Midseason Pick-Ups and Fighting Regression

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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Jeff made Lookout Landing a thing, but he does not still write there about the Mariners. He does write here, sometimes about the Mariners, but usually not.


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Aaron (UK)
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Aaron (UK)
2 years 2 days ago

Could this be the effect of September call-ups for the non-contending teams? What happens to .540 teams that don’t make pickups?

DavidKB
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DavidKB
2 years 2 days ago

I was going to write this exact thing. Your conclusion would really benefit from a control group that doesn’t make an acquisition. Despite that criticism, this is a very interesting and nuanced finding.

Pat Burrell
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Pat Burrell
2 years 2 days ago

I kept trying mid-season pickups, but my numbers never, ever regressed back to my average.

jeff
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jeff
2 years 2 days ago

So is the increase more than team that did not more an acquisition? The acquisition also has impact that another team has now weakened itself.

Pale Hose
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Pale Hose
2 years 2 days ago

“If a player has been really good for a time, odds are, going forward, he’s going to be less good.”

Respectfully, Jeff, I’m going to have to disagree on this. It may be nitpicky, but I think “really good” should be replaced with “better than expectation” to describe regression. Your sentence implies more of a change in talent level.

The Stranger
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The Stranger
2 years 2 days ago

I think both are true, and useful. In the aggregate, if you take all the players or teams who performed above-average over a period of time (whether it’s a month or a year) more of those will decline than improve in the future, which I think is the point Jeff is making. It is also true that of those, the ones who outperformed their true talent are substantially more likely to perform worse than the ones who were at or below their true talent. But given an arbitrary sample of .540 teams, you’d expect them to, in the aggregate, do a bit worse going forward (not to play .500 ball, but to do a bit worse than .540). The point of the article is that adding an impact player mid-season appears to successfully offset that and then some. (I too would like to see the control group of over-.500 teams that didn’t make a move, though.)

The Stranger
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The Stranger
2 years 2 days ago

This is one of those things that was kind of unexpected, but possibly obvious in retrospect. That average 3.4 WAR player was probably 2-3 wins better than the guy he replaced, and those teams improved by 2-3 wins. It feels like it shouldn’t be that simple (regression, other moves, etc.), but OTOH it’s exactly the result you’d expect if it was that simple.

Pirates Hurdles
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Pirates Hurdles
2 years 2 days ago

It is 3.4 wins over the entire season, not 2 months. You wouldn’t expect more than a 1-1.5 win bump and only if they are replacing a 0 WAR player.

The Stranger
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The Stranger
2 years 2 days ago

The change Jeff cited was from an 88 to a 90-win pace over a full season, which is indeed about 1 win after the deadline. I followed Jeff’s lead in using full-season numbers, that’s all. I assume most of these players replaced 0-1 WAR players, because that’s probably the 5th starter or the worst position player on a contending team.

Pirates Hurdles
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Pirates Hurdles
2 years 2 days ago

Not sure I understand the assumption – ” 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.”

Why would we assume this? What if the teams true talent is at 87-88 win pace, or what if its is even higher (or if it is 87-88 wins, but now they get better luck)? I would expect some teams to regress, some to maintain pace, and some to even increase without any change of the roster.

DNA+
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DNA+
2 years 2 days ago

Yes, this is correct. Regression does not mean “get worse”. Regression means approach the true level, whatever that is, with greater sampling. Regression can be positive or negative, and certainly when looking at multiple teams, some would be expected to get worse, some better, and some to stay about the same (if they are winning at their true talent level).

The Stranger
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The Stranger
2 years 2 days ago

The reason you’d expect those teams to regress is because, on average, those teams probably weren’t true-talent 87-88 win teams. Part of regression is that, given a sample of high-performing teams or players, in the aggregate they’re almost certainly outperforming their true talent. Jeff’s point is that his sample’s true talent level was probably in the 84-85 win range.

Pirates Hurdles
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Pirates Hurdles
2 years 2 days ago

But, how can that be known without looking at each team. Is there a study that demonstrates the the average true talent over 128 team sample is 3-4 games lower?

DNA+
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DNA+
2 years 2 days ago

Sampling variation is random, so each team has an equal chance of outperforming or under-performing their true talent level. If you only sample way out on the tail (outliers), those teams probably are outperforming their talent more often than not. However, Jeff didn’t sample way out on the tail. He took all teams that added a 2 WAR player. Those teams were biased towards good teams, but I’m not sure there is any reason to think it was biased towards overachieving teams. Surely, some teams think they are contenders and look to add talent simply because they think they have underperformed.

I think Jeff is showing an interesting result: adding players does seem to help teams on average. However, the sampling bias before and after the trade should be the same (equal chance of being greater than or less than the true talent level).

DNA+
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DNA+
2 years 2 days ago

I’d be interested to see a histogram of the winning percentages of the teams in the samples (before and after).

The Stranger
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The Stranger
2 years 2 days ago

The thing is, it’s not a random sampling of teams. It’s a selection of teams that have performed at an above-average level so far. Yes, some of them are performing at or below true talent, but as a group they’re almost certainly outperforming their true talent by some amount (the exact amount is uncertain). That’s because true talent for teams clusters around .500 – there are more 80-85 win teams than 85-90 win teams, and even fewer 90+ win teams. So if you have a sample of teams performing at 85-90 wins over a short period, you’ll have more “hot” 80-85 win teams than you do “slumping” 90+ win teams.

If true talent were evenly distributed, you’d be correct, but because there are more average teams than elite teams, that means that an above-average sample is more likely to be overperforming than underperforming its true talent. The true talent of the sample is still above-average, but not by as much as the performance of the sample to date.

DNA+
Guest
DNA+
2 years 2 days ago

What you are saying is possible, but it is not necessarily correct. This an empirical question that you have to measure (i.e. by looking at some measure of talent that is independent of wins).

Jeff is not just sampling all good teams. He is only sampling teams that have added a 2 WAR player. That means there are plenty of teams that were playing at a good winning percentage that did not add players and are not included in this sample. It may be the case that actual overperforming teams sometimes decide NOT to add players, because they know their team is unlikely to be good enough in any case. They might actually decide to become sellers. On the other hand perhaps teams that decide to add players are biased towards underachievers because they’ve already got a good talent base to build upon. We really just do not know.

The Stranger
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The Stranger
2 years 2 days ago

I agree that it’s possible that the teams that add players aren’t representative of all contending teams, and that it would be best to have some measure expected performance before predicting regression.

However, that’s a lot of work and I think regression has to be the null hypothesis here. You can speculate about why overperforming or underperforming teams might or might not add players, but absent any firm evidence of a bias there, I think it’s fair to assume that a large sample of teams playing .540 baseball will probably regress toward .500. I agree that it’s a probability and not a certainty, and I can’t tell you how much regression to expect, but if you had to slap a projected winning% on those teams for the remainder of the season, I don’t think you’d want to use .540.

DNA+
Guest
DNA+
2 years 2 days ago

Well, the evidence we have from Jeff’s analysis is that those teams got better! How good do you think those added players were to have not only compensated for regression from overachieving, but also added a couple of wins in such a short time frame?

The Stranger
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The Stranger
2 years 2 days ago

Well, the improvement from the major additions more or less accounts for the added wins. As for overcoming the regression, I imagine most of these teams made other, smaller moves – picked up bullpen help or fourth outfielders, for instance. As I’ve said, we don’t know how much regression there was to overcome, just that some probably would have been expected.

Thiago Splitchange
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Thiago Splitchange
2 years 2 days ago

My thoughts exactly. If a team is on an 87-88 win pace, but are underperforming based on their run differential, they’ll regress to performing at their expected level by run differential, leading to a 90-91 win pace (for example) without even making any acquisitions. When discussing regression, it must be done by looking at individual metrics regressing to their mean, rather than just saying an entire team will regress to the mean without understanding what would drive that.

#KeepNotGraphs
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#KeepNotGraphs
2 years 2 days ago

#KeepNotGraphs

Nick O
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Nick O
2 years 2 days ago

Part of it may be that contending teams tend to have an easier go of it in September, when the non contenders shut guys down and the AAAA guys start getting some burn.

George Resor
Member
2 years 2 days ago

first isn’t a replacement level player by definition below average. I’m not convinced that they player replaced by the acquired players are necessarily below replacement level player (there are not a lot of below replacement level player on contenders). Can part of the improvement of contenders during the second half be a result of all the non contenders trading away there best players, making them easier opponents for the contenders to beat?

Declan in Boston
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Declan in Boston
2 years 2 days ago

Yes, regression is to true talent level, not to average – average is way below replacement, and that piece of regression is called aging. I’d guess that teams playing below true talent, but still in contention, are those most likely to upgrade. And, of course, teams that decide to go for it are likely to have better records (for the rest of the year) than those that don’t.

Catoblepas
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Catoblepas
2 years 2 days ago

I wish you hadn’t used “statistically significant”. For all I know, that means you get a confidence level of 94% instead of 95%, or 88% instead of 90%. Be Bayesian! Tell me how confident you were, or how big the predicted range was, or anything other than whether or not the results cleared an arbitrary cutoff.

Joel
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Joel
2 years 2 days ago

I could see someone like the Mariners going out and getting a bat that would be worth those 2, 3 extra wins (or a couple bats) — but then have them not address the pitching (because it’s been great) or in order to get the bats, they had to trade some of that pitching. And then the pitching regresses, and it’s all just becomes a wash or worse.

DNA+
Guest
DNA+
2 years 2 days ago

That wouldn’t be the pitching regressing, that would be the talent level actually changing.

Joel
Guest
Joel
2 years 2 days ago

Oh, true in the case of them trading their pitching. But if they didn’t trade the pitching, I bet they’re still in for a bit of regression in that bullpen….so I guess one of the points in the article is that the FO would need to be out in front of that, instead of just assuming the pen/rotation will be nails the rest of the way..

Jim Kelley
Member
Jim Kelley
2 years 2 days ago

“I remember… some of the details about the clearest time regression to the mean was ever explained to me.”

So I’m no grammar expert, but I’m fairly certain that this is not a sentence.

PackBob
Guest
PackBob
2 years 2 days ago

Enough of a sample size can get past noise but I have no idea if this is a large enough sample size. Intuitively it makes sense that teams would on average improve, since they would have a half season or so of performance to judge and would know where they lack.

I wonder if this could be broken into teams that exceeded expectations and those that underachieved before making the moves.

David K
Guest
David K
2 years 2 days ago

I often have a hard time grasping the concept of “regressing to the mean” in the context of all those people in Vegas at the roulette wheel who track the previous spins, thinking that if there were more reds than blacks in the past, there is a greater chance of seeing more blacks in the future, and betting accordingly.

If a guy is a .300 lifetime hitter, and he’s batting .240 at the all-star break (assuming he’s not injured, and hasn’t hit he wall age-wise), he’s not likely to bat .360 to get is average up to it’s yearly career norm. He’s probably more likely to hit close to his lifetime average of .300 the rest of the season to get his average that year up to .270. So if the latter is the kind of regression (or in this case progression) we’re talking about, I can buy it, but not the former.

jdbolick
Member
Member
2 years 2 days ago

You’re referencing what is known as “the gambler’s fallacy.” That is not regression to the mean.

Kev
Guest
Kev
1 year 11 months ago

this is a very good post

Kev
Guest
Kev
1 year 11 months ago

amazing

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