Friday, September 24, 2010

Are Traded Players "Lemons"? An updated study

Here's something kind of shocking I found when I looked at the performance of traded players.

I took all batters from 1901 to 1975 who started a season with a new team. I eliminated all players whose Marcel predictions had them projected to have fewer than 400 PA that year. I also eliminated all players who had less than 1,000 Runs Created for their career so far. So I'm left with 102 full-time players with good careers so far.

Then, for each of those players, I used similarity scores to find a control, the closest match in Marcels for that year among non-traded players. The control had to be the same age and play the same position.

So now I have two groups of 102 players each, controlled for age and position, with almost identical projections for that year. The only difference appears to be that one group was traded, and the other was not.

How do you think their actual performance would compare for the subsequent season?

If you thought the two groups would have similar performance that year, you'd be right. Their composite batting lines were very close.

So far, no surprises.

Now, consider moving beyond that season. You still have the same two groups, who are the same age, play the same position, had identical Marcels last year, and performed identically last year. The only difference between the two groups is that, in one of the groups, every player was traded before last season.

How would you expect the rest of their careers to match up?

This time, if you thought they'd be nearly identical, you'd be very wrong. It turns out that the control group played 60 percent longer than the traded group, and, in addition, was more productive -- by almost three quarters of a run created per 27 outs.


Why does that happen? I'm not sure, but I have some guesses (and full details with all the numbers) in a draft of a followup to my 2004 "Are Traded Players Lemons?" study. The draft of the new study is here (and contains a link to the old study).

I'd appreciate any comments you might have on the new study, and any other hypotheses you might have that I didn't think of.


(P.S. Many thanks to Jeff Sackmann, who published a database of Marcels last month, making the study possible.)


UPDATE: in light of some of the comments, especially from Guy, I've updated the study ... before, I thought there might be a lemons effect. Now, I'm not so sure.

Use the same link.

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At Friday, September 24, 2010 1:23:00 AM, Blogger Hank Gillette said...

Maybe baseball GMs took to heart Branch Rickey’s maxim, “It’s better to trade a man a year too soon than a year too late.”

At Friday, September 24, 2010 1:59:00 PM, Blogger Cyril Morong said...

Hank, good point.

Phil, if the traded guys tend to be lemons, did their new team get them at a discount? Are both teams in the trade trading lemons? I know not all of these guys were traded. Maybe some got released (but maybe not too many if you tried to only include players who were good before).

Would the market tend to correct itself over time? Wouldn't GMs start to see this kind of pattern and then offer lower "prices" for trades?


At Friday, September 24, 2010 2:02:00 PM, Blogger Phil Birnbaum said...

That's a good point about some of those players having been released ... although, since all of them were projected to get 400 PA, I bet it's not very many of them. And the same "lemons" argument would apply to released players.

I don't know if there's anything in the theory of lemons to predict whether the buyer gets a good deal or not. It's very possible that the buying team is aware of the possibility of a lemon, and offers lemons in return. I didn't analyze specific trades, just players who switched teams.

So the market may have corrected itself, or it may never have been inefficient -- maybe trades have always been lemon for lemon, with both sides understanding that that's what's going on.

At Friday, September 24, 2010 2:12:00 PM, Blogger Cyril Morong said...

When my wife and I bought a used car back 1998, we had a company called "lemon busters" check it out. Maybe baseball needs something like that.

My understanding of the theory for lemons is that some good cars are not even offered for sale. Suppose that your car is truly worth $1000. Alot of people won't believe it is worth that much. So maybe they offer you $800. But you may not want to sell at that price. So quality cars get pulled off the market.

Maybe good players, whom teams think have a real future, don't get traded (which may be related to Hank's point). They are like the cars that are truly worth $1000 but no one believes it and won't offer enough for them.

It would probably be alot of work to figure out if the traded players were fetched at a discount price (maybe only 1 minor leaguer instead of 2 or something like that). But if this is still going on, the question would be why. Are some GMs just not getting it or are the prices discounted? I don't have any idea how to figure that out.

At Friday, September 24, 2010 2:20:00 PM, Blogger Phil Birnbaum said...

Right, that's the theory. And it makes sense ... if you look at the first couple of charts of the study, the traded players are definitely worse than the non-traded players.

That isn't necessarily lemons, though ... even if there were no lemons, nobody wants to trade a huge popular star like Pujols or Mauer or Jeter.

I definitely agree with you that it would be hard to figure out whether other GMs know what's going on and make worse offers because of that.

At Friday, September 24, 2010 4:41:00 PM, Anonymous Guy said...

Phil: one possible explanation is that only the traded players are required to have 1000 career RC pre-trade. That means they were generally extremely productive players when they were young. Their matched control player has been equally productive over the past 3 seasons, but may have been a much inferior player prior to that. So I would guess that your traded players are more likely to be in a measurable steep decline. What happens if you match them only to other 1000 RC players? Or if that's too difficult, how do the two groups' current Marcel compare to say their average Marcel 4-6 years earlier? Have the traded players been declining at a faster rate, in terms of performance and/or playing time?

At Friday, September 24, 2010 5:05:00 PM, Blogger Phil Birnbaum said...

Hi, Guy,

My thought was that most of the control players would also have 1,000 RC, or close to it, just because of the matching. But I'll investigate.

I like the "traded players are already in decline" theory, but that doesn't explain why it takes a year or two for that decline to kick in.

At Friday, September 24, 2010 5:26:00 PM, Anonymous Butler Blue said...

Phil - Great stuff. Never thought of applying the market for lemons to baseball. And you beat me to the point on my one criticism, that this could be the causal effect of trades on performance, rather than lemons. I think it's probably lemons, too, but it's hard to say for sure. If we could find some players who were forced to relocate but not through trades (i.e. like the Expos moving to Washington), maybe it would be possible to see if relocating really is a big deal.

At Friday, September 24, 2010 5:34:00 PM, Anonymous Butler Blue said...

@Guy: I think that the fact that they're matched on age will help avoid this, right? If there's two guys who've performed the same over the past three years that are both 32, then I would think they aren't trending apart that much. If this were about pitchers, then maybe there's arm fatigue or injuries. But for batters, it seems ok to me. Anyway, I'll be interested to see how that turns out once Phil checks.

At Friday, September 24, 2010 7:14:00 PM, Anonymous Guy said...

Phil: I'm not sure where you are finding all these 1000 RC players to study. According to B-Ref, there were only 131 such players in the years 1901-1975 -- and that's for their entire career. If 102 of them were traded, you must be comparing them to a matched sample of lesser players. But it sounded like your earlier study had a lot of these players in both the control and traded samples. What am I missing?

At Friday, September 24, 2010 9:06:00 PM, Blogger Phil Birnbaum said...


A player can appear more than once if he switched teams more than once after getting to 1000RC. Also, a player can appear as a control for a season in which he was not traded.

I've posted the full list of 102 pairs (traded players and their comparables) at

BTW, Guy, you're right ... most of the comparables are short of 1000 RC, some of them substantially. The RCs are listed in the above file.

At Friday, September 24, 2010 9:26:00 PM, Blogger Phil Birnbaum said...

Okay, I reran the critical comparison, but this time I insisted that the control group players all had at least 1000 RC before the control season.

The results were about the same -- actually, slightly more extreme than before.

Originally, the controls beat the tradeds, 143367-103242 AB.

Now, the controls beat the tradeds even worse, 147443-102867 AB.


In unrelated news, the original difference in AB (143367-103242) is statistically significant at p=.0008 (80 times in 100,000 simulations). The corresponding difference in RC/G (5.62-5.12) was statistically signficant somewhere between .02 and .035 (can't tell for sure because of rounding errors).

At Friday, September 24, 2010 9:29:00 PM, Blogger Phil Birnbaum said...

Further to the first part of the previous comment: the traded AB dropped from 103242 to 102867 because one of the tradeds didn't have any possible comparables with 1000RC, and so was dropped from the sample.

At Friday, September 24, 2010 11:49:00 PM, Anonymous Guy said...

Thanks for the clarification. But I now have some sample size concerns about this exercise, given relatively small number of players, the fact a player can appear twice in the same sample, and (I think) can even appear in the other sample! I also wonder how good the matching can be given such a tiny pool of players to choose from. If you find the same thing for, say, all players with more than 4,000 prior PAs, that would seem more meaningful.

On the playing time issue, couldn't some of that be a function of the non-traded players being stars with long seniority on their team? They may sometimes get playing time in excess of what they earn, while traded players don't have a history with their current team and so may have to earn their playing time.

At Saturday, September 25, 2010 12:57:00 AM, Blogger Phil Birnbaum said...

Hi, Guy,

Re: the sample size issue: the significance level of .0008 accounts for that. What I did, basically, is randomly switch every pair of players with probability .5 (so that the traded becomes the control and the control becomes the traded). Of 100,000 randomly switched runs of the study, only 80 came out at least as extreme (either way) than the real one did.

Yup, it certainly could be that the non-traded players earned their time through seniority. I'll add that as a possibility.

At Saturday, September 25, 2010 11:20:00 AM, Anonymous Guy said...

Hmm. What we're mainly looking at here is the final few seasons of great players. Some of them change teams, including some multiple times (Al Simmons alone is about 4% of your sample). I'm not sure it's really surprising that the guys who are released by their team perform worse than those who are not, even accounting for their Marcel.

This would only be evidence of an information asymmetry if the teams picking up these aging players are overpaying for them, by trading good talent for them. But for many of these players, especially in the early years, that doesn't seem to be the case. Just picking a few of the older players at random, Babe Ruth, Tris Speaker, Eddie Collins, George Davis all seem to have moved via free agency. Same for all 5 of Simmons' moves (though once he was purchased for a considerable sum). I certainly don't think you can title the paper "traded players", as I'm not sure even half of them were traded.

In many cases, the acquiring team is taking a low risk by signing these faded stars. They aren't giving up any talent, the player may have something to contribute, and maybe they think it will help at the gate. Did Boston think more of Babe Ruth's talent than the Yankees did in 1935? Probably not. In any case, I don't think the analysis tells us a lot without knowing what price the acquiring team paid.

Final thought: Just looking at a few of these players, it does appear to me that a lot of the traded players had a sharp decline in their final pre-trade season. It could be that Marcel underestimates the meaning of that drop because it doesn't "know" the player is in his mid-30s when it weights the 3 prior seasons (it only applies a generic age adjustment). Maybe a severe drop at this age has more predictive value than a similar drop earlier in a career.

At Saturday, September 25, 2010 12:23:00 PM, Blogger Phil Birnbaum said...


I suspect you're right that Marcel underestimates the meaning of a sudden drop at an advanced age. The effect could be evidence of a limitation in Marcel as much as it could be evidence of a lemons effect.

Even if there's no information asymmetry, we still gain some valuable information. If it turns out that players who are traded/released turn out to be worse than their Marcels suggest, then at least we know that teams -- the trading team, and perhaps also the new team -- realize something that the statistics don't.

Of course, as we agree, it could just be that Marcel fails to capture something obvious.

Does the fact that the more recent trades (1949-1975) show a similar effect (although delayed two years instead of one) change anything? All the examples you cited were old-timey.

At Saturday, September 25, 2010 1:07:00 PM, Blogger Phil Birnbaum said...

Checking how each group did the season before the trade, vs. the season after the trade:

The traded group was almost absolutely flat. The non-traded group declined by about 3.6 runs per 500 PA. This is using RC27, I haven't switched to LW yet.

From this one season, it looks like the non-traded players were declining but the traded players weren't.

I'll try two years before ...

At Saturday, September 25, 2010 1:30:00 PM, Blogger Phil Birnbaum said...

Guy's right. Here are the RC27s for last three seasons and next one season for the traded players:

6.23, 6.13, 5.34, (trade), 5.33

And for the non-traded players:

5.75, 5.63, 5.69, (trade), 5.40

So the traded guys were traded because they appeared to have had a big decline in the season before being traded. Some of that one-year decline was probably luck, because they were able to avoid a decline in the following year.

The non-traded guys were holding steady, but declined a bit in the following year.

The Marcels for the fifth season in these lines would be based on

6.13, 5.34, 5.33

for the traded guys, and

5.63, 5.69, 5.40

for the non-traded guys. So non-trade should beat trade, which it does.

Gonna think about this a bit more.

At Saturday, September 25, 2010 1:44:00 PM, Anonymous Guy said...

Phil: the result for the 1949-75 period is intriguing, but now you're getting down to a very small sample. Plus the free agency period result is not consistent.

I think you'd have to look at the transactions, and see A) how many were really traded, and B) how many of them were traded for more than a "bag of balls." The players in the 50s and 60s do seem to have been traded for the most part, but often for guys I haven't heard of. The question is whether they were real prospects or not.

But I'm not sure it's worth figuring this out. Even if you feel pretty sure that "HOF players who are released/traded late in their career will probably decline a lot over the next few years," I'm not sure how much utility that information has. It's just a very small universe of players.

Seems more interesting to me to broaden the study, and see if traded veterans in general do underperform their Marcels. Or at least those with a dramatic decline in the pre-trade year.

At Saturday, September 25, 2010 10:49:00 PM, Blogger Phil Birnbaum said...

Here's an update.

For the four years before the trade and three years after, the RC27s (multiplied by 100) are as follows. First the trades, then the non:

672 623 613 534 t 533 530 530
603 575 563 569 t 540 562 567

So: the traded guys were traded perhaps because they had been dropping, and had a BIG drop in the year before the trade. The non-traded guys dropped only a bit. And, it looks like the "540" in the year following the trade might be a fluke.

So the effect is probably just that the traded guys got worse than the non-traded guys, despite their similar Marcels, as Guy suggested.

So what I did instead is this: instead of matching the players by similarity of Marcels, I matched them by similarity of the actual results in each of the last two years before the trade, and again on the SUM of the last two years before the trade. That is, I calculated three similarity scores. I took the weighted average, with weights of 3/2/1, the "3" being two years ago.

Also, I relaxed the age requirement. The control player could now be up to 1 year younger, or 2 years older, than the traded player. (The asymmetry was to make the average age about the same overall, which it was.)

The results now:

Season two years before: tradeds +27 Linear Weights per 550 PA (using -.25 for the out), non-tradeds +23 LW per 500 PA. Tradeds had 1% more PA.

Season one year before: tradeds +18 LW, non-tradeds +17 LW. Non-tradeds had less than 1% more PA.

Season immediately after trade: +18 to +17 again. Non-tradeds now had 8% more PA.

Marcels for the above season: +18 to +15. About the same PA. So, compared to the Marcels, the non-tradeds were relatively a bit worse, but had substantially more PA.

Finally, career: +16 to +17 (rate) in favor of non-tradeds. The non-tradeds had 15% more PA overall.

My thinking is that none of this is significant, either in statistical or baseball terms. But I await other opinions.

At Sunday, September 26, 2010 1:07:00 AM, Blogger Hank Gillette said...

Maybe this is too blindingly obvious to be mentioned, but I do not think that a rational GM is going to trade away a player that he sees a long-term upside for. Of course, mistakes can be made, as when the Reds traded Frank Robinson roughly 10 years too soon.

It's not unusual for a team in contention to trade for a fading star on a non-contending team and give up prospects that may prove to be more valuable than the star is worth. Presumably, the GM doing this thinks that increasing the chance of winning now is worth the gamble. The non-contending team is not going to win anything anyway, so why not trade away a declining talent for possible future wins?

At Sunday, September 26, 2010 7:38:00 AM, Anonymous Guy said...

This is an interesting result:
672 623 613 534 t 533 530 530
603 575 563 569 t 540 562 567

Maybe a player's rate of decline provides information not already captured in the Marcel weights? Might we worth looking at players who decline but are not traded/released. And how much does age matter? Does a decline from age 28 to 30 mean anything?

At Sunday, September 26, 2010 11:24:00 PM, Blogger Phil Birnbaum said...

I've updated the study. Same link.

At Monday, September 27, 2010 2:06:00 PM, Blogger Vic Ferrari said...

Cool stuff, Phil. Terrific commentary as well.

On the issue of fewer PAs for the players in the following season, your point re survival bias is well taken. If Hank Gillette's theory has merit, shouldn't we also see a platoon split advantage for the traded players? The thinking being that if most of these guys were moving from weaker to stronger teams, they'd be rested in more games against same-handed pitching because the new team would be more likely to have a better opposite handed hitting option on the bench.

Also, as another tes of Hank's theory:
The sum totals of the marcel forecasts ring in very close for both groups, does the same hold true at the player level? i.e is the sum of variances (and absolute deviations) of results minus forecasts for both groups the same?

I hope you don't mind the request. I could check myself using your player list and JS's marcel database, but I'm not very fast at scraping this data together, and you have the data to hand.

At Monday, September 27, 2010 6:00:00 PM, Blogger Phil Birnbaum said...

I don't have data easily at hand to check platoon splits, but I can check the mean square error for players ... will try to get to that soon.

At Monday, October 11, 2010 5:48:00 PM, Blogger Joakim Stålebrink said...

Assuming there is a lemon effect, is it preferable for clubs to "pay" with players over draft picks since there is an information asymmetry in the former but not in the latter? Or do the market even this out by the value of the pick?


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