  In the National Basketball Association (NBA), teams must make choices about
which players to acquire, how much to pay them, and other decisions that are
fundamentally dependent on player effectiveness. Thus, there is great interest
in quantitatively understanding the impact of each player. In this paper we
develop a new penalized regression model for the NBA, use cross-validation to
select its tuning parameters, and then use it to produce ratings of player
ability. We then apply the model to the 2010-2011 NBA season to predict the
outcome of games. We compare the performance of our procedure to other known
regression techniques for this problem, and demonstrate empirically that our
model produces substantially better predictions. We evaluate the performance of
our procedure against the Las Vegas gambling lines, and show that with a
sufficiently large number of games to train on our model outperforms those
lines. Finally, we demonstrate how the technique developed in this paper can be
used to quantitively identify "overrated" players who are less impactful than
common wisdom might suggest.
