Far East Rumors and Game Theory

Lately, there have been persistent rumors that Major League Baseball and Nippon Professional Baseball (NPB) are considering a major change to the posting system – perhaps in time to affect Masahiro Tanaka. One of the most commonly rumored proposals is a system that would allow three teams to “win” the post. In New York beat writer Joel Sherman’s words:

There had been speculation the system would undergo radical changes, with perhaps even the teams with the three highest posting bids all gaining the rights to negotiate with the players.

He goes on to note that the posted player may get the opportunity to pick one of three top bidders. For the sake of simplicity, let’s leave that wrinkle aside for now.

Our own Eno Sarris has already provided some helpful analysis on these rumors from the perspective of the different stakeholders in the process. For those who are unfamiliar with or need a refresher on the posting system, I recommend this short wiki-style post on baseball-reference.

In brief, the posting system is designed to allow Japanese players to leave Japan for American professional baseball prior to their free agency – which typically takes 10 seasons. Usually the player requests to be posted, but that’s not a hard and fast rule and the Japanese team is under no obligation to post a player, even if he wants to be posted. The posting fee itself is meant to compensate the Japanese team for losing a good player.

We can only speculate as to why the MLB and NPB are interested in negotiating a new system, but the impetus is probably financial in nature. The most specific comment I can find is a not-quite-quote from MLB executive Kim Ng that they have talked about issues involving the posting process.

In recent seasons, posting fees have grown dramatically, as evidenced by Yu Darvish‘s record $51.7 million posting fee prior to the 2012 season. Tanaka is expected to easily exceed that posting fee despite that scouts uniformly agree that he has less upside than Darvish.

One reason why posting fees have grown is the new Collective Bargaining Agreement that was negotiated prior to the 2012 season. Changes to the draft, international spending, and luxury tax system have constrained clubs from spending excess funds in traditional ways. However, posting fees are not considered part of a team’s international budget or payroll. In other words, teams can spend as much as they want on posting fees without the luxury tax or draft pick penalties coming into play.

By allowing the three top bidders to compete, the player will likely sign a more lucrative contract than under the current system. Ostensibly, major league owners expect posting fees to decrease while Japanese owners must expect similar overall fees or some other form of compensation. With all the stakeholders featuring competing interests, agreeing to a change will be difficult.

We can tinker with Game Theory to test whether or not the rumored proposal makes sense. Game theory is designed to simulate the decisions of two players, so in this case let’s start with a game between Team A and Team B in a hypothetical two team league, with the winner getting the opportunity to negotiate with the player. Let’s assume that both teams want to win the post, they have comparable resources, and there is no opportunity for collusion. They can submit either a high bid or a low bid, but the specific amount in either case is unspecified.

2x2 Game

The top left box is considered the equilibrium choice in this game. All participants know that the only way to win the player is to Bid High. In fact, if the team wants to win the posting, the decision is really Bid High or Bid Higher. Multiple iterations lead the optimal strategy towards ever higher bids, which is part of the reason why Tanaka’s post is expected to exceed Darvish’s record.

And this was only a two participant game. In reality, there are 30 participants and any number may choose to bid.

Now let’s considered the rumored proposal to allow the top three posting teams to negotiate with the player. This scenario is too complicated to capture with a simple 2×2 table, so let’s talk through it instead.

Let’s say that 10 teams are interested in signing Tanaka and that the top three posting teams will get to negotiate with him. Team A has to Bid High for a chance to win, but it’s likely that they have to actually Bid Higher(ererer). All other participants also see this and it becomes a guessing game as to how many orders of “higher” are necessary to be in the top three. Just thinking through this scenario, it doesn’t appear as though we can expect posting fees to decrease substantively.

Furthermore, a team that wants to flex their financial might could opt to submit an enormous bid. Whether the posting fee is ultimately the highest bid or an average of the top three highest bids, an enormous bid would push the cost of entry higher. If multiple teams – say the Yankees and Dodgers – executed this same strategy simultaneously, the result would be a very high posting fee.

So we’ve identified that players will cost more and posting fees will probably continue to escalate under the rumored change. If that’s the case, why would major league owners agree to a system that causes them to spend more money?

It may be a matter of preference. Like with traditional free agency, the proposed rumor makes it very likely that the team with the highest overall budget for a given player will win him. Using Tanaka as an example, let’s say the Yankees, Dodgers, and Angels are the three teams who get to negotiate with him and that the average post is $65 million. Let’s also say that for the posting fee plus salary, the Yankees planned to spend $150 million, the Dodgers $140 million, and the Angels $130 million. For the sake of the example, let’s say those are fixed budgets. In this case, unless Tanaka has a strong preference to pitch in Los Angeles (or maybe he really wants to bat), he’s going to end up signing with the Yankees.

From an economist’s perspective, there’s a certain beauty to seeing the team with the highest overall valuation win the player. But given the asymmetrical distribution of financial resources around the league, that’s an extremely unfair approach. Of course, the current system is also unfair.

Having completed this thought experiment, I have to conclude that the MLB and the NPB are unlikely to agree upon the most commonly rumored change to the posting system. An as yet unspecified change could be made or small adjustments to the current system, but the three bidder approach has a lot of downside and very little upside for major league owners. My best guess is that the MLB wants posting fees to count against the luxury tax or international budget in some way.

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Brad is a former collegiate player who writes for FanGraphs, MLB Trade Rumors, The Hardball Times, RotoWorld, and The Fake Baseball. He's also the lead MLB editor for RotoBaller. Follow him on Twitter @BaseballATeam or email him here.

26 Responses to “Far East Rumors and Game Theory”

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  1. baruchk says:

    why wouldnt posting fees decrease substantially? Lets say under the old posting rules, team A would bid 65 million in an attempt to secure Tanaka. Under the new posting rules, would that team really spend that much? In my opinion, they would probably spend more like 50 million. Salaries for these Japanese players tend to be similar, if not more, than the posting fee. How many teams can you logically see spending over 100 million on an unproven commodity? To me, you have the new york and LA teams, and possibly a surprise contender. And lets say you bid 50 million and somehow don’t end up in the top 3. Now 3 big market teams have their hands tied trying to negotiate with Tanaka and are probably out of the market for alot of other free agents at the moment, leaving you with more options, especially if team A doesn’t have a payroll around the luxury tax already

    I just can’t see how this new system wouldn’t lower the posting fee when all you have to do is get into the top 3 to have a shot.

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    • piratesbreak500 says:

      Interesting take, though the idea of “unproven commodity” isn’t as relevant as it used to be. There’s now been a pretty decently large number of folks who have come from across the pond, so we’ve got a pretty good idea of what his performance would look like in the US. The only big question is the recent drop in strikeout rate.

      SO yes, he hasn’t pitched in the US, but with scouting and stats, we have a solid idea of probable performance level.

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  2. Dave says:

    Interesting take. I think it depends a lot on whether they take the average of the top three bids, though. If not, it could have the opposite effect. Take your scenario:

    “Using Tanaka as an example, let’s say the Yankees, Dodgers, and Angels are the three teams who get to negotiate with him and that the average post is $65 million. Let’s also say that for the posting fee plus salary, the Yankees planned to spend $150 million, the Dodgers $140 million, and the Angels $130 million. For the sake of the example, let’s say those are fixed budgets. In this case, unless Tanaka has a strong preference to pitch in Los Angeles (or maybe he really wants to bat), he’s going to end up signing with the Yankees.”

    If the top three bids were Yankees (80 mil), Dodgers (65 mil), and Angels (50 mil), then the player would actually have an incentive to sign with the Angels, since even though they have the smallest overall budget, they will have the most money leftover available to give to the player himself. In that case, teams might be incentivized to NOT bid way over the top, as if there is a large gap between their bid and the other winning bids, they might discourage the player from choosing their bid. In this case, bids could actually come back down.

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    • Brad Johnson says:

      I can’t imagine either league would give the player any ability to affect the posting fee like that. I would expect that the options are either an average of the three bids or the top bid.

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      • B N says:

        Taking the average wouldn’t make any sense though. How are you supposed to place a bid when you know that your bid is going to be averaged with two others that you have no idea about?

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        • octelium says:

          Then you bid low to bring the other bids down.

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        • pft says:

          If the average is too high for you, you simply don’t make an offer to the player

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        • olerudshelmet says:

          Previously the posting would have been won by one team. Naturally an average will be less than the high bid. The other two teams would have not even had the opportunity to negotiate previously. Although I’d imagine that any one of the final three teams could decline to pay the average price or match the high bid.

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        • Simon says:

          Presumably you wouldn’t be under any obligation to actually make an offer if the average was too high. I mean, if the bids were Yankees $60 mill, Dodgers $60 mill and Pirates $20 mill, then the Pirates would likely drop out gracefully at that point.

          Anyway, it’s hardly any less logical than a system where the highest bid is used.

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  3. Jim says:

    I’m a professor of economics and teach game theory. The example and matrix in the article need a bit of work and explanation before they are useful.

    First we need payoffs that are either numbers or at least magnitudes. The key question in analyzing a game is “given what my opponent did, am I happy with my choice?” In this case, if the other team bids high, do I want to bid high or low? If the other team bids low, do I want to bid high or low? If each team is happy with its bid given the bid by the other team, we have an equilibrium that we can view as our prediction of the outcome.

    We could easily imagine a situation in which both teams bid low and are happy with their choice. Under the old regime, if both bid low only one team will win and get to negotiate, so each team has an incentive to “bid up” to try to win, assuming they value the posted player more than they will ultimately have to pay in bid plus salary. Under the new regime, this may no longer be the case: each team will earn the right to negotiate simply by being one of the top two high bidders, and so the incentive to bid up is reduced.

    Of course which outcome we should predict depends heavily on the precise structure of the auction, which as the article notes is not fully known yet. In particular it will be important whether all the top bidders have to pay their bid (or the average bid) or whether only the high bidder will have to pay.

    Finally, the branch of economics called auction theory is the study of these type of games. One key result in auction theory is that if bidders are symmetric in the sense that their valuations of the player are drawn from the same distribution, then we should expect different auction designs to yield similar revenue for the seller. But if bidders are asymmetric—as they are likely to be in MLB given different revenues and different locations on the marginal value of a win curve—in general we see that the design of the auction matters a lot for revenues, and, importantly, we can no longer be confident that the player will go to the team with the highest valuation of the player. This is because of a tradeoff inherent in lowering my proposed bid: I may win the player at a lower price, but I lower my probability of winning because there is a bigger chance that another team has a high valuation and so bid higher than my new, lower bid.

    In sum, the difference between the old and the new posting system is likely to be a complicated proposition that will require some pretty heavy analysis. My intuition though (acknowledging the uncertainty in the design of the new system) is to expect the highest bid to be lower than the previous high bid, the sum of the three top bids to be higher than the previous high bid, the player to more frequently go to a team other than the one that values him highest, and the player to earn more in the contract.

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    • Jim says:

      Also I should have said thank you to Brad for opening this discussion and bringing my attention to this potential change!

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    • Brad Johnson says:

      Thanks for the post, I appreciate it. Most of my more advanced undergrad work was done on the Winner’s Curse, so I’ll admit I’m a bit fuzzy on game theory specifics. I did try to relay that I was using a bastardized version of game theory to draw my conclusions, but you did a nice job here of cleaning things up for me.

      One thing I did a poor job highlighting is that not all Japanese prospects are created equal. The Nori Aoki’s of the world who only see a couple teams interested in them should be expected to have lower bids, but players who have upwards of 15 teams involved like Tanaka may =still see very high bids. And repeated games should continue to inflate the bid price more than typical MLB inflation, subject to the money actually being available. At least that’s my best guess.

      Also, if you know your bid will be averaged and you have the financial resources, there is some incentive to attempt to offer the highest bid. The team would know that the average bid will be less than their bid, another winning team may opt not to pay the average, and the player will have been signaled that your team values him most.

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      • Simon says:

        I doubt the player really cares who bids the highest, especially assuming that the Japanese club gets the same money whoever signs him.

        The other thing with these systems, which I don’t think has been pointed out, is that they can be gamed by MLB clubs colluding. Not that MLB clubs would ever collude in any way, but theoretically, at least, some of those who are most interested in Tanaka could save substantially if they share some information. While it’s likely to be partially offset by having to pay the player more, it does seem to be a potential issue.

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  4. Ed says:

    Generally in the past, the rumors have been of one team bidding way higher than the others. If you only have to be in the top 3, I think that takes away some incentive to blow everyone else away. Now that just being close to the top is sufficient, I think teams are less likely to try to try to drastically outbid everyone else.

    I also think they’re most likely to make the posting fee be the lowest bid of the top 3. Doing anything else screws over the #3 team if they placed an honest bid – possibly even the #2 in a case where the #1 blows everyone else away. Using the average or highest also works against the goal of keeping the fee down.

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    • Simon says:

      Why would the Japanese clubs go along with such a system?

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      • Brad Johnson says:

        And that’s pretty much my point. If you adjust the proposal so that it makes sense for MLB teams, then NPB has no reason to participate. And vice versa.

        The players seem to be winning here, but they’re the only stakeholders with no leverage or control over the situation. You would expect any change to claw back money from the player like with the amateur draft and international free agents.

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        • TKDC says:

          There really is nothing other than a gentleman’s agreement and perhaps the honor of individual Japanese players keeping MLB from just letting any Japanese player either be drafted or signing as free agents (or matriculating to MLB teams in any other way they see fit). There isn’t some international Baseball treaty between the countries. MLB would obviously not want Japanese teams to possibly pouch players, but some level of negotiating for a fair outcome for all parties seems plausible, and that might mean a bit less for the Japanese teams.

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  5. pft says:

    Your premise that posting fees will continue to escalate is false, or at least it is not very well supported.

    Logically, the posting fees are as high as they are only because the team that wins the bid has no competitors and can lock in the player at below market rates. The change in the posting process means higher salaries, and less benefit to avoiding the tax, so obviously posting bids will be lower since the benefit of a bid in the top 3 is not as high as it was when only the top bidder could negotiate with the player. Not to mention the effect when the 3rd lowest bidder wins the negotiation because he has more money to spend on salary given his lower bid.

    Furthermore, from a competitiveness issue, MLB does not want high revenue teams to have a competitive advantage. Short of counting the posting fee as salary in some way, or taxing the posting fee in its entirety regardless of the teams salary, the best strategy is to reduce posting fees and increase salaries required to sign Japanese players. This proposed system seems to do that.

    From the players side, the Japanese players are the driving force obviously since they will benefit enormously.

    The MLBPA can not be happy with the teams having a loophole to avoid the tax and cheaper alternatives to the free agent market. In a bizarre world where paying 50+ million in posting fees makes financial sense to avoid a few million in luxury tax, this can only suppress salaries of MLB players. Instead of the Yankees for example bidding competitively for one of the free agent pitchers in this years pool, and resigning themselves to pay some tax, they instead will be looking overseas and spending money to enrich some Japanese teams pockets while taking a huge risk on a mature rookie with declining K rate, despite huge failures of the posting system in recent years or pitchers like Daisuke and Igawa.

    As far as I can see, the only losers here are Japanese teams, who are likely moving forward as a result of pressure from the Japanese players union.

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  6. Erik says:

    If they are looking to make things more fair for the Japanese players they might consider going to a system where the player chooses the winning bid, but has to pay his club the difference in posting fees.

    Of course the more teams the player is allowed to chose between the lower the posting fee is likely to become. As it stands I believe every proposed change is likely to lower the amount of money the controlling club takes home.

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  7. joe says:

    It seems to me your analysis is based on the idea that the posting fee would be the average of the three bids. But what if that is not the case. What if it is either average or original bid (the higher one). There the team will need to bid enough to ensure a top 3 bid, but that also cuts into money they will offer the player. For example, if the Yankees bid 80 million instead of 65 million, their available funds would fall to 135 million, meaning they loose to the Dodgers,

    It also seems to me that a neglected part of this is the impact on second-tier Japanese players. For example, the Brewers stole Aoki for 2 million (they were surprised to win) and turned that into a 2 year, 3 mil deal with a 2 million dollar option for this year. If there was a top 3 system, more teams would submit such speculative bids, driving the player’s salary up and perhaps getting the suprise candidate as posting the highest price.

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  8. flailing says:

    Doesn’t google award the winner of its adword bidding to the highest bidder but they pay they price of the second highest bidder plus a penny. Varian worked through the math and showed this was the optimal auction process that encouraged bidders to put in higher prices. In this case, the posting fee would be the the 3rd highest and the top 3 would be able to negotiate.

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    • Brad Johnson says:

      You’re referring to a Vickery style auction. That is one possible alternative, but I’ve not seen any rumors about it being on the table. It will be interesting to see what they decide since they’ll need to put a system in place pretty soon.

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  9. Mr Punch says:

    Agree with Ed’s point – plan removes incentive to blow competition away. For example, I’m pretty sure Boston’s unprecedented posting fee for Matsuzaka was predicated on avoiding an exchange of bids with the Yankees.

    But isn’t the biggest issue here the matter of in effect buying players from other teams for cash? The more MLB implicates itself in the posting system, the less it can justify barring its own teams from selling talent. Or is that in fact the intent? As Bill James noted decades ago, the current ban tends to raise the cost of free agents.

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  10. Spencer Dean says:

    One thing, why does everybody assume the Japanese team gets the only the highest bid? Is not the system designed so that they now receive ALL THREE bids? In which case, npb teams stand to make far more money

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  11. chuckb says:

    It seems to me that teams are now (or will be) competing not with the 2nd highest bidding team but with the 4th highest bidding team in order to gain the right to negotiate with the free agent. There’s no need to be 1st, to have the highest bid. Teams just need to be better than 4th. It seems, then, that a 2×2 payoff matrix could still be constructed between any given team and the 4th place bidder. We don’t know which team that would be or what their bid would be but it seems that the only 2 bids that really matter are the 3rd and 4th place bids.

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  12. tz says:

    How about just having an agreement that the MLB team signing a “posted” Japanese player pay a posting fee equal to a fixed percentage (say 50-100%) of the total value of new MLB contract?

    The players get to negotiate with multiple teams, the Japanese team gets compensation, but there’s no need for the MLB teams to sweat out a game of “chicken” on how much to overpay the Japanese team just for the right to sign the posted player.

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