It is natural to suppose that a prosecutor's conviction rate - the ratio of convictions to cases prosecuted - is a sign of his competence. Prosecutors, however, choose which cases to prosecute. If they prosecute only the strongest cases, they will have high conviction rates. Any system which pays attention to conviction rates, as opposed to the number of convictions, is liable to abuse. As a prosecutor's budget increases, he allocates it between prosecuting more cases and putting more effort into existing cases. Either can be socially desirable, depending on particular circumstances. We model the tradeoffs theoretically in two models, one of a benevolent social planner and one of a prosecutor rewarded directly for his conviction rate as well as caring about convictions and personal goals. We also look at anecdotal evidence from Japan and detailed U.S. data drawn from county-level crime statistics and a survey of all state prosecutors by district. We find that prosecution rates vary little with budget, but conviction rates do increase, and that the conviction rate declines in the number of cases prosecuted and with the crime rate of a district.