At Marathon in 490 B.C. Athenian hoplites showed that heavy infantry could resist massive amounts of missile fire from the archery-centric Persian forces. At Carrhae in 53 B.C. Roman legionnaires were not able to withstand missile fire from the similarly archery-centric Parthian forces. Why were the legionnaires, with their larger shields and more developed formations, seemingly not able to withstand missile fire as well as the citizen hoplites of Athens?
According to Herodotus the Athenian hoplites charged the Persian line at a run. So while the Persians had a large number of archers the Athenians were exposed to effective archery fire for a relatively short period of time before they closed the gap and engaged in hand to hand combat. By contrast the Parthian horse archers were able to harass the tightly packed legionnaires more or less with impunity. When the Romans tried to engage the Parthians in combat the horse archers retreated firing Parthian shots. When Crassus sent Publius to clear the horse archers they retreated and drew off his forces until Publius and his troops were isolated then the Parthian cataphracts attacked while the horse archers blocked their retreat. The Parthians were well supplied with arrows and able to continue shooting until nightfall.
The hoplites were exposed to archery for the time it took them to charge the Persians line at a run. The legionnaires were exposed to archery for the duration of the battle because they could not engage the Parthian horse archers.