Greedy base sizes for sporadic simple groups

A base for a permutation group G acting on a set is a sequence B of points of such that the pointwise stabiliser G₁ is trivial. Denote the minimum size of a base for G by b (G). There is a natural greedy algorithm for constructing a base of relatively small size; denote by G (G) the maximum size of a base it produces. Motivated by a long-standing conjecture of Cameron, we determine G (G) for every almost simple primitive group G with socle a sporadic simple group, showing that G (G) =b (G).