Why were the early Islamic armies so good?

Actually, Akram spends a lot of time talking about logistics and the state of the armies (he points out that most of the Romans units and formations in the Yarmuk campaign were from Italy and Greece and had consequently little idea of campaigning in that terrain, the formations that had served in the region earlier had been decimated by the Persian war), and in this he is far better than most writers on military affairs generally. It helps that he was a career army officer himself (and actually served in the region in WW2).