I remember… some of the details about the clearest time regression to the mean was ever explained to me. It wasn’t explained to me personally; it was a blog post somewhere, or maybe a print-published article, and it simply showed league-leading batting averages, and then the batting averages for the same players the next season. If you’re familiar with the concept of regression, of course you know that, the next season, the batting averages were pretty much all down. It couldn’t have been more simple, and it couldn’t have been more helpful, and regression is so common a term now within baseball analysis that we all get to feel like part-time mathematicians. Especially around here, most people are smart enough to factor regression into almost everything.
It applies between seasons, and it applies within seasons. It’s a little like gravity — it’s always a factor, whether you like it or not, and it’s built into good player projections. It’s built into good standings projections. If a player has been really good for a time, odds are, going forward, he’s going to be less good. If a team has been really good for a time, odds are, the same thing. Regression is among the more powerful forces, but there is some evidence of teams being able to fight it off. Let’s talk about midseason trades.
Trade talk is all the rage right now, with the soft deadline coming up in just over a week. It’s possible there could be some true blockbusters, if the Rays decide to move David Price, or if the Royals decide to move James Shields, or if the Red Sox decide to move Jon Lester. It’s also possible it could be a real boring pile of crap, if teams on the fringes decide they’re still in the hunt. For all I know, we’ve already seen all the big moves we’re going to see. But in theory, anything’s possible, and I found myself wondering about the history of teams who’ve made significant midseason acquisitions. How much did those acquisitions actually help? I wasn’t necessarily going for anything with the research; I just wanted to have an answer.
So I examined the wild-card era, between 1995 – 2013. Using the FanGraphs leaderboards, I found qualified position players and starting pitchers who changed teams in those seasons. I set a minimum season threshold of 2 WAR, having determined that a player worth more than that can be called a significant pick-up. Checking with Baseball-Reference for every single player, I confirmed trades and trade dates, and I narrowed the list to players added by contending teams. I made sure that the teams had at least 40 games played prior to the acquisition, and at least 40 games played following the acquisition. I was left with a sample numbering 128. Not too big, not too small; enough to conclude, I don’t know, something.
So we’ve got 128 significant midseason pick-ups by contending teams. This ignores relievers and guys who got hurt, but, oh well. Now, at the time of the pick-ups, the teams all had an average winning percentage of .541. They had a median winning percentage of .535. That translates to either about 88 wins over a full season, or about 87. That makes perfect sense — they’re good, contending teams doing the adding, because they want to improve their standing in the race.
Forget about the additions for a moment. Now remember what you know about regression to the mean. We’re looking at a sample of teams, much of the way through the season, on pace to win 87 – 88 games. The rest of the way, then, you’d expect them to regress, perhaps to an 85-win pace, or 84. That is, without any extraordinary moves being made. Success generally equals success plus luck, and so on and so forth, you know these principles by now.
Back to the additions. All the 128 players, by the way, averaged 3.4 WAR. Before the additions, the teams had an average winning percentage of .541, and a median winning percentage of .535. After the additions, the teams had an average winning percentage of .553, and an identical median. Over a full season, that would be a 90-win pace. So not only did the teams not regress; they actually improved, which of course was sort of the point. But when I was gathering these numbers, I expected for the teams after the additions to play maybe just as well as they already had. I didn’t think they’d step up. I thought the additions might just somewhat counter the coming regression, evening things out.
I don’t know how much to make of this, and of course every situation is different for every team and every transaction, but remember also that those added players probably aren’t replacing replacement-level players, exactly. They likely would’ve been replacing below-average players, and that’s different. By overall average, the teams improved from an 88-win pace to a 90-win pace. Using the medians, they improved from an 87-win pace to a 90-win pace. There’s plenty of noise in either direction, but the sample isn’t small.
The numbers aren’t statistically significantly different, so I suppose it’s possible this means nothing. Also, sometimes contending teams make multiple upgrades in the middle of the year, so as to have the best stretch run they can. They try to fill all the holes somehow, and those little additions can add up. But, the idea behind a significant midseason addition is to improve, and that’s by and large what’s happened, with teams fighting off regression to the mean. They haven’t just improved their levels of true talent. They’ve improved their levels of performance, and that’s not an easy thing for teams already performing quite well.
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