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.