The Research Experience for Teachers Program
http://www.cs.appstate.edu/ret
A Statistical Analysis of
Basketball Comebacks
Presenters:
Jessica Jenkins and Adam Benoit
Watauga High School
Lincolnton High School
Inspiration
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
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
Comparison of Comeback Probabilities
at the start of the 4th Quarter for
Deficits up to 20 Points
Point
Differential
1
Empirical
Estimate
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
Point
Differential
10
11
12
13
14
15
16
17
18
19
20
z(x,y)
Empirical
Estimate
0.1119
0.0882
0.0382
0.0485
0.0260
0.0126
0.0383
0.0221
0.0000
0.0189
0.0066
z(x,y)
0.1100
0.0946
0.0813
0.0699
0.0601
0.0516
0.0444
0.0381
0.0328
0.0282
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
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•
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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_lea
d_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/