Thanks! So basically it comes to a combination of equipment + discipline on both sides, but feudal heavy cavalry was much harder to get properly disciplined, and so infantry prevailed? What about disciplined cavalry, such as Matthias Corvinus' Black Army, versus disciplined infantry?
Yes I think it comes down to all those things that are hard to pinpoint down: morale, experience, discipline on that day etc. Given the right equipment and training I am sure either side, calvary or infantry could break each other. My tentative guess is that, on balance, it usually went to the infantry. Why? Simply because they are cheaper: to train, to arm, to gain experience, and there were a lot more of them. But as the wikipedia article states there were cavalry units famous for charging - one assumes that took a lot of training and experience to pull off though. So yes I am sure there are instances of elite cavalry charging and breaking elite pike/heavy infantry face to face.
But what about the value of men behind those three lines? In Byzantine military manuals it is implied/stated that heavy cavalry can break spears of opposing infantry, so it may come down to having physical mass to stop the cavalry charge. Meaning that men behind first three lines may still matter, even if their spears do not.
On the defensive against cavalry I can think of one good reason for more than three ranks. What a cavalryman does not want is to lose his momentum in the charge and find himself at a stop in enemy lines. So a determined scrum of men in depth would dissuade nervous cavalry from just rushing in. A cavalry soldier has an advantage over an individual foot soldier with his weapon...but if you've come to rest completely surrounded by enemy, you are very likely going to to pulled down and then you're toast. A unit with just three ranks, would be easier for aggressive cavalary to just crash through to the other side and escape, I would think.
I have found both arguments, but personally I believe they will. I know of cases when horses charged into solid objects, large masses of people, or both; and these were racing horses, not trained cavalry horses.
Example. There is also the fact that Byzantine military manuals - with few of which I am intimately familiar - either suggest or outright state that, yes, horses will indeed charge into infantry lines. And Byzantine infantrymen were not pushovers, they would stand their ground - yet you see progressively deeper infantry lines as Caliphate cavalry gets heavier. So while wild or light cavalry horses may not charge into pikes, heavy cavalry horses - bred and trained for the purpose - probably will.
I would (again tentatively!) suggest that while cavalry horse were indeed trained to charge into masses of enemy, it would still be a very bad idea to take on a pike unit face on. And if you put a gun next to my head, I say that the pike unit, in such circumstances will win nine times out of ten. But flanking a pike unit, so avoiding all the pointy bits - that would be good.
Very simply (too simply!) after the peak of the Roman Empire, I believe Western European battle tactics shifted towards mobility and cavarly. Phalanxes and legions needed expensive training and were a lot of manpower. The states left over shifted to smaller armies, and many (but not all!) of the enemies coming in, utlised horse armies. To counter this armies like the Bzyantines had to respond and change also. There was a definite tilt to heavy cavalry and that became the elite aristocratic unit to have - helped very much by the Normans!
Now I'm not saying that infantry at that time were bad, just that advances in calvary tactics and technology, horse breeding, changes in societies expectations (a knight charges gallantly against the enemy on his horse of course!), and aggressive use of heavy cavalry (by said Normans for example) made them the pre-eminent unit. You would have your elite infantry units - as I am sure you are aware, the Varangian guard for the Byzantines, but I would (again tentatively!) suggest that a lot of the other infantry would be of lower quality and quite a lot of 'filler' - levies etc.
That may be one of reasons, but Byzantine manuals specifically specify increasing infantry / spearmen depth in order to resist charge of progressively heavier cavalry. But that is 10th century, so it does not really help with 15th century warfare. Hence my asking.
By the time you get to the 15th century I believe you are getting the end result of two trends.
Firstly, because of the predominance of heavy cavalry in the early period, others rediscovered the utility of heavy pike infantry. Scotland did it with the schiltron as I've stated ~1300, but there we are really talking about the famous Swiss pike formations and the German Landsknecht. These then led to the Spanish Tercio's, the Swedish innovations later on etc. This, as I've argued, balanced the effect of heavy cavalry and would usually dictate the actual use of horses most of the time. By the late 15th century the infantry will have been getting very good at it.
Secondly the battles are getting smaller. Even the most prosperous of European states can't afford to have huge armies - logistics was rearing its ugly head. So armies became more 'quality not quantity'. Those low quality levi spearmen tended to dissappear. (Unless, of course, it was an 'asymmetrical war', say Kings putting down peasant uprisings etc.) So effectively you were left with the 'cream of the crop'. The hardened and experienced warriors/mercenaries who could afford all the kit were the ones on the field most of the time.
Your Wikipedia link suggests, as I already stated, that it came down to discipline first and foremost, and problem was that feudal cavalry was sh*t at that particular thing. But there were few disciplined heavy cavalry armies in 15th century - Hungarian Black Army and French Compagnies d'Ordonnance. So you definitely could see disciplined cavalry charging disciplined infantry - but I have not found sufficient sources myself to reach any final conclusion.
My guess is that, because a knight in western European was also a member of societies elite, they were less likely to be cohesive as a unit. To be an effective shock trooper on horseback takes training and following orders. Would all these lordlings get on well with each other? Or were they more concerned with jousting and going starry-eyed about one-on-one combat? Hence my guess at the effectiveness of orders of knights such as the Hospitallers and Templars who submitted their egos to their organisations - at least in the tactical sense.
I'd suggest that because heavy cavalry was not as effective as it used to be, what we are seeing was these armies 'rediscovering' the tactics of Alexander the great. Hammer and anvil. Use the infantry to pin the enemy then use the cavalry to flank and charge into a weak point. Cause a rout then run down all the fleeing soldiers. I note that the Hungarian Black Army you talk about was famous for its cavalry but still had a lot of infantry at its core.
Certainly a well-timed cavalry charge could be the decisive point of a battle, but discipline was crucial. How many battles have been lost by one sides flanking cavalry winning, chasing the defeated units off the field, only to return to discover the rest of their army has been soundly crushed!