It was the earliest arms race.
Armor was developed, in part, as a defense against the missile. The idea it was developed as a defense against the melee weapon strike is untrue. The shield and the parry (as well as greaves to protect the leg below the shield) was the original primary defense against melee.
The Welsh longbow was developed as a way to punch through armor.
Another bow that did this earlier and even better was the steppe composite recurve bow. The Mongols developed specialty arrows (they looked like mini chisels) specifically to punch through even plate armor.
Eventually armor became so weighty it was an unlucky soldier who fell in battle. The advent of the ultimate missile, the firearm, ended most of the age of armor.
The tactics of missiles (skirmishers) was to weaken or disrupt the main line of battle so your main line of battle could break through. Some of the more advanced mounted missile societies (Huns, Samanites, Mongols, Parthians) had a much smaller melee contingent relying on the missile to win the battle and the melee arms to mop up suvivors.
One of Rome's worst defeats was Crassus against the Parthians, who used mobility and missile barrage to destroy most of the Roman legions. Historians estimate the battle of Carrhae had 35,000 Roman legionnaires attacking 10,000 Parthian cavalry. The Romans suffered 25,000 estimated casualties.
Jammer