Pirates pitchers hit more batters than any team in the majors this year, 75. They also led in 2014. And 2013. That’s unusual. The only teams to have led the majors in hit batters for three or more straight seasons since 1901 are the 1921-23 Phillies, 1930-32 Cardinals, 1938-40 Senators, 2002-04 Rays, and the 2013-15 Pirates.

The Pirates also got hit more than any team in the majors this year, with 89 hit batters. On one hand, that makes sense, given baseball’s Book of Exodus stance: A hit batter for a hit batter. On the other hand, and more significantly, it’s been a rare occurrence. Since 1931, only 14 teams have led their league in both pitcher and batter HBP (1943 Giants, 1947 Dodgers, 1955 Dodgers, 1963 Reds, 1966 White Sox, 1968 Astros, 1980 White Sox, 1982 Angels, 1983 Expos, 1996 Astros, 2009 Phillies, 2012 White Sox, and 2013/2015 Pirates). Only 8% of teams in that timespan have led their league in both categories–pure random chance would put that figure above 9%. It just doesn’t happen very frequently.

I should interject that I fall in the anti-hit batters camp. I don’t like seeing anybody getting hit by pitches. Sometimes they shake it off. Sometimes they miss time. Sometimes it’s horrifying. But when you consider that there were 1,602 batters hit last year, 844 on fastballs, and the average fastball velocity is 92.1 mph—well, they’ve all got to hurt. As I’ve discussed in previous posts, some hit batters are clearly accidents, often occurring when a pitcher, ahead in the count, comes inside on a pitch and misses. But some undoubtedly are a form of message-sending, with the message coming as a hard object thrown at a speed that would constitute assault were it not on a baseball diamond. (A notable case occurred when Cole Hamels hit Bryce Harper in 2012, then justified it on the grounds of “that old-school prestigious way of baseball.”) Intentionally throwing at hitters to exact some sort of vengeance, sorry, is dumb. But how often does it happen?

The Pirates provide a good test case, since by leading the league in hit batters on both offense and defense, they provide a decently large sample size. Here’s how large: Pirates batters were hit 89 times, tying them for 11^th among the 1,926 team-seasons since 1931. Their pitchers hit 75 batters, tying them for 43^rd. If you saw a lot of Pirates games, you saw a lot of batters getting hit.

And you heard a lot of excuses. The Pirates encourage pitching inside, drawing the ire of other clubs. But Pirates backers also point to the large number of Pirates batters who get hit, and the need for the pitchers to “protect” Pirates batters. You hit my Andrew McCutchen, I hit your Joey Votto. That sort of thing.

How often does that happen? Is protection–really, retaliation–a significant factor in batters getting hit? To try to answer, I classified every hit batter in Pirates games last season—164 in total—into three different categories:

• First Blood: Named in honor of the great American thespian Sylvester Stallone, the standard by which actors have been judged. (The New York Times memorably described Arnold Schwarzenegger as “the thinking kid’s Sylvester Stallone.”) First Blood (the initial work in Stallone’s Rambo oeuvre) occurs when a batter is the first one hit in a game or series.
• Retaliation: As a follow-up to First Blood, Retaliation occurs when a batter is hit by the pitcher whose teammate was last hit.
• Piling On: This occurs when a team, having already had a batter hit, suffers another, with no intervening Retaliation.

(I realize that I’m ignoring hit batters as retaliation for things like inside pitches, hard slides, and being Bryce Harper. Those don’t show up in game summaries, and besides, that’s more two-eyes-for-an-eye and therefore less acceptable.)

The timeframe is important here. Hit batters occur in the context of a game, but the casus belli can stretch out longer. Al Nipper hit Darry Strawberry with a pitch in spring training of 1987, allegedly in retaliation for Strawberry taking a slow trot around the bases after hitting a home run off Nipper in the prior year’s World Series. So I looked at hit batters in three settings:

• The game being played
• The series between the teams, to see whether retaliation carries over from one day to the next
• The season series, to capture longstanding grudges.

For example, on July 12, the day before the All-Star break, the Pirates’ Arquimedes Caminero hit the Cardinals’ Mark Reynolds with a pitch in the tenth inning. The next time the two teams played was on August 11. The Cardinals’ Carlos Martinez hit Pirate Aramis Ramirez in the first inning. That’s First Blood for the game and series, but Retaliation for the season series, since the prior hit batter, albeit a month earlier, was a Cardinal. Two days later, Pirates catcher Francisco Cervelli was hit by a pitch from Lance Lynn in the first inning. That was First Blood for the game, but Piling On for both the series and season series, as it followed his teammate getting hit. The next time the teams played, on September 4, Pirates reliever Jared Hughes hit Reynolds with a pitch in the ninth inning. That counts as First Blood for the game and the series, Retaliation with respect to the season series. The following day, the Pirates’ Starling Marte was hit by Jaime Garcia in the second inning. That was First Blood for the day, Retaliation for both the series and the season series. In the bottom of the second, Charlie Morton hit Jon Jay. That’s Retaliation in the context of game, series, and season series.

(Another aside: I am opposed to the use of plunked as a synonym for hit by pitch. Plunk is what happens when you’re rearranging books on your bookshelf and a paperback falls from a high shelf and hits you in the shoulder, or when you’re walking in the woods and an acorn hits your head. A 92.1 mph fastball is not a plunk.)

You may be thinking: This is pretty stupid, categorizing hit batters, what’s the point? The point is that if the Pirates pitchers are hitting opposing batters for some sort of tribal/protection/vengeance thing, we should see a lot of Retaliation. If that’s nonsense, it’s not the case.

Say a team plays 19 opponents, as the Pirates did (every National League team, plus the American League Central). Let’s also assume that the team’s pitchers hit 75 batters, as the Pirates did, and the team’s batters were hit 89 times, again as the Pirates were. If hit batters are random, we’d expect the team to be throw 19 x 75 / (75 + 89) = 8.7 First Blood pitches and get hit by 19 – 8.7 = 10.3 such pitches in season series. Thereafter, the odds of a hit batter being Retaliation or Piling On would be 50/50, subject to the distributional difference between 75 and 89. So the team would log 33.2 Retaliation and Piling on hit batters, and get hit by 39.3 of each type of pitch. Again, this assumes that hit batters occur completely randomly.

Here are the actual totals:

This kind of refutes the self-defense argument, doesn’t it? A Pirates batter was hit by a pitch before an opponent was in 61 games, accounting for nearly 70% of the team’s hit batters. But Pirates pitchers drew first blood in 56% of their games as well. Overall, retaliation accounted for only 20% of batters hit by Pirates pitchers in games. Over the course of a series, when my hit batter today can result in your hit batter tomorrow, retaliation explains only 32% of Pirates opponents hit. Even with the most liberal definition of retaliation, when it can be spread over the weeks or months of a season series, it still accounts for just 43%, less than half of batters hit by Pirates pitchers. Not that it was different on the other side: Pirates hit in retaliation accounted for only 15% of hit batters in games, 33% in series, and 39% in season series. The majority of hit batters occurred without seeming provocation.

Let’s compare the results of the Pirates games to those of the random distribution presented above. For Pirates pitchers, a random distribution would be 9 First Blood, 33 Retaliation, and 33 Piling On. Actual figures: 9, 32, 34. For Pirates batters, a random distribution would be 10 First Blood, 39 Retaliation, and 39 Piling On. Actual figures: 11, 35, 43. Those distributions (1) are pretty close to random and (2) feature less retaliation than a random distribution would suggest.

So what does it mean? Well, retaliation definitely does occur. We saw it the National League wild card game, when Pittsburgh reliever Tony Watson pretty clearly hit Cubs pitcher Jake Arrieta on purpose, in response to Cervelli and Josh Harrison getting hit by Arrieta, resulting in the silly spectacle of the benches clearing. But the example of the Pirates’ regular season, when there were a lot of hit batters, shows that retaliation isn’t as common as either code-of-honor defenders like Hamels nor hand-wringers like I might think. The numbers instead suggest that hit batters are, in fact, pretty random. Which would seem to make intentionally hitting batters a really uninformed idea as well as a bad one.