Thursday, February 9, 2017

Why three point shots are the best in basketball

Basketball coach Dan D'Antoni uses expected value per attempt to explain why his team takes so many 3-point shots:
"If you can get a layup and it's clean — it's not one that's highly contested — it's [worth] 1.8 points [per attempt]. It's 1.3 from that corner, 1.27. Do you know what a post-up is, with a guy standing over top of you? It's 0.78. So you run your team down there and we'll see how long you can stay with teams that can play the other way. You've seen it in the NBA. The last two championships have been Cleveland and Golden State. What do they do? You don't see anybody post up. They just spread that thing out and go."

HT:  Jason


  1. This was a cool article! I was not aware of how granular coaches get as to breaking down the probability of points per attempt from different areas on the court. It’s surprising to see the “post up” shots actually equate to the lowest points per attempt at 0.78. My whole life playing basketball the message was always to work the ball down into the post player for the closer shot, and in reality, that statistically isn’t the best option for the team to put points on the board. The 3-point shot has really changed the game between 2005 and 2012 Six of the seven NBA champions averaged at least 18.5 three-pointers during the regular season. In 2012, both Miami and San Antonio averaged over 21 attempts per game (Babb, 2013). This is mind blowing to see the strong correlation between teams that lead in 3-point field goals and the corresponding NBA champions. Analytics have revolutionized sports in recent years, more and more teams look at data now to decide which players they want to draft or trade for. Once, the dominant way of judging how well a player or team would perform was the “eye-test”—the organic, gut-instinct impression that came simply from watching a game unfold. But that time has been replaced by an era in which coaches and their backroom staff pore over formulas and figures—how many mid-range jump shots a team uses versus attempts near the hoop, or how many three-point shots versus two-pointers—to predict the most effective methods for winning (Ross, 2015). Statistical data and algorithms have changed every aspect of sports in the last 20 years. All the way down to where to take a shot from on the basketball court. It’s a different NBA and different sports arena now, I’m curious to see how the development of coaches change in the future, are analytics going to become as important as motivation, and team building? Will future coaches have a background in statistics?


    Babb, Stephen. Bleacher Report. How the 3-Pointer has Revolutionized the NBA. August 1, 2013.

    Ross, Terrance. The Atlantic. Welcome to Smarter Basketball. June 25, 2015.

  2. Although I haven’t watched basketball in a LONG time (I’m too busy writing response posts like this for my MBA!), this blog post piqued my interest. In the article, Coach Dan D’Antoni argued that post-up shots were the worst type of shot to take, claiming that they are worth 0.78 points per shot (Davis, 2016). From an economic perspective, this is really an argument supported by analysis of expected values.

    Coach D’Antoni’s brother, Mike, is head coach of the Houston Rockets in the NBA. During the 2015-2016 season, the NBA league average for completing two-point and three-point shots was 49.1% and 35.4%, respectively (2015-16 NBA Season Summary, n.d.). Calculation of expected value shows the following:

    Two Point Shot Expected Value: (0.491*2) + (0.509*0) = 0.982
    Three Point Shot Expected Value: (0.354*3) + (0.646*0) = 1.062

    During the same time, the Houston Rockets did slightly better than league average in two-pointers (51.4%) and slightly worse for threes (34.7%) (2015-16 NBA Season Summary, n.d.), yielding the following calculations:

    Two Point Shot Expected Value: (0.514*2) + (0.486*0) = 1.028
    Three Point Shot Expected Value: (0.347*3) + (0.653*0) = 1.041

    The numbers are closer, but jive with the league totals. Three pointers, on average, prove out to be the better shot to take, for both the Rockets and the League overall. I suppose the numbers are only part of the story, since teams have to have capable players and favorable league rules, say on distance of the three-point line. I’ll leave the argument of what makes a more exciting game (hard fought battles in the paint versus a shooting spree) to the pundits and fans.


    2015-16 NBA Season Summary. (n.d.). Retrieved April 8, 2017, from Basketball Reference:

    Davis, S. (2016, December 29). Marshall men's basketball coach gave a great breakdown of why 3-pointers are the best shots in the game. Retrieved April 8, 2017, from Business Insider:

    Froeb, L. M., McCann, B. T., Shor, M., & Ward, M. R. (2016). Managerial Economics: A Problem Solving Approach. Boston, Massachusetts: Cengae Learning.

  3. “Collective bargaining negotiation between labor unions and corporate employers create a particular area in the field of general negotiations, but the fundamental legal and relationship characteristics make them distinct. Unlike a general business negotiation and law suit negotiations that are not controlled by constitutional provisions, a collective bargaining negotiation is directed and administered by external laws”. (Craver, Charles B. n.d.)
    “Strategic view of bargaining can be looked at like the game of chicken whereas the capability to pledge to a position gives one player bargaining power over rivals. Let’s look at a situation where a manager who works at a college is bargaining with a labor union over a fixed sum and that each player has two possible strategies, which are bargain hard or accommodate. If they both bargain hard, then they will never reach a deal and neither profits from this. If one bargains hard and one accommodates, then the one who bargains harder will probably get a better deal. In the game of chicken, but parties will try to push for what they want for their prefer equilibrium by committing to a position. If you see that you cannot convince your rival to come around to your side, then you might want to consider accommodating. Unions will threaten to strike if they do not agree with what management is presenting, but this is usually due to the fact that the union representatives do not believe that management is going to do what they say. Management has to insure that their threat is credible”. (Froeb, L. m., B.T. McCann, M. Shor, and M.R. Ward. 2016)

    Craver, Charles B. n.d. Retrieved from internet:
    Froeb, L. m., B.T. McCann, M. Shor, and M.R. Ward (2016). Managerial Economics: A Problem Solving Approach. Boston: Cengagebrain.

  4. This comment has been removed by the author.

  5. Marshall Men’s basketball coach, Dan D’Antoni brings up a very interesting point when breaking down the math as to why three point shots are the best shots in basketball. Having been to many college basketball games I had always wondered as to why the player didn’t drive the hoop and try to make the layup or post up shot. I had figured this was the best option as you were closest to the hoop. After reading the article posted by Scott Davis, Dan D’Antoni gave me a whole new perspective on the various types of shots in basketball. Minimizing Expected Error Costs is an economic concept that can be related to the game of basketball. Froeb, McCann, Shor and Ward say that rather than making decisions that maximize expected profits, it is sometimes useful to think instead about minimizing expected “error costs” (Froeb, McCann Shor, Ward, 2016, pg. 224). With that being said, going for the three pointer each time will get you the maximum number of points per shot. However, it may be better to drive the hoop to get a lay-up or maybe even a foul shot although you will not be getting as much “profit” or most number of points out of it. In a sense the safer, least amount of error may be more beneficial in the long run as three pointers can be harder to shoot as they are farther away from the hoop. Every time a shot is taken in basketball there is some risk and uncertainty to each shot. Risk versus Uncertainty is an economic concept that can be applied to the game of basketball. Uncertainty can be described as something that can be quantified using random variables; that is, you can list the possible outcomes and assigned probabilities to each of those outcomes (Froeb, McCann Shor, Ward, 2016, pg. 224). Just as Dan D’Antoni did in his article, he portrayed the possible outcomes per shot type, a layup being worth 1.8 points per attempt, 1.3 from that corner, and 1.27 from the far corner (Davis, 2016). These outcomes he predicted were affected due to those random variables; a person blocking the shot, shooting over somebody, etc. There is always risk when taking a shot in basketball no matter what those variables are, there is risk of missing the shot each time one occurs. After reading the article it helped me better understand the economic concepts related to uncertainty, and making decisions with uncertainty.

    Davis, S. Marshall men’s basketball coach gave a great breakdown of why 3-pointers are the best shots in the game. 2016. Retrieved from dantoni-why-3-pointers-are-best-shots-in-basketball-2016-12. December 2017.

    Froeb, L. M., McCann, B. T., Shor, M., Ward, M. R. Managerial Economics a Problem Solving
    Approach. Fourth Edition. Boston, MA: Cengage Learning, 2016.

  6. D’Antonio’s statements bring up not only a trend in basketball, but a trend in all sports in recent times- The mining of data analytics to improve player and team performance. Teams are combating the economic concept of uncertainty by analyzing performance metrics in detail. With this data teams are able to make more informed decisions and reduce the uncertainty of certain outcomes. When we’re uncertain about what value a variable will take, we identify the situations in which it takes on different values, list possible values, and assign a probability to each value. (Froeb, L. m., B.T. McCann, M. Shor, and M.R. Ward. 2016). The NBA coaches have identified the values and probabilities of various shot locations on the court and found the three point shot to have the highest probability for success. When you’re uncertain about the costs or benefits of a decision assign a simple probability distribution to the variable and compute the expected costs and benefits. (Froeb, L. m., B.T. McCann, M. Shor, and M.R. Ward. 2016). The probability distribution has been assigned to a selection of shots with the costs and benefits weighed for each shot attempt. The three point shot has the highest benefit and given the recent success of teams that frequently shoot the three there is evidence that applying this model can reduce the uncertainty of an unsuccessful losing outcome.

    Froeb, L. M., McCann, B. T., Shor, M., & Ward, M. R. (2016). Managerial Economics: A Problem Solving Approach. Boston, Massachusetts: Cengae Learning