The Face on Mars and Wins Produced

Posted on April 26, 2007 by

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As Dave has blogged earlier – we employ a team statistical adjustment (i.e. team defense) measure as part of the Wins Produced metric.  This measure incorporates the opponent’s field goals made, opponent’s turnovers, and team rebounds into our analysis of individual players.

Now this may come as a shock to you but we have critics.  I know, but it’s true. One critique is that we only present Wins Produced with the team adjustment but not without the team adjustment.  Specifically we have been asked “… how well does Wins Produced with the team adjustment predict team wins?  For the sake of intellectual honesty please make this information public.”

Dave provided an answer to this question, but I thought I would chime in with a few more thoughts.  Let me begin with a quick linear regression review.  One of the main assumptions of the linear regression model “… is that the dependent variables can be calculated as a linear function of a specific set of independent variables, plus a disturbance term.”  (Kennedy p. 43, A Guide to Econometrics 3rd ed.)  If this assumption is violated you have a specification error.  One type of specification error is an omission of a relevant independent variable (i.e. the team adjustment in question).  If we did not include the team adjustment measure then our econometric model would be mis-specified.  Consequently our coefficient estimates would be biased and our inferences would be inaccurate!

Think about it this way – for years people believed that there was a “face on Mars”.  Examining fuzzy pictures from the Viking Orbiter 1 space craft we see a fuzzy picture of a hill that is “face-like.”  From that fuzzy picture some have concluded that this hill is an artificially shaped alien artifact.  The problem is that the resolution of the 1976 Viking Orbiter was not strong enough to provide a clear picture of this hill.  With the

2001 Mars Global Surveyor’s higher resolution Mars Orbiter Camera the “face-like” hill is well…. just a hill.

In the same manner if we estimated Wins Produced with the team defense adjustment our estimates would be like the original fuzzy pictures and could lead to inaccurate conclusions.  Thus “[f]or the sake of intellectual honesty …” I would respond that by looking at how well Wins Produced without the team adjustment is like drawing conclusions from fuzzy pictures since the model is mis-specified.  Hence, by not estimating a mis-specified model we are being as intellectually honest as possible.

I suspect that this explanation will not satisfy all of those who “know we are wrong or are hiding something up our sleeves”.  Such is life.  We have learned over the last year that you can’t make everyone happy.  We do feel fairly confident that our fully specified model – based on the theoretically sound proposition that wins are determined by offensive and defensive efficiency — provides an accurate picture of player performance in the NBA.  And although that picture might just be a hill in economics, it is our happy little hill (okay, my metaphor is getting away from me).

– Stacey

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