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How the Spurs beat the Heat: the principle of financial arbitrage

San Antonio Mayor Julian Castro, whatever his other talents, has failed to do anything about his city's oppressive heat. Fortunately for the fine people of San Antonio, last night the city’s NBA team, the Spurs, finally took care of the Heat. And the reasons why have some useful lessons for basketball, and finance and management more generally.

The Spurs trounced the Miami Heat on Tuesday night in Game 3 of the NBA finals. And they did it on the backs of two guards named Gary Neal and Danny Green, obscure role players who combined for 51 points. LeBron James, the greatest player of this age, scored 15.

To understand why the Spurs won — and why they have been one of the best teams in the league over the last decade-plus — it helps to read a certain 1990 paper in an economics journal. “Arbitrage in a Basketball Economy,” by Kevin Grier and Robert D. Tollison, explained a principle that remains useful: Successful basketball strategy resembles the financial concept of arbitrage.

Arbitrage is the principle that when there is a mispricing in a market, someone will trade to exploit the difference, making a profit for themselves and ending the mispricing. For example, the exchange rate between the dollar and the yen should be consistent with the dollar-to-euro and euro-to-yen exchanges rates. If those prices don’t line up — if there is free money to be made by trading dollars for yen, then exchanging the yen for euros, then euros back to dollars — somebody will do it almost instantly, and the mispricing will evaporate.

So, what does that have to do with the NBA?

In their paper in the journal Kykos, Grier and Tollison asked whether the question of who takes shots on a basketball team could or should obey the same principle.

Think of it this way: A basketball team has five players on the floor at any given time, and any of them can shoot from any point on the floor. Each shot has an “expected value” in terms of points. For a point guard shooting from just behind the three-point line, there might be a 45 percent chance of scoring three points if he sinks the shot, a 10 percent chance of being fouled and getting foul shots, a 25 percent chance of missing the shot but a teammate getting the rebound and allowing another scoring opportunity, and a 20 percent chance of missing and the opposing team getting the rebound. Multiply those out as a weighted average, and you would expect something like 1.4 points, on average, for every time the point guard takes that shot.

What you want as a coach (or a fan, for that matter) is for every shot your player takes to have the same expected value. Your star forward driving to the lane? A big-but-slow center hogging the space under the basket and putting up an easy shot? A mid-range jumper by your journeyman point guard? They should all have the same expected value when all the possible outcomes and their relative probabilities are factored in.

If that’s not the case — say, your journeyman guard’s jumper has a higher expected value than your star forward’s inside shot — there's an arbitrage opportunity. The coach should demand more shooting by the guard and less by the forward.

The best players will still end up taking more shots and scoring more points than the weaker players. But if defenses are guarding the stars more tightly and leaving easier opportunities for weaker players, a well-coached team will exploit the opportunity. Yes, to be a successful team you need to have good players. But to be a great coach, you need to deploy those players smartly so that there is no low-hanging fruit of higher-than-average expected value shots not being taken.

In their 1990 study, Grier and Tollison found that coaches’ success on this frontier — not just of winning more games or fewer, but on properly arbitraging what shots are taken —matters. “We show that managers who allocate shots better increase team victories and improve their own job security,” they wrote.

Which brings us back to Gary Neal and Danny Green, the stars of last night’s NBA finals game. The Heat defense was focused on stopping the Spurs' biggest stars, Tim Duncan, Tony Parker and Manu Ginobili. Those three combined for only 25 points, less than half that of the Neal-Green combo. In the first half, even as the Spurs were leading, Duncan looked physically dejected at times.

But because he is a great coach, Gregg Popovich, ensured that his team was able to exploit whatever opportunities the opposing defense left open. And in this case, the fact that Neal and Green are journeymen who will probably never star in a sneaker commercial wasn’t a reason why they shouldn’t lead the Spurs offense. As the Bleacher Report puts it, “Spurs coach Gregg Popovich is the kind of guy who discovers $20 bills in his laundry, finding money seemingly everywhere he looks.”

Exactly. He’s really good at identifying arbitrage opportunities, which, last night at least, was enough to beat the Heat.