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Changing Nash Equilibrium in NBA Free Agency

This past round of free agency marks the beginning of a significant change in business. The catalyst for this is the soaring salary cap. Grantland’s Zach Lowe reports that the cap will jump from 67 million this year, to 90 million next year, to 108 million the year after. In a sense, this makes what was an expensive and risky signing of a player before, a bargain risk now. Any contract, even a max contract, will seem like just a mid-level deal in a few years. This gives teams incentive to lock up as many players as they can under the cheaper salary cap that is currently present. Using Game Theory, we can understand how strategies are being affected by this change.

Here’s a consideration of two teams’ payoffs under a normal salary cap and a soaring one, if the ultimate goal is to win a championship:

Normal cap:

The top left box shows competition in Free Agency for Team A and Team B. Ultimately, Team B will win out and attract good free agents because it is better, so Team A will be stuck spending money on maybe a single role-player, not improving itself much. Team A can’t spend money on multiple free agents because it can’t sustain having a high payroll with a losing record; it will lose money.

The bottom left box benefits Team B even more since competition won’t drive up prices for a free agent, but Team A will also have a chance to obtain a star on the cheap from the draft.

The top right box shows a situation where Team A will be able to attract a good free agent since it doesn’t have competition, but Team B will decide to tank in order to obtain a better draft pick. This is counter intuitive since Team B was already a good team.

The bottom right box shows a situation where both teams tank, so Team A will receive a better draft pick since it was already worse, and Team B will get worse without receiving a good pick.

The only Nash Equilibrium here is the bottom left, showing that better teams will build through the draft, and worse teams will tank. This explains the phenomena in recent years where there were so many teams tanking to get good picks (Celtics, Lakers, 76ers, Bobcats, Cavaliers). Hurting the competitive balance of the league, this incentive made it so only a few teams were good and relevant(Heat,Pacers,Thunder,Spurs).

(Worse Team A, Better Team B) B: Build through Free Agency B: Build through draft
A: Build through Free Agency 2,4 4,2
A: Build through draft 4,6 3,1


Rising Cap:

Now, the top left box shows the same competition as before, but with an important difference. Driving up prices through competition doesn’t matter for Team B since the deals will be considered cheap in a few years anyway. And for Team A, the future flow of money means that it doesn’t have to settle for signing one role player, it can sign many. This will actually improve the team significantly and excite the fan base.

The bottom left box now has less incentive for Team A because a draft pick takes time to develop. The team will continue to struggle for a few years and this isn’t a good option. Furthermore, the team will have unused money and that will make it seem cheap, angering the fan base.

The top right box now shows a little more payoff for Team A because it will get someone on a good deal.

The bottom right box remains the same.

In this case, the Nash Equilibrium moves to building through free agency, and this is what the NBA is seeing now. Many teams are throwing around max contracts and spending all their money. Free Agents have more power as they have multiple suitors, driving up their prices(Tyson Chandler, Greg Monroe). And most importantly, less teams are openly tanking, meaning the competitive balance of the league is returning.

(Worse Team A, Better Team B) B: Build through Free Agency B: Build through draft
A: Build through Free Agency 4,6 5,2
A: Build through draft 3,6 3,1

Dallas Mavericks owner Mark Cuban has remarked about this change when he was asked what his team would do, if they knew they weren’t going to sign Deandre Jordan earlier, rather than be surprised by it last second. He noticed that because of this change in Nash Equilibrium for most teams, that there would be very few teams tanking next year, making it so that one could obtain a higher draft pick without having to be terribly bad. He said that they were seriously considering trying for a draft pick if they knew they wouldn’t be getting Jordan.

Ironically, this shift in Nash Equilibrium might provide more payoff to those in the future who are the pioneers in tanking once again.



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