A Statistical Analysis of Basketball Comebacks Presenters: Jessica Jenkins and Adam Benoit Watauga High School Lincolnton High School

Inspiration What was the likelihood of the http://www.nba.com/hawks/sites/hawks/files/imagecache/image_gallery_default/photos/HWK_Tmac_Moment1.jpg What was the likelihood of the "Greatest" NBA Comeback of All Time?

Abstract Likelihood of an NBA comeback based on the time remaining and point differential Data mining strategies Visualization Modeling the empirical data with a function

Introduction NBA regular season games from 2002 – 2013 Two factors: time and point differential Modeled with exponential function

Literary Reviews Factors: possession, home-team advantage, current ranking Bill James’ formula Seconds = (lead – 3 ± 0.5)2 +0.5 if the leading team has the ball -0.5 if the trailing team has the ball Research prior to 2000

Empirical Data

Empirical Data

Empirical Data 95% Confidence Interval The most frequent probability of a comeback is 0.1420; however, the 95% confidence interval is from 0.1126 to 0.1757.

Function z (x,y) = 0.5e -Ry x + C -178.3099y x + 457.8600 z represents likelihood of a comeback, x represents time remaining, and y represents point differential The coefficient (R) and the constant (C) were found using nonlinear regression in MatLab z = 0.1128 for the previous example

Function and Empirical Data

Comparison of Comeback Probabilities at the start of the 4th Quarter for Deficits up to 20 Points Point Differential Empirical Estimate z(x,y) 1 0.4235 0.4298 2 0.3975 0.3694 3 0.3581 0.3175 4 0.3108 0.2729 5 0.2531 0.2346 6 0.2722 0.2016 7 0.1859 0.1733 8 0.1522 0.1489 9 0.1210 0.1280 Comparison of Comeback Probabilities at the start of the 4th Quarter for Deficits up to 20 Points Point Differential Empirical Estimate z(x,y) 10 0.1119 0.1100 11 0.0882 0.0946 12 0.0382 0.0813 13 0.0485 0.0699 14 0.0260 0.0601 15 0.0126 0.0516 16 0.0383 0.0444 17 0.0221 0.0381 18 0.0000 0.0328 19 0.0189 0.0282 20 0.0066 0.0242

Function and Empirical Data Deviation

Conclusions Function reasonably models the data Better predictor at specific points in game

Back to the Inspiration

Further Research Home-team advantage Quantify game momentum Possession Different Function

Acknowledgments Co-author Dr. Mitch Parry Dr. Rahman Tashakkori Dr. Mary Beth Searcy National Science Foundation ASU Computer Science Department Watauga High School Lincolnton High School Fellow RET Members

References [1] H. S. Stern, “A Brownian Motion Model for the Progress of Sports Scores” J. Amer. Stat. Assoc., vol. 89, no. 427, pp. 1128-1134, Sep. 1994. [2] Paramjit S. Gill , “Late-Game Reversals in Professional Basketball, Football, and Hockey” The Amer. Stats.,vol. 54, no. 2. pp. 94-99. May. 2000. [3] B. James, (2008, March, 17). The Lead is Safe. [Online]. Available: http://www.slate.com/articles/sports/sports_nut/2008/03/the_lead_is_safe.3.html [4] (2013, May, 29). Root-mean-square deviation. [Online]. Available: http://en.wikipedia.org/wiki/Root_mean_square_deviation [5] (2013, July, 17). ESPN NBA. [Online]. Available: http://espn.go.com/nba/