The Run Expectancy Matrix, Reloaded for the 2020s

This is a public service post of sorts. If you’re like me, when you type “Run Ex” into Google, it will auto-complete to “Run Expectancy Matrix.” It knows what I want – a mathematical description of how likely teams are to score in a given situation, in aggregate. I use this extensively in analysis, and I also use it in my head when I’m watching a game. First and third, down a run? That’s pretty good with no outs, but isn’t amazing with two.

There’s just one problem with that Google search: It’s all old data. Oh, you can find tables from The Book. You can find charts that are current through 2019. There’s a Pitcher List article that I use a lot — shout out to Dylan Drummey, great work — but that’s only current through 2022. And baseball is changing so dang much. Rather than keep using old information, I thought I’d update it for 2025 and give you some charts from past years while I’m at it, so that you can understand the changing run environment and use them for your own purposes if you so desire.

First things first: Let’s talk methodology. I downloaded play-by-play logs for all regular season games played between 2021 and 2025. For each play, I noted the runners on base, the number of outs, and then how many runs scored between that moment and the end of the inning. I did this for the first eight innings of each game, excluding the ninth and extras, because those innings don’t offer unbiased estimates of how many runs might score. Teams sometimes play to the score, and the home team stops scoring after the winning run. If you have the bases loaded and no one out in the bottom of the ninth, one run will usually end it, and that provides an inaccurate picture of run scoring. That’s also why I skipped 2020; the seven-inning doubleheaders and new extra innings rules produced a pile of crazy results, and the season was quite short anyway. No point in trying to wade through that maze.

That’s a pretty simple process – the hard part is the data wrangling, which I’ve already done for you. So let’s talk about the results. First, here’s 2025, with the caveat that we’re still early in the season:

Hey look, a table! I know that’s not all that useful on its own and stripped of context, but you can do some fun things even with just this one. For example, you can see that a runner on second with one out carries a run expectancy of 0.67. With a runner on third and one out, that rises to 0.86, an increase of 0.19 runs. That’s the value of stealing third with one out – naturally, it’s also the value of advancing on a wild pitch or balk. Compare that with the cost of getting caught. No one on and two outs has a run expectancy of 0.1, a decrease of 0.57 runs. Succeed three times and fail once, and you’re breaking even.

In fact, whenever you hear people talk about breakevens in baseball, they’re looking at charts like this. Steals, sacrifices, intentional walks; you can think of this as the baseline way of evaluating the cost and benefit of those actions, and then change the specifics based on the identity of the batter, pitcher, baserunner, and so on. It helps set expectations, too. If you have the bases loaded and one out, anything less than three runs is a slight disappointment.

Check out how things have changed over the past half decade. Here’s 2021:

Here’s 2022 (the slight differences between my table and Drummey’s likely arise from my throwing out the ninth and extra innings):

Here’s 2023:

And here’s 2024:

Lastly, here’s the average of the four previous years:

If you’re looking for a takeaway as to what’s different about 2025, it’s too early to say. But if you’re looking for what has happened to the run environment in recent years, that’s easier. I ran the same data for 2015 through 2019 to get a baseline comparison. Here’s that half decade, leaving out the mini-Deadball Era of the first half of the 2010s:

Do those look similar to the current era to you? You’re not wrong. Here’s the difference between the two, where a positive number means more runs scored in recent years than they did in the past:

Yeah, basically nothing. But if you’re wondering how much baseball has changed since, say, the early 2000s, what about looking at 2000 through 2004 by the same metric? Here it is:

And the differences:

Now we’re getting somewhere. There’s an across-the-board decline in scoring with no outs. But with one out, and particularly with two, scoring hasn’t changed much. That feels like something actionable and interesting, and the reason why is intuitive.

From 2000 to 2004, hitters struck out 16.8% of the time. From 2021 through 2024, that was 22.7%. Clearly, then, the lack of contact has weighed on teams’ chances of scoring multiple runs in an inning by stringing together balls in play. But on the other hand, the home run rate has increased by about 10%. From 2001 to 2004 (four years, to match the recent years), the league hit 21,175 home runs. In the past four years, they’ve hit 22,480. And that’s despite nearly 20,000 fewer plate appearances – on-base percentage is way down, thanks to those dang strikeouts.

Why hasn’t two-out scoring fallen as much as no-out scoring? Because hitters these days are a lot more likely to run into one, no stringing together of hits necessary. Fewer runs are being scored – and they’re being scored in different ways, too. Getting to third with no one out is a lot less valuable than it used to be. Juicing the bases early in the inning isn’t quite as good for the batting team or as dangerous for the pitching team. Intentional walks are more defensible when there are so many strikeouts in the game, at least when they come against home run threats who could flip the table on its head in a single swing.

I hope these run expectancy tables are helpful to you. I’m certain they won’t be as useful to you as they are to me – I use them in the background for a ton of articles, and now I have them all in one place – but as far as the nuts and bolts of baseball analysis go, I think this stuff is indispensable.