I went through a section of the Iliad (book 1, lines 1-230) and tried to get insight into when the copula is explicit and when it’s omitted. I tried to find every instance where ἐστί(ν) was used as a copula, and every instance where there was an implicit copula. I didn’t try to systematically record or analyze other forms of the verb such as the subjunctive or the first person. A summary of the examples is at the end of this post. Does the following analysis seem right?
One reason to make the copula explicit would be if the tense or mood is not the default. By design, my survey didn’t cover those usages, but we do have examples like lines 136 and 171.
The verb εἰμί seems to have three main senses: (1) the copula, (2) “there is” constructions, and (3) εἰμί+dat., which is literally a “there is” but actually is a way of expressing “to have.” All three of these can be done either by using the explicit verb or omitting it.
It’s hard to be sure based on the small sample size, but one pattern that does seem to spring out at me is that the explicit εἰμί seems to be mandatory in comparisons with the genitive. There also seem to be cases where the sentence could be read with an emphasis on the verb (1.63), and it may be that the explicit verb is apt to be used in a speech that is an emphatic statement.
Explicit uses of ἐστί(ν)
1.63 - ἢ καὶ ὀνειροπόλον, καὶ γάρ τ’ ὄναρ ἐκ Διός ἐστιν,
seemingly optional; can be read with emphasis on is
1.107 αἰεί τοι τὰ κάκ’ ἐστὶ φίλα φρεσὶ μαντεύεσθαι,
copula, but closely allied with “have” expressions using ειμι+dat.; seems like it would be hard to parse without the explicit copula; speech is an emphatic statement
1.114 κουριδίης ἀλόχου, ἐπεὶ οὔ ἑθέν ἐστι χερείων,
stating the copula explicitly makes it clear that the basic statement being made in the clause is complete at the end of the line; without it, we might think that we were just beginning a clause of the form “since her inferior is not…;” speech is an emphatic statement; comparison
1.169 νῦν δ’ εἶμι Φθίην δ’, ἐπεὶ ἦ πολὺ φέρτερόν ἐστιν οἴκαδ᾽ ἴμεν
without the copula, this could be taken to mean “for to go to a better home;” speech is an emphatic statement; comparison
1.229 ἦ πολὺ λώϊόν ἐστι κατὰ στρατὸν εὐρὺν Ἀχαιῶν
speech is an emphatic statement; comparison
Implicit copulas
1.80 κρείσσων γὰρ βασιλεὺς ὅτε χώσεται ἀνδρὶ χέρηι·
comparison, but not a comparison with a genitive
1.156 ἐπεὶ ἦ μάλα πολλὰ μεταξὺ οὔρεά τε σκιόεντα θάλασσά τε ἠχήεσσα·
a “there is” expression
1.174 πάρ ̓ ἔμοιγε καὶ ἄλλοι οἵ κέ με τιμήσουσι, μάλιστα δὲ μητίετα Ζεύς.
a “to have” expression, implicitly εἰμί+dat.