Pondering Single-Game Home Run Records

I like to think that I’ve asked a lot of questions about baseball in my life. It comes with the territory: my job is to write about those exact baseball questions, which gives me plenty of incentive to come up with them. But crowdsourcing is a powerful thing, and on a recent episode of Effectively Wild, I heard a question I’d never pondered before.

The major league record for home runs in a single game by a single team is 10. It was set on September 14, 1987, by the Toronto Blue Jays. That’s not an historically powerful team, nor was it an historically powerful era. Those Jays finished the season with 215 home runs, a mark 10 teams surpassed in 2021. But it stands alone as the most prolific single-game home run outburst, and it’s part of a broad trend that doesn’t make a lot of sense if you think about it.

Home runs have exploded since the ball became livelier in 2015. Despite that, only four teams have set new single-game home run records in that time. It doesn’t add up; home runs are flying out of ballparks like never before, and yet teams are mostly looking up at records set in earlier eras.

On the podcast, Ben Lindbergh and Meg Rowley mentioned a few hard-to-measure ideas. Maybe players are easing off the gas pedal more in blowouts, or managers are taking their best players out for rest more often. Maybe the deeper bullpens on modern teams mean fewer chances to pile on a reliever who just doesn’t have it that day.

Maybe, they also mentioned, it’s just math. After all, there might be a lot of home runs now, but there were a lot of games then. Any individual game might be less likely to result in an offensive outburst, but play enough of them, and the math starts to change. Ten games in a low-homer environment are less likely to produce a home run record than 10 games today, but what about 100 games, or 1,000 games?

I don’t have a strong feeling about the qualitative factors, but I can at least test the math part of it. There’s an easy way to do it, provided you’re willing to simplify the game significantly. If you treat each batter as identical and each event as independent of each other (no pitching changes, no change in outcomes based on base/out state, etc.), you can just roll a bunch of dice – digitally, in my case – and see how often a team puts up a gaudy single-game home run total.

As an example, I set the likelihood of each outcome to the average across the entire major leagues from 1970 to 2001. I thought that roughly captured the home run environment in the past, though your mileage may vary. The specifics are less important than the setup, at least in my opinion, so in either case, let’s start here.

Next, I simulated 80 162-game seasons with those rates for each outcome. I kept track of how many home runs were hit in each game, then looked for the highest single-game total after those 80 seasons were over. This is more telling than showing, but as an example, my first run topped out at an eight-homer game, so I (well, my computer program, but you get the idea) wrote down “8” as the record going into 2015.

Then I ran another simulation, with only seven years (counting the abbreviated season and the piece of 2022 we’ve already played as one combined season) but with modern rates for each outcome. In particular, home runs per plate appearance went from 2.25% to 3.15%. In the first simulation I ran here, the most home runs I got in a single game was six, so I had the computer program write down “6,” then compare the two numbers. Six is less than eight, so in this particular team’s case, the old record stood up despite increased home run likelihood in recent years.

Of course, that’s just one run of history, and the advantage of simulating things rather than observing them in real life is that we can do it an arbitrarily high number of times. I told my computer program to replicate this comparison – 80 years of low offense and seven years of high offense – a thousand times. Then, I simply looked at how frequently the seven high-offense years surpassed the previous 80 years of low offense.

Sound simplistic? Perhaps it is, but some of the best ways to get results are the simplest ways. In my 1,000 simulations, old records held up 76.7% of the time. In other words, we’d expect roughly 23 out of the 30 teams to still have pre-2015 home run records, even with the significantly higher rate of home runs in modern baseball. That’s pretty close to the real number of 26: the Orioles, Diamondbacks, Mets, and Padres are the only teams to have actually set new home run records in my narrowly defined modern era.

Case closed? It could be. Waving my hands and saying “four is close to seven” is probably enough to get me out of this article. But I decided to go one step further, because I think there’s actually a good reason that real life teams have done worse at breaking old home run records than this very naive estimate would suggest.

See, I used league average rates of offensive outcomes up above, and that’s a fine way to get an average of what we can expect. That’s why I used the word average, after all. But we’re not looking for averages, we’re looking for individual outlier games. Teams have good and bad home run seasons; when you put together a bopping team or the league has a high-home run year, you’re far more likely to set an all-time record. The past wasn’t all played with an exactly identical home run environment; it varied year-to-year, with ups and downs over time making each season either more or less likely to produce a record that will stand for all time.

To replicate this, I took the easy way out and had my computer program vary each year’s home run rate randomly. More specifically, I changed the rate by a randomly and normally distributed amount of percentage points, with one standard deviation equal to half a percentage point of home run rate. Now, every year brings with it a new offense. In some years, a team will assemble a squad of boppers and have a home run rate well above league average, and vice versa. That makes for a higher likelihood of extreme outcomes – math is neat that way.

With our new randomly varying home run rate in tow, I ran the same simulation again. This time, the old records held 80.6% of the time, or for roughly 24.2 out of 30 teams on average. Now we’re getting pretty close to what actually happened in reality. Score one for modeling the past.

Last thing to consider: some teams have longer or shorter histories than the 80 162-game season equivalents I used for this exercise. Just to get a rough idea, I repeated the exercise with a hypothetical shorter past; only 20 seasons before the recent home run boom era. This time, it was much easier to catch the past. Teams with short histories set new single-game home run records in the recent high-homer era 57.4% of the time.

Put another way, it’s no coincidence that the Diamondbacks, Padres, and Mets all feature on the list of teams that set new home run standards in recent years. The shorter your history, the more likely you are to do something new and unprecedented in a given year. There’s a saying that I mostly found reductive when I worked in finance: “It’s not about timing the market, it’s about time in the market.” In that context, it means that you should worry less about whether you’re buying at the perfect time and more about owning investments for the long haul.

That glosses over the fact that timing really does matter, but I think it makes a good point about our baseball hypothetical. Why aren’t teams setting more home run records? It’s not because they aren’t hitting the ball out of the park left and right, or because this isn’t a perfect era for new home run records. It’s just time in the market. Play enough games, and something weird will happen – frequently, something so weird that it could take decades or even a century to replicate.