Louis Brehier, who wrote a book called, Les institutions de l’empire byzantin cited the following statistics regarding the transition of Imperial authority between the Roman Empire and the Medieval Roman Empire(Byzantine).
When it comes to Romans from Caesar to Valentinian II (44 BC-AD 392): 39 emperors were murdered or deposed; 5 were killed in battle; 19 died peacefully.
63 emperors in total, 39 out of 63 murdered or deposed. Therefore, 62% irregular succession
When it comes to the "Byzantines" from Theodosius I to Constantine XI (395–1453): 65 emperors were deposed, 41 died violently and 8 killed in battle. 39 died peacefully.
112 emperors in total, 65 out of 112 murdered or deposed. Therefore, 58% irregular succession.