 Solution

Using 50 controls per UTC can reduce sampling variance by averaging over more control outcomes. The gain has sharply diminishing returns because controls matched to the same UTC are not 50 independent treated-control contrasts.

The disadvantage is poorer covariate balance: the 50th-nearest school will usually be much less comparable than the fifth-nearest school, increasing residual confounding and changing the target population. A caliper or variable matching ratio should therefore prevent distant matches even if many controls are available.