The Law of Diminishing Returns and the NBA

Posted on May 3, 2006 by

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The Phoenix Suns finished the 04-05 season with 62 wins.  Before the 05-06 campaign began the Suns lost three very productive performers – Quentin Richardson, Joe Johnson, and Amare Stoudemire.  How productive were these players?  In our book we detail how the statistics tabulated for the players can be used to measure a player’s Wins Produced.  As noted in the sample material posted on our website, team wins basically equals the Wins Produced accumulated by the team’s players.  For example, Wins Produced for the Suns players in 2004-05 sum to 60.3.

Of these, a bit more than 25 wins can be attributed to Richardson (6.1 Wins Produced), Joe Johnson (5.9 Wins Produced), and Amare Stoudemire (13.5 Wins Produced).  Although the Suns did add players like Boris Diaw, one wonders how the Suns still managed to win 54 games in 05-06 with so much production leaving the building? Well, as we say in the book, let’s get all academic for a moment.  In our book we discuss the Law of Diminishing Returns, which basically states that if other inputs in production are fixed, one can expect adding additional workers will lead to less productivity from a firm’s labor force.  Or if we go in reverse, taking workers away can lead to more productivity from the remaining labor.  If we apply this law to basketball we can expect to see a player’s productivity decline as the productivity of his teammate’s increases. Again, taking this process in reverse, if a team loses productive players, it is possible for other players to “step it up.” 

With the Suns we see evidence of this phenomenon.  Steve Nash’s produced 16.1 wins en route to winning the MVP award in 04-05.  Shawn Marion was a bit better, producing 18.6 wins last season.  This year both players improved. Nash produced 18.6 wins this year.  Marion, who again bested Nash, finishing the year with 22.6 Wins Produced.  Does all this mean that the Suns are better off without Amare?  No, but we can expect when he returns next year that the productivity of his teammates will dip slightly. 

This discussion highlights a key distinction we make in the analysis of an NBA player’s productivity.  Our measure of Wins Produced paints an accurate picture of “how” productive a player has been.  To understand “why” a player is productive is a bit more difficult.  The Law of Diminishing Returns is not the only force acting on player performance, but it is an issue to address in understanding why players get better or worse from season to season.  I think our view of how to measure player performance in the NBA, and the specific role Wins Produced can play in the process, can best be summarized with the following quote from our book:  “One cannot end the analysis when one has measured the value of player performance. Knowing the value of each player is only the starting point of analysis. The next step is determining why the player is productive or unproductive. In our view, this is where coaching should begin. We think we can offer a reasonable measure of a player’s productivity. Although we have offered some insights into why players are productive, ultimately this question can only be answered by additional scrutiny into the construction of a team and the roles a player plays on the floor.”– DJ