The ground was wet and the horses ran into the stakes the English had planted in front of their bowmen.
This is another example of how "modern" English military thinking of the day was. When Simon de Montfort, Earl of Leicester and brother-in-law of King Henry III had rebelled in the mid-13th century, his most important ally was Llewellyn the Great. Henry had intended to make his son Edward the Prince of Wales, but that would only have been a glorified title, whereas Llewellyn aimed at the actuality of ruling Wales. Many of de Montfort's allies were also Welsh borders, English lordlings who held lands on the Welsh border. With them out of the equation, Llewellyn was better able to secure the adherence of Welsh magnates who might otherwise have opposed him. In effect, Montfort and Llewellyn were scratching one another's backs.
Montfort eventually captured Henry and Edward. Edward escaped, and in a subsequent battle that same year (1265?), Montfort was killed and Henry liberated. Attempts to unseat Llewellyn, however, failed, and in large measure because of the Welsh bowmen who devastated the feudal cavalry.
Edward had a sharp mind. He was also vengeful and brutal, but that is no reason to ignore his intelligence. He adopted many of the measures which his enemies used when he became King in 1272. Montfort had called a parliament of the baronage and knights of the counties in an effort to gain broad-based support. Edward carried it a step further, establishing a permanent parliament, and one in which there was a Commons as well as a House of Lords. This meant that Edward could appeal directly to the Commons to vote him the supplies he needed. He was usually successful--the Commons were flattered to have the official, public notice of the King. They also routinely wrested "freedoms" from the King in return for supporting his policies and voting him supplies. The Lords were often willing enough to endorse revenue legislation coming from the Commons because it didn't come out of their own pockets, and they were not clever enough to see the long-term implications of a King who was not dependent upon their largesse and their troops.
Because something else Edward had learned was the unreliability of the feudal levy and feudatory loyalty. Montfort had relied upon the direct, material support of the baronage, and to a large extent of the Marcher Lords, the men with estates on the Welsh border, where magnates maintained large bodies of men at arms. That was fine for so long as Montfort could rely upon their support, but when things looked dicey (the French King and the Pope condemning Montfort), they quickly changed sides, and in the same summer. Montfort fell because so much of his army had changed sides, and a good deal of what remained melted away as the lordlings grew nervous about being involved in a defeat. Of course, their hesitation lead to that defeat.
So Edward wanted armies of hired troops, or of the retainers of men who owed everything to him, and who could not afford to turn their coats. This he accomplished by handing out to those men the lands confiscated after the settlement of the Montfort rebellion. Then he would not be dependent upon the feudal levy. Traditionally, the Marcher Lords were to deal with the small Welsh raiding parties, and the feudal levy would assemble at Chester for a summer campaign against Wales. But the feudal levy was sufficiently unreliable that it was never fully assembled at Chester until the summer was almost over, and the Welsh could survive the brief foray against them. But Edward had a paid, standing army, and he was able to rely upon the Parliament to vote him the supplies he needed, so that he could prepare for campaigning over the winter and get a start as soon as enough grass had grown in the Spring to provide fodder for the horses.
Edward didn't convene his parliaments, though, until 1295. Before that time, he allowed the feudal magnates to meet their feudal obligations with cash, and even offered a discount, so that he would be free of the necessity of relying upon them militarily. He also extended his divide and conquer program to Welsh magnates, and his first big coup in 1272 was to separate Powys from the rest of Wales. The Welsh bowmen came mostly from South Wales, so Edward was able to turn their own weapon upon them.
Powys had been an independent "kingdom" after the Romans withdrew from Britain, and even though it had long ceased to be anything resembling a kingdom, the Lords of Powys in the south always resented the dominance of Welsh princes from Gwynned in the north. Llewellyn ap Griffith, grandson of Lewellyn the Great, had just conquered Powys in the 1260s, so the de la Pole family were quite willing to side with Edward against Gwynned. This is the same sort of short-sightedness which afflicted the English magnates. Edward made the de la Poles essentially Marcher Lords, but defeating Lewellyn ap Griffith did not lead to their own independence.
So Edward was free of the feudal levy (and establishing the Parliament twenty years later assured this), and his appearance early in the year with a professional, paid army loyal only to him as paymaster was a much a threat to the Marcher Lords as it was to the Welsh. The same would be true when he attempted the conquest of Scotland. The Marcher Lords in the west, and the Borderers in the north had lost a great deal of their power, and were no longer in a position to threaten the crown, or to rebel with impunity.
When Edward had dealt with Wales, and finally settled the Marcher Lords, he turned his attention to Scotland. The newly minted Parliament was a part of this plan. This was the era when William Wallace arose to prominence. One of Wallace's techniques on the battlefield was to form his spearmen into circular formations known as shiltrons, with stakes driven into the ground before them, and with the spearmen wield long, heavy pikes--both measures to negate the effect of traditional heavy cavalry. It is believed that at Falkirk, the English bowmen simply stood back and slaughtered the Scots in their shiltrons.
Whatever the truth about Wallace and the English (and truth is probably a rare commodity in those tales), Edward incorporated yet another tactical method into his military doctrine. By the time his grandson Edward III began the Hundred Years war, it was standard practice for the bowmen to erect a hedge of stakes in the ground to protect them from heavy, armored cavalry. So Edward I's measures gave the English a standing army, paid by the King and loyal only to him, large bands of well trained archers, and a tactical doctrine which called for them to stand on the defensive and receive the enemy attack before going over to the offensive. In most feudal era warfare, this was decisive. But if the enemy wouldn't play, it was useless--and worse than useless, as your army ate up their rations, and emptied your treasury without providing any results. So many expeditions during the reign in France of Charles V simply marched from Calais to Bordeaux, without accomplishing anything. This was what was happening to the Black Prince in 1356, when Jean le Bon, the father of Charles V, stupidly attacked the English near Poitiers. They need only have surrounded them and waited for them to surrender, which likely would have happened very quickly. Charles was captured there along with his father, and it seems he learned that lesson well.