A Rough-cut Probability Analysis of the Hawks Lottery Situation

1. A Rough-cut Probability Analysis of the Hawks Lottery Situation Steve Walton, Ph.D.

2. 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

3. Relevant Data

4. 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%

5. Technical Results

6. 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%

7. 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%