I find naval battles to always be a little (so as not to say a lot) more confusing than land battles and I've tried a number of fancy looking and on paper effective fleet setups but in the end, I always find myself going back to something like artillery ships (usually balistae cause they actually fire pretty quickly and I like their range, I've tried some onager ships but they're not as nice imo) and then ships with javelinmen on them. The reason I prefer javelin men over archers is because they have a higher rate of fire (even though not as much range but that's part of why I like javelins)
I've given up trying to micro naval battles, so I always just make two groups, one artillery and one eh... point defense laser javelins from hell (at a ratio of 1:2). Then I send the javelin ships ahead, turn on fire javelins and leave them clustered up so they can support each other. There really don't seem too many ships that can stand up to combined flaming javelin spam from 2 or 3 ships at once.
Then I just micro the artillery ships and shoot whatever the javelins are not shooting.
Upside... I have not lost a battle like that yet but I usually outnumber my enemies in fleets at the point in the game.
Downside... It's expensive. Expect your javelin ships to do a pretty good job at soaking up fire themselves. After every major battle, the fleet needs a turn or two in port.
Another downside: I'm not sure if barbarian factions can build artillery ships. The last time I got my hands on them as the Gauls it was cause I captured a Roman town that could build them and for some reason that let me build them, which was pretty cool. They were even called 'Roman Light Artillery Ship' or something but were all crewed by Gauls.
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