We study the factors that predict medical malpractice ("med mal") insurance premia, using national data from Medical Liability Monitor over 1990 to 2017. A number of core findings are not easily explained by standard economic theory. First, we estimate long run elasticities of premia to insurers' direct cost (payouts plus defense costs), allowing for lags of up to four years, of only around +0.40, when one might expect elasticities near one. Second, state caps on malpractice damages predict a roughly 50% higher ratio of premia to direct costs even though, in competitive markets, a damages cap should affect premia primarily through effect on cost. A difference-in-differences analysis of the "new cap" states that adopted caps during the early 2000's provides evidence supporting a causal link between cap adoption and the ratio of premium to direct cost. Third, the premium-to-cost ratio, which one might expect to be fairly constant over time, instead varies widely both across states at a given time and within states across time. Our results suggest that insurance companies do not fully adjust revenues to changes in direct costs even over long time periods. Insurers in new-cap states have been able to charge apparently supra-competitive prices for a sustained period.