Equal opportunity, widely invoked in popular discourse as a goal for policy, seems at odds with the welfarist approach that is standard in economics. But are they really different? We consider a canonical class of resource allocation problems and ask whether the allocations chosen by an equal-opportunity criterion could also have been chosen under some welfarist criterion. Typically, no such welfarist criterion exists. However, for a rich class of problem specifications, it does exist, and we characterize this class. When the welfarist criterion does exist, it can use either the sum or the min to aggregate individual welfares; the freedom to use more exotic aggregators does not expand the possibilities.