In Tiberius's write-up on the new heroic actions, he took a detailed look at what each of them do and when you might call them based on their utility. All but two were found at least some utility. The unfortunate misfits? Heroic Shoot and Heroic Strength.
Following Thumper's maxim, I shan't say anything about Heroic Shoot. But I read Tiberius's post shortly after a TMAT Tournament where I made frequent (albeit unexpected) use of Heroic Strength in all three of my matches. While it's not the sort of heroic action you would automatically call every turn, I believe there are situations--and several of them--where it adds clear value.
Tiberius was kind enough to give me a chance to explain. So here's the first of three write-ups examining the case for Heroic Strength.
(Also, there be some maths ahead...)