Wednesday, February 09, 2022

Tanking in professional sports as a Mirrleesean optimal tax problem

 In the current baseball lockout, the players are rightly focused on the problem of tanking, while the owners are oddly verging on indifferent to it. (Their proposed revision to the amateur draft rules is ludicrously short of the mark.)

Since clearly it is good for the sport (in terms of fan interest, likely revenues, and aesthetics) to limit the current level of tanking, I can only presume that the owners sufficiently value the downward pressure on salaries that tanking presumably creates to be happy to make things worse overall. This could either be a financial calculation about their share of the overall take, or (given how poisonous the labor relations in baseball appear to be) they may even value hurting the players financially as an end in itself. Or, perhaps they figure that the players care more about it than they do, so they can use an inadequate proposed response to extract leverage in the bargaining process.

To explain: Suppose a given team isn't going to do well this year no matter what. But they hope to be better in the future, e.g., after their minor league prospects get a chance to develop. It makes perfect sense for the team to trade current value (e.g., an aging star who is still very good) for future value (e.g., promising minor leaguers). They are trying to trade current wins for future wins, because the latter are expected to have greater marginal value. After all, the aim isn't just to maximize overall wins over time, but to make the playoffs and win championships.

That is not tanking, and there is probably no reason to limit it. The key is, under the problem as stated so far, the team still wants to win as much as possible this year - they just are willing to reallocate expected wins from the current to the future given how the marginal value of a win depends on its other wins for the same season.

A team that does this will still be trying to win every game it can this year (subject to the roster moves that serve its long-term goals). And its fans will still be rooting for it to win every game it can, even if they are realistic about how good this year can actually be. 

Then we get to the actual system, where draft position depends on your won-lost record, in the inverse. Now a bad team, even taking its roster as given, actually wants to lose each game it can (or should want to, from an incentives standpoint). Sophisticated fans also want it to lose and lose. (E.g., as a New York Jets fan, I was disappointed by their wins last year that took them out of the running for Trevor Lawrence.)

But when a team is rationally wanting to lose, and even if its fans are rationally on the same page, it diminishes the sport. Things are worse and less interesting all around. So, while I wanted the Jets lose and was disappointed by their (with typical stupidity and incompetence) stumbling into a couple of ill-needed wins, that simply reflected the current design. Wanting your team to lose under the current rules does not logically require wanting there to be rules under which you will want your team to lose.

On the other hand, there is a reason for having teams with worse won-loss records get higher draft positions. This helps promote long-term equality in how well different franchises do, which I would argue is good for each of these sports on multiple grounds.

How can these points both be true? Easy. It's the classic tradeoff between incentive and distributional goals. The James Mirrlees optimal tax set-up involves a very similar problem. From a distributional standpoint, at least within the model we should 100% equalize after-tax-and-transfer resources. But this would destroy incentives to earn. So the optimal solution involves a tradeoff between the right distributional answer (100% earnings tax to fund a demogrant) and the right incentives answer (no earnings tax).

A sport like baseball, football, and basketball tracks right onto this model. No draft preference for the losing teams is bad on distributional grounds. But an overpowered draft preference for losing creates undesirable incentives to tank. 

Currently in both baseball and football, I get the sense that incentives to tank are overpowered. In baseball, it's quite extreme, as the Astros and to a lesser extent Cubs success stories of almost a decade ago help to show. Basketball, by contrast, seems to have gotten it more into the right range. From a purely distributional standpoint, it is unfortunate and suboptimal that the very worst team in the league has only a relatively small chance at the #1 pick. But it does mean that teams aren't battling so hard to be the worst, even when there is a consensus #1 pick out there, since the payoff is only a modest increase in one's likelihood of landing that player. And to get yourself into the NBA draft lottery, you actually have to miss the playoffs. Given that the best non-playoff team has only a small chance of rising a great deal, teams are generally trying to win - and less prone to tanking - creating a better sport with better games and, I would think, greater fan interest (late in the year especially) than in the alternative.

Returning to baseball, the owners are proposing a lottery only for the three worst records. That simply doesn't do enough, or even close to it, to address tanking. Baseball tends not to have as clear a standout #1 pick as basketball more often does, anyway. So the players are right - more of a lottery would be good for the sport, and if the owners disagree (as opposed to just pretending to do so for now) then it is because they are short-sighted at best and malevolent at worst.