Are the Rays Playing a Zero-Sum Game in the International Free Agent Pool?

No one would ever associate the Tampa Bay Rays with spending money. But in this past year’s international free agent (IFA) signing period, they did exactly that. As Robbie touched on a while ago, the Rays spent a lot of money in the IFA pool and are subsequently getting punished for it. As you can see here in the CBA, there are levels of penalties for going over your allotted Signing Bonus Pool. 

Tampa Bay was allotted $2.9 million for the 2012-13 international free agent signing period, they then proceeded to break the bank in signings as they have currently spent over $3.7 million. $1.55 million went towards Jose Castillo, a Venezuelan LHP with huge upside and another $1 million towards promising right-hander Jose Mujica, and between them and catcher David Rodriguez, who got $600,000, the Rays were already over the $2.9 million maximum between those three alone.  The steepest penalty for international signings was going 15% over 2.9 million for a total of $3.335 million- the Rays actually went 28% over the allotted pool and it will certainly cost them. They will pay $812,000 in taxes (100% of the amount they went over), and will not be able to sign any player in 2013-14 for more than $250,000. But here is a thought, was Tampa Bay playing a Zero-Sum game in the IFA pool this year?

Game Theory is the concept that you always want your average yield from a game, say a lottery, to be greater than the price you pay to enter. Using the lottery ticket example, let’s say there’s a simple lottery when you pay $1 to enter and there are two possible results: you don’t win and lose your money or you win $1 million, with the chances of that happening being 2 million to 1. The average winnings from a ticket would be 1,999,999/2,000,000 multiplied by 0 plus 1/2,000,000 multiplied by $1 million, which would be 50 cents. That seems nice- your average result from your ticket is positive!- but Game Theory tells us that really you have to subtract that 50 cents number from the $1 you paid to get the ticket, meaning that your average result is to lose 50 cents so you shouldn’t participate in the lottery (and whoever is running the lottery will make a lot of money as long as enough people enter). The 1 million number looks shiny (and real lotteries have all sorts of other outcomes to make the odds of winning look much better), but Game Theory tells us only to gamble when the potential reward exceeds the risk. That’s a concept that can be applied to international free agents as well.

When you’re signing a 16 year old international free agent, their are a variety of outcomes, with the most likely being that the player never pans out and fails to get out of rookie ball and the best being that the player lives up to all of his potential and becomes a major league superstar. For each player, teams have to evaluate whether his potential of becoming a big league player outweighs the risk of him falling apart along the way. Expectations can vary substantially based on how much you’re paying to sign each prospect- when you sign a prospect for $1 million you’re taking a much bigger risk than when you sign a prospect for $20,000 and have to be sure that the player is extremely talented and has a relatively reasonable chance of making his potential into reality to warrant such a gamble. For a lottery or for an IFA prospect, even when your net result is positive it doesn’t mean that you’re going to win- but you want to pick your spots to find gambles where the potential reward outweighs the risk and you hope that if you find enough worthy gambles, eventually you’ll come ahead in one of them. However, there’s a major difference between a lottery and IFA market: it makes no difference to you who else participates in the lottery and especially who wins if that person isn’t you, but in baseball, teams are directly competing with their biggest rivals, and signing a player isn’t just buying a lottery ticket but also making sure your competitor can’t do the same.

A zero-sum game is when your gains from entering a game (known as the utility) are equal to your opponents’ losses from playing the game and losing. Put another way, when the Rays signed Jose Castillo, the other 29 MLB teams lost out on the opportunity to sign him. But aren’t there plenty of talented international free agent prospects? And what about the tax? Doesn’t that negate, at least to an extent, the benefits Rays are getting by signing these guys? The answer is that the players the Rays signed were top-of-the-top prospects, and those are in short supply. Once the Rays scooped them up, the money rival teams had allotted to sign them had to go to either a lesser prospect or none at all, forcing them into a riskier situation or prompting them not to take the risk at all and have no possibility of success. And while the Rays would have loved not to be taxed for going over the $2.9 million maximum, the taxes are only marginal costs in Game Theory lingo. While the Rays did have to pay an additional fee, that was only because they succeeded- if they had failed to sign Castillo or Mujica, they would not have payed the tax- and that trade-off was worth the added risk as not only did the Rays get the players they desired, but also they forced other teams into worse situations, giving them a competitive advantage for the long-term.

If you want to see how this theory plays out, you can look no further than the Rays’ signing of Mujica. Mujica was a highly-regarded prospect and the Rays were obviously not the only team interested. One other team that went for him was, in fact, the Rays division rival Toronto Blue Jays, who at one point were considered the favorites for his services. After the Rays swooped in and signed him, the Jays turned around and signed Venezuelan shortstop Luis Castro for $800,000- but then Castro failed his physical and the Blue Jays negated the signing and ended up with nothing, only signing a few vastly inferior prospects after that. In signing Mujica, the Rays didn’t just get themselves an outstanding pitching prospect but also set the Blue Jays back significantly the rest of the international signing period, and the Rays’ reward coupled with the Jays’ loss was easily worth the additional money in taxes.

Even if we conclude that the Rays’ willingness to exceed the $2.9 million dollar cap was really an extremely beneficial move for them for this year’s international free agent market, aren’t we overlooking the second half of their penalty? Because they surpassed the cap so exorbitantly, the Rays won’t be able to sign any prospects for more than $250,000 in this coming year’s signing period. Didn’t the Rays sacrifice this year’s class to pay for last year? The knee-jerk reaction to that is to say that the Rays believed that they got a group of talented prospects and that letting the opportunity to sign them go by, even if it would have allowed them to avoid penalties, would have been something they would have regretted for a long time. But there are also two other factors that make the Rays’ move look even smarter. The first is that next year’s class is considered to be weak, so the Rays are not losing out nearly as much as they would have in a different year. Secondly, part of the game with international signings is that the high-profile signings aren’t always the best one. Enny Romero who is now a top-10 prospect in the organization despite being an unheralded signing, and the same is true with Cristian Toribio, the Rays’ shortstop prospect who signed for just $65,000 in 2012 but immediately impressed in his pro debut. Being forced to keep their signings under $250,000 simply forces the Rays to get more creative and sign more sleeper prospects as opposed to the high-profile players- and considering how the Rays have become renowned throughout baseball for their astute moves in the draft and on the trade market, that sounds like something right up their alley.

Despite how good their gambles are looking right now, the Rays took plenty of risk in this year’s international free agent market and that risk is only magnified by the money in taxes the Rays have already paid in exchange for getting their players signed. However, through the scope of Game Theory or not, the Rays saw the taxes and penalties in front of them as only a minor concern compared to the potential reward of the prospects they signed and also the additional havoc they wrecked on their rival teams by forcing them to look elsewhere and sign riskier players. What other teams saw as a deterrent, the Rays saw as an opportunity for an edge, and they executed their plan flawlessly.