Optimal Shot Selection Strategies for the NBA MARK FICHMAN & JOHN O’BRIEN Tepper School of Business, Carnegie Mellon University MathSport International Conference June, 2017, Padua (Italy)
Basketball is Changing • “The NBA’s most efficient offenses seek out layups and threes. A high school in Minnesota takes the idea to the extreme.” (Ben Cohen, The Basketball Team That Never Takes a Bad Shot WSJ January, 2017) • The Rockets have taken 46 percent of their shots from 3-point range, the highest rate in NBA history. (John Schuhmann NBA.com , “One Team, Three Stats: Rockets Launch from deep at a record rate”) Optimal Shot Selection Strategies for the NBA
Basketball is Changing • An issue with articles on previous page is their total emphasis upon shot locations without considering defense • Objective of this paper is to solve for the mixed strategy Nash Equilibrium for offense/defense defined over court locations – first lets consider the phenomena Optimal Shot Selection Strategies for the NBA
Basketball Strategy: Facts and Coaching • Facts: • Prior to 1979, the NBA only had 2-point field goals • In 1979, the NBA introduced the 3-point shot • Initially only 3% of shots attempted were 3-pointers • In the 2013 season, 24.4 % of all shot attempts in the NBA were 3-pointers. It is now 31.6% for the 2016-17 season. • NBA coaching strategy has changed • Warriors power forward David Lee in relation to “Stretch 4s”: • "The game is changing," Lee said, "and I think one of the things is not telling '4s' (power forwards) they're going to be in the post all the time. Instead, teams are giving them the option to shoot mid-range shots and threes. Then the defense has to make the adjustment." Source: Fichman and OBrien JSA (Forthcoming 2017) • Source: http://www.sfgate.com/sports/kroichick/article/Stretch-4s- changing-NBA-dynamic-5011347.php Monday, November 25, 2013 • In addition there is a tradeoff that must be made between risk and expected payoff 7/24/2017 Optimal Shot Selection Strategies for the NBA 4
NBA Expected Payoffs => Importance of Risk and Return � Source: Fichman and OBrien JSA (Forthcoming 2017) If teams were risk neutral they would have shifted to 100 % 3 point shooting in 1987. They did not do that as we saw earlier. 7/24/2017 Optimal Shot Selection Strategies for the NBA 5
Basketball today consists of mixed 2- and 3-point shot strategy – along with an increasingly significant number of 3-point shots http://grantland.com/the-triangle/trio-grande-valley-daryl-moreys-d-league-plan-to-do-away-with-midrange-shots/ 7/24/2017 Optimal Shot Selection Strategies for the NBA 6
Constructing a Mixed Strategy Equilibrium (Offensive/Defensive) • Adopt a Nash Equilibrium approach - given a mixed strategy ( w ) defined over court locations • Offense maximizes risk adjusted payoffs made • Defense minimizes risk adjusted payoffs given up • Maximize difference between natural log of offensive and defensive Sharpe Ratios • Sharpe Ratio = expected payoff/(risk = standard deviation) • Equivalent to: • Maximizing the growth rate of point production per unit of risk taken by the offensive team net of the opposing team defense's attempt’s to minimize the growth rate of point production • Restricts attention to constant mixed strategies (log utility is a member of the iso-elastic utility functions – CRRA optimal strategy is independent of the SR) Optimal Shot Selection Strategies for the NBA
Analytical Objectives • The maximization problem is defined as follows and solved for every pair of teams in the NBA (970 optimization problem permutations): 𝜈 𝑃𝑔𝑔𝑓𝑜𝑡𝑓 𝜈 𝐸𝑓𝑔𝑓𝑜𝑡𝑓 • 𝑁𝑏𝑦𝑗𝑛𝑗𝑨𝑓 𝑥.𝑠.𝑢. 𝜕 ln − ln( 𝜏 𝐸𝑓𝑔𝑓𝑜𝑡𝑓 ) (1) 𝜏 𝑃𝑔𝑔𝑓𝑜𝑡𝑓 • • Subject to: σ 𝑘 w 𝑘 = 1 w 𝑘 ≥ 0 . • w = a vector of eleven shot location weights (figure 1), 𝑞 the probability of success from each shot location, and s T the possible points from each location. Expected points from the mixed strategy is defined as: 𝜈 = 𝑡 𝑈 w 𝑈 𝑞 𝑝 and the variance covariance matrix for different shot locations is: 𝜏 = w 𝑈 Σ 𝑝 w , Optimal Shot Selection Strategies for the NBA
Advantages of a Theoretical Approach • Generalizes across games e.g., from NBA to NFL to other sports • Every sport manages risk and return in payoffs • Every sport faces the problem of quantifying strategy to enable optimization theory to be applied • Extends to multiple shot types – e.g., 11 key locations on a basket ball court corresponding to finer shots (following slide) • In principle permits a basketball team to be engineered 7/24/2017 9 Optimal Shot Selection Strategies for the NBA
Shot Locations Optimal Shot Selection Strategies for the NBA
2015/16 Regular Season and Playoff Data • Data: play-by-play log data from nbastuffer.com • Database provides plays tagged by game clock time, 24-second clock time elapsed, play descriptions, shot types, and shot locations • Offensive and defensive statistical distributions estimated by shot location • Each team played 82 regular season games • Equilibrium was solved for every pair of teams (30x29) Optimal Shot Selection Strategies for the NBA
What should you do across 11 zones? • One argument, the Houston Rockets argument following on the Vipers experiment is only 3 pointers and 2 pointers within 5 feet of the basket. They are now doing that. • But there is a struggle between offense and defense 7/24/2017 Optimal Shot Selection Strategies for the NBA 12
Predictions when the Best and Worst are Paired! • Both best teams are clearly favored to defeat the worst • 0.376 offense versus 0.209 defensive • 0.709 offense versus 0.311 defense • Offensive power of GSW comes through and defensive strength of CLE (or offensive weakness of PHI) – but consider next slide 7/24/2017 Optimal Shot Selection Strategies for the NBA 13
Within Season Analysis • The sign of the difference between the offensive and defensive equilibrium for any pair of teams predicts the outcome of the game • The within season equilibrium difference provides a very strong description of the predicted versus actual winner (p<0.0000) which supports the observation that both risk and expected payoffs matter w.r.t. game outcomes • Raises the question can this theory be applied to predict and interpret playoff game outcomes? • Overall the answer is yes – correlation between equilibria difference and realized spread is positive (r=0.20, p < 0.03) using a relatively small sample • Out of sample analysis also raises the question did each team play their predicted strategies and how does this impact outcomes? • Explore this question via the final series
What happens when GSW is paired with CLE? • Against the league average, the analysis predicts GSW shoots 74% 3- pointers and CLE 56%! (both very high in theory) but when specifically paired against each other CLE their defensive strengths come through and GSW’s 3 -point predicted percentage drops to 21.1% whereas CLE drops to 45% predicted 3-point shots • In final series GSW started near the predicted equilibrium when playing against CLE with 68.5% 2-point shots but then almost monotonically GSW moved in the direction away from the equilibrium prediction to shooting too many 3-point shots. • On the other hand, over the series, CLE drifted closer to their predicted equilibrium. 7/24/2017 Optimal Shot Selection Strategies for the NBA 15
Deviation from Predicted Strategy – Chi Square Analysis 7/24/2017 Optimal Shot Selection Strategies for the NBA 16
Observations on Golden State – Cleveland final Veteran reporter when asked by Mark: `Hi, I am a lifelong basketball fan (just to establish my basketball bona fides, I saw Kareem play at Power Memorial) and a professor. I am also a fan of your reporting over the years. I heard you say on the Sports Reporters last week that you think Golden State should have shot more 2 pointers in last year's finals against the Cav's. I agree. I came to that conclusion using some basketball analytics two of us (me and another professor at Carnegie Mellon, John O'Brien) created precisely to address that question (what is the right number of 2 and 3 point shots to take). My question, if you don't mind my asking, is how you came to that conclusion? His answer: ``All they needed at some point in the final 2 minutes was a lousy little 2. But the only thing on their minds was jacking up 3s.’’ Bob Ryan Did GSW get it right this year? 7/24/2017 Optimal Shot Selection Strategies for the NBA 17
Suppose the optimal strategy for 2016 applies to 2017? Optimal Shot Selection Strategies for the NBA
Thank You Contact Information: Mark Fichman mf4f@cmu.edu John O’Brien jo0x@andrew.cmu.edu
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