Agincourt? I thought it was Hastings where the longbow came to prominence. Of course, I could be wrong. it's happened before.
The Normans brought the bow and calvary to the battle of Hastings, while the Saxons relied on their shield wall tactics. The bow definately played an important roll in the battle, as the Bayuex tapestry depicts Harold being killed by a Norman arrow through the eye.
But the importance of the long bow at Agincourt is that Henry’s army was comprised primarily of archers, and they were outnumbered by the French. But when the heavily armored French troops became bogged down in the mud, the English archers were better able to move on the field and defeat the more heavily armored French force.
Over a span of 100 years Agincourt, Crecy, and Poiters were the three signature battles of the longbow. They all involved the repetitive mauling of French armies by English bowmen. I saw a recent history channel production that credited the victory at Agincourt to overcrowding of the battlefield by the French where one horse falling caused a chain reaction where hundreds fell and were unable to disentangle themselves and rise from the muddy field. The armored riders were helpless and swarmed by the lightly armored Brits. They actually demonstrated that the bodkin tipped arrow was incapable of penetrating the armor of the day. Under the circumstances it was a miracle that the Brits won.