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Hit By Pitch vs Home Runs

Posted by Andy on November 8, 2010

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.

12 Responses to “Hit By Pitch vs Home Runs”

  1. Ellis Says:

    So awesome, great post. Maybe we can brainstorm some more reasons why HBPs have accompanied HRs (I'm not sure I by the retaliation) thing. Since this doesn't look individual players' correlation between HRs/HBPs, a lot of other factors could be in play here. Maybe as pitchers started throwing upper-90s fastballs recently they just couldn't control their pitches as much?

  2. Frank Clingenpeel Says:

    Ellie has a point, but we can't ignore the retaliation issue. I can even recall a father-son game back in the fifties in which Early Wynn {now there's a great name for a pitcher!} "dusted off" HIS OWN SON ! I must admit that while I approve of the more stringent contrals over the practice, it used to add interest to the game.

  3. Larry R. Says:

    You didn't want to come to the plate after someone homered against a guy like Drysdale or Gibson. It was different back in the day. Of course, some guys, like Frank Robinson, would get dusted and then homer in the same AB if he was able to avoid getting hit.

  4. kds Says:

    How about the armor and pads that batters wear today that they did not have before? (And helmets too.) All this protection allows the batter to crowd the plate with less risk of getting hurt. If there is no retaliation effect whatsoever, one would expect a percentage pattern of pitches off the plate, and the closer the batter is the more often he is hit. Presumably setting up "on top" of the plate will also help the batter hit home runs. So the protection technology may lead to increases in both HR and HBP without any change in pitcher behavior.

    MLB's efforts to prevent beanball wars and bench clearing brawls may have reduced the percentage of HBPs that were intentional. This may have increased total HBPs as batters felt safer setting up closer to the plate since they would mostly be hit by pitcher mistakes rather than pitches aimed to hit them.

  5. BSK Says:

    Could this also be impacted by strike zone? Pitching approaches? Aggressive pitching inside could lead to both more HBP and more HRs. Get it all the way inside and you intimidate. Miss and better hitters will punish it.

    Perhaps, in the early years, pitchers could throw inside as much as they wanted since no one had the power or the approach to really make them pay for mistakes. Naturally, more inside pitches mean more guys getting hit.

    As guys bulked up and the HR became a weapon, pitchers had to start using the outside corner more and HBP went down.

    Eventually, offensive players got so good that pitchers had to come back inside, push them off the plate (or at least try), and HBP went up. But the strategy was not effective and HRs continued to climb.

    I realize this is more narrative than fact, but it seems at least plausible, no?

  6. Cyril Morong Says:

    Great post, glad you brought this up. I like the non-linear relationship you found. I have looked at this (mainly since the 50s in terms of data). I have a link that summarizes my findings and has links to the other posts

    Here is a summary of what I found

    -There is a significant positive relationship between a pitcher's walk rate and his HBP rate

    -In the 1960s, a pitcher who gave up more HRs hit fewer batters but today a pitcher who gives up more HRs hits more batters.

    -For both leagues, the HBP/Walk rate has been rising since 1980 (so poor control is not the only reason for more HBP).

    -In recent years (up through 2007), the HBP/HR rate has been relatively high, even adjusting HBPs for control as measured by the walk rate.

    -players who hit HRs more frequently are now more likely to get hit by a pitch than in the the 50s, 60s and 70s.

    -hitting a HR in the 1990s was 83% more dangerous than it was in the 1960s in terms of causing the player to be HBP.

    From 2000-2009, here is the equation

    HBP% = 0.0477*HR% + 0.009

    The denominator for both HBP & HR was AB + HBP. The t-value for HR% was 1.97. The equation from the 1960s was

    HBP% = 0.0311*HR% + 0.0058

    Since .0477/.0311 = 1.53, it means that hitting a HR from 2000-2009 was 53% more likely to get you hit by a pitch than in the 1960s.

  7. Guy Says:

    I think the HR-HBP connection is not only, or even mainly, a story of retaliation. The issue is that pitchers have to try to move power hitters off the plate, to stop them from hitting HRs, and that results in more hit batters. It's not intentional (usually), just a cost of pitching inside to great hitters. When the HR rate goes up, there are more hitters dangerous enough to be worth busting inside and taking the risk of a HBP. (Hitting a weak hitter gives him a free pass to 1B, so pitchers avoid that as much as possible.)

    My guess is that HBP rates lag HR rates a bit. As HRs increase, and more guys become power threats, pitchers adjust and start pitching inside to a higher proportion of hitters. But it takes a little time for pitchers to realize they need to do this. So a one-time jump like 1987 (presumably a lively ball effect) doesn't impact pitchers' behavior. But if HR rates climb continuously, THEN pitchers do respond.

    Clearly, the dynamic was different in the 1920s and 1930s. Probably a function of social norms following Chapman's death, and a lack of good protective equipment. But for the past 50-60 years, pitchers have clearly responded to HR increases by pitching inside more aggressively.

  8. John Autin Says:

    @7, Guy -- I don't actually see pitchers making more effort to drive batters away from the plate, and given the costs of doing so -- potential ejection, plus more batters nowadays are willing to just take the HBP -- their behavior may well be justified.

    I think the relationship between HRs and HBP is more direct: On average, batters stand closer to the plate in this era than ever before. They do this in order to hit more HRs, and it works. It also results in more HBP that are purely a byproduct of the pitcher's ordinary wildness, with no specific brushback purpose involved.

  9. Detroit Michael Says:

    Fascinating post. Thanks.

  10. Tuesday Links (9 Nov 10) – Ducksnorts Says:

    [...] Hit By Pitch vs Home Runs (Baseball-Reference). From the article: “It turns out that there is a fairly strong correlation between HBP rates and HR rates.” Charts and stuff… pretty cool. [...]

  11. Bob McDittin Says:

    I don't think there is any correlation. The stats don't look at individual players.

  12. The AL/NL gap in hit-by-pitch rates » Baseball-Reference Blog » Blog Archive Says:

    [...] up on my earlier post about HBP rates, let's take a look at the split in HBP rates by [...]