The bow has a slow rate of fire, you can't hold a longbow in firing position for long (150+lbs of force required hold the drawn back bow), and you are only accurate from 300-800 feet (add 15% if in a high tower). That means charging calvary will reach your archers in 10-15 seconds and moderately paced walking infantry unit will be on top of your archers within 20-30 seconds of entering range. That leaves time for a few arrows. The bunched up, tight formations formed a reasonable defense - your outer troops would take the hits from the archers for the 20 seconds it took to get to the archers.
We romanticise the longbow because our frame of reference is a rifle. For modern people, it is hard to understand how superior the musket was to any bow. A rifled muzzle loader made up for it's slow rate of fire with lethality and a range of 350-1000 M. 1000M is not a sprint - it will take infantry 20 minutes, at a minimum (more likely 30-40 minutes). Additionally, at close range, a musket could tear through several soldiers...
It seems to me that at Agincourt the archers place obstacles in front of their position--sharpened stakes. That would have provided some protection against a cavalry
Agincourt was interesting because mud (a combination of rain and fresh plowed fields) reduced infantry and cavalry mobility. The opening cavalry charge made the muddy battlefield worse, and the combination of mud and stakes on the ground injured the horses. The French were heavily armored, causing men-at-arms to sink up to their knees in mud. English longbowmen were able fire arrows into the french men-at-arms who were literally stuck in the mud until they ran out of arrows. The decisive moment was when English archers ran out of arrows and attacked the exhausted French with the hatchets and mallets they used to make and drive the stakes into their defensive positions.
To be fair, an arrow released from a bow with a draw weight of over 150 pounds could easily launch an arrow that could pass through multiple people at close range -- depending on how light their armor was.
I've seen bows with a third of that draw weight completely pass through a deer.
Obviously, certain factors have to be met -- distance being the most important and then shot placement.
Why would anybody ride a horse directly towards archers? If an arrow can make the horse fall or buck, the guy riding it with any sort of heavy armor is probably coming down hard.
Same reason mounted military & police do in riot-control today: heavy training of those horses shifts the initial balance from "what will my horse do if injured?" to "will these guys break ranks and run before many horses are injured?".
We romanticise the longbow because our frame of reference is a rifle. For modern people, it is hard to understand how superior the musket was to any bow. A rifled muzzle loader made up for it's slow rate of fire with lethality and a range of 350-1000 M. 1000M is not a sprint - it will take infantry 20 minutes, at a minimum (more likely 30-40 minutes). Additionally, at close range, a musket could tear through several soldiers...