When the Home Runs Are Hit

Are home runs more likely at the beginning of games when the air temperature is typically marginally warmer than at the end? That is the question that I recall in my head, but I am unsure if it drove me to split home run rates by inning or if it formed as a question that could possibly be addressed by data cross tabbed in that manner. Regardless of which came first, I did end up looking at home runs per inning, but I don’t think you can say much of anything about temperature changes during the game from this.

Here I charted the 2011 home run rate in each half inning against the rate for the team (either home or road) overall. Home teams enjoy a slight but meaningful advantage in hitting home runs and I wanted to normalize for that. In the above graph, the points at the second inning show that road teams are more likely to hit a home run in that inning relative to all other top half innings.

The dramatic difference between the top of the third and top of the fourth surprised me, especially since the home teams showed a much more gentle increase. In the other seven innings, the home and road squads track closely to each other, but not in those two innings. One year of data is hardly a definitive sample though and there’s no reason to stop there, so onward I went to the entire Retrosheet era.

That certainly got rid of any discrepancies between home and away, but the general pattern in the 2011 data held and just became more concrete. I expected the graph to look something like an arc and instead got something more like arches. The fourth and sixth innings are baseball’s home run innings and it’s not close. I internally guessed that starting pitcher fatigue would have the middle innings be the most prone for home but that’s also why I expected an arc-like curve descending as the relievers took over. What’s going on in the fifth? Batting order plays a prominent role, but whether that’s the whole story is worth a deeper look.

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Matthew Carruth is a software engineer who has been fascinated with baseball statistics since age five. When not dissecting baseball, he is watching hockey or playing soccer.

42 Responses to “When the Home Runs Are Hit”

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  1. Ballens says:

    The guy who gave up all the home runs in the 4th got yanked for the long reliever who the other team didn’t get to until the 6th?

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  2. Hason Jeyward says:

    Could the 5th inning homer-drought be a result of which part of the batting order typically comes to the plate in the 5th? If the middle of the order typically comes to bat more in the 4th and 6th, that would leave the top or bottom for the 5th.

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    • CircleChange11 says:

      By this point, everyone should know that pitchers do worse the 2nd and 3rd times through the lineup, as compared to the first time through the lineup.

      We also all should know that in the 4th inning, the 3-4-5 hitters are likely up quite often, as compared to the 1st where maybe just one approaches the plate, or the second where maybe only 2 of the 3 get a PA in the same inning, etc.

      It should come as no surprise to saber friendly fans that there are more home runs hit in the innings that would feature the 2nd and 3rd times through the lineup with the same starting pitcher. In other words, before more effective relievers enter the game and/or specialist relievers.

      The combination of the two presents a larger threat to SPs.

      We see the same thing in the 6th, where the teams likely are bringing the lineup around a 3rd time against a now tired and less effective SP.

      It is very cool that if we took the sabermetric data from just [1] effectiveness through times in the lineup, and [2] what lineup slots come up more often, with the knowledge of how pitchers are used … we could have probably drawn a “prediction graph very similar to one representing the actual results.

      I’m hearing MGL saying that managers leave SPs in too long, much of the time. After the 5th inning seems to be a good time to take out your 4-5 starters, or any starter that’s not above average. An average reliever should be more effective than they are the 3rd time through the lineup. Sure, it drains the bullpen more, but there’s also quite a bit of evidence that shows that relievers can, and have, handled much greater workloads than the average reliever handles currently.


      I know I’ve said this before, but I would love to conduct a simulation experiment with a team using 3 starters per game, 2-3 innings each, and have them pitch every other day, with relievers filling in as needed. No guy goes through the lineup more than 1.5 times. SPs might pitch more total innings, and they might not ever pitch “fatigued innings”.

      I’m curious as to whether it would play out at the MLB level, if we can set aside things like “pitcher wins” and basing salary and awards off of them. I am talking, literally, if it would be more effective for pitching staffs. I use this same type of thing in travel ball, although I wouldn’t just pitch the best pitcher first either, but perhaps arrange the order according to velocity, or alternate RHP-LHP-RHP, or things of that nature.

      In the end, I’m just curious if it would lead to more/less fatigued innings pitched by SPs, and/or more effective innings pitched as a whole.

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  3. kylemcg says:

    Interesting. First thing that comes to mind is the fact that many of the 3rd-5th hitters in MLB lineups will have more power. They are likely to come up in the 6th. For instance this guy:


    Almost always hits #4. He has the most at-bats in the 1st, 4th, and 6th innings, and the most HRs then too. It would be interesting to see the ISO’s of hitters that appear in each inning, if that makes sense?

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    • kylemcg says:

      Another example:


      Tends to hit 4th or 5th with some 3rd mixed in. Definitely a power guy, and has had the most opportunities in the 2nd, 4th, and 6th innings. Has had the most HRs in the 4th and 6th, but curiously, more HRs in the 7th than in the 2nd. Apparently doesn’t fare so well in his first appearance.

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    • More examples of a different sort says:

      These were just the first three guys that came to mind, but it certainly appears that the bottom of the order is more likely to bat in the 5th.

      Don Sutton
      Career PAs in the 4th: 192
      Career PAs in the 5th: 295

      Greg Maddux
      Career PAs in the 4th: 230
      Career PAs in the 5th: 382

      Tom Seaver
      Career PAs in the 4th: 184
      Career PAs in the 5th: 277

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  4. Basil Ganglia says:

    My gut reaction is that the fourth inning spike has to do with lineup turnover. Fourth inning is the second time through the lineup and will usually bring up the heart of the batting order, with those batters having already had one turn through the lineup.

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  5. doug says:

    The fifth inning is most likely when the 8-9-1 guys would be up, if the hitting team left 1 man on base or scored 1 and left 0 men on base each inning, and it would be 7-8-9 if 3 men total were left on base/scored up until that point.

    Hypothetically speaking, it would make sense for any hitter’s ability to hit a certain pitcher to go up with an increased amount of AB’s, and this may in fact be true. However, this increase in productivity in a hitter’s 2nd and 3rd AB might come at the sacrifice of not trying to swing for the fences. I have no evidence to support this, it’s just my 2 cents.

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  6. Eric W. says:

    This is absolutely fascinating. I think what really gets me is the more subtle yet undeniable trends that manifest themselves even in such a short period of time (ie. one season) when compared to the 60 year chart. Like if you look at the 1st to 2nd inning trends, it’s basically exactly the same on both charts. It’d be really interesting to try and map out exactly what is happening each inning on these charts.

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    • Gus says:

      I agree this is more interesting than I would have expected it to be. I’m also interested/curious that home run rate in the later innings isn’t higher in the aggregate graph. If you bin your analyses by decade (or 20yr period), is there a marked difference between the “era of the reliever specialist” and the bad old days of complete games? It seems like you could use 1970 as a safe cut off.

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  7. Telo says:

    One year of data… useless.

    There will obviously be some biased because higher quality hitters are slightly more likely batting more in the 1st, 4th and likely 6th inning, but these numbers are >50% noise only using 1 year. What possible reason is there for using just 1 year besides being lazy.

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    • Scott says:

      Lazy commenter who cannot read an entire article calls an author, who did use more than one year of data, lazy. Irony!

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    • KitchenSink says:

      Telo, you’re no Tulo!

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    • cwendt says:

      1. Wrong. There are 162*15 observations in this sample…more than enough to start drawing an inference about the difference between innings, though it might not be a representative sample.
      2. The author did look at other seasons to confirm the trend. Lazy commenter is lazy.

      When I read this, what I like is the HR depression by the late inning guys. Also, home teams hit more HR in the late innings. I’m sure that has nothing to do with never bringing in your closer in a tie game on the road.

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    • Hason Jeyward says:

      You’re going to miss everything fun and die angry.

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    • Notrotographs says:

      Telo doing his thing.

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      • joser says:

        I keep telling myself I’m not going to read any more of Telo’s comments but he crowns himself with the most Marlinesque of public asshats in this way just frequently enough that I keep coming back. It’s almost like it’s intentional — surely no one keeps making these kinds of mistakes over and over?

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  8. Pfafftown says:

    How about the starting pitcher buckling down in the 5th so as to make it far enough to be eligible for a win?

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  9. dougiejays says:

    I’d think if anything the fifth would be more susceptible to managers leaving fading SPs in 10-4 games to get the win, which would lead to more homers.

    But as for explaining the graphs…The idea that 4th inning=first lineup turnover for the best hitters makes sense, especially when 3-4-5 are usually power guys. The 6th is the third lineup turnover against a decent SP, and it’s also when teams burn their lowest-on-the-depth-chart RPs.

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  10. reillocity says:

    I propose that we prospectively refer to the 3rd through 7th innings as the “inverted W home run innings” rather than the “middle innings”.

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  11. BbnT says:

    The 2nd inning still intrigues me on the 60 year graph

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  12. Marver says:

    I think the most interesting observations here is the difference in home/road rate in the 6th inning. The 6th is the inning in which the pitcher is most frequently pinch-hit for. Hence, the road team will be using a fresh arm more often than the home team in the 6th inning, which may be the source of the 6th inning difference.

    The 9th inning difference is another game-dependant difference. The home team can only hit if it is tied or losing. In cases in which the home team is losing big, I’d imagine the road team has a poor pitcher in. The road team hits in all scenarios, however, including those in which it is barely winning (and facing, in all likelihood, a decent pitcher).

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    • delv says:

      “The 6th is the inning in which the pitcher is most frequently pinch-hit for.”

      Split the graphs by league!! Let’s see if the 6th inning hump is less pronounced for the AL.

      Also, I agree about the 9th being game-dependent.

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    • siggian says:

      If you hypothesis about the 6th inning is correct, the AL graph should look different from the NL graph. There’s no pinch hitting for the pitcher happening in the AL.

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  13. timmyt says:

    This is whack. Im thinking the 5th inning drought is due to the bottom of the lineup coming up after the top part of the lineup, and maybe feeling like they dont need to push as hard if a lot of runs were scored in the previous inning

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    • Husker says:

      My favorite player, a bottom-of-the-lineup guy, often tweets in the 5th inning with something like, “Scored a lot in the 4th. Don’t think I’ll try this AB.”

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  14. Robert E says:

    Interesting the road team has an edge in the later innings (6-8). I was not expecting that. Why do you think that’s happening?

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    • Greg says:

      Here’s pure speculation, but it’s based on an educated guess:

      We would have to examine if there is a noticeable difference between the leagues from 1973 to the present. If NL road teams are performing significantly better than their AL counterparts during the 6th to 8th innings, then it is possible that NL managers are more inclined to leave in a tiring pitcher, or fail make a pitching change to exploit the platoon advantage, because the pitcher’s spot in the lineup is due in the next half inning. In contrast, a NL road team would have already pinch-hit for the pitcher in the top half of the inning, and so a fresh pitcher would be facing the home team’s lineup in the bottom half of the same inning.

      With the DH rule, managers can make pitching changes more freely because they do not have to worry about pinch hitting for the pitcher. AL managers are less likely to stick with a pitcher who is tiring or struggling than their NL counterparts.

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    • Road teams do not have an edge in later innings.

      the home run rate in each half inning against the rate for the team (either home or road) overall

      Road teams are more likely to hit home runs in later innings relative to other road (i.e. top half of) innings than home teams are relative to other home (i.e. bottom half of) innings

      Home teams have an edge in absolute HR rate across every 1-9 inning.

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  15. Jason461 says:

    This is really neat. It would be interesting to do this exercise while controlling for expected HR rate. That is, how many HRs would be expected given the spots in the order coming to bat in the inning. That might do a decent job of sussing out how much of a factor temperature is, for example.

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    • jesse says:

      If you hated your interns a lot, you could probably project temperature data on every inning and just go ahead and regress.

      Really interesting work, can’t believe the spikes are that defined. I bet its a combination of lineup iso and the sample selection bias of pitchers getting yanked in 4 on bad days and in 7+ on good days.

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    • Husker says:

      Despite the introduction, this article turned out not to have anything at all to do with temperature.

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  16. JWTP says:

    Maybe need to separate AL and NL not just for pinch hitters but also for the DH? Might need to separate day and night games to eke this out as well. Yeah I know that’s a lot of work.

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    • BiChiBri says:

      Agree. For day games, it’s a mistake to assume that the temperature is lower in the ninth than it was in the first.

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