It has been argued, particularly by the French evolutionist Michel Raymond et al, that left-handedness confers an advantage in combat (and by corollary in fighting sports and other one-on-one sports - see the section on Handedness and Sport), an idea that is sometimes referred to as the Fighting Hypothesis.

The basis of this “infrequency advantage” is that the vast majority of opponents faced by left-handers are right-handers (the majority of the population), so that they are well practised at dealing with the kind of asymmetry offered by other right-handers. It is, however, relatively rare for a right-hander to face a left-hander (which make up a small minority of the population), and are therefore much less practised at dealing with the different angles, stances, etc, employed by left-handers.

The Fighting Hypothesis also claims to explain the greater frequency of left-handed males than left-handed females, which is repeatedly found in studies, on the grounds that male-male fighting is a more common occurrence than other combinations and so it is the males who stand to profit the most from the left-handed fighting advantage.

Although far from conclusive, a 2004 study by Charlotte Faurie and Michel Raymond of nine undeveloped societies in five continents found some support for their hypothesis that left-handed combatants in such societies hold an advantage. They found that, in those primitive societies with higher levels of violence and higher murder rates, the incidence of left-handedness was higher, (ranging from 3.4% among the largely pacifist Dioula community in Burkina Faso, to 22.6% in the notoriously violent Yanomamo culture in South America), perhaps indicating that such violent societies favoured left-handed criminals.

Spiral staircases and towers in castles typically spiral clockwise going up, and this was purportedly a deliberate design to afford an advantage to the (largely right-handed) defending soldiers at the top of the stairs, who had plenty of room and good angles to swing their weapons at the (largely right-handed) attackers below, who had little room and were impeded by the central column of the stairs. Left-handed attackers, it is argued, therefore held an advantage (or at least less of a disadvantage) in such circumstances.

The famously left-handed Kerr clan supposedly built anti-clockwise spiral staircases in Ferniehirst Castle in the Scottish Borders during the Middle Ages in order to give themselves a similar advantage (although one would have thought that this would also yield an advantage to the right-handed attackers below!)