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September 19, 2001

## Hit-by-Pitch Rates

This week's question come from P. N., who asks:

I'm an Oakland A's fan and there's been a lot of talk lately about how the A's are leading both leagues in the number of batters hit by pitches. Tim Hudson has suggested that the pitching staff needs to be more aggressive in protecting the hitters.

Although I am sympathetic to my guys, I'm wondering if the A's HBP numbers aren't at least partly a function of their greater plate discipline. After all, if you see more pitches, the odds of your getting hit by one ought to increase. Any way to find out if this hypothesis is correct?

Thanks for the question, P.N.; let's take a crack at testing this hypothesis.

If the A's HBP totals were solely due to seeing more pitches per plate appearance (and teams otherwise had no ability to induce more HBP), we should see a relationship between the HBP rate (HBP per PA) and the number of pitches seen per PA (NP per PA). Plotting them for each team during 2001 to date (through September 17):

There's not much of a linear relationship. We have examples of teams that see a lot of pitches, and get hit a lot (which happens to be Oakland), but we also have teams that see even more pitches, and are among the lowest teams in the rate at which they get hit (San Diego). We've got outliers at just about every corner. Computing the correlation between HBP/PA and NP/PA yields +0.130, which at best indicates a mild relationship, given these relatively few data points.

Perhaps that not the right approach. Taking lots of pitches can lead to taking more walks. Could a high OBP lead to more opportunities to get hit by a pitch, thus increasing the team totals? There's a bit of a complicating factor in that getting hit by a pitch directly increases OBP, and yields another PA in which a batter could be hit. However, the frequency of HBP is small enough where we can ignore it for now.

One way to test this alternative theory would be to compare HBP per game to plate appearances per game. If a team has a high OBP, they will have more plate appearances per game (excluding extra-inning games), which would in turn give more chances to get hit per game. I've done this analysis, and the correlation between the two stats (HBP/G and PA/G) is +0.199, slightly better than we saw before, but not that strong of a relationship.

I've included the data for each team's HBP, PA, and NP rates at the end of the article, including how each team ranks among all 30 major-league teams. It's interesting to note how different the Astros and Padres are in the HBP/NP and NP/PA categories: Houston ranks first in times getting hit per pitch, but 28th in pitches per PA. The Padres are the opposite, ranking dead last in how likely a single pitch is hit a Padre batter, but first in how many pitches they see each time they come to the plate. Though these two examples might lead you to think that there's some kind of inverse relationship between the two categories, that's not the case. The correlation between NP/PA and HBP/Pitch is virtually zero (+0.044), indicating that the two categories have no relationship (positive or negative) to each other when you look across the entire league.

So it doesn't look like the A's propensity get plunked can be blamed on their taking more pitches. There's a slightly positive relationship, but the primary explanation lies elsewhere: either in the batting styles of the A's players themselves, taking stances closer to the plate, or perhaps a coaching strategy to get them to "lean in" to a pitch that's a little too far inside.

Or maybe Tim Hudson was on to something...

```
Team  Lg   G  HBP    PA     NP  PA/G  HBP/G  HBP/PA  HBP/NP  NP/PA
ANA   A  144   68  5497  20744  38.2   0.47   0.012  0.0033   3.77
BAL   A  142   68  5330  19974  37.5   0.48   0.013  0.0034   3.75
BOS   A  141   60  5466  20489  38.8   0.43   0.011  0.0029   3.75
CHA   A  144   46  5416  20507  37.6   0.32   0.008  0.0022   3.79
CLE   A  144   62  5616  21343  39.0   0.43   0.011  0.0029   3.80
DET   A  143   46  5395  19929  37.7   0.32   0.009  0.0023   3.69
KCA   A  143   39  5429  19762  38.0   0.27   0.007  0.0020   3.64
MIN   A  144   59  5491  20603  38.1   0.41   0.011  0.0029   3.75
NYA   A  143   55  5521  20998  38.6   0.38   0.010  0.0026   3.80
OAK   A  144   81  5665  22031  39.3   0.56   0.014  0.0037   3.89
SEA   A  144   54  5713  21767  39.7   0.38   0.009  0.0025   3.81
TBA   A  143   44  5346  19788  37.4   0.31   0.008  0.0022   3.70
TEX   A  144   68  5672  21548  39.4   0.47   0.012  0.0032   3.80
TOR   A  143   64  5526  20595  38.6   0.45   0.012  0.0031   3.73
ARI   N  144   50  5536  21082  38.4   0.35   0.009  0.0024   3.81
ATL   N  143   38  5369  19440  37.5   0.27   0.007  0.0020   3.62
CHN   N  143   58  5374  20484  37.6   0.41   0.011  0.0028   3.81
CIN   N  144   59  5505  20458  38.2   0.41   0.011  0.0029   3.72
COL   N  143   54  5548  20478  38.8   0.38   0.010  0.0026   3.69
FLO   N  144   58  5457  20203  37.9   0.40   0.011  0.0029   3.70
HOU   N  143   80  5530  20236  38.7   0.56   0.014  0.0040   3.66
LAN   N  144   50  5406  20223  37.5   0.35   0.009  0.0025   3.74
MIL   N  145   65  5429  20638  37.4   0.45   0.012  0.0031   3.80
MON   N  144   58  5294  19635  36.8   0.40   0.011  0.0030   3.71
NYN   N  145   61  5463  21088  37.7   0.42   0.011  0.0029   3.86
PHI   N  144   38  5487  20868  38.1   0.26   0.007  0.0018   3.80
PIT   N  144   61  5313  19866  36.9   0.42   0.011  0.0031   3.74
SDN   N  144   38  5573  21945  38.7   0.26   0.007  0.0017   3.94
SFN   N  144   41  5616  20773  39.0   0.28   0.007  0.0020   3.70
SLN   N  144   59  5398  20020  37.5   0.41   0.011  0.0029   3.71

------------ RANK ------------
Team  Lg   G  HBP PA/G HBP/G HBP/PA HBP/NP NP/PA
ANA   A  144   68   14     4      4      4    13
BAL   A  142   68   25     3      3      3    16
BOS   A  141   60    7     9     11     11    15
CHA   A  144   46   21    24     24     24    12
CLE   A  144   62    4     8     10     12    10
DET   A  143   46   19    23     23     23    26
KCA   A  143   39   17    27     27     27    29
MIN   A  144   59   15    12     15     16    14
NYA   A  143   55   11    18     18     19     7
OAK   A  144   81    3     1      2      2     2
SEA   A  144   54    1    20     20     20     5
TBA   A  143   44   28    25     25     25    24
TEX   A  144   68    2     4      5      5    11
TOR   A  143   64   10     7      7      7    19
ARI   N  144   50   12    21     22     22     6
ATL   N  143   38   23    28     28     28    30
CHN   N  143   58   22    15     14     17     4
CIN   N  144   59   13    12     16     14    20
COL   N  143   54    6    19     19     18    27
FLO   N  144   58   18    16     17     15    23
HOU   N  143   80    9     2      1      1    28
LAN   N  144   50   24    21     21     21    17
MIL   N  145   65   27     6      6      6     9
MON   N  144   58   30    16     12      9    21
NYN   N  145   61   20    11      9     13     3
PHI   N  144   38   16    29     29     29     8
PIT   N  144   61   29    10      8      8    18
SDN   N  144   38    8    29     30     30     1
SFN   N  144   41    4    26     26     26    25
SLN   N  144   59   26    12     13     10    22
```

Keith Woolner is an author of Baseball Prospectus. You can contact him by clicking here.

Keith Woolner is an author of Baseball Prospectus.
Click here to see Keith's other articles. You can contact Keith by clicking here

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