I think what made the longbow a significant part of how we see medieval english armies today is not necessarily the quality of the bow, but the quantity. Archery training was as common as fast food in medieval england, and sunday was even a day dedicated to nothing but longbow training?
Side note- On the ringmail, the rings worked really well at stopping a slashing sword attack, but the rings were prone to not necessarily break apart, but part when something pierced instead of slashed. So against a sword cut, the ringmail was effective, but against a bodkin arrow? Not at all.
I think the solution for the English is to increase ROF for longbows. If you take it in a historical sense, a large portion of the english population were trained as opposed to able. In a game mechanics sense, the English are the retarded cousins of the French, who have everything the english have and then a whole bunch more (like an effective crossbow unit, better cannon selection, better cavalry, and better spear infantry, a good pike unit, and Scot's guards which are retinue longbowmen with armor plating... Not to mention horse archers.)
If English bowmen had a higher rate of fire, then an english army that was primarily made up of bowmen (which seems historically accurate) would give a french army a run for their money. This is what england needs in my opinion.
Bookmarks