The longbow is credited with the English victory at Crècy (1346) and Poitiers (1356). Because an arrow fired from a longbow could pierce chainmail armor, it gave to common footsoldiers a weapon that could withstand the nobility. Not surprisingly, both crossbows and longbows were despised by the noble class.
A Longbow was reasonably cheap to make and Edward III was able to require all able-bodied Englishmen to become proficient in its use. Archers alone were not enough to win the day, but they modified battlefield tactics, serving as mobile field artillery. Not to push modernism too far, but a better analogy would be armored infantry, for the archers, after the enemy had closed and the bows were no longer effective, dropped their longbows and fought with knives and swords.