a rough-cut probability analysis of the hawks lottery situation

A Rough-cut Probability Analysis of the Hawks Lottery Situation

Steve Walton, Ph.D.

Summary of the Problem If the Hawks’ lottery position is 4 or lower, the pick goes to Phoenix

If the Pacers’ lottery position is 11 or lower, the pick goes to the Hawks

What is the chance that each of the following scenarios will play out:

Hawks keep their pick and gain Indiana’s

Hawks keep their pick but don’t get Indiana’s

Hawks lose their pick to Phoenix but gain Indiana’s

Hawks lose their pick to Phoenix and don’t get Indiana’s

Relevant Data

ODDS PROBABILITY OF PICK 1 TO 14

per1000 1 2 3 4 5 6 7 8 9 10 11 12 13

1 Memphis 250 25.00% 21.50% 17.75% 35.74% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

2 Boston 199 19.90% 18.80% 17.11% 31.85% 12.34% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

3 Milwaukee 156 15.60% 15.73% 15.57% 22.55% 26.49% 4.05% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

4 Atlanta 119 11.90% 12.59% 13.29% 9.85% 35.02% 16.08% 1.27% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

5 Seattle 88 8.80% 9.65% 10.67% 0.00% 26.15% 35.92% 8.44% 0.38% 0.00% 0.00% 0.00% 0.00% 0.00%

6 Portland 53 5.30% 6.03% 6.98% 0.00% 0.00% 43.95% 33.06% 4.57% 0.13% 0.00% 0.00% 0.00% 0.00%

7 Minnesota 53 5.30% 6.03% 6.98% 0.00% 0.00% 0.00% 57.24% 22.60% 1.82% 0.03% 0.00% 0.00% 0.00%

8 Charlotte 19 1.90% 2.23% 2.68% 0.00% 0.00% 0.00% 0.00% 72.45% 19.64% 1.08% 0.01% 0.00% 0.00%

9 Chicago/New York 19 1.90% 2.23% 2.68% 0.00% 0.00% 0.00% 0.00% 0.00% 78.41% 14.27% 0.50% 0.0035% 0.00%

10 Sacramento 18 1.80% 2.12% 2.55% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 84.62% 8.74% 0.18% 0.0007%

11 Indiana 8 0.80% 0.95% 1.15% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 90.74% 6.28% 0.08%

Summary of Relevant Data The chance the Hawks move up is 38%

The chance the Hawks don’t move up is 62%

The chance the Pacers move up is 3%

The chance the Pacers don’t move up is 97%

Technical Results

Indy moves up Indy doesn’t move up

ATL moves up ~.01 ~.37 .38

ATL doesn’t move up ~.02 ~.60 .62

.03 .97 1.00

Managerial Results What is the chance that each of the following scenarios will play out:

Hawks keep their pick and gain Indiana’s = ~37%

Hawks keep their pick but don’t get Indiana’s = ~1%

Hawks lose their pick to Phoenix but gain Indiana’s = ~ 60%

Hawks lose their pick to Phoenix and don’t get Indiana’s = ~2%

Technical Notes The probabilities of the Hawks moving up and the Pacers moving up are not

independent

“Joint probabilities” are presented in the body of the table on the “Technical Results” slide

“Marginal probabilities” are presented outside the body of the table on the “Technical Results” slide

The actual joint probabilities should be constructed using Bayes’ Rule

However, the additional precision gained by applying Bayes’ Rule is not offset by the time required to complete the analysis

Therefore, the numbers reported are consistent with the correct application of probability theory, but are not the precise answers

The answers presented are likely within plus or minus 1%