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.

Thank you for reading

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Wow. This is really fantastic. I've always felt that game theory has a big place in baseball analysis (see The Book) but I'm not smart enough to figure it out myself. Very nice job applying it to something that never totally made sense to me before either.
This is the first of the Prospectus Idol columns I read and I have to admit, I got pretty into it. I was just thinking about this problem literally a couple weeks ago - I see now my error, or my confusion, was in not thinking along division lines, as most teams realize that once your in the playoffs it's a crapshoot, so to speak, in which obvious differences along 162 games might not manifest in a best of 7...if they're all this good - I'll be pretty into seeing how this all shakes out suddenly. Good luck!
Great job. The explanation is crystal clear.
To the author: Were you advised by Victor Rios-Rull? I am a PhD candidate in the Minnesota Economics department and I had him for part of my first-year macro sequence last year. Always good to see fellow Economists doing work in baseball.
Not advised by him, but I did take his first year course in macro a few years ago! Congrats on surviving that course...I think that was the hardest first year course for me.
Actually, I found him the easiest, as he didn't require us to do homework! V.V. Chari was by far the worst; he tries to cover a ridiculous amount of money in 8 weeks.
Some constructive criticism offered to help you do well with voters in the future:

"In this article, I will utilize the repeated prisoner’s dilemma to illustrate what is going on." Fancy that up a little; it still reads a little dry.

A major feature of the prisoner's dilemma that is being left out is the element of trust. In the abstract, it's about rational calculation. In more vibrant uses of the situation, it's a test of how well you know your partner and how much they trust you to do the right thing by you. That element of actual interpersonal relationships is missing from your analysis.

This calculation, incidentally, is one reason why organized crime has such a prohibition against testifying or ratting out your confederates:: you may not be able to trust your partner (and thus should confess), but you can trust us to punish you worse than the feds (and thus you should deny everything.

I go into this issue at length, because clearly the issue of trust for one's sporting competitors but business partners and MLB itself is a factor in how teams approach this issue. You come close to this understanding when you talk about the AL East and the NL East. But you need to consider that MLB can't do very much to punish teams that bust their draft slot. It's as if there was no 15 year penalty.

I think you're focusing on specific applications of the repeated prisoner's dilemma. The prisoner's dilemma has a lot of interpretations, and trust can only be viewed as one of them. At the risk of getting overly technical, there are a variety of equilibria that can arise. When you say "trust", you're taking one view of a general idea, which is "what you believe your partner's strategy is." The pure repeated prisoner's dilemma generally does not include a decision to say one thing or the other, so rather than calling it "trust", think of it as a probabilistic "belief" about behavior. In many real life scenarios, there is an interpersonal interaction, but most of those are explained by some of the criteria above. Why are people nicer in small towns? Some of that is simply that they interact with these people more...which is why they trust them. But that falls under the general umbrella of the first criteria, which is "the chance of future rounds occurring is the highest." I see your point, and that is one angle that is taken, but keep in mind that what we are talking about here-- collusion-- is illegal. There's no talking/trust in that interpretation so I left that out of the article.

It's important to remember, by the way, that the "punishment" I referred to is not by the MLB but by the other teams who start drafting better players later in response. The payoff of -15 was the disappointing situation when you have drafted a player who required a cheap bonus and your division rival has drafted a player who required an expensive bonus and gotten much better than you in the process.
I liked the guy that had to quit a lot, but of the remaining ten, I'm pulling for Matt. I would postpone sex to read his work.
Ha! But if you postpone sex, thereby attempting to both read baseball analysis and get some (the best possible outcome), do you trust your partner to still be primed for action after you are done reading your article? If you put her off, would she be less enthusiastic in the sack? Would she "deny" altogether?

It seems to me that the potential gain of reading the article is not worth the potential loss involved here. Particularly if we're talking about a Strasburg-like talent that has a 60-70 chest and scores 80 on the freaky scale.
LOL. Randy just won the BP Idol comment section competition for me.
The BP Fan's Dilemma

Husband/Wife Read Sex
Read 0,0 0,9
Sex 6,0 6,9
Another example of how bad formatting can ruin a good joke.
Good stuff guys!
Great article. Game theory is a very interesting subject and its nice to see it used for baseball analysis. I haven't read any of the other submissions yet, but this will probably be one of the best.
Excellent article - would love to see more discussion of game theory applied to both baseball business decisions and on-field strategy.
This was terrific. Very well written and well argued. The best of the entries that I've read so far.
Um, I guess I read a different article. I like the concept of using the prisoner's dilemma to analyze the decision of signing people at or above slot bonus, but some of the assumptions and conclusions are problematic.

My main disagreements start with the introduction. Words like "fairly common", "on average", etc are used to describe the logic of paying above slot value but then the question is asked "Why do teams refuse to draft those players who will require this kind of money to sign?" This would imply, then, that the logic on slot values is _not_ "fairly common", nor average.. and also does not account for the idea that different organizations value players differently.

It is also assumed that "The number one factor for how much a team earns in revenue is how many games they win and whether they make the playoffs". That logic would imply that, over the last 5 years, the Red Sox and Angels generate more revenue than the Yankees and that the Twins and White Sox generate comparable revenue.

And the prisoner's dilemma assumption "If you agree to pay the recommended slot values, you may encourage your competitor(s) to do so in the future" might sound ideal in a "Beautiful Mind" John Nash "good for the group and good for me" sense... except collusion is not allowed. Even in the current environment, while it might benefit teams not to overpay for free agents, teams still end up doing so. There's also a scarcity of resource issue to consider. Superstars are rare players and can be worth paying a premium for, even if it is an overpayment. Sometimes teams overpay for certain players not just to acquire the player, but to deny their rivals from acquiring that player.

Finally, let's theorize a bad team has the #1 pick in this year's draft and that player would net the team that drafts it an extra 5 wins a year. By the logic of "The number one factor for how much a team earns in revenue is how many games they win and whether they make the playoffs", then that bad team would be at the biggest disadvantage in revenue. The bad team would have signed the #1 pick for the lowest cost to itself and improved in 5 wins. From the perspective of the bad team, their revenue would increase from the additional wins. However, those 5 wins (and the accompanying revenue) would have to be subtracted from some combination of the 29 other teams in the league. Though the bad team benefits from the slot values, the other teams in the league are potentially harmed from sticking to those slot values.

If you give the worst teams in the league the best picks and keep the costs to the #1 pick's slot value, more wins and more revenue gets subtracted from the better teams... so you wind up with a league of 81-81 teams with slight deviations around those numbers. So, from the perspective of a good team, it is to their benefit to pay above slot value for a prospect because it increases the slot value cost for the low win, low revenue teams. Paying above slot value keeps the good teams good and pressures the weak teams into staying weak.

So, in a theoretical cooperative system that functions efficiently, there'd be thirty 81-81 teams and a series of one game tiebreaker playoffs at the end of the regular season to determine who would be the actual playoff winners. However, baseball is competitve and not cooperative. It is inefficient (since money can be misspent). And it makes sense for good teams to pay above slot value to acquire talent (either via free agency or through the draft) to stay good. Thus, the prisoner's dilemma with the assumptions made in this article do not apply correctly to the situation at hand.
Let me try to respond to each of these criticisms individually. In general, I think you're missing the spirit of this kind of article and the generalization aspect to analysis like this, but I'll hit on each point individually rather than just being dismissive.

When I said the logic is 'fairly common', I said among baseball fans and experts. Specifically, I meant BP writers and readers, scouts, and some more aware commentators. I am explaining the decision to people who at first glance believe that teams are making an error in judgment by refusing to draft some elite talent.

I did not say that the #1 factor in estimating the revenue of any team is its wins. I said that the #1 factor in improving your revenue for an individual team is wins. The 80-win Yankees will make less revenue than the 95-win Yankees. The 80-win Royals will make less revenue than the 95-win Royals. That is quite different than saying the 95-Royals make more than the 80-win Yankees. That is false. The prisoner's dilemma works with asymmetric numbers.

You say that collusion is not allowed. That is true. But they tried it anyway in the 80s with free agency and got sued by the player's union. There is no draftee's union-- so they can get away with IMPLICIT collusion which is tough to prove, but happens all the time. Think energy, think airlines. Implicit collusion is tough to prove.

The scarcity of resource issue is precisely what the benefit to defecting on a collusive agreement is-- you can pay less than value. But this is not a complete market and there is benefit for a player to sign below their true market value, if they have no other choice.

I am pretty sure that you are making some kind of logic mistake with your argument about the worst and best teams, but I have to say that I do not follow your argument. There is some additional assumption that you are making but not articulating that if you teased out, I could respond. In general, all teams are going to have short term harm (or at least medium term harm by not getting to use those players after developing them), but gain in the long run as everyone agrees to pay less for talent. They tried this with free agents in the 80s, but it didn't work, so they have tried this.

You would never have a league full of 81-win teams plus or minus deviations. These teams have different free agent capabilities, different development abilities, different scouting abilities, and a million other things. The symmetry was for simplicity in the article, but it is not at all a requirement for the model to work.

If you want to discuss the worst/best teams thing a little more, I'd be happy to discuss, but I'm not following the argument as you presented it. Thank you very much for the comment...and the opportunity to explain in more detail what I could not in the 1500 word limit :-)
You said: ""The number one factor for how much a team earns in revenue is how many games they win and whether they make the playoffs"."

That seems very similar to: "the #1 factor in estimating the revenue of any team is its wins".

There is no mention of "improving" revenue anywhere in your article. I think you are trying to say the following... the number one _baseball_ability_related_ factor for how much a team earns in revenue is how many games they win and whether they make the playoffs.

Market size, corporate sponsorships, memorabilia sales, stadium ticket prices, fan popularity etc have stronger overall affects on revenue than win total. Take the Chicago Cubs, who have lost for most of the last few decades but were generating tons of revenue, or the Marlins who have won two World Series and a fair share of baseball games but don't generate as much revenue.

Either way, I didn't misquote you and I apologize if you thought I did. You are also pretty sure I am making a logical mistake though you aren't quite sure why, which is also a bit dubious. I may not understand my tax returns, but that doesn't mean I automatically assume a mistake has been made. Let's see if we can get past the misunderstanding about the citation first and I'll try to rephrase what I meant.
I have come up with a number of criticisms against the usefulness of this analogy, arguments against the assumptions you have made, and have come to see this idea, in general, as an extreme oversimplification of a complex market.

However, this is the fourth time I've started to respond to this post, and I've finally decided that the above sentence is as critical as I want to be. I don't really want to address any of those issues directly.

What I will say about this article is: I read it about 2 hours ago and it has taken up my time ever since. It has spurred a great conversation between myself and my brother. It has helped get my creative juices flowing and made me really think about where this analogy falls short, where it could be improved, if it can actually be used to explain teams behavior (as you seem to assume), and what other methods/analogies may work better.

If for no other reasons, those things makes this article great. I love thinking about things like this, and working through these kinds of issues and the practicality of such methods.

I know that my comment is very vague. If you would like more specific criticism or someone to play Devils advocate, let me know.

I look forward to reading similar attempts at explaining other baseball related issues.
Thank you for your comments. I certainly welcome the criticism and open dialogue. This article came from extensive arguments with people who disagreed with the premise, and I have learned a lot about the details of the draft during those arguments.

In general, I'll preempt some of the arguments just a little bit by making a quick comment. You are right that it is an oversimplification of the market. Rightly or wrongly, that is the point of theoretical economics. The idea is to take a complex situation with many moving parts and highlight some clear tradeoffs that decision makers face. In this case, you get the benefit of underpaying for talent if you defy the commissioner's recommended bonus levels, but you suffer the consequence of your rivals underpaying for it more often in the future. The four things I list that make collusion more likely to occur cover a lot of the complexities. There are a lot of other factors in play, but the point of an article is to highlight a clear tradeoff that people are responding to differently due to the magnitude of those costs and benefits.
Underpaying for talent or overpaying for talent? I thought the decision was to either pay the recommended commissioner slot levels, or for teams with later round draft picks to overpay to acquire talent (or place pressure on teams drafting higher in the round to also overpay).
By "underpaying for talent", I meant paying below market rate for the elite players by drafting them and paying them more than the recommended slot bonuses. You're right that it is "overpaying" in the sense that you are paying over the recommendation, just getting a better bargain for the skill level.

It's kind of like if you decide not spend $1 for something worth $2, and instead spend $1.50 for something worth $5, did you underpay or overpay? I meant underpay to mean spend $1.50 for something worth $5. Semantics, I guess, but thanks for letting me clarify.
In isolation, spending $1 for something worth $2 and spending $1.50 for $5 are both forms of underpaying.

If, before given the choices of what I could buy, I decided I was going to spend $1 and instead spent $1.50... I wouldn't call it overpaying, I would call it overbudget.
I'm adding my judging comment to each article:

Swartz, Matt -- 9. Wow, I'd publish that right now, as is. That is a strong, strong piece. Well thought out, well written, well presented. There's almost nothing out of place. His writing reminds me of Shawn Hoffman, which is high compliment. Moreover, his thinking reminds me of Shawn too, which is even higher.
Wow, just the opposite. Perhaps, I'm tired, but I thought this was one of the least well written entries. It was a bit sloggy for me. It is a premise worth conjecturing, thanks, but I think it could have been done in half the words.

The other 750 words might have been devoted to some actual cases. For example, find some teams' stated reasons for avoiding over-the-slot players and test how grounded they were.
As I've gone through many of the articles, comments, and Will's comments, I find it interesting that there are many different viewpoints about which article people like and which they don't.

Similarly, there have been numerous times on American Idol, when after a vote has occurred, and Simon Cowell says, "America, you got this one wrong."

Will definitely has his own taste on what he likes, but while aligned with BP readership, it may not completely reflect what the BP subscribers want.

This is going to be a fun competition!
There's a slight difference though. Contestants on American Idol generally don't seem to work with the judges besides Simon once the competition is over... for this competition, whoever wins will be working with all three of the judges. All three judges for the BP competition have a vested interest in who wins.
Good point, Tim. There's a couple things -- first, I can't do the math, so the more data-heavy pieces lose me. I try to grasp them as best I can, but there's a point where I stop trying. I also have a more mainstream bent on what I like to read rather than the more sabermetrically rigorous pieces. It forces someone who does that to really write well and explain well for me to get it -- Nate and Keith have always done that and the finalists do as well, to some extent.

There's also an element of stewardship in my judging. I want the winner to really deserve it, to have worked hard, done amazing work, and to come out with a check AND to be ready to write alongside the rest of us.

Finally, I'd note that the comments might not be the best gauge of readership. We have a small amount of active commenters, but a large casual readership who may or may not read or even vote in the contest. I'll be curious to see how it breaks down. The hardcore sabermetric audience is a finite set (though I'm scared I just used that mathematical term incorrectly.) Remember how when you read Rob Neyer the first time, it was like discovering a new food and you just wanted more? Now, you read him and say "eh, more Neyer." Too many people think Rob's gotten "worse" but Rob's educated them so well that they've 'graduated'. He's the gateway drug.
I first got an understanding of the definitions of sabremetrics through Rob Neyer. I'm glad he's writing articles instead of blogs again.

And yeah, comments might not be the best gauge, especially with how spammy I am.
I love the creativity involved in this piece and am always interested in the application of economic theory to the game. But I think you may be giving ownership more cedit than they deserve. For the most part, it is ownership making the decision to go over-slot-- they're the ones approving the increased budget. Many ownership groups often fail to appreciate the relationship between the draft and the long-term success of the organization, and would rather invest that money into current free agents or pocket it themselves. I guarantee you every front office in the game would love to go over-slot every year, but getting the approval from ownership is the problem. I guess I see it more as much simpler case of greed and/or ignorance at the level of ownership rather than a case of the prisoner's dilemna. Either way, like I said creative and thought-provoking.
I understand what you're saying and I'm sure most GM's and their staff would love to bust slot, just like they would love to sign every superstar free agent they could. That's very true.

I had ownership in mind, rather than the GMs. I do think you're right that many owners fail to understand the relationship, but they don't really need to. Bud Selig and the commissioner's office recommend bonuses with the owners' collective goals in mind. The recommendations don't serve any purpose other than to find an agreement for collusion. While the owners might not understand the prisoner's dilemma they're in, they probably understand Bud is trying to help them out by holding bonuses down when he tells them how much to pay.
I have issues with the Prisoner's Dilemma generally (it's not a dilemma, first of all - betrayal dominates silence in the original construction), and that really ruins the whole article for me.
Great article, makes you think. Sort of reminds me of the early 60's and the AL being dominant thus ignoring minority players. It wasn't league wide as far as the National League was concerned.

Also, yet another reason the MLB draft does not have the recognition that it should. There is absolutely no way the casual viewer could watch it with any sort of clue as to what was happening.
Nice work. Draft strategy is a topic screaming for more research. I have now read all 10 and this one would rank 3rd for me. Good job.