Linda Gorman explained the problem of pay-for-performance with teachers: because of the small number of students per teacher, average student test scores can be more influenced by outside-the class-room size than by what the teachers are doing. As a result, a P4P scheme can end up rewarding bad teachers and penalizing good ones.
Austin Frakt has identified an additional problem in rewarding Accountable Care Organizations for their performance. In order to get around the small sample size problem, ACOs have to have at least 5,000 patients. But the larger the number of patients, the more physicians that are needed. And if gains are shared equally (rather than apportioned on the basis of marginal product) the larger the number of doctors, the less incentive anyone of them has to meet group goals.