At Agincourt the first charge of the knights was premature and they had become seriously disrupted before they reached the English lines, the mud mainly slowed their charge down and allowed the archers to fire a couple of extra volleys. It was of coerce a disaster, most scholars that I have read seem to conclude that the result would probably have been the same anyway, it was the premature charge that was the primary factor for the French to loose the battle. If they had just continued advancing with a combined force of dismounted Men-at-Arms supported by crossbow fire they would most likely have won the battle on attrition alone.
There are a few important things to understand about cavalry, their use and importance on a battlefield. Their main advantage is mobility and chock. The way you can quickly mount an aggressive offensive against a weakened or unprepared enemy formation is the single most important use of cavalry in conjunction with mobile firepower.
The one problem with cavalry is that they can never match the power of force of a unified infantry line. In an unbroken and well led infantry line every horsemen are usually outnumbered at least five to one in any given point at a battle line if the infantry is armed with any sort of spear or pole-arm weapon. Cavalry have a very hard time attacking in more than one rank at a time while good order and trained infantry can use three or more ranks and each cavalryman faces at least two (perhaps more) infantrymen in width per mounted soldier.
If the infantry hold and don't run on the initial impact most cavalry will quickly get overwhelmed by the cheer number of attacks coming their way. If the first rank of cavalry cant break into the formation then they either have to retire so the second rank can engage or simply be bogged down. This has always spelled doom for cavalry since the dawn of time.
Good cavalry on the other hand could attack and retire and keep doing this until the enemy either tired and ran away or got so sick and tired that they tried to chase after them. If either of that happened it often ended in disaster for the infantry. In open space all the favor are in the mounted soldiers side because now it is they who will get local superiority in strength.
Believe me when I say it is very hard to find many battle recount of a cavalry formations successfully charging headlong into a good order infantry formation and routing it without either being far superior in numbers or being up against peasant levies.
Even in the time before the "100 Years War" in the earlier periods of the middle ages commanders almost never sent in the cavalry before first engaging their archers and infantry. It was a well known fact that a strong spear formation could form a wall of spears and just hunker down behind their shields. They would then use skirmishing archers to take potshots at the cavalry. There are many such references made on battlefield tactics.
A very good example of this is the "battle or Arbedo". It is a rather classical pitched battle with a smaller Swiss force against a larger Milanese force is 1422. Just the total number of knights were larger than the Swiss force but the Swiss had advantage of terrain in that their force could not be flanked. The cavalry made several failed and costly attacks at the Swiss (equipped mostly with halberds).
When the cavalry failed to break the enemy they dismounted their knights who instead used their lances as pikes and together with crossbowmen could beat back the Swiss who had to retreat. With their lances used as pikes they would outreach the Swiss halberds, they could not on horseback.
This is not the only example, there are many such examples and very few that say otherwise.
One big thing to understand is how hard it is to find a good solid battleground in Europe where you really can utilize the full force of cavalry with thousands upon thousands of mounted warriors. This is also a rather great factor to consider. As long as the cavalry can not use their mobility to surprise and chock an experienced and trained infantry formation it will become an impenetrable wall.
One of the other key strength of cavalry was the ability to move an army quickly, deploy quickly and charge early. If you had a large cavalry force you could be able to deploy and charge before the enemy deployed properly and you would use the confusion to your advantage. Some English armies in the "100 Years Wars" would actually be fully mounted, even the archers as I understand it. They would raid and plunder and avoid the enemy and then draw up a battle on a suitable spot to their advantage. They could now prepare their defenses and that way gain a superior advantage. That way they were a good mounted infantry force since most of the Men-at-Arms would fight in a dismounted formation as well.
A perfect use of cavalry can be seen in the Battle of Poitiers by the English that use their reserve of lighter mounted sergeant to flank the French force after fierce fighting. Their cavalry had been hidden in a small wooded are in the English rear. This was what broke the French army that day, it is not certain the English could have won the battle without this move.
Eastern heavy cavalry was far more effective than western heavy cavalry. They used lighter and faster horses and many formations also carried missile weapons. This gave their cavalry a whole new meaning when deployed on the more common open plains. But even such armies would have huge difficulties fighting on the European scene and would still be at the mercy of combined missile and heavy infantry formations, still they were of much higher quality overall.
So don't get what I say as if I don't think that cavalry was important or potent, or that heavy cavalry was weak. They were neither of those things. It's just that the myth of the head on charge is too widely spread when the strength of cavalry had so many other uses that made them important.
My conclusion is, that, no matter what armor or training you give the mounted warrior they can never overcome the shear local superiority of an infantry line of defense. So, without infantry being either weak, ill trained, low on moral, fatigued or disrupted you would have very low chances to charge with impetus alone. My research in the matter see this as irrefutable facts from ancient times until the disuse of cavalry.
Sorry for another long wall of text...
** Edit **
Here is an interesting article on medieval warfare and the Myths about it... http://deremilitari.org/2013/06/the-myt ... l-warfare/
It does imply that infantry was a greater part of medieval warfare. I have also read some of the sources given in the text.
