Greedy base sizes for sporadic simple groups

A base for a permutation group G acting on a set Ω is a sequence B of points of Ω such that the pointwise stabiliser GB 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).