The Optimal NBA Roster Updated

4 Sep

The Optimal Roster


As shown in 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 15 players that comprised the ‘Optimal Roster’ taken from a pool of all players currently in the NBA?

My concept of the “Optimal Roster” uses the Excel Risk Solver software to create an optimal NBA roster of 15 players while staying in the confines of the salary cap or potential tax level based on the 2011 CBA agreement for NBA teams.

Using John Hollinger’s GameScore calculation averaged over an 82-game regular season and adjusted to per 48 minutes played,, 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 15 players cannot exceed a given limit, in this case I used a ceiling that was a calculation of the average NBA team salary in the 2012-13 season.   An additional constraint was added such that only one player from each position may be chosen to build the starting lineup and each roster must have two back up players at each position.   Given each team may carry 15 players, but can only have 12 active for a game, it made sense to build the model to accommodate all 15.

The main focus of this research is to be able to understand small variances in spending and to place a framework around how a team can go about statistically maximizes roster to meet given expectations.   In other words, 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.  Lastly, if a team were to lose a few players in the offseason due to Free Agency, are we able to take a pool of undrafted collegiate prospects, international NBA eligible players and current NBA free agents and use this model to find the ideal solutions to the vacated roster holes?  These are the ideas that are being explored using this model.

The last question in the preceding paragraph is largely dependent on the ability to standardize collegiate and international players with current NBA players in order to compare apples to apples.  This would require a projection model to attempt to predict the output of college players at the NBA level, and a similar conversion model to convert international player productivity to the NBA game.    In the current optimization model, we are only using a pool of current NBA players to build the ideal roster because the framework for the projection models is not currently in place.   I wanted to take a moment to acknowledge the next steps in the process that I have yet to achieve, but certainly plan to do.

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

Jordan Jhabvala 


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