The following logic is fairly common among baseball fans and experts today: "The expected gain in wins (and hence, 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 by doing so."

 [Note by jonk, 04/21/08 5:28 AM EDT ]Bumped to front page

First, it’s important to understand some basics of why baseball teams make money.  This should be mostly obvious to many but for the sake of thoroughness, I will include this logic.  The number one factor for how much an additional 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—in an auction format.  The other is to “grow your own” players, and use the limits of the MLB’s rules for paying players who have not yet earned free agency by having six years of service time—you can use these players yourself, or swap these players for other players who also have lower service time, or for players who have been signed as free agents whose value to you in revenue now exceeds the value of their contract.  The second method—“growing your own”—is primarily where profit comes from.  The Phillies’ success of the pass few years has been a product of the fact that they have paid below market value (as measured by the expected revenue that they generate) for players like Howard, Hamels, and Utley, and can make up the difference between a team made of these stars and a bunch of T.J. Bohns and a playoff team by paying for market value on guys with six years or more of service time like Rollins, Burrell, Moyer, and Gordon.  With those players and the guys that they have in place, they made the playoffs last year, and a lot of money.  Signing guys like Howard, Utley, and Hamels as free agents instead would have led to the team losing money despite making the playoffs.  It would have been smarter to put together a 65-win team on the cheap.  The format of an auction can be somewhat manipulated if the buyers (teams) try very hard, but it is clear that the revenue generated by players signed as free agents is very similar on average to their salaries.  There are small opportunities to have little advantages in evaluating worth, but the vast majority of profits come from players with less than six years of service time.

As a result, if you draft a player who understands that he will be paid less than his expected revenue generated, accounting for the odds of him making it to the majors in the first place and how well he may do upon getting there, he will want to receive more money.  Luckily, 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.  Doing so will cost you a year of free agency in the future, though, so unless Scott Boras is your agent in the mid-90s and he gives you bad advice that costs you a year of free agency in the future so as to help himself be a more feared bargainer in future dealings, you won’t generally do so in most circumstances.  Therefore, it is frequently players considering other sports or college who will ever be able to receive a higher than normal bonus.  If certain teams are likely to do so, then that gives the draftees a bit of leverage in negotiations.   So the league—interested in the owners’ profits—tries to come up with suggestions that they believe can be sustained (more on this later) for what teams should pay.  These values are intentionally less than the expected revenue gained by having them in your control until they become free agents less the amount that you would be expected to pay them.  (Note: all of this is averaged over all possible outcomes.)

We have established that there is a clear logic to the original statement that I quoted at the beginning of this—if you pay above slot values, you can get better players than other teams, and still pay them less than you would if you signed the same quality players as free agents.  The question now becomes why teams do not do 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 following 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, we will offer the following deal—if you confess and your partner denies it, you will receive only two years in prison and your partner will receive fifteen years in prison.  He is being offered the same deal.  The following table depicts the situation in terms of how many years will be spent in prison (negative to show that it’s 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—what is the best thing to do if my partner denies the murder, and 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.  So it is smart to confess either way, for both people, and the equilibrium outcome is that both people will spend 10 years in jail.  The disappointing part of this situation is that they would be collectively better if they had both denied it—but because they are each better off by confessing than going along with the denial, and this cannot be sustained if these are the only two options.

Now, let’s 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 don’t win enough games to make back your saved money.  Instead, you pay above slot, you get the equivalent of 10 years in jail—your 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 has reached.  However, it doesn’t stop there.

Consider now, an alternative depiction of the situation is that the mafia controls these people in the following way—confess and you will be killed fifty years before your time.  Now the new situation appears as follows:

Player 1 \ Player 2     Deny     Confess

Deny                          -3, -3     -15,-50

Confess                      -50,-15    -50,-50

Unsurprisingly, it is best to deny the murder regardless of what your partner does.  This would be analogous to baseball making rules that punish you a lot financially if you pay above slot.  The major league players association would never stand for this situation.

So, we must move onto the other method of collusion in this situation.  Now, let’s say that you repeatedly murder and kidnap people and the police continuously require a confession and offer the same deal.  In this case, you consider playing the original game two times.  Suppose that by denying the first time around, you can get people to deny the second time around.  Then you could each get only 6 total years in jail instead of 20.  However, that breaks down for the following reason: suppose that you have both agreed to play the strategy that you will deny the second time around if you both have denied it the first time around.  It is still wise to confess the second time around—and therefore, knowing this, no one would ever do it the first time around either.  The same logic would be applied to playing this game three, four, or a million times.  You confess in the last round regardless of what has happened.  You confess in the round before that understanding it will not force your partner to deny the murder earlier on.  In each previous round, it is wise to confess and people will always confess.

However, suppose that this game will be played an infinitely amount of times.  In this case, people will deny the crime in the prisoner’s dilemma!  Suppose that you have 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 thereafter.  Unless you value the short-term way more than the long-term, this is not worth it.  The reason that you go against your short-term gain is to encourage your partner to do what benefits you in the future.  If that helps you more than you hurt yourself now, then you will do this.  The “grim trigger” strategy described above is not the only way to get collusion—any way that encourages your partner to help you later on helps.  In laboratory environments, the most successful strategy tends to be to start off denying, and to copy your partner’s strategy in the previous round each time.  It is important to remember that this doesn’t need to actually be played an infinite number of times.  All that needs to happen is that any time you play the game, there needs to be a sufficiently high chance of playing the game again in the future at some point.

Collusion can be achieved more often in some circumstances and less often in others.  The best circumstances for collusion are those when the chance of future rounds occurring is highest, the gain to defecting now is smallest, the gain to future cooperation by your partner is highest, and the present is relatively less valuable.

The analogy to baseball should be pretty clear.  If you agree to pay the recommended slot values, you may encourage other teams to do so in the future.  Undoubtedly, this does happen.  In fact, it is the reason that teams make significant profits at all.  If teams paid players the expected revenue gain above their salaries before hitting free agency, they would make little money.  As free agent’s salaries are nearly the same as expected revenues that they will generate, teams would make little profit if this system broke down entirely.  However, if teams never paid any money to draftees, the gains to deviating in the short-term would be too large—any team could easily deviate and make such huge profits that the suggested slot payments wouldn’t be the same.

This type of analysis holds pretty easily when more than two people are playing this kind of game.  Any game where one person can gain at the expense of others, yet both would have been better off by not undertaking this action is a prisoner’s dilemma.  If at any time that you play this game, there is a chance of playing the game in the future with some of the same people you played with this time, it is an infinitely repeated prisoner’s dilemma.

So why do teams ever deviate?  Well, the Red Sox and Yankees deviate because of a few reasons.  One is that they are in the unique situation where paying free agent’s salaries is still probably profitable to them.  They stand to lose less by the system breaking down.  Also, because the other deviates, they stand to lose more by playing by the rules.

Undoubtedly, the Phillies would help their team if they drafted a guy like Porcello and paid him the money they paid him.  They certainly would if they did this all the time.  However, they would encourage other teams to do the same, and increase the chances of a future with payrolls that nearly match revenues in the future.

As long as teams in direct competition with the Phillies do not pay above slot values, it is unlikely that they will do so.  The Red Sox and Yankees have significantly wounded the Blue Jays, Rays, and Orioles chances at profit in the future, and if they were not already able to generate so much revenue already, they would be endangering a lot of their own profits too.  The Phillies are not in direct competition with the Yankees and Red Sox.  If they do make the World Series, that mostly comes down to luck anyway.

I’m not saying that I wouldn’t be thrilled with the Phillies paying above slot.  I route for their place in the standings, not their bottom line.  But I would be happy if they grabbed a bunch of superstar free agents without tightening the purse strings else where.  I simply don’t get mad at a team for not losing money for the sake of my happiness.