When does the Roman Army become "professional"?

[SigniferOne]

We need to distinguish "professional" from "good quality" troops. Troops under Marius and afterwards were professional in the technical sense, of being divorced from their economic station and spending their full time in the military; of making the military their "profession". But in terms of good quality, I don't know if the Roman legions were ever as good in the Republican period as right after the 2nd Punic War, when something like half or quarter of the entire Roman people had been militarized, and were trained through the school of Africanus and Marcellus. These were fierce men and the kind of formation evolutions that they were performing in battles like Ilipa boggle the mind.