How to Argue About Momentum

I’m sorry, assorted old people and grumps of the world. Michael Baumann got you all riled up yesterday by looking into whether clutch exists. It does! It’s inarguably a real thing. It’s also not very predictive, and even maybe not predictive at all. I know! It’s shocking (note: it’s not shocking). After reading that, I had no choice but to look into that other baseball truism: momentum.

There have been plenty of studies about it. The findings are consistently uninteresting. It’s basically this: Momentum probably has some effect, but it’s minimal. You can slice it a ton of different ways and get some version of that conclusion, whether you’re talking about a big win helping the next day or a string of important games begetting more.

I thought I’d add to the literature with a different study. I can’t remember which game in particular, but I was watching some ball last week when a team tied the game in the bottom of the fifth or sixth. One announcer mentioned offhandedly that they were heading in the right direction and had the opposition right where they wanted them. This isn’t rare. If you watch baseball, you’ve heard some version of it for sure. I tuned out before the end of the game, so I can’t tell you whether they were right, but I made a note to look at it later.

That particular definition of momentum – rallying to tie the game in the bottom half of the inning – felt ripe for study. I grabbed game logs from every game played since 2000 to take a crack at finding this effect. I went through the score after every half inning and noted a few things. First, I noted the score differential. Next, I noted the change in differential since the last half inning. Finally, I checked who won the game in the end. That let me find whatever subset I wanted and study the difference between games that were tied when the half-inning began and the ones where the home team tied it up during that half-inning.

As an example, I found 1,982 games where the home team rallied back from a deficit to tie things up in the bottom of the third inning. Those teams ended up winning the game 52.8% of the time. There were 13,881 total games in my sample that were tied after the third inning. In those contests, the home team won 52.3% of the time. Hey look! It’s momentum.

One critical point here: Yeah, that’s probably not momentum. A statistical test would consider those numbers to be pretty much equal. But we’re not limited to just the third inning. We have tons more data. Here’s a table of win percentages by inning, both for all tie games and for games where the score became tied in that particular half inning:

In all, that’s 107,470 tie half-innings, and 15,516 games that became tied in that exact half-inning. That’s a pretty robust sample. As you can see, the home team wins more than half the time. We know that, of course: It’s home field advantage. As you can also see, the win percentage for the two sets is ever so slightly different.

Now, is that number statistically significant? No. More specifically, it’s insignificant at pretty much any level. The difference between 52.55% and 52.98% is just too small to be sure that there’s an effect here. In other words, we can’t reject the null hypothesis that tie scores that result from comebacks and regular old ties are drawn from the same sample.

That’s a pretty milquetoast conclusion. It doesn’t track with how things feel. Coming back from a three-run deficit to tie things up should tilt the playing field. Those dastardly opponents should feel demoralized, and our plucky heroes should have adrenaline pumping through their veins, unlocking higher levels of performance. Maybe I didn’t do a good enough job selecting the comebacks. What if we limit it to times where teams came back from multiple runs down to tie the score?

There were 5,034 instances of a home team erasing a multi-run deficit and ending the inning with a tied score. Those teams won… 52.9% of the time. There were 1,593 instances of erasing a deficit of at least three runs, and those teams won 53.0% of the time. We’re getting squarely into silly season, but there are 448 instances of scoring four or more to tie it up, and those teams won 54.5% of the time. Hey, maybe we’re on to something! But that’s not statistically significant either; in samples that small, variance is much larger.

You can slice these data over and over and end up with basically the same result. There’s a tiny increase in winning percentage for teams who tied the game after trailing relative to teams who entered the half-inning tied and left it tied, but it’s not statistically significant in any sample. Even if it were significant, I don’t think this is what the momentum crowd means – half a percentage point isn’t something you can perceive. Play 200 games where you tie the game up in the fifth, and then 200 where you start and end the inning tied, and you might win one more if we accept the numbers at face value. That’s just… that’s nothing.

This doesn’t disprove momentum, of course, but it does a fair job of disproving this particular type of claim. Forget the theory. We’re using the actual games on the field, and there’s no evidence of a strong effect. Major leaguers do about as well in games that have been tied all along as they do in games where they rally back to tie things up.

I thought I’d check one more limited example of where you might expect momentum to work before I finish up for the day. What about games where teams rally from behind in the bottom half of an inning and end the inning ahead by a single run? That sounds like a true momentum-changing time at bat. I found 6,906 times where that happened, and the teams won a whopping 70.1% of the time. Hey! Now we’re cooking with gas.

Bad news, though: Obviously they won a lot! They finished the inning ahead. I found 34,862 instances of a team starting the inning up by a run and then finishing the inning still up by a run. Not so much momentum there. Those teams held on to win 71.6% of the time. Turns out, being up a run is really valuable, and it’s not because of how you got there.

That dataset actually needs a bit of adjusting, because the specific inning matters a lot more when the game isn’t tied. Being tied after three innings isn’t so different, in terms of expected winning percentage, from being tied after seven. Being up by a run after three is clearly less beneficial than it is after seven innings, though. I controlled for that by taking the proportions from the comeback sample and seeing how often the teams would have won if the “true likelihood” of a win from each position was defined by the bigger sample: innings that a team started and ended with a one-run lead. Using that criteria, we’d expect a 71.2% winning percentage. If you throw out the first inning (we don’t have any data for teams that entered the first inning up a run), that’s exactly what has happened.

Is this news? Not really. It’s one of the many implicit assumptions that go into baseball analysis. If the game has a path-dependent memory, then just saying ‘tie game in the bottom of the sixth’ doesn’t mean much. If you’re trying to calculate run expectancy, win expectancy, really any state-based probability at all, you need to assume that what happened before matters almost not at all. That feels weird! It doesn’t feel like how we experience sports at all. The impulse to question it is understandable. But if you look at what the players have actually done on the field, in major league games in the 21st century, you’ll find that the momentum of a game has essentially no effect on what happens from there on out. That’s good to know – unless you’re rooting for the team that just roared back to tie things up.