  Team performance is a ubiquitous area of inquiry in the social sciences, and
it motivates the problem of team selection -- choosing the members of a team
for maximum performance. Influential work of Hong and Page has argued that
testing individuals in isolation and then assembling the highest-scoring ones
into a team is not an effective method for team selection. For a broad class of
performance measures, based on the expected maximum of random variables
representing individual candidates, we show that tests directly measuring
individual performance are indeed ineffective, but that a more subtle family of
tests used in isolation can provide a constant-factor approximation for team
performance. These new tests measure the "potential" of individuals, in a
precise sense, rather than performance, to our knowledge they represent the
first time that individual tests have been shown to produce near-optimal teams
for a non-trivial team performance measure. We also show families of
subdmodular and supermodular team performance functions for which no test
applied to individuals can produce near-optimal teams, and discuss implications
for submodular maximization via hill-climbing.
