How to Properly Score Pickup Basketball
Have we been playing basketball wrong this whole time? Kirk Goldsberry, of ESPN’s Grantland.com, writes a fascinating article about how the commonly accepted scoring system in most pickup basketball games is fundamentally unfair. Ideally, in any sport, all strategies are equally fair in leading a team or player to victory, with success relying on how well the strategy is executed. Goldsberry argues that playing basketball with baskets made inside the three point line counting as 1 point and outside the arc counting as 2 points produces a scoring system which unfairly favors the effectiveness of the long range shot. I believe that this type of argument relates specifically to the topic of game theory we have discussed in the course thus far.
In his piece, Goldsberry cites an independent study from Cornell grad Samual Reis-Dennis, who observed average player shooting percentages from different areas on a court at the University of North Carolina at Chapel Hill. Reis-Dennis recorded that players made 28% of shots from outside the arc while shooting 42% inside the arc. Let’s produce a game theory table as we have in class with player 1 being a basketball player, whose scoring percentages equate to the above mentioned averages, with the following two (2) shooting strategies: (1) shooting from inside the arc; or,(2) shooting from outside the arc. Furthermore, let this player respond to three (3) different scoring systems: (1) where all shots made produce one (1) point; (2) where baskets inside the arc are worth one (1) point, and baskets outside the arc are worth two (2) point; and, (3) a final system where shots made from inside the arc earn two (2) points, and shots made from outside the arc earn three (3) points. Based upon this player’s shooting percentages, his expected payoffs from his two (2) shooting strategies are as follows:
| Player Strategy | All shots: 1 point | Inside the Arc: 1 point
Outside the Arc: 2 points |
Inside the Arc: 2 points
Outside the Arc: 3 points |
| Shot from inside the Arc | (0.42)*1 = 0.42 | (0.42)*1 = 0.42 | (0.42)*2 = 0.84 |
| Shot from outside the Arc | (0.28)*1 = 0.28 | (0.28)*2 = 0.56 | (0.28)*3 = 0.84 |
To maintain the integrity of the sport, the best case scenario results in a scoring system that creates proportional payoff for a player shooting the safer short range shot as well as the player opting for the riskier long range shot. We can see from this table, however, that the scoring system itself influences the player to favor one shooting strategy over another. In the first case of all shots being equal to one (1) point, the player will clearly be motivated to take all his shots from inside the arc, since the safer shot produces a payoff that is equal to that of a player opting for higher-risk, long-range attempts from outside the arc. Similarly, the most common of all pickup scoring systems, with 1’s and 2’s being awarded as between short and long-range baskets, respectively, we see that players should always shoot long range shots since they produce a richer payoff. Finally, the optimal scoring system, with 2’s and 3’s serving as the respective short and long-range point values, has equal payoffs for both shot- types. Therefore, we see that in terms of basketball game theory, this final scoring system creates the most equitable reward environment for both short and long-range shooting strategies. . So, always remember, to play your next pick-up using the 2’s and 3’s scoring system, or risk damaging the competitive balance of shot selection.
Source:
Goldsberry, Kirk. “Video: How to Fix Pickup Basketball With Analytics.” Grantland, 2 Sept.
- Web. 14 Sept. 2015. <http://grantland.com/the-triangle/video-how-to-fix-pickup
basketball-with-analytics/>.