The important statistic for cost effectiveness is really the cost effectiveness of the marginal grant. If the marginal grant is very cost effective, then money is being left on the table and we should be awarding more grants! Conversely, if the marginal grant is very cost ineffective, then grant making is inefficiently large even if the average grant is cost effective. In that situation we could improve cost-effectiveness by eliminating some of those marginal grants.
The distance between the marginal grant and the average grant is increasing in the fat-tailedness of the distribution, so for very fat tailed distributions, this difference is extremely important.
The important statistic for cost effectiveness is really the cost effectiveness of the marginal grant. If the marginal grant is very cost effective, then money is being left on the table and we should be awarding more grants! Conversely, if the marginal grant is very cost ineffective, then grant making is inefficiently large even if the average grant is cost effective. In that situation we could improve cost-effectiveness by eliminating some of those marginal grants.
The distance between the marginal grant and the average grant is increasing in the fat-tailedness of the distribution, so for very fat tailed distributions, this difference is extremely important.