My name is Matt Swartz, and I am a Ph.D. candidate in Economics at the University of Pennsylvania, and I will be completing my degree this Spring. In my dissertation, I have applied economic theory to study dating and marriage, as a metaphor for how learning and matching work together. Meanwhile, I have gotten married myself as I worked on this, which I use as a justification that I must know what I am doing. Using this success as a blue print, I recently turned to writing my most recent paper on interviewing for jobs with graduation coming soon. In the past few years, I have come across sabermetrics, and I have spent a significant amount of time since then learning about baseball. Last year, I was invited to join the Phillies‘ blog “The Good Phight”, and this year I was also invited to join the sabermetrics blog “Statistically Speaking.” My baseball analysis ranges from economic modeling of baseball decision making to more hardcore statistical analysis. The piece that I am submitting is clearly not a hardcore statistical analysis, but I am well trained in looking at non-experimental data, and I have the baseball fan background that many academics lack when they dabble in performance analysis. It is this combination of being a sabermetrician, sabermetrics consumer, economist, writer, and baseball fan that I believe makes me uniquely qualified to work at Baseball Prospectus.

Why Teams Do Not Spend More on the Draft

The following logic is fairly common among baseball fans and experts today.

“The expected gain in revenue by paying above the recommended slot values for draft picks is higher than paying the equivalent amount of money for free agents.”

I would not attempt to argue with this logic. On average, it is overwhelmingly true. The question then becomes:

“Why do teams refuse to draft those players who will require this kind of money to sign? Teams that draft and pay these players gain an advantage.”

Whether teams choose to draft players who command these bonuses does not seem to follow a clear pattern. Large market teams like the Yankees and Red Sox regularly bust slot, but so do poorer teams like the Rays. Some large market teams like the Phillies and Mets generally adhere to recommended bonuses, however. In this article, I will utilize the repeated prisoner’s dilemma to illustrate what is going on.

The number one factor for how much a team earns in revenue is how many games they win and whether they make the playoffs. There are two main ways to get players. One of them is to sign free agents. The other is to “grow your own” players, using the limits of the Major League Baseball’s Collective Bargaining Agreement. You can use these players yourself, or use them as valuable assets to trade. The second method is primarily where profit comes from.

While the player knows he is worth more than his bonus, his only avenue to get another offer is to wait another year to be drafted by another team who has the same dominating position over him. Therefore, the players considering other sports or college are the only ones who will have bargaining power. So the league-interested in the owners’ profits-tries to come up with suggestions that they believe can be sustained for what teams should pay these guys. The question now becomes why teams do not do abide by this. I will start this with an analogy that many people are familiar with-the prisoner’s dilemma.

The prisoner’s dilemma is a typical game theoretical model, and the basic background is the following: there are two men who have committed a kidnapping and murdered the person. The police have proof that they committed the kidnapping, but will need a confession to lock them up for the murder. They put them in separate rooms and explain the rules: if neither of you confess, we will only be able to put you into jail for three years each. If you both confess, we will be able to put you into jail for ten years each. However, if one of you confess and your partner denies it, you will receive only two years in prison and your partner will receive fifteen years in prison. The table below depicts the situation in terms of how many years will be spent in prison (negative to show that years in jail are bad).

Player 1/Player 2    Deny   Confess
Deny                -3,-3    -15,-2
Confess             -2,-15   -10,-10

Each player should consider the situation this way: (1) what is the best thing to do if my partner denies the murder, and (2) what is the best thing to do if my partner confesses? As -2>-3 and -10>-15, it is clear that is best to confess regardless of what your partner does. It is smart to confess either way, for both people, and the outcome is that both people will spend 10 years in jail. The intriguing part of this situation is that they would be collectively better off if they had both denied it-but because they are each better off confessing, mutual denial cannot be sustained.

Now, let us make an analogy for baseball. “Denying” is like paying the suggested slot values. “Confessing” is paying above slot values. You do better either way. If the other teams pay above slot values, you avoid getting the equivalent of 15 years in jail-your team is bad and others are good, and you do not win enough games to make back your saved money. Instead, you pay above slot, you get the equivalent of 10 years in jail-you are competitive but have spent a lot of money. If other teams do not pay above slot values, you get the equivalent of three years in jail by doing the same-you each have comparable teams (holding all else constant), and you have each saved money (or seven more years in jail). However, you can make money by getting better players while other teams do not-and make up your expected expense by winning more games and making the playoffs more often than other teams (receiving two years in jail).

This is the level of analysis that the original statement at the beginning of the article has reached. However, that is not the whole story.

When the prisoner’s dilemma is to be played infinitely many times, or at least the horizon is unclear, this game should be played differently. Suppose that by denying the first time around, you can get people to deny later on. In this case, people will deny the crime in the prisoner’s dilemma! Consider the following strategy: deny the first time, and deny in any subsequent round when your partner has denied in all previous rounds. If your partner plays the same strategy, neither of you will ever have any incentive to deviate. Any deviation will save you one year in the short-term, and cause you to lose seven years in each subsequent round. The reason that you go against your short-term gain is to encourage your partner to do what benefits you in the future.

The analogy to baseball should be clear. If you agree to pay the recommended slot values, you may encourage your competitor(s) to do so in the future. Undoubtedly, this does happen. In fact, it is the reason that teams make significant profits.

The best environments for collusions occur when:

  1. the chance of future rounds occurring is highest
  2. the gain to defecting now is smallest
  3. the gain from future cooperation by your partner is highest
  4. current payoffs are relatively less valuable

So why do teams ever deviate? The Red Sox and Yankees deviate for several reasons. One is that they are in the unique situation where paying free agent’s salaries is probably still profitable to them, so the relative gain from future cooperation by other teams is not that high. Secondly, because the other deviates, they stand to lose more by playing by the rules. The rest of the AL East deviates as well-they cannot coerce their competitors to adhere to slot recommendations, so even the small market teams like the Rays bust slot regularly. The Rays might have a large incentive to have the system work, but they are unlikely to coerce the Red Sox and Yankees to avoid drafting these players merely by playing along. Many other teams in of the American League bust slot as well to compete with the AL East teams who frequently take the Wild Card.

On the other hand, the NL East mostly adheres to the recommended bonuses, despite containing several large market teams, and even though it is a highly contested division. Any team could take an advantage by busting slot significantly one year, but the other teams would subsequently bust slot thereafter and the gain would be minimal. The Mets and Phillies are only in slightly smaller markets than the Red Sox and Yankees, but since their gain is slightly higher to collusion, these two hated rivals pass over elite talents who command high bonuses. The Nationals seem eager to bust slot, but remain uncompetitive in the near future, and so the payoff for the Mets, Phillies, and Braves to cooperating remains strong.

If teams that are cooperating and playing by the commissioner’s suggested rules ever consider deviating, this will have a positive effect on their profit in the next few years as these players add a lot of value. However, if their competition in the league begins to follow suit, they will end up no better off in the win column and lower in the profit column. The commissioner’s office arbitrarily lowered the recommended slot values in 2008, and teams defected wildly. The gain from paying these elite draftees suddenly became too high.

From a fan’s perspective, we do not care about the team’s bottom line. We want our teams to succeed. It is somewhat frustrating when the ownership does not go out and spend the money to bring in a big name free agent, but we accept that the team is trying to maximize profits. However, many people are unable to make the jump and realize that when our team does not draft that superstar athlete with a football scholarship and lets another team pay him that large bonus, they are not being foolish. They are colluding.