
43 2 Eddie Plank 193 4227.33 3746 1018 2099 16685.07 0.0116 2.06 0.239
49 T42 Greg Maddux 97 3550.67 3206 760 2523 13978.89 0.0069 3.32 0.230
55 1 Walter Johnson 203 5914.67 4907 1363 3509 22949.37 0.0088 2.57 0.228
57 24 Darryl Kile 109 2080.33 2053 890 1618 8809.53 0.0124 1.82 0.225
63 T59 Tim Wakefield 88 1512.67 1498 644 1020 6407.73 0.0137 1.58 0.218
64 6 Bert Blyleven 155 4970 4632 1322 3701 19969.40 0.0078 2.80 0.217
65 T75 Cy Young 81 3634.33 3237 449 1678 13934.81 0.0058 3.74 0.217
68 28 David Cone 106 2880.33 2484 1124 2655 11730.53 0.0090 2.36 0.213
69 T176 Bret Saberhagen 59 2562.67 2452 471 1715 10149.73 0.0058 3.64 0.212
76 T50 Chief Bender 95 2839.67 2447 675 1622 11129.87 0.0085 2.40 0.205
78 T18 Doc White 119 3040.67 2743 670 1384 11987.69 0.0099 2.07 0.205

"HBP Rank," above, is where the pitcher resides on the all-time career total list of HBP.  "Rate Rank" is where the pitcher ranks, in terms of Brushback Average, all-time, of pitchers with 25+ career HBP who pitched from 1900 to 2001.

At this junction, it is significant to again stress that the statistic of BBA should be thought of in terms of a "probability" (or intent) ratio.  The higher the ratio compared to other pitchers, the greater the probability of the pitcher's intent to brushback and/or hit batters.  However, while it is not a "real number," as long as the equation is applied universally to all pitchers in a study, it does allow for some comparative analysis.

And, the analysis here is that Pedro Martinez is head and shoulders the leader of the class.  It is somewhat safe to assume that, if you were a batter hit by one of Pedro's pitches, Mr. Martinez has some intent behind his offerings.

In fact, only seven pitchers in the history of the game (with 25+ career HBP during 1900-2001) have a BBA of .400 or greater.  And, Pedro is still the top of that chart as well.  

What follows are the top twenty, in terms of BBA, for all pitchers with 25+ career HBP - - during the years 1900 through 2001:

Rate Rank HBP Rank PITCHER HBP IP H BB SO eBF HBP/eBF Command BBA
1 T95 Pedro Martinez 75 1692.67 1262 467 1981 6502.33 0.0115 4.24 0.489
2 T163 Rolando Arrojo 61 618.67 632 228 461 2604.65 0.0234 2.02 0.474
3 T604 Esteban Yan 32 368.67 410 136 309 1585.65 0.0202 2.27 0.459
4 T367 Scott Sullivan 42 534 457 194 443 2156.88 0.0195 2.28 0.445
5 T308 Jeff Weaver 46 592.67 616 176 402 2463.33 0.0187 2.28 0.427
6 T604 Ryan Rupe 32 376.67 418 136 281 1616.21 0.0198 2.07 0.409
7 T225 Jeff Nelson 53 620.33 494 331 648 2574.33 0.0206 1.96 0.403
8 T773 Paul Wilson 27 351.33 360 139 268 1489.75 0.0181 1.93 0.349
9 T732 Steve Woodard 28 632 739 136 438 2657.24 0.0105 3.22 0.339
10 T816 Mike James 26 302.67 273 144 237 1270.53 0.0205 1.65 0.337
11 T660 Kerry Wood 30 478 356 264 582 1967.96 0.0152 2.20 0.336
12 T557 Harry Krause 34 525.67 446 146 298 2074.39 0.0164 2.04 0.335
13 13 Randy Johnson 125 2748 2113 1160 3412 11022.36 0.0113 2.94 0.334
14 T7 Don Drysdale 154 3432 3084 855 2486 13617.24 0.0113 2.91 0.329
15 T95 Mark Leiter 75 1184 1205 424 892 4967.88 0.0151 2.10 0.318
16 T435 Doug Jones 39 1128.33 1155 247 909 4583.89 0.0085 3.68 0.313
17 4 Jim Bunning 160 3759.33 3433 1000 2855 15034.31 0.0106 2.86 0.304
18 T476 Mel Rojas 37 666.33 591 254 562 2724.05 0.0136 2.21 0.301
19 T557 Bob Wells 34 577.33 610 184 387 2422.07 0.0140 2.10 0.295
20 T557 Steve Reed 34 641 583 217 488 2607.62 0.0130 2.25 0.293
21 T57 Pedro Astacio 89 1742.67 1798 572 1366 7284.33 0.0122 2.39 0.292

As before, "HBP Rank," above, is where the pitcher resides on the all-time career total list of HBP.  "Rate Rank" is where the pitcher ranks, in terms of Brushback Average, all-time, of pitchers with 25+ career HBP who pitched from 1900 to 2001.

What is very interesting about this list is the presence of so many current day pitchers.  No wonder why we see so many highlights (?) of batters charging mounds following brushbacks on ESPN's "SportsCenter" every evening.

For those interested in how the Top 100 all-time HBP leaders (from 1900-2001) rank in terms of BBA, the following chart is included:

Rate Rank HBP Rank PITCHER HBP IP H BB SO eBF HBP/eBF Command BBA
1 T95 Pedro Martinez 75 1692.67 1262 467 1981 6502.33 0.0115 4.24 0.489
13 13 Randy Johnson 125 2748 2113 1160 3412 11022.36 0.0113 2.94 0.334
14 T7 Don Drysdale 154 3432 3084 855 2486 13617.24 0.0113 2.91 0.329
15 T95 Mark Leiter 75 1184 1205 424 892 4967.88 0.0151 2.10 0.318
17 4 Jim Bunning 160 3759.33 3433 1000 2855 15034.31 0.0106 2.86 0.304
21 T57 Pedro Astacio 89 1742.67 1798 572 1366 7284.33 0.0122 2.39 0.292
23 T42 Jesse Tannehill 97 1940 1886 323 739 7679.80 0.0126 2.29 0.289
25 T18 Kevin Brown 119 2776 2588 768 2021 11184.32 0.0106 2.63 0.280
26 T25 Rube Waddell 108 2868.33 2374 783 2267 11245.69 0.0096 2.90 0.278
37 T80 Aaron Sele 79 1466.33 1580 548 1082 6263.05 0.0126 1.97 0.249
38 T10 Roger Clemens 129 3886.67 3306 1258 3717 15524.41 0.0083 2.95 0.246
43 2 Eddie Plank 193 4227.33 3746 1018 2099 16685.07 0.0116 2.06 0.239
49 T42 Greg Maddux 97 3550.67 3206 760 2523 13978.89 0.0069 3.32 0.230
53 22 Jack Warhop 114 1412 1366 400 463 5747.84 0.0198 1.16 0.230
55 1 Walter Johnson 203 5914.67 4907 1363 3509 22949.37 0.0088 2.57 0.228
57 24 Darryl Kile 109 2080.33 2053 890 1618 8809.53 0.0124 1.82 0.225
63 T59 Tim Wakefield 88 1512.67 1498 644 1020 6407.73 0.0137 1.58 0.218
64 6 Bert Blyleven 155 4970 4632 1322 3701 19969.40 0.0078 2.80 0.217
65 T75 Cy Young 81 3634.33 3237 449 1678 13934.81 0.0058 3.74 0.217
68 28 David Cone 106 2880.33 2484 1124 2655 11730.53 0.0090 2.36 0.213
76 T50 Chief Bender 95 2839.67 2447 675 1622 11129.87 0.0085 2.40 0.205
78 T18 Doc White 119 3040.67 2743 670 1384 11987.69 0.0099 2.07 0.205
79 T39 Don Cardwell 98 2122.33 2009 671 1211 8664.97 0.0113 1.80 0.204
90 T88 Al Leiter 77 1690 1490 805 1449 7060.80 0.0109 1.80 0.196
92 T42 Frank Lary 97 2161.67 2123 616 1099 8834.91 0.0110 1.78 0.196
103 T50 Cy Morgan 95 1445.67 1180 578 667 5834.79 0.0163 1.15 0.188
106 T95 Dennis Eckersley 75 3285.67 3076 738 2401 13079.59 0.0057 3.25 0.187
108 T72 Otto Hess 83 1419.33 1355 448 580 5805.51 0.0143 1.29 0.185
109 T29 Jim Lonborg 105 2464 2400 823 1475 10171.48 0.0103 1.79 0.185
113 T34 Jack Chesbro 102 2747.67 2477 631 1237 10856.43 0.0094 1.96 0.184
114 27 Barney Pelty 107 1918.67 1663 532 693 7605.65 0.0141 1.30 0.183
115 21 Orel Hershiser 117 3130.33 2939 1007 2014 12773.53 0.0092 2.00 0.183
118 64 Mike Boddicker 87 2123.67 2082 721 1330 8791.75 0.0099 1.84 0.183
124 T72 Todd Stottlemyre 83 2171 2174 809 1575 9105.22 0.0091 1.95 0.177
126 T10 Dave Stieb 129 2895.33 2572 1034 1669 11770.83 0.0110 1.61 0.177
133 T7 Joe McGinnity 154 3074.67 2918 719 994 12307.57 0.0125 1.38 0.173
137 T95 Willie Mitchell 75 1632.67 1464 605 921 6673.13 0.0112 1.52 0.171
152 T10 Frank Tanana 129 4188.33 4063 1255 2773 17129.09 0.0075 2.21 0.166
156 T47 Harry McIntire 96 1650.67 1555 539 626 6748.89 0.0142 1.16 0.165
159 T84 Dwight Gooden 78 2800.67 2564 954 2293 11415.89 0.0068 2.40 0.164
161 T59 Jakie May 88 1563 1645 617 765 6669.66 0.0132 1.24 0.164
164 54 Mickey Lolich 92 3640 3366 1099 2832 14729.80 0.0062 2.58 0.161
169 T39 Jack Billingham 98 2230.67 2272 750 1141 9312.49 0.0105 1.52 0.160
175 3 Charlie Hough 174 3801.33 3283 1665 2362 15667.75 0.0111 1.42 0.158
180 T88 Dazzy Vance 77 2966.33 2809 840 2045 12014.05 0.0064 2.43 0.156
190 T34 Bob Gibson 102 3885 3279 1336 3117 15570.70 0.0066 2.33 0.153
191 T29 Jeff Pfeffer 105 2408.33 2320 592 836 9703.49 0.0108 1.41 0.153
193 T31 Long Tom Hughes 104 2643 2610 853 1368 10916.26 0.0095 1.60 0.153
194 53 Ed Willett 93 1545.33 1450 491 508 6298.83 0.0148 1.03 0.153
198 T59 Scott Erickson 88 2106 2281 745 1152 8964.92 0.0098 1.55 0.152
205 T70 Ferguson Jenkins 84 4500.67 4142 997 3192 17830.89 0.0047 3.20 0.151
207 15 Jim Kaat 122 4530.33 4620 1083 2461 18478.53 0.0066 2.27 0.150
212 T66 Tom Candiotti 85 2724.33 2662 883 1735 11227.61 0.0076 1.96 0.149
215 5 Nolan Ryan 158 5386 3923 2795 5714 21906.52 0.0072 2.04 0.147
222 T75 Danny Darwin 81 3016.67 2951 874 1942 12332.01 0.0066 2.22 0.146
224 T78 Omar Olivares 80 1591.33 1678 685 853 6850.55 0.0117 1.25 0.145
225 T55 Joe Coleman 90 2570.67 2416 1003 1728 10668.29 0.0084 1.72 0.145
235 65 Harry Howell 86 2340.33 2172 597 926 9368.73 0.0092 1.55 0.142
248 T31 Ed Reulbach 104 2363 1884 823 1020 9370.66 0.0111 1.24 0.138
253 T84 Sam Leever 78 2248.67 2070 460 711 8871.25 0.0088 1.55 0.136
254 T18 Dennis Martinez 119 3908.67 3788 1146 2087 15956.45 0.0075 1.82 0.136
258 T66 Hippo Vaughn 85 2730.33 2461 817 1416 10977.53 0.0077 1.73 0.134
277 T80 Kevin Gross 79 2487.67 2519 986 1727 10520.23 0.0075 1.75 0.132
280 T59 Rick Reuschel 88 3548.33 3588 935 2015 14529.29 0.0061 2.16 0.131
287 T25 Gaylord Perry 108 5350.33 4938 1379 3534 21404.93 0.0050 2.56 0.129
294 T47 Togie Pittinger 96 2040.33 2017 734 832 8504.73 0.0113 1.13 0.128
297 T66 Lefty Leifield 85 1838 1673 554 616 7410.16 0.0115 1.11 0.128
323 T50 Rube Benton 95 2517.67 2472 712 950 10283.83 0.0092 1.33 0.123
337 T88 Bill Duggleby 77 1677.33 1766 405 440 6901.07 0.0112 1.09 0.121
346 T84 Tully Sparks 78 2158.33 2039 543 725 8668.49 0.0090 1.34 0.120
351 T95 Casey Patten 75 2063 2154 557 757 8528.66 0.0088 1.36 0.120
358 T80 Bob Welch 79 3092 2894 1034 1969 12647.44 0.0062 1.90 0.119
363 T47 Earl Moore 96 2581 2290 1009 1307 10577.42 0.0091 1.30 0.118
368 T59 Jack Coombs 88 2320.67 2034 841 1052 9419.29 0.0093 1.25 0.117
374 T95 Chuck Finley 75 3006.33 2886 1254 2436 12617.85 0.0059 1.94 0.115
385 9 Howard Ehmke 132 2767.33 2804 1017 1012 11624.87 0.0114 1.00 0.113
390 T70 Wild Bill Donovan 84 2851.67 2508 977 1505 11526.71 0.0073 1.54 0.112
425 T75 Jack Powell 81 3448 3313 762 1380 13798.36 0.0059 1.81 0.106
433 T91 Tom Seaver 76 4782.67 3971 1390 3640 18848.13 0.0040 2.62 0.106
435 T16 George Mullin 121 3451.33 3275 1131 1394 14138.75 0.0086 1.23 0.105
440 T34 Chick Fraser 102 2204.33 2175 836 792 9227.21 0.0111 0.95 0.105
446 T42 Vic Willis 97 3343.33 3080 947 1371 13455.19 0.0072 1.45 0.104
447 T66 Tommy Byrne 85 1362.67 1138 1037 766 6017.73 0.0141 0.74 0.104
448 74 Don Sutton 82 5282.33 4692 1343 3574 20931.17 0.0039 2.66 0.104
449 38 Wilbur Cooper 100 3482 3415 853 1252 14087.24 0.0071 1.47 0.104
458 14 Phil Niekro 123 5404.33 5044 1809 3342 22093.21 0.0056 1.85 0.103
470 23 George Uhle 113 3119.33 3417 966 1135 13179.51 0.0086 1.17 0.101
487 T80 Charlie Root 79 3197 3252 889 1459 13156.54 0.0060 1.64 0.099
488 T91 George Mogridge 76 2256 2350 565 679 9276.92 0.0082 1.20 0.098
500 T16 Hooks Dauss 121 3390.33 3407 1064 1201 14031.73 0.0086 1.13 0.097
522 T78 Jim Perry 80 3286.33 3127 998 1576 13392.45 0.0060 1.58 0.094
537 T39 Tommy John 98 4710.33 4783 1259 2245 19325.13 0.0051 1.78 0.090
558 T91 Rip Collins 76 1712 1795 674 569 7296.84 0.0104 0.84 0.088
567 T57 Carl Mays 89 3020.67 2912 734 862 12164.29 0.0073 1.17 0.086
602 T84 Jack Quinn 78 3319 3614 732 1047 13705.58 0.0057 1.43 0.081
633 T55 Lee Meadows 90 3150.67 3280 956 1063 13120.89 0.0069 1.11 0.076
644 33 Red Faber 103 4087 4106 1213 1471 16844.34 0.0061 1.21 0.074
711 T42 Burleigh Grimes 97 4180 4412 1295 1512 17494.60 0.0055 1.17 0.065
730 37 Earl Whitehill 101 3563 3917 1431 1350 15395.66 0.0066 0.94 0.062
786 T91 Eppa Rixey 76 4494 4633 1082 1350 18388.08 0.0041 1.25 0.052

Again, "HBP Rank," above, is where the pitcher resides on the all-time career total list of HBP.  "Rate Rank" is where the pitcher ranks, in terms of Brushback Average, all-time, of pitchers with 25+ career HBP who pitched from 1900 to 2001.

Note the placement of some of baseball's "celebrated" and reputed brushback artists on this list.  Carl Mays, Burleigh Grimes, Bob Gibson, Dennis Martinez, Danny Darwin, Kevin Gross - - sure, they have some high totals of HBP; but, based on their BBA, the issue of "intent" is not as clear as it is with Pedro, Randy Johnson, or Drysdale.

Also interesting, in expanding the list to capture the Top 100 HBP leaders, are some of the one-on-one comparisons which arise via the BBA rankings.  For example, Roger Clemens, often labeled as one not afraid to provide a close shave to a batter, has a BBA (.246) which is comparable to Aaron Sele (.249).  Yet, you rarely hear about "Sele the Intimidator." 

Seeing both Leiter brothers in Top 90 of BBA certainly makes one ponder how many plunkings occurred between the two brothers, as they grew up, playing whiffle-ball in their backyard in southern New Jersey?

Lastly, it seems that a brushback artist (as defined by BBA) was more common place in the periods 1900 to 1929, 1950 to 1969, and 1990 forward.  Tannehill, Plank and the Big Train were around in the early 1900s.  Drysdale and Bunning were the BBA kings during the '50s and '60s.   And, in the 1990s, along came the Big Unit and Pedro.

The '30s, '40s, '70s and '80's seemed peaceful, by BBA standards.  In fact, if you look at the Brushback Average leaders during the periods 1930 to 1949 and 1970 to 1989, you will find the following as the "Top Tens":

1930 to 1949:

PITCHER HBP IP H BB SO eBF HBP/eBF Command BBA
Tommy Byrne 26 375 244 329 251 1630.50 0.0159 0.76 0.122
Ed Holley 25 517 571 154 159 2182.94 0.0115 1.03 0.118
Roy Parmelee 54 1114.1 1062 528 513 4731.76 0.0114 0.97 0.111
Bill Swift 36 1637.1 1682 351 636 6649.62 0.0054 1.81 0.098
Chief Hogsett 59 1192 1477 492 432 5330.44 0.0111 0.88 0.097
Charlie Root 48 2048 2121 536 914 8432.36 0.0057 1.71 0.097
Boom-Boom Beck 37 973 1052 316 329 4111.86 0.0090 1.04 0.094
Dizzy Dean 27 1967.1 1919 453 1163 7919.22 0.0034 2.57 0.088
Harry Brecheen 27 1386.1 1242 378 666 5528.80 0.0049 1.76 0.086
Earl Caldwell 25 553 610 242 196 2411.46 0.0104 0.81 0.084

1970 to 1989:

PITCHERS HBP IP H BB SO eBF HBP/eBF Command BBA
Mitch Williams 32 356.1 251 272 347 1527.20 0.0210 1.28 0.267
Mike Smithson 73 1356.1 1473 383 731 5680.20 0.0129 1.91 0.245
Horacio Pina 25 354 290 174 222 1462.28 0.0171 1.28 0.218
Bert Blyleven 143 4703 4319 1268 3562 18849.46 0.0076 2.81 0.213
Bob Johnson 32 691 643 268 506 2859.62 0.0112 1.89 0.211
Roger Clemens 32 1284.2 1088 371 1215 5080.44 0.0063 3.27 0.206
Bill Greif 36 715 747 287 442 3050.30 0.0118 1.54 0.182
Frank Tanana 102 3405.1 3252 966 2345 13820.38 0.0074 2.43 0.179
Dave Stieb 108 2458 2158 873 1432 9962.56 0.0108 1.64 0.178
Fred Scherman 30 532.2 516 245 294 2261.80 0.0133 1.20 0.159

In these two periods, there was no one near the .280+ range - which is an indicator of the probability of serious brushback intent.  The establishment of the lively ball (1930-40s) and the advent of the lowered pitcher's mound and designated hitter (1970-80s), basically introductions favoring offense, perhaps impacted pitcher's "Command" and thus enabled the masking of "intent" (BBA)?

Well, at least, that's my theory.

In any event, while the "Big D" (Drysdale) and Bunning were once once the kings of Brushback Average, the truth is now:  If, as a batter,  you're questioning if Pedro "slipped" with a pitch, - - - don't.  He probably nailed you on purpose.  (And, John Kruk and Larry Walker probably did have a reason to fear Randy Johnson.)

In closing, the "master" Brushback Average list -- all pitchers (1900-2001), career 25+ HBP, ranked by BBA -- is available by clicking here.

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