Price Ceilings and the New Posting System

Yu Darvish arrived a rock star, but Masahiro Tanaka's contract dwarfs even his (via Mike LaChance).

Yu Darvish arrived a rock star, but Masahiro Tanaka’s contract dwarfs even his (via Mike LaChance).

Masahiro Tanaka was set to be the third pitcher to produce a hefty posting fee for a Japanese baseball team until Major League Baseball and Nippon Professional Baseball agreed to make the maximum posting fee $20 million. Since Daisuke Matsuzaka had generated a $51.11 million posting fee in 2007 and Yu Darvish $51.7 million in posting in 2012, this odd price ceiling was bound to have some odd results. Tanaka had a stronger NPB career than either, so the assumption was that he would generate at least this much.

After months of back and forth, the Rakuten Golden Eagles decided to accept the $20 million fee. Rejecting this reduced sum would not have been surprising, because this is frequently the result of markets with barriers like this. The result would have been that Major League Baseball was deprived of talent that it would have had under the previous posting agreement. Just because it didn’t happen this time doesn’t mean that we aren’t eventually going to see a great player failing to cross the Pacific because of this rule.

The goals of the posting agreement are to allow NPB players to compete in the majors, to allow NPB teams to be compensated for lost talent, and to bring the best players in the world into Major League Baseball. This new agreement fails to accomplish these goals. Installing market barriers rarely produces better outcomes, but later I will discuss what MLB might have had in mind when distorting the market.

To understand what this kind of barrier does, let’s talk about what market effects determined the posting fee under the prior agreement. This will require using a technique called backward induction, the process of reasoning backward in time from an ultimate set of possible final outcomes to determine the correct strategic approach.

It usually shocks outsiders unfamiliar with the system that major league teams paid $50 million just for the opportunity to negotiate with Matsuzaka and Darvish, but the reasoning makes sound economic sense. Since these pitchers have no other options for negotiating partners, the major league team has enough bargaining power in an exclusive agreement to extract a $50 million surplus. Of course, when 30 teams compete for that surplus, they will offer nearly this amount in equilibrium.

Let’s start by discussing what happens to a player who has two years remaining until free agency, which was the case with Matsuzaka, Darvish and Tanaka. According to some very helpful discussions with Patrick Newman of NPB Tracker, any of these three pitchers might have expected something in the neighborhood of $8 million during their final two years in Japan (and probably less), and any major league team negotiating exclusively with Tanaka would know this. Let’s assume that it was known in advance that a six-year deal was being discussed. This is generalizable, as is the assumption of two years remaining until free agency, but it simplifies the analysis to fix these amounts.

When Darvish was negotiating with the Rangers going into 2012, the Rangers knew that he was going to earn about $8 million per season for 2012 and 2013 in Japan, but that if he then leaped over to the U.S. via free agency and tried to seek a four-year deal, he would get substantially more because all 30 teams could bid for his services. Suppose both the Rangers and Darvish suspected that he would get a four-year, $41 million deal. Obviously he would get more than this now, but given how often pitchers get hurt and decline in two-year time spans (think about Daisuke Matsuzaka and his 5.53 ERA in the last four year years of his agreement with the Red Sox), the expectation was that he might get about $41 million.

This concept is known as a BATNA, or Best Alternative To Negotiated Agreement. In this case, Darvish’s BATNA was to receive $57 million over six years. Knowing this, the Rangers offered him $57 million and he was willing to take this, because he was likely to get only $16 million in 2012-13 in Japan and $41 million in 2014-17 in the majors.

Of course, Darvish was likely to produce far more value than $16 million during the first two years of his agreement in 2012-13 in the United States. We know this because we know that the Rangers ponied up about $108 million to receive six years of his service.

What we do not know is how exactly that value would be broken up by year, but let’s use an example. You can write this schedule to be less steeply declining, in which Darvish is risk-averse and, while expecting to receive more than $41 million if he waited until after 2013 to become a free agent, he would be willing to accept $41 million now as a discount on some larger amount. This is a more realistic but tedious to model, though it is a direct extension of the below framework.

Year Value BATNA Surplus
2012 $37 $8 $29
2013 $30 $8 $22
2014 $22 $22 $0
2015 $13 $13 $0
2016 $4 $4 $0
2017 $2 $2 $0
Total $108 $57 $51

This is where the backward induction strategy comes into play. Every team has a different value, and chances are that the Marlins would have been hard-pressed to generate $108 million of revenue with six years of Darvish’s services, but suppose that at least a couple of teams had about this schedule of expected values—maybe the Red Sox and Rangers.

If the Rangers had to bargain with Darvish in the absence of any posting fee that they owed, it’s possible that Darvish’s agent would have been able to negotiate for more than $57 million. After all, we know that the Rangers would have been happy to pay as much as $108 million (because they did). However, if the Rangers had to pay a $20 million posting fee, they would be willing to pay only $88 million because they could keep their posting fee otherwise—signing Darvish to an $88 million deal with a $20 million posting fee costs $108 million. What about a $40 million posting fee? In that case, they would be willing to pay up to $68 million.

You can probably see where this is going. The Rangers are willing to offer as much as $51 million to obtain negotiating rights, at which point their hands are tied, and they are willing to pay only $57 million. Since by assumption the Red Sox are also willing to pay $50.999 million (or $51 million “minus a biscuit” as my British adviser used to say), the Rangers trying to offer any less will just lead to a loss of the opportunity to negotiate.

Sometimes this is easier to see graphically, so let’s draw this one up.

The full boxes’ height each year represents what Darvish would be worth to the Rangers in each year. The red boxes’ heights represent the amount Darvish could earn each year if he did not reach agreement with the Rangers—low for two years in Japan but higher starting in year three once he could be a major league free agent. The two gray boxes within the larger boxes representing years one and two show the surplus value that could be gained by negotiating with Darvish if he had no bargaining power—they are the gap between his major league value and his hypothetical NPB salary (his BATNA).

Since we used backward induction and determined that the bidding team would offer Darvish’s team the full surplus value to get this right, we know that the sum of the red boxes represents Darvish’s salary totals, while the gray boxes represent the posting fee that his team received.

There are a bunch of little bells and whistles that you can throw into this model, including uncertainty, risk-aversion, discounting, and opening up other negotiating points of contention like the length of the deal or perks. Introducing slightly different values among elite teams and teams that shade down their bids from their indifference point is more realistic. But these do not qualitatively change the results, and they have minimal quantitative impact in equilibrium anyway. The general structure will remain, and it’s why you end up with posting fees in the neighborhood of $50 million.

Now let’s change the rules, but assume for simplicity that Tanaka is equally valuable but no more valuable than Darvish. The Red Sox and Rangers will be our dueling teams (yes, I know that this should be generalized to include more teams), but neither can offer more than $20 million. Now Tanaka is allowed to let them both bid on his services. Obviously anything less than $20 million would kick them out of the bidding, but once they are both in, they are willing to pay $88 million — and will have to because anything less will be outbid by the other.

Either way, a team will spend $108 million. The new way, Tanaka gets more money and the Golden Eagles get less money. That’s a pretty amazing outcome for Tanaka at first glance, considering that when MLB and NPB hammered out their new agreement, he wasn’t even at the negotiating table!

But there’s a problem. Go back up and look at the table of potential values for Darvish by year (again assuming that Tanaka is just as valuable). What do the Golden Eagles get under the new system if they post him after his first year? They get $20 million. And what if they wait a year and post him after the 2014 season? They get $20 million. Based on the numbers that I wrote above, teams would be willing to bid up to $22 million so they would pay up to the price ceiling of $20 million.

This begs the question: why not wait to post Tanaka until next year? He would not have been useless in 2014. On the contrary, I’m sure the very fact that Rakuten floated the concept of an $8 million salary means he was probably worth more than that in revenue. If the Golden Eagles had been willing to take the risk, and expected that they would be able to get a $20 million posting fee during the 2014-15 season offseason anyway, they might have waited.

Now, the reason the decision was far from a slam dunk is because of how close that number is to $20 million. If we expected him to generate an $18 million bid after 2014—which is very reasonable under slightly different assumptions—then they may have been better off posting him now. The question is why either league would let this happen.

Let’s walk through the effect of the price ceiling on all parties. If Tanaka gets posted anyway, he wins out at the expense of the Golden Eagles, but if he does not he risks an injury or an ill-timed decline in talent, in which case he would never earn the way he would have under the previous agreement. The Golden Eagles obviously lose out here—no ambiguity there. And realistically, the potential major league team that would agree to dish out more than $100 million to some combination of the Golden Eagles and Tanaka, is also losing out.

On its face, this seems like an inefficient outcome. Tanaka would be worth something close to $40 million on a one-year, no-strings-attached deal to a major league team and about $10 million to a Japanese team. There’s money that seems to be left on the table. A properly negotiated agreement should be able to distribute that $30 million of extra value between the parties to make them all better off than a situation in which Tanaka stays in Japan.

One sneaky way around the rules was proposed here by Ben Badler. It involves posting a second player who will also generate a $20 million posting fee but will not be worth it on his own—this would only be because his agent and the Golden Eagles have a firm agreement to negotiate both deals or neither. But the incentives to create black markets like that are why economists usually advise against price ceilings in the first place. Plus, chances are either NPB or MLB, or maybe both, would have struck down something like that.

So, is MLB run by idiots? Did they not foresee this result? I doubt it. I’m sure that someone voiced the possibility that the Golden Eagles might opt out during all those discussions.

For one thing, MLB’s stated objective was to reduce the posting fee because that money was not subject to the luxury tax. That’s all well and good, until you realize that MLB could have just said that any posting fee in excess of $20 million would count toward the luxury tax. The same result would happen—the team that values the player most would still be the one to end up with him and the team would spend the same amount, but the possibility of waiting a year to post would be eliminated. So that doesn’t explain it.

Here is where I think Major League Baseball was going with this: Why did the Rangers value Darvish at $108 million? Was this all Japanese television rights and jerseys? That is doubtful. Most likely, they were paying for wins (and the ensuing impact on their playoff potential).

Here’s the thing—the market is not guaranteed to be efficient when there are externalities involved, and that’s exactly what more wins for the Rangers are: externalities. If Darvish adds five wins to the Rangers, Major League Baseball still finishes the season with 2,430 wins. There are still 10 playoff teams. The wins and playoff appearances Darvish’s team enjoys get taken away from other teams.

The net effect is that one of those teams paid money to create an externality on its opponents—more losses and a lower playoff probability. This externality creates inefficiencies from the teams’ collective perspective. Actually, this is why baseball lets only about a third of its wins created (in terms of WAR) be eligible for competitive bidding in free agency; the rest of players are subject to either arbitration or the reserve clause and earn less than their free market value.

This agreement is just another form of limiting the amount of WAR that will be paid for at the market price. As a whole, major league teams will generate nearly the same revenue as they would have. Maybe there would be a little more advertising revenue from Japanese viewers, a few more jerseys, and the effect on revenue of a slightly higher league talent level, but the impact on ticket sales would be minimal. However, the total costs of all 30 teams combined would be just a little bit higher.

Does that mean this was the efficient move? No, it does not, even though the players collectively might be getting about $108 million more and the teams might be losing a few million combined. Teams would not quite lose $108 million more, because presumably the five losses spread through the league would cost some revenue, but not enough to offset the full effect on the winning bidder. Even if they would lose $100 million (to pick a number), the teams together would be better off by $8 million.

However, in aggregate, Tanaka would still generate more revenue stateside than he would in Japan. This is mainly because of all the publicity and because a higher overall talent level has to help MLB.  The problem here is simply a matter of incentives, which is that the 30 MLB teams collectively lose out if more money is spent on salaries. Since they can act collectively in negotiating with NPB, they have enough bargaining power to create an agreement which leads to less money being spent.

The Coase Theorem guarantees that an efficient solution could be reached with no costs of negotiating as long as all property rights are defined, and it is actually quite straightforward what should happen: MLB should get a chunk of the posting fee. It should let the posting fee go all the way up $50 million or higher (I had heard $75 million was possible for Tanaka), and MLB should take enough of a cut from the Japanese team that after distributing it across the league, the 30 owners would collectively be better off.

The remainder left over for the Golden Eagles would just need to be high enough to get them to post Tanaka. To entice them, MLB would only need to create the system in which posting Tanaka after 2013 would generate a sufficiently higher fee than waiting until after 2014, which was clearly not true in this case and almost derailed the posting.

This would have been a far better alternative and would help avoid the damage of a price ceiling on posting fees when this ceiling discourages a Japanese team from posting a superstar in the future. Perhaps when this agreement is renegotiated in three years, MLB will heed this warning and construct an agreement that puts a better product on the field.

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  1. Jason said...

    I think you are ignoring MLB’s nuclear option, which would be to treat NPB contracts like college coaches treat contracts. MLB could simply treat Japanese players as free agents, and let them negotiate their own breach-of-contract with their former Japanese team. If Tanaka were worth $10M to Rakuten, then it is hard to see where they would be able to claim losses on the contract of greater than $20M. This, as far as I know publicly unspoken option, limited NPB’s negotiating power. It ends up with more money in the hands of players or MLB team owners and less in the hands of NPB teams. This is what I perceive to be the goal of the agreement from the MLB/player’s association point of view.

    • Simon said...

      It ends up with less money in the pockets of MLB teams too. Tanaka got far more than Darvish, despite being an inferior option. While there’s undoubtedly been inflation over the two years since Darvish signed, it hasn’t been anything close to the difference in the two deals.

      • Matt Swartz said...

        I think it’s far more likely that Darvish raised expectations for Tanaka. Translating Japanese statistics is a process plagued by small sample size. According to your explanation, teams were willing to pay $50MM more to negotiate with Darvish, overestimated Darvish’s eventual contract by $50MM, or some combination of the two– but simply left that money on the table.

      • Simon said...

        I think the difference is largely due to the way that the process is handled. A traditional free agency approach, where the player and his agent can play teams off against each other (as happened with Tanaka), will likely generate a better deal for the player than the previous posting system where the initial bids were blind and on a one-off basis, and the subsequent negotiations were impacted by the various factors you mentioned.

      • said...

        Here’s the problem with that. Nobody forced the Yankees and several other teams to pay this much money. The bidding process may have pushed them into offering it, but clearly they were willing to pay $175 for seven years. If you’re right that Tanaka and Darvish were viewed as having a similar talent level, then teams were willing to pay around $150 million for six years given salary inflation.

        Anybody could have seen that Darvish would about $57 million to play. That means that if push came to shove, the “right” bidding process could have goaded any number of teams to offer $93 million as a posting fee. But nobody offered more than $52. So several teams left close to $41 million on the table that they would have been willing to pay but for the bidding process was sealed? No team could have predicted that anyone would have spent $52 million and decided to drop a $53 million number into the hat? Is that really more likely than the fact that just maybe Darvish made NPB look like a higher caliber league than before and upped the estimate for the Tanaka’s value?

  2. Carl said...

    Matt – Great article – as always and congratulations on being chosen to write the lead-off article on the new HBT.

    Jason – MLB and NPB need to work together to avoid destroying NPB by depriving it of all the league’s stars. neither side (more American players play in Japan than Japanese players play in MLB). Also, don’t forget about exchange rates. While the Yen is weak now and the dollar strong , there have been, and will be again, times when the Yen is strong and Japanese players wont have an economic incentive to play in MLB.

  3. said...

    This is phenomenal work Matt.

    I agree that there are better ways to handle the bidding/posting system, and you outlined a solid alternative, but how likely are we to see this be altered (much) once this initial agreement is over if the NPB is able to secure upwards of $20MM through the posting system for lesser talent at positions that are scarce for talent in MLB?

  4. said...

    Thanks for your comments.

    The point is that MLB probably wants to limit the amount of money spent on players– it’s not about maximizing their profits plus player salaries, just about maximizing their profits. Having an agreement that limits the amount spent on salaries & posting fees is beneficial.

    You make a good point about how the MLB benefits from Japanese baseball being popular. An international sport makes more money nationally. However, I think the exchange rate issue, while relevant, is going to be overrated here. The potential salary is so much higher in dollars that even exchanging it back for yen isn’t going to adjust. Plus, the exchange rate will move based on inflation (buying power) anyway. It’s an interesting factor in this whole thing though.

    • Jason said...


      Yes, but if it’s a zero-sum game as assumed here, i.e. Texas will spend the same money whether it goes to the player or as a posting fee, then you have to assume MLB would rather keep their players happy than the Japanese owners.

      And at any rate, the bidding for a right to post (The old system) was much more ripe for underhanded manipulation of the process than the current system. There was nothing to prevent, say, the Red Sox from offering $200 million to Rakuten and then not following through with the negotiation just to keep him out of New York at no cost to themselves.

      At the end, it is not a perfect system but it seems like they probably hit the balance pretty well.

      • Matt Swartz said...

        If you look at the link to Ben Badler’s suggestion in the article, you’ll see that there are plenty of ways to manipulate this system too. The reason that nobody would bid $200MM and refuse to negotiate was a matter of respecting the system so that it would not be changed. It is no less manipulable now with a market barrier.

        Also, my main proposal was to NOT make it a zero-sum game: instead they should let a share of the posting fee be distributed to the other 29 teams. MLB owners come up further ahead that way, and there isn’t as high of a risk of unposted players.

  5. Jason said...

    But there were eight times the previous system broke down in just such situations, where teams won the bidding and then failed to negotiate. The extent to which they negotiated in bad faith is impossible to determine, but it is almost certain that it was abused. But at any rate, 8 times the previous system failed to get the player into MLB. The current system has been tested once, in a scenario which has made it more likely than any previous in history for a team to not accept the new system. And they still accepted it and posted him for the cool $20M. How likely is it that another player will come along of Tanaka’s caliber, under multiple years of team control, before 2016 when this deal will be re-worked? Very, very little risk at all.

    • Jason said...

      Actually I am wrong about the 8 unsuccessful postings. There is still the case of Hisashi Iwakuma, of course, but I clearly overstated my case. Nonetheless, buying two $20M postings, when one was obviously not worth it would be a pretty overt way to skirt the rule and would involve lots of people holding up their end of a shady deal, compared to the relative ease of outbidding a posting by a few million and then making an extremely halfhearted negotiation. I don’t think you can overstate the problems with the previous system.

      • Matt Swartz said...

        Eight times didn’t sound right. Whether there is a Japanese player who is as good as Tanaka in the next three years I can’t say. Eventually there will be a better player and eventually $20 million will shrink relative to MLB salaries. Anyway, if you wanted to fix the old system but leave the framework in place, you could make a portion of the fee non-refundable, maybe $1MM or something. There are almost always better ways than a price ceiling or price floor to distort the market the way you want.

  6. Paul said...

    Great article, but I have a couple of questions which I’ve asked to quite a few baseball writers through e-mail, Twitter, etc. that I’ve never received a reply: What is the impact of television revenue to the team that signs the Japanese player?

    When the Red Sox signed Dice-K it turned into a giant media event, and throughout the course of his first couple of seasons with Boston there was a never ending stream of Japanese reporters and television people following his every move. Because the Red Sox own NESN, do they benefit from the broadcasts in Japan? If so, how much? Is it worth paying these Japanese star players the amounts they do because of the potential future revenue which the team does not have to share with MLB?

    All the articles criticizing teams “wasting” money on these Japanese stars might need to be reconsidered if the economic impact to the team is substantially lowered due to the amount of dollars taken in from Japan. A Tanaka or Dice-K signing would then be similar to a Matt Garza deal instead of colossal waste of money.

  7. Morris said...

    Really enjoyed the article, but one question I have is:
    Is it possible that Japanese pitchers want to play in America for more than just the money reasons? Why would they leave their home country where they’re already a legend and likely will receive the exact same sum of money as offered by an MLB team unless there’s an appeal to play in America?

    If this is the case, is it possible that for certain Japanese players who especially want to play in the MLB, under the old bargaining agreement, teams had extra leverage and could thus go slightly “over-slot” on their bids for rights to negotiate but make up for it by slightly “lowballing” the free agent? Perhaps Yu Darvish would’ve commanded more than $57 in the market if he was clearly stating that he was indifferent in playing in the MLB vs. Japan, and money was the chief concern. Let’s say that he could command 1MM/year extra in Japan, at $63 MM total. Then, teams would pay a posting fee closer to $45 MM. According to wikipedia, of the 16 Japanese players who received bids under the old rules, 14 in the end signed with the MLB team. It seems quite likely that posted players are very likely to play in the MLB once a team bids on them, possibly because there’s a selection bias in the players who are posted (aka, they may be posted partially as a result of expressing a great desire to play in the US). I am wondering if the new collective bargaining agreement prevents “lowballing” contracts from happening by preventing teams from jacking up bids beyond the equilibrium point for the exclusive negotiation rights. This is purely speculative, I don’t really have evidence of this phenomenon existing, but theoretically, could it impact the decision on putting such a price ceiling in place?

    • said...

      Morris, this is an interesting point, but it will not actually adjust the amount paid in equilibrium, only the split between Japanese player and NPB team. If a team knows that there is a premium associated with playing in the MLB, they would determine the contract needed to sign the player to be less by the amount of that premium, and then bid more under the old system. In the current system, that money goes to the player. But the key is that it would go to the bid before. The team still backwards induces what it will take to sign the player and subtracts that from their maximum willingness to pay. Combined, they pay their maximum willingness to pay.

  8. Paul B said...

    I feel like MLB put a price ceiling on the posting system to try and squash the NPB somewhat. I think that the MLB would rather that the money go to the players in their own league and not to another competing league. By giving players from Japan more money it gives them more incentive for those stars to come over to the US, which in turn hurts the Japan league.

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