Left handed men in cohorts were placed on the right in close formation like the turtle. You see, a man who is left handed will use the right as the shield arm. Left handed men were very appreciated in armys, both in Rome and Greek hopolites. In case of Greek hopolite battles, many times the battle was decided by in how much time the right flank of an army crushed the left flank of the others army. This wsa because commanders used their best men on the right flank to keep them safe from skirmishers (remember they are carrying the shield on the left, and so, mainly safe from arrows/javelins). Left handed men could fit in a formation to deny the enemy the possibility to kill valorous warriors with a lucky shot (like Richard the Lion Heart, killed by a revel crossbow bolt).