Some non-healthcare reading from Wages of Wins as the NBA playoffs are upon us. Should a coach bench a starter in foul trouble? Doesn’t reducing a high-quality player’s aggregate minutes adverse affect a team and thus coaches should let players play regardless of the number of fouls they have?
It turns out that the optimal strategy looks something like this: bench starters in foul trouble only if it is early in the game and the player has a strong backup on the bench. The specifics are of course in the paper but the basic idea can be explained using option pricing.
Option pricing is the most common example of derivatives valuation in the field of finance. It is also the most notable, being the source of the famous Black-Scholes pricing formula under specific assumptions about the underlying process for which Robert C. Merton and Myron S. Scholes won their Nobel prizes in 1998 (two of us worked with them at Long Term Capital Management, the hedge fund where they were partners)…
In the context of basketball, benching a player creates an option for the coach. The coach has the choice to put him back in the game at a critical juncture later in the game. In options terminology, the coach has the right to exercise his option early, by letting the player play through his foul trouble, but he risks that the player fouls out and will be unavailable at the end of the game, when matchups become important…
We had prior beliefs that benching was universally bad; we were wrong.