NBA All-Star Game Prediction

Pouya FatemiAlex WuZinnia Horne

$3.57 Billion in Revenue in the ‘07-’08 season1

Games broadcasted in over 215 countries and territories 2

Fans in New York paid $74 million for tickets in the ’04-’05 season 2

1http://www.plunkettresearch.com/Industries/Sports/SportsStatistics/tabid/273/Default.aspx 2 http://www.forbes.com/2005/12/22/nba-team-valuations_cz_mo_1222nbaintro.html

Why do we care?

How can we most accurately predict the winner of the NBA All-Star Game?

What is the probability distribution of the points scored by an NBA All-Star team?

Probem

Pw = total points scored by Western Conference = ∑ POSi

N = number of possessions per team per game

POSi , discrete random variable with possible values [0,1,2,3,4] – This represents the possible number of points scored in each possession

Variables

Model Formulation

• Most likely outcome (mode) after a possession is to score 0 points.

• The next likely outcome is scoring two points. • The average number of points scored is 1.0973, with a standard

deviation of 1.1074.

Normal Approximated Distribution for Pw

• Mean = N * [E(POSi)] = 90 * 1.0973 = 98.757• Standard Deviation = (√N) * STD of POSi = (√90) * 1.1074 = 10.506• Assumption: N (# of possessions team obtains in a game = 90)

Sensitivity Analyses# of Posessions vs. E(Points)

70.0075.0080.0085.0090.0095.00

100.00105.00110.00115.00120.00

75 77 79 81 83 85 87 89 91 93 95 97 99 101 103 105

• Relationship between # of possessions (x-axis) and expected # of points scored (y-axis).

• Assumed value in our model was N = 90

P(2 pt shots) vs. E(Points)

88.0090.0092.0094.0096.0098.00

100.00102.00104.00106.00

0.5

0.52

0.54

0.56

0.58 0.6

0.62

0.64

0.66

0.68 0.7

0.72

0.74

0.76

0.78 0.8

0.82

0.84

0.86

0.88 0.9

• Relationship between percentage of 2-pointers (x-axis) and expected # of points (y-axis).

Effect of momentum Treat seconds spent each possession as a

random variable bounded by 0 < seconds spent <24

Possible Extensions