Monday, June 16, 2014

Within NBA Team Income Inequality and Player Performance

Nobody has a strong preference to be a "low ranked monkey".  Whether in the NBA or at the University of California,  workers are unhappy when they know they are below the median earners.   But does being "unhappy" translate into being unproductive?

In this blog post, I will provide a sketch of a good undergraduate economics honors thesis.  There are many economics students with strong quant skills who aspire to be the next Nate Silver.

Suppose that a student can access the universe of all player statistics for every team for the last 30 years.  For each team in each year, the researcher would calculate the income inequality measure for the team in that year and knowing each player's salary and the median salary could calculate whether the player's salary is above or below the median.

Key outcome statistics for the team would be its wins and how far it went in the playoffs

Key personal stats for the player would be some "sabermetrics" indicator of points, rebounds, assists, turnovers,  shooting efficiency, defensive prowess, etc.   Time varying controls would include the player's age and cumulative minutes played and recent injury history.  Suppose this can be boiled down to a single variable called X for each player in each year.  So if a team has 12 players this is a 12 dimensional vector each year. A similar metric could be constructed for the coach's quality based on past playoff and winning percentages.

The following multivariate regression would then be run;

Using the team/year aggregate data: a conditional logit model could be estimated of the form:

probability team j wins the title in year t =  f(X ,  coach quality,  team income inequality)

If the team income inequality variable has a negative coefficient then this indicates that team income inequality is "bad" for performance.

The player/year level micro data could then be used to test whether player performance suffers when they are on a team that has more income inequality and they are a low ranked monkey (LRM).

Define X1 as  a player's single quality index for that year (as defined above) and define X2 as his teammates scores for that year (this variable could be lagged).

The researcher would estimate:

X1 =  player fixed effect + player age + player injury + coach fixed effect + B2*X2 +  B3*team income inequality +  B4*LRM  +  B5*LRM*team income inequality +  final year of contract  + U

The income inequality is "bad" hypothesis would posit that    B4 is less than 0 and B5 is less than zero.

Why is NBA data important?  It isn't but it represents a collectable measure of productivity across hundreds of millionaires.  These guys have no real wants or needs.

The ambitious researcher could then re-estimate the micro regression above and study whether the player was traded in the subsequent year.  Traded players may indicate that the player was unhappy in the situation and disgruntled .

For those interested in other work investigating how individual performance is affected by the composition of the group one participates in, take a look at my paper with Dora Costa from 2003.