Game Theory of Basketball and Legal Scholarship
By Mike Dorf
A couple of weeks ago, I participated in a 3-on-3 basketball tournament as part of a fundraiser for students doing pro bono work in Louisiana: Participating teams each paid a registration fee, which then went into the pool of funds; the winning team and the runner-up team received donated prizes. In order to ensure that all participants got to play at least two games, the organizers of the tournament announced that the 16 teams would play an initial round of randomly paired games, with the eight winning teams then going to the "winners' bracket" and the eight losing teams going to the "losers' bracket." Each bracket would then play single-elimination games until the championship game featured the winner of the winners' bracket against the winner of the losers' bracket. Nearly everybody participating should have understood that this arrangement created an incentive for teams to deliberately lose their first-round game, so as to have an easier road to the the championship game--having only to defeat three teams that had all lost their initial game. But of course everybody also should have realized that because everyone else should have realized the same thing, perhaps the easier path would be in the winners' bracket, and so on. You don't need to be John Nash to realize that, other things being equal, it should have been perfectly unclear whether your team would be better off winning or losing the first game.
My own calculation was that it would be advantageous to lose the first game, despite the game theory. I figured that some teams would not have bothered to read the rules. Others who had done the math would think it unsporting to deliberately lose a game or, even if they thought it not unfair, would have found it psychologically difficult to lose deliberately. And that turned out to be true. My team lost our first game (albeit not deliberately) but then proceeded to win three elimination games in the losers' bracket to make the finals, where we lost pretty badly. I have little doubt that we would have been eliminated in game 2 if we had won our first game--because we would have then faced the team that ultimately beat us in the final game. And my team was pretty mediocre: In a field of 25-year-olds, we were three middle-aged law professors. We were good enough to beat about half the teams in the tournament, and under the rules as distributed, that meant we ended up finishing second out of sixteen, a result that while fair in the sense that it conformed to the rules known to everyone ex ante, was not exactly "accurate." (The runner-up prize was a $100 gift certificate for a bar review course for each member of our team. Because that was of no use to any of us--all having passed the bar long ago--we donated our prizes to the members of the team that lost to the championship team in the final game of the winners' bracket, i.e., the "real" runner-up team.)
This little episode encapsulates for me a key limitation of conventional game theory: It depends on the assumption that your opponents will act rationally. If you have reason to believe that they will not, then you need to build that into your model to get the optimum strategy. Now I'll consider another example, which will come with some practical advice for legal scholars and aspiring legal scholars.
Legal scholars publish some of their scholarship in books and peer-reviewed journals, but most legal scholarship appears in student-edited journals. Within the world of legal academe, there is a reasonably well-understood pecking order among journals, with prestige attaching in roughly (but not exactly) the same measure as it attaches to the schools with which the journals are affiliated. Thus, it's more prestigious to publish in the Stanford Law Review than in the Eastern North Dakota Law Journal (and not just because the latter doesn't exist; I didn't want to insult any real journal, but you get the idea). It's also more prestigious to publish in a law school's "flagship" journal (e.g., the Cornell Law Review) than in one of its specialty journals (e.g., the Cornell Journal of Law, Psychology, and Hackysack, which also doesn't exist). Just how much more prestigious it is to publish in a flagship journal than a specialty journal depends on the school and the journal, and there is undoubtedly a large element of subjective judgment here, but legal scholars understand the basics.
Unlike most peer-reviewed journals in law and other fields, the student-edited journals accept multiple simultaneous submissions (although some will promise a relatively quick decision for an exclusive submission). So if you're a beginning scholar--perhaps a lawyer hoping to land a job as a full-time academic one day--and you're not sure that your article draft will appeal to the top law reviews, you will send it out to a great many journals, perhaps as many as a hundred or even more (or so I've heard). This is made quite easy through a website to which you can upload your article and then click on all of the journals to which you want it delivered for a modest fee of $2/journal.
The risk of sending to too many journals is that you may get an offer from an obscure journal in which you would rather not publish your article. An author who receives such a publication offer will quickly notify the more prestigious journals to which she has sent her manuscript, asking them to "expedite" their consideration of her manuscript. Indeed, for many junior scholars, the whole point of sending the article to journals down the food chain is precisely to get an offer that can then be leveraged for an expedite, because the journals up the food chain are so flooded with submissions that they may not otherwise even bother to read the submission before they have accepted enough articles to fill the entire volume of the next year's journal.
One has to be careful in playing the expedite game, however, for two reasons. First, the editors of a top journal are not going to drop everything to consider an article by someone they've never heard of just because she has a publication offer from the Central Alabama Journal of Firewalking and Law. Accordingly, the best practitioners of the expedite game seek expedited reviews in waves: Get an offer from a fourth-tier journal; use it to get expedited reviews at third-tier journals; get an offer from the third-tier journal; lather, rinse, repeat.
But that brings me to the second risk. Law journal editors understandably don't like being used in this way, and so they will often give short deadlines. For example, a number of them say that if an author seeks an expedited review and gets an offer of publication, the author has an hour or less to decide whether to take the offer. This is not enough time to use the offer to try to expedite somewhere else. Journals further down the food chain lack the leverage to make such exploding offers, but they can put some pressure on authors with relatively short deadlines, thus playing on authors' risk aversion.
When I first started out as a legal academic almost 20 years ago, the system just described had a bit more slack built into it, partly because hard-copy submissions were then the norm. It also used to be the case that the submissions "season" was longer, with a "window" from mid-February to late April and another window from mid-August to early October. It now appears that the fall window is much smaller, with journals mostly filling up in February and March. That in turn has led savvy authors to try to get their articles into the journals when they have the most openings.
These days, much of my knowledge of the law journal process is based on what I have been told by my former students who are trying to break into or have recently broken into legal academia. In many years, I don't write anything "on spec," because between books, book chapters, and invitations to write for symposia, I don't have the time. But through happenstance, I had two papers to send out through the general process this spring, and so I've now become closely acquainted with the system again. (The papers are here and here. They'll be published in the Virginia Law Review and the Duke Law Journal, respectively. Apparently, my current work has special appeal below the Mason-Dixon Line.)
My re-acquaintance with the journal submission circus now leads me to question the conventional wisdom that it's best for authors to submit their papers at the very start of the submission season. Picture the situation facing a new board of 2L articles editors in mid-February. On their very first day reading articles they find literally hundreds in their inbox. Why? Because the timing of when the boards turn over is not exactly uniform or transparent, the savvy authors have all tried to get to the top of the queue by sending their manuscripts in early. But now you have editors with no experience having to sort through many more articles than they can possibly read. If you are a new/unknown legal scholar, the best that you can hope for under these circumstances is that the editors at the top journals simply ignore your submission for a while, because if they need to make a decision, they'll likely rely on shortcuts like your c.v. to reject it. (Some journals use blind reads for some parts of their processes but most don't.) At least if the editors leave it in the inbox, there's a chance it will get serious consideration following a request for expedited review.
But if a novice scholar is better off with her article not being considered by the more prestigious journals right at the beginning of the submissions season, then she is better served by not submitting her article to the more prestigious journals until at least a few weeks into the season, say March 1 at the earliest. And that is where the analogy to the 3-on-3 basketball tournament may come in: If everybody reasons this way, then it really would pay to submit early, because then the journals would not be flooded, and you could get your piece read by being at the top of the queue.
In theory, there ought to be a natural sorting: Established scholars (like yours truly) should submit their articles early in the cycle, when the overwhelmed student editors are using shortcuts (like letterhead, c.v., etc) to decide which articles to read and even to decide which articles to accept. (Some student-edited journals include a blind peer review stage in the review process but many don't.) Meanwhile, novice scholars should be sending their articles to the less-prestigious journals first, but holding back for at least a couple of weeks before sending to the more-prestigious journals, so that the editors there first look at it upon receiving an expedite request.
In practice, however, it looks like everybody in a position to do so is simply sending out their manuscripts at the beginning of the season, much like the basketball teams in my 3-on-3 tournament simply tried to win their first games. That means that the sophisticated game theorist should be able to garner at least a small advantage in the submissions game by timing her submissions strategically. Of course, it also helps to have written an interesting article on a topic of interest to student editors, but that's a different story.
A couple of weeks ago, I participated in a 3-on-3 basketball tournament as part of a fundraiser for students doing pro bono work in Louisiana: Participating teams each paid a registration fee, which then went into the pool of funds; the winning team and the runner-up team received donated prizes. In order to ensure that all participants got to play at least two games, the organizers of the tournament announced that the 16 teams would play an initial round of randomly paired games, with the eight winning teams then going to the "winners' bracket" and the eight losing teams going to the "losers' bracket." Each bracket would then play single-elimination games until the championship game featured the winner of the winners' bracket against the winner of the losers' bracket. Nearly everybody participating should have understood that this arrangement created an incentive for teams to deliberately lose their first-round game, so as to have an easier road to the the championship game--having only to defeat three teams that had all lost their initial game. But of course everybody also should have realized that because everyone else should have realized the same thing, perhaps the easier path would be in the winners' bracket, and so on. You don't need to be John Nash to realize that, other things being equal, it should have been perfectly unclear whether your team would be better off winning or losing the first game.
My own calculation was that it would be advantageous to lose the first game, despite the game theory. I figured that some teams would not have bothered to read the rules. Others who had done the math would think it unsporting to deliberately lose a game or, even if they thought it not unfair, would have found it psychologically difficult to lose deliberately. And that turned out to be true. My team lost our first game (albeit not deliberately) but then proceeded to win three elimination games in the losers' bracket to make the finals, where we lost pretty badly. I have little doubt that we would have been eliminated in game 2 if we had won our first game--because we would have then faced the team that ultimately beat us in the final game. And my team was pretty mediocre: In a field of 25-year-olds, we were three middle-aged law professors. We were good enough to beat about half the teams in the tournament, and under the rules as distributed, that meant we ended up finishing second out of sixteen, a result that while fair in the sense that it conformed to the rules known to everyone ex ante, was not exactly "accurate." (The runner-up prize was a $100 gift certificate for a bar review course for each member of our team. Because that was of no use to any of us--all having passed the bar long ago--we donated our prizes to the members of the team that lost to the championship team in the final game of the winners' bracket, i.e., the "real" runner-up team.)
This little episode encapsulates for me a key limitation of conventional game theory: It depends on the assumption that your opponents will act rationally. If you have reason to believe that they will not, then you need to build that into your model to get the optimum strategy. Now I'll consider another example, which will come with some practical advice for legal scholars and aspiring legal scholars.
Legal scholars publish some of their scholarship in books and peer-reviewed journals, but most legal scholarship appears in student-edited journals. Within the world of legal academe, there is a reasonably well-understood pecking order among journals, with prestige attaching in roughly (but not exactly) the same measure as it attaches to the schools with which the journals are affiliated. Thus, it's more prestigious to publish in the Stanford Law Review than in the Eastern North Dakota Law Journal (and not just because the latter doesn't exist; I didn't want to insult any real journal, but you get the idea). It's also more prestigious to publish in a law school's "flagship" journal (e.g., the Cornell Law Review) than in one of its specialty journals (e.g., the Cornell Journal of Law, Psychology, and Hackysack, which also doesn't exist). Just how much more prestigious it is to publish in a flagship journal than a specialty journal depends on the school and the journal, and there is undoubtedly a large element of subjective judgment here, but legal scholars understand the basics.
Unlike most peer-reviewed journals in law and other fields, the student-edited journals accept multiple simultaneous submissions (although some will promise a relatively quick decision for an exclusive submission). So if you're a beginning scholar--perhaps a lawyer hoping to land a job as a full-time academic one day--and you're not sure that your article draft will appeal to the top law reviews, you will send it out to a great many journals, perhaps as many as a hundred or even more (or so I've heard). This is made quite easy through a website to which you can upload your article and then click on all of the journals to which you want it delivered for a modest fee of $2/journal.
The risk of sending to too many journals is that you may get an offer from an obscure journal in which you would rather not publish your article. An author who receives such a publication offer will quickly notify the more prestigious journals to which she has sent her manuscript, asking them to "expedite" their consideration of her manuscript. Indeed, for many junior scholars, the whole point of sending the article to journals down the food chain is precisely to get an offer that can then be leveraged for an expedite, because the journals up the food chain are so flooded with submissions that they may not otherwise even bother to read the submission before they have accepted enough articles to fill the entire volume of the next year's journal.
One has to be careful in playing the expedite game, however, for two reasons. First, the editors of a top journal are not going to drop everything to consider an article by someone they've never heard of just because she has a publication offer from the Central Alabama Journal of Firewalking and Law. Accordingly, the best practitioners of the expedite game seek expedited reviews in waves: Get an offer from a fourth-tier journal; use it to get expedited reviews at third-tier journals; get an offer from the third-tier journal; lather, rinse, repeat.
But that brings me to the second risk. Law journal editors understandably don't like being used in this way, and so they will often give short deadlines. For example, a number of them say that if an author seeks an expedited review and gets an offer of publication, the author has an hour or less to decide whether to take the offer. This is not enough time to use the offer to try to expedite somewhere else. Journals further down the food chain lack the leverage to make such exploding offers, but they can put some pressure on authors with relatively short deadlines, thus playing on authors' risk aversion.
When I first started out as a legal academic almost 20 years ago, the system just described had a bit more slack built into it, partly because hard-copy submissions were then the norm. It also used to be the case that the submissions "season" was longer, with a "window" from mid-February to late April and another window from mid-August to early October. It now appears that the fall window is much smaller, with journals mostly filling up in February and March. That in turn has led savvy authors to try to get their articles into the journals when they have the most openings.
These days, much of my knowledge of the law journal process is based on what I have been told by my former students who are trying to break into or have recently broken into legal academia. In many years, I don't write anything "on spec," because between books, book chapters, and invitations to write for symposia, I don't have the time. But through happenstance, I had two papers to send out through the general process this spring, and so I've now become closely acquainted with the system again. (The papers are here and here. They'll be published in the Virginia Law Review and the Duke Law Journal, respectively. Apparently, my current work has special appeal below the Mason-Dixon Line.)
My re-acquaintance with the journal submission circus now leads me to question the conventional wisdom that it's best for authors to submit their papers at the very start of the submission season. Picture the situation facing a new board of 2L articles editors in mid-February. On their very first day reading articles they find literally hundreds in their inbox. Why? Because the timing of when the boards turn over is not exactly uniform or transparent, the savvy authors have all tried to get to the top of the queue by sending their manuscripts in early. But now you have editors with no experience having to sort through many more articles than they can possibly read. If you are a new/unknown legal scholar, the best that you can hope for under these circumstances is that the editors at the top journals simply ignore your submission for a while, because if they need to make a decision, they'll likely rely on shortcuts like your c.v. to reject it. (Some journals use blind reads for some parts of their processes but most don't.) At least if the editors leave it in the inbox, there's a chance it will get serious consideration following a request for expedited review.
But if a novice scholar is better off with her article not being considered by the more prestigious journals right at the beginning of the submissions season, then she is better served by not submitting her article to the more prestigious journals until at least a few weeks into the season, say March 1 at the earliest. And that is where the analogy to the 3-on-3 basketball tournament may come in: If everybody reasons this way, then it really would pay to submit early, because then the journals would not be flooded, and you could get your piece read by being at the top of the queue.
In theory, there ought to be a natural sorting: Established scholars (like yours truly) should submit their articles early in the cycle, when the overwhelmed student editors are using shortcuts (like letterhead, c.v., etc) to decide which articles to read and even to decide which articles to accept. (Some student-edited journals include a blind peer review stage in the review process but many don't.) Meanwhile, novice scholars should be sending their articles to the less-prestigious journals first, but holding back for at least a couple of weeks before sending to the more-prestigious journals, so that the editors there first look at it upon receiving an expedite request.
In practice, however, it looks like everybody in a position to do so is simply sending out their manuscripts at the beginning of the season, much like the basketball teams in my 3-on-3 tournament simply tried to win their first games. That means that the sophisticated game theorist should be able to garner at least a small advantage in the submissions game by timing her submissions strategically. Of course, it also helps to have written an interesting article on a topic of interest to student editors, but that's a different story.