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

2. Inspiration What was the likelihood of the
What was the likelihood of the
"Greatest" NBA Comeback of All Time?

3. 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

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

5. 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

6. Empirical Data

7. Empirical Data

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

9. 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 = for the previous example

10. Function and Empirical Data

11. 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

12. Function and Empirical Data Deviation

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

14. Back to the Inspiration

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

16. 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

17. References
[1] H. S. Stern, “A Brownian Motion Model for the Progress of Sports Scores” J. Amer. Stat. Assoc., vol. 89, no. 427, pp , Sep
[2] Paramjit S. Gill , “Late-Game Reversals in Professional Basketball, Football, and Hockey” The Amer. Stats.,vol. 54, no. 2. pp May
[3] B. James, (2008, March, 17). The Lead is Safe. [Online]. Available:
[4] (2013, May, 29). Root-mean-square deviation. [Online]. Available:
[5] (2013, July, 17). ESPN NBA. [Online]. Available: