Abstract: Aggressive herding of females is a frequent but not invariant response by male savannah baboons,Papio cynocephalus, to encounters with other troops. While males in some troops are consistently more likely to herd than those in others, not all inter-troop encounters result in herding, even within particular troops. This suggests that males assess the risk of male invasion posed by each encounter and respond accordingly. We used data from baboon troops in the Drakensberg mountains to determine the rules males follow in deciding whether to herd. Consistent differences between troops were explained only by the adult sex ratio. Males were more likely to herd if the sex ratio of their own troop was female biased, a finding that is concordant with the observation that males are more likely to immigrate into troops where the sex ratio is more female biased than the population average. Differences within troops were a consequence only of encounter distance, with herding being more likely at closer distances. We found a negative correlation between the angle of approach to the other troop and the subsequent angle of deflection. We interpret this to mean that herding functions to increase the distance between the interacting troops, thereby curtailing opportunities for strange males to inspect the troop and determine its sex ratio. In this way, possibly unlike those in other populations, the decision rules of these male baboons are geared to protecting longer-term reproductive prospects.