On whose traditions did the Romans base their poetry?

The Greeks.

Explanation:

It said before that, "The Romans got their ideas of poetry by the Greeks.."

i just did something on this guy a few days a go give me two minutes to find it in my notes.

“the iliad” (gr: “iliás”) is an epic poem by the ancient greek poet homer, which recounts some of the significant events of the final weeks of the trojan war and the greek siege of the city of troy (which was also known as ilion, ilios or ilium in ancient times).