Unarmed attacks have a recovery time of 60.
Staves have a recovery time of 100.So you get 1.67 times as many hits per second unarmed as you do with a staff.
Armsmaster makes the ratio even more severe. e.g., if you had 10 ranks in Armsmaster, the recovery times would be 50 and 90. So unarmed would be 1.8 times as fast as staff.
Also, small and fast attacks are more efficient than large and slow attacks, because they don't waste as much damage on the last hit. So more of your "damage per second" can be applied to your next target (if there is one), to bring them down faster.
BV