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, RotoWorld, and Rotoballer. Follow him on Twitter @BaseballATeam or email him here.

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