  We consider a study of players employed by teams who are members of the
National Basketball Association where units of observation are functional
curves that are realizations of production measurements taken through the
course of one's career. The observed functional output displays large amounts
of between player heterogeneity in the sense that some individuals produce
curves that are fairly smooth while others are (much) more erratic. We argue
that this variability in curve shape is a feature that can be exploited to
guide decision making, learn about processes under study and improve
prediction. In this paper we develop a methodology that takes advantage of this
feature when clustering functional curves. Individual curves are flexibly
modeled using Bayesian penalized B-splines while a hierarchical structure
allows the clustering to be guided by the smoothness of individual curves. In a
sense, the hierarchical structure balances the desire to fit individual curves
well while still producing meaningful clusters that are used to guide
prediction. We seamlessly incorporate available covariate information to guide
the clustering of curves non-parametrically through the use of a product
partition model prior for a random partition of individuals. Clustering based
on curve smoothness and subject-specific covariate information is particularly
important in carrying out the two types of predictions that are of interest,
those that complete a partially observed curve from an active player, and those
that predict the entire career curve for a player yet to play in the National
Basketball Association.
