It turns out that there is a fairly strong correlation between HBP rates and HR rates.
I guess this isn't entirely surprising. A fair fraction of hit-by-pitches occur after one or more home runs, so when there are more homers, there are more batters getting hit by pitches.
Click through to look in more detail at the data.
Here's a scatter plot of HBP vs HR rates for each season since 1901:
This plot looks like a smile, doesn't it? It makes me smile too.
My first instinct upon looking at this plot was surprise that HBP rates were higher at both low HR rates and high HR rates.
I started thinking that it made sense. The higher HBP rates at high HR rates are clear--as per what I wrote above, more batters get hit after homers, so more homers means more HBP. I was thinking that there also might be more HBP when HRs are low because there's lower risk that the HBP would come back to haunt the pitcher.
But then I took another look at the raw data. All of the years in which the HR rate was under 0.30 per game came before 1921. Back then, HBP rates were quite high. In 1921, HR rates jumped up suddenly (hello Babe Ruth) while HBP rates continue to decline very gradually. I am not sure why HBP rates started high and went down very slowly but it took another 20+ years (until the mid 1940's) for HBP rates to bottom out.
So look again at the plot above. Every single point to the left of 0.3 HR per game is from 1920 or earlier.
Let's look at the plot again with a few drawings added by me:
I've put ovals around 3 distinct zones. The left oval is the one I was talking about above--the pre-1921, low-HR rate part of baseball history since 1901.
The middle oval is all the years from 1921 to 1993, before the current high-offense area. Over a large range of HR rates (basically 0.3 per game up to just under 1.0 per game) HBP rates are fairly low compared to the other ovals.
The right oval is 1994 to present, where HR rates and HBP rates have both been really high.
Notice that for all of these 3 ovals, none of the HR rates overlap. In other words, I drew 3 ovals that separate chunks of points entirely by HR rate.
Eagle-eyed viewers will notice, however, that two points escaped my ovals. These are outliers.
Let's look at the outlier on the lower right. Let's see--it has a HBP rate from the 1921 to 1993 period, but an unusually high HR rate. What year do you think it is? Can you guess?
Yup, it's 1987. That year sticks out on every study that tracks HRs, including this one. Something weird was happening that year. The thing that's weird about 1987, though, is that HBP rates weren't up at all. They were 0.19 per game in 1986 and 0.22 in 1988, and right at 0.19 per game in 1987. Home runs were up, but apparently retaliatory HBPs were not up--so maybe retaliatory HBPs don't really happen? It's unclear.
The other outlier--the one at 0.95 HR per game and 0.32 HBP per game...what year was that?
It was the quite unusual 2010, of course. We already know that offensive levels this year were the lowest since pre-1994. HBP rates were still high, but HR rates dropped down some such that it should have been in the middle oval, not the right oval.
What does this tell us? It suggests that HBP are more a part of baseball culture than retaliation specifically from HRs. Home run rates dropped off, and so did HBPs, but not as much as we might have guessed. However, if HR rates continue to drop, I think we'll get more years smack in that middle oval coming up.
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