The Optimal NBA Roster

1 Apr


Following the movie Moneyball, the use of data analytics has played an ever growing role in decisions made by professional sports teams.

My concept of the “Optimal Roster” was developed after an Optimization class at Carnegie Mellon’s Tepper School of Business.  In a particular class discussion, my professor attempted to maximize the return of a bond portfolio by choosing an ideal group of five bonds, out of a possible ten, given a specified dollar amount to invest.   In order to do this, he used Excel Risk Solver to help identify the optimal solution/portfolio of bonds to choose.

This discussion led me to the optimal roster concept.  What if I replaced bonds with NBA players?  What if instead of an investment portfolio, I optimized the selection of players within the constraints of a team’s Salary Cap?   What if instead of considering bond coupons (interest), maturity and risk, we looked at a player’s points, rebounds and assists?  Lastly instead of a having to choose five bonds out of a possible ten, what if we had to choose five players, one player at each position, out all NBA players currently in the NBA?

My concept of the “Optimal Roster” uses the Excel Risk Solver software to create an optimal starting lineup of an NBA team while staying in the confines of currently salary cap for a team.

Using a simplified version of John Hollinger’s PER calculation, I was able to rank players based on position.  Then adding in their Salary information, I was able to set the constraints in Risk Solver stating the total money spent on the five players cannot exceed the percentage of the salary cap inputted.   Also, only one player from each position may be chosen in order to maximize total team PER.

The main focus of this research is to be able to understand small variances in spending.  Meaning, if half of a percent more of the salary cap was dedicated to spending on the starting five players, how much greater does total team PER become.   Does it make sense to potentially over spend and dip into the luxury tax just to gain more productivity from players?   Or can you find ways to save money while still getting productive output from your lineup.  These are the ideas that are being explored using this model.

The ideal scenario in this case is to be able to build a team of 15 players; however the student version of Risk Solver limits us to 200 variables so this isn’t possible.   Also, the next step in this research is to be able to account for rookie salaries versus veteran deals which certainly skew the results.   Nonetheless, the framework from the model is in place and I will continue to post more once I am able to do more of the variance research resulting from having more variables to work with.

If you have any questions or thoughts on this model and research, please contact me at

Jordan Jhabvala 


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