Both teams scored a run in every inning.

The question of how often this might have occurred over the course of baseball history first struck me about 20 years ago, while standing in the parking lot of Kauffman Stadium, the home ballpark of the Kansas City Royals. I was there with my father, Lary Bump, a sportswriter and member of the Society of American Baseball Research. It was that organization’s annual convention which had me thinking, in my own numbers-centric way, about the history of the sport.

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Both the Internet and I were too young to be able to answer the question easily back then. We’ve each since matured to some extent.

Now, there’s a site called Retrosheet, which uses an army of volunteers to cobble together as complete a set of data about professional baseball games as possible. They provide files of information stretching all the way back to the earliest years of play, allowing me to run through every game on file and figure out when and if a box score had wound up free of zeros. And, as it turned out, a number of other little details about the history of the game.

In total, Retrosheet had scoring lines for 377,340 games over the course of 146 seasons from 1871 through 2016. For a number of years in the late 1800s, no box scores were available. But among those years for which they were, ballplayers tallied a total of 1,678,194 runs.

How that number looked each season correlated, as you might expect, to the number of games played, which itself was a function of the number of teams. The season in which the most runs was scored came in 2000, when teams put up just shy of 25,000 runs according to Retrosheet’s data. The effects of the two labor strikes in 1981 and 1994 are obvious on the run totals.

Having this data broken out by inning, though, meant that I could figure out some more information about the flow of those 377,000-plus games.

For example: In about 27 percent of innings (that is, a team’s half of an inning) a run is scored.

This has been fairly consistent over time. Beginning in 1909 (as far back as Retrosheet’s annual data goes without interruption), the percent of innings in which a run was scored was generally a bit under 30 percent. A bit over half the time one run was scored; a bit under half, more than one.

The inning in which a run is most likely? Interestingly, the first.

I asked my father for his thoughts on why this might be.

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“Often, a pitcher isn’t right in the first inning, for a number of reasons,” he said, then listing some likely factors (which I’ve edited slightly).

Especially on the road, he might not be comfortable on the mound or the environs of the stadium.

Ever since I’ve been listening to baseball on the radio/TV, commentators have said, “If you don’t get to him early, you might not get to him at all.” A good pitcher especially will make adjustments if they encounter trouble during the game, reducing runs in later innings.

Perhaps the most obvious is that in every first inning, both teams start with what the managers feel is their best lineup grouping coming to the plate — a speedy leadoff batter who can steal bases, followed by a player with good bat skills who can hit behind a runner so that he advances even if there is an out, then the highest-average hitter, then the big power hitter.

As baseball has evolved, teams have added more starting pitchers to their rotations. Pretty much by definition, the second starting pitcher added behind Old Hoss Radbourn and others in the 1800s wasn’t as good. When teams went to three starters (maybe the 1890s or early in the 20th century), that third guy wasn’t as good as the other two.

“In the ’70s,” he added, “teams added a fifth starter, who is considerably worse than the starter. I had a brief interview with Nolan Ryan shortly after he complained because his team (I think the Angels) went to five starters. He was not happy about it.”

That pattern has held over time.

Note that, particularly in more recent decades, the likelihood of runs being scored in an inning drops in the eighth and ninth innings — likely a function of specialized closers.

The data also bolsters the first point above — the existence of home-field advantage. The home team is consistently more likely to score runs in an inning than the away team.

All of these charts cut off at the 11th inning (with the first nine highlighted). The longest game stretched 26 innings; the most runs in an inning was 18.

I was curious, too, about how the number of runs related to the inning. The inning in which it was most common to score one, two, three, four or five runs was the first. After that, the most common innings for big scoring bursts came later. The most common inning for scoring six runs was, coincidentally, the sixth. This didn’t happen very often.

There have been a number of times since 1871 that teams have scored in every inning at bat — mostly by home teams that then don’t have to hit in the bottom of the ninth. (The most recent example in the Retrosheet data was when the White Sox did it against Cleveland last September.) On Sept. 13, 1964, the Cardinals scored in all nine innings against the Cubs.

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But as far as I can tell — and baseball historians will let me know if the data missed something — the only time both teams scored in all nine innings was that Athletics-Haymakers game, back in the first year in which a professional baseball league played any games at all.