Lebron James behaving in an Instrumentally Rational Manner

In PLSC240 today, I introduced you to the rational choice theory (RCT), an increasingly important explanatory mechanism in political science. The basic idea behind RCT is that one can analyze political outcomes on the basis of understanding individual behavior. The fundamental assumption regarding individual behavior is that all human beings (regardless of where they are from) act in an instrumentally rational manner. What does this mean? It means selecting the means or action (instrument) that will maximize one’s expected utility. Huh? Well, here’s an explanation by way of an example from King James. Click on the picture to link to a page where you can view the video clip.lebron.jpg

In that clip, we saw Lebron James hit a “step-back 3”; in other words, he stepped his right foot back behind the 3-point line so that his shot (were it to go in the basket) would be worth three points rather than two. You often see players do this. In so doing, they are acting in an instrumentally rational manner by maximizing their expected utility. Follow along for the logic, and for some mathematical notation.

We all value things in life, and an NBA player–during the 48 minutes (or portion thereof) that he is on the floor values points (among other things). He wants to score as many points as possible, other things being equal. Because he values points, they give him utility. From a rational choice perspective, an individual is acting in an instrumentally rational manner if she takes the action/behavior that will maximize her expected utility. Moreover, she should be consistent–i.e., given the same utility and environmental constraints the individual should select the same action/behavior every time, and any other individual would do the same.

In the NBA, some shots from “the field” are worth 3 points, while others are worth 2. Thus, Lebron in the situation shown in the video clip can quantify the utility of his preferences: they are u(3pt) = 3, u(2pt) = 2. In other words, the utility (u) to Lebron of making a 3-point shot is 3, and of making a 2-point shot is 2. Deciding whether to take a 3-point shot or a 2-point shot would be a straightforward task if he knew for certain that the ball would go in the hoop every time he shot. Of course, he isn’t certain. What are his beliefs about the probability of each of these shots going in?

Well, fortunately the NBA keeps statistics on these types of things. He shoots 33% from beyond the 3-point line, and 40% from a foot inside that line. Thus, his beliefs are Pr(2pt )= 0.4, and Pr(3pt) = 0.33. The probability of successfully making a 2-point shot–one foot inside the line–is 0.4, etc. Given that we now know both his preferences and beliefs, we can determine what is the instrumentally rational action for Lebron to take.

What is his expected utility (EU) of attempting a 2-point shot?

EU(2pt) = Pr(2pt) · u(2pt), which is 0.4· 2 = 0.8

What is his expected utility (EU) of attempting a 3-point shot?

EU(3pt) = Pr(3pt) · u(3pt), which is 0.33· 3 = 0.99

Since 0.99 > 0.8, Lebron is “maximizing his expected utility” by “stepping back to hit the three.” Isn’t rational choice fun?