Hypothetical question.

[onejayhawk]

What current player, on his last year, would you give up for Byron Buxton plus thee option years? Assume you have no chance for the title.

J

[Don Quixote]

That could hinge on whether I think I have a shot at the title next year. Assuming I think I can make a run next year, I'd probably give up my second-best stud.

[Gregg]

Any one of them. If I know I am not going to win and have no chance, I would trade any single layer that is in their last year. That said I am not sure that one player will get it done.

[Big Tymer]

Right, this is a silly in question in that in any sort of keeper / dynast format you are now talking about an absurd package required to acquire Buxton. Plus, if the team who has him is not in contention this year (and they would know if they are before the season starts) then he is literally unavailable.

[Fresno Bob]

Any one of them. If I know I am not going to win and have no chance, I would trade any single layer that is in their last year. That said I am not sure that one player will get it done.

gregg beat me to it

[onejayhawk]

Right, this is a silly in question in that in any sort of keeper / dynast format you are now talking about an absurd package required to acquire Buxton. Plus, if the team who has him is not in contention this year (and they would know if they are before the season starts) then he is literally unavailable.

How about a more practical player, say Puig or Segura?

J

[mjl]

This is turning out way longer than I thought it would. Maybe I'll submit this to FanGraphs to get some commentary on it, and/or actually do the math for real at some point.

I don't know if this is related to the discussion we had a little while ago in the basketball thread, but the first questions I'd have are how many other teams are in the same "no hope for this season" position, whether Buxton is the best available keeper (at least in your opinion), and how many players you can keep. Another factor is how certain the team you're trading with is about winning this year.

I'm going to make a couple of completely indefensible assumptions and throw some numbers out, just to give you a framework for how I'd think about it and how the various knobs would affect my thinking.

12-team league, one keeper, entry fee is $50, payouts are 300/150/90/60. Note that in a league with minimal keepers like this, the best keepers still won't be evenly distributed, since if you have a cheap Trout and Puig, you're already in great shape for this year and next year you'd much rather Puig be at full price in the auction.

Let's say that in the three years where you have Magical Rookie (henceforth MR) at your bargain-basement price, you automatically move up a spot in the final standings. In my experience there was a pretty high correlation in keeper leagues over the last couple years between having Mike Trout and winning, at least compared to other teams that didn't have some other insane bargains. Then in the next three years where you have this guy at his extended price, you move up a half-place.

In the first three years, the EV of having him is equal to the first prize in the league. Your normal EV is 1 (1/12 * the payout for each place in the standings). Your EV with MR on your team is 75 for the first three years (2/12 * 300 + 1/12 * 150 + 1/12 * 90 + 1/12 * 60) and somewhat less, we'll say 62.5 for lack of doing math where I explicitly define "half-place", for the next three years. If you don't discount future earnings, the marginal value of MR is $112.50.

Given that, whatever you give me has to be enough to move me from a totally average team to something around 2nd or 3rd place quality. (Brief digression: Note that we are assuming here that I don't already have MR on my active team and that he wouldn't even be up this year at all, so basically this is pricing Bryce Harper right after he was drafted or something like that; if MR is already on my active roster you also have to replace all of his performance.) Given our assumption that MR is worth one place right now, and that value is linear, this means you probably need to give me four expiring guys of his value, which would move me from slot 6.5 to slot 2.5. If MR is an active player, a Puig instead of a Buxton, it's five players since you have to replace his performance as well.

Presumably if I'm willing to talk to you about this deal, my team isn't currently average though, and since there's no value to coming in "higher" than first, I might be willing to take a bit less because anything more would be irrelevant, but because of injuries (and because there's no benefit for me to give you a discount) I probably wouldn't.

That feels about right to me. If there's only one keeper, and I'm replacing MR with someone only decent going forward, I have to be comically certain of winning this year to give up that advantage for the next six years.

Factors ignored:
The primary factors being ignored are the time-value of money and the risk of league failure over the next six years. If there's a chance the league disappears over the course of MR's contract, or that the league changes structure in some manner that devalues the contract, you need to take that into account for the future value. I'm not going to do the math correctly right now (and for a lot of us the money we're talking about here is beer money and thinking about investing it is kind of silly), but if you figure some amount of real-world inflation, the value of investing your winnings over the next six years, and the chance that the league fails, the price definitely drops. Again throwing in arbitrary terms, if you say that each year that you can earn 2% over inflation, inflation is 2%, and the league has a 10% chance to fail each year, trading is worth about $127 in six years and not trading is worth about $101, so maybe drop one player from what you need to make the trade. (Math here.)

This is also assuming that if I don't keep MR that I don't have a keeper at all. If the replacement value of a keeper is something non-zero, then the marginal value of MR goes down.

Of course, looking at this from your side, if you know that you're not going to be competitive, you only get one keeper, and MR is the best available keeper, rationally you should be willing to trade your entire team for him, so the only questions are whether you have enough talent to make this worth my while and if anyone else has more. If you have the second-best available keeper, it would even be in your best interest to trade him to another hopeless team for all of their talent and then bundle both groups of players for MR. Silly, but economically accurate! Although this would probably increase the risk of league failure so that would reduce the future value enough that it's not really correct.

okay it's gotten really late and I am not going to do the rest of the math for how it changes when you allow more than one keeper, but clearly each keeper that you add dampens this, since it may be preferable for you to get the #3 and #4 targets than #1 alone, and now that we have to take into account the possibility of multiple trades things get much more complicated.

Anyway, this is why I think keeper leagues that have a very small percentage of players being kept are dumb.

[joncarlos]

In a league with no farm system and one keeper, Buxton is probably not one of the best 12 keepers. Let's say I have Miggy, Cano or Cutch expiring. I would probably rather trade them for Trout or Harper or Puig who has 1 year left, than get Buxton for 3 years.

In a more realistic scenario where everyone gets multiple keepers and Buxton doesn't have much of an opportunity cost (ie, he's a free farm keeper), I'd trade quite a lot for him, but obviously the key question is opportunity cost. Maybe there's a $15 Goldschmidt on a long term deal that I could get for Miggy AND Cano.

[james33]

Any one of them. If I know I am not going to win and have no chance, I would trade any single layer that is in their last year. That said I am not sure that one player will get it done.

Agree with this.

But mjl had a good point re: risk of league failure. Assuming it is a longstanding league so little to no risk of league failure, I'd give any single player up for Buxton. I see the math as fairly simple.

I'm assuming this question is post-auction. Pre-auction, of course the best player's salary matters, and I'd be even more likely to trade my best player with an expiring contract for Buxton.

The best player in the league is worth what, $48? So you are losing $48 worth of a player, all $48 coming during a year you don't care about anyway. And, in exchange, you are getting $1 Buxton for five years. If his average worth is just $11, you are coming out ahead ($50 vs. $48) in the deal.

[mjl]

@jc: If you're trading for someone who only has one additional year of value, and the trade is happening immediately post-auction (so you're trading one year of McCutchen for two years of someone)... I'm even less sure how this math should work because I think maybe you want to look at standard deviations above the mean instead of linear value above the mean, but if you figure the average player is worth $11 and McCutchen is worth $35, you should probably expect to get two years of someone with about $12 of excess value on their contract, like a $10 Freddie Freeman ($23). However this assumes that the other person can replace Freeman with a $10 player for free, which is unlikely to happen, so either you have to throw in a $10 player or they won't be willing to give up as much, so now you're looking at McCutchen and Ryan Howard for Freeman. Of course, the current year's value is kind of meaningless to you, but that's what the other person would probably be willing to give up. But then you get into questions about whether Freeman is one of the best keepers available to you and whether you even want to do this trade or if you'd be better off trading multiple guys for someone like Goldschmidt, as you said.

Note that since the profit you make off Freeman in the current year has no value to you, you are really only getting about $12 of useful value out of this, and you'd probably still be better off trading for Buxton and concentrating all of the profit into the next year. Also if the other person isn't losing any value for this year, they won't need quite as much back.

Anyway, as the question is framed, obviously you would give up whatever was necessary to get him because all of your expiring guys are valueless and you should cash them in for whatever you can, and the more interesting version of the question is how much the other guy requires to make the trade.