I've been making some recordings of grammar drills for Homeric Greek (1, 2), and have been wrestling with the question of how to deal with cases where the user is supposed to produce some Greek, but there is more than one form used in Homer. This occurs in singular genitives of second-declension nouns (-ου/-οιο), and also for past-tense verbs that Homer uses both with and without the augment. Thinking about how to approach this, I read up on what causes Homer to use the augment in some cases and not in others:
Drewitt, J. A. J. (1912). The Augment in Homer. The Classical Quarterly, 6(01), 44. doi:10.1017/s0009838800017523
Decker (2015). The augment in Homer, with special attention to speech introductions and conclusions, https://core.ac.uk/download/pdf/322539654.pdf
The Decker paper seems pretty complete and gives the impression that this is well understood, and although it's somewhat complicated, basically there is a list of criteria that pretty much determine whether the augment is used or not. In particular, the augment is likely to be omitted in narrative (as opposed to dialog), in verse-initial position, in the iterative forms, in root aorists, when the verb is an aorist that refers to the past (rather than an aorist that refers to the present), in the imperfect, in amphibrachs (ἄϋσε), and in non-sigmatic aorists. Some of these are absolute rules, others just statistical tendencies.
I've noticed that there are some verbs that simply never take the augment, but it's not clear to me why this would be based on any of the known criteria. For example, I went through a list of common verbs in homer beginning with omicron:
sometimes augmented: ὁμοιόω ὀνομάζω ὀπάζω ὁρμαίνω ὁρμάω ὀτρύνω ὀφείλω ὀφέλλω
never augmented: ὀλέκω ὀνειδίζω ὀρούω ὀρύσσω
Some of these verbs are used enough times that I'm pretty sure it's not a coincidence. For example, here's a count of aorist forms of ὀρούω, to rush:
ὄρουσαν (6), ὄρουσε (1), ὄρουσεν (6), ὄρουσ᾽ (2)
Does anyone have any hypothesis about why this is? So far my guess is that maybe the never-augmented ones are just verbs that are only used in narrative, never in dialog. However, I haven't yet checked that hypothesis, which would be somewhat time-consuming. Another possibility is that these are all archaic verbs (e.g., I think ὄλέκω is); the augment is seen less often for archaic words (which is why the dual and root aorist don't get augmented).
Is there some obvious reason for this that I'm missing?