Despite the modern view that longbows had trouble penetrating high quality plate armour after about 1350, as late as 1415, the hail of arrows created by massed ranks of thousands of longbowmen helped to win the battle against plate armoured French knights at Agincourt. The French mounted charge against the English defensive position was ineffectual. The vast majority of the French knights advanced on foot, but exhausted by walking across wet muddy terrain in heavy armour and being buffeted by thousands of arrows, they were overwhelmed when the English longbowmen (using their swords and mauls) joined the hand-to-hand fighting in support of the English men-at-arms.
So basically the damn things are pathetic against anything higher then transitional armour...
More cool stuff from your own sources:
The range of the medieval weapon is unknown, with estimates from 165 to 228 m (180 to 249 yds). Modern longbows have a useful range up to 180 m (200 yd). A 667N(150 lbf) Mary Rose replica longbow was able to shoot a 53.6 g (1.9 oz) arrow 328 m (360 yd) and a 95.9 g (3.3 oz) a distance of 249.9 m (272 yd).[18] A flight arrow of a professional archer of Edward III's time would reach 400yds. It is also well known that no practice range was allowed to be less than 220yds by order of Henry VIII.[19]
The longbow had a long range and high accuracy, but not both at the same time. Most of the longer range shooting mentioned in stories was not marksmanship, but rather thousands of archers launching volleys of arrows at an entire army. Longbowmen armies would aim at an area and shoot a rain of arrows hitting indiscriminately at anyone in the area, a decidedly un-chivalrous but highly effective means of combat. An archer could hit a person at 165 m (180 yards) "part of the time" and could always hit an army.[citation needed]
Gerald of Wales commented on the power of the Welsh longbow in the 12th century:
... n the war against the Welsh, one of the men of arms was struck by an arrow shot at him by a Welshman. It went right through his thigh, high up, where it was protected inside and outside the leg by his iron cuirasses, and then through the skirt of his leather tunic; next it penetrated that part of the saddle which is called the alva or seat; and finally it lodged in his horse, driving so deep that it killed the animal.[20]
In a modern test, a direct hit from a steel bodkin point penetrated Damascus chain armour.[21][22]
However, even heavy draw longbows have trouble penetrating well made steel plate armour, which was used increasingly after 1350. A 2006 test was made by Matheus Bane using a 75 lbf (330 N) draw (at 28") bow, shooting at 10 yards; according to Bane's calculations, this would be approximately equivalent to a 110 lbf (490 N) bow at 250 yards.[23] Measured against a replica of the thinnest contemporary "Jack coat" armour, a 905 grain needle bodkin and a 935 grain curved broadhead penetrated over 3.5 inches (89 mm). ("Jack coat" armour could be up to twice as thick as the coat tested; in Bane's opinion such a thick coat would have stopped bodkin arrows but not the cutting force of broadhead arrows.) Against "high quality riveted maille", the needle bodkin and curved broadhead penetrated 2.8". Against a coat of plates, the needle bodkin achieved 0.3" penetration. The curved broadhead did not penetrate but caused 0.3" of deformation of the metal. Results against plate armour of "minimum thickness" (1.2mm) were similar to the coat of plates, in that the needle bodkin penetrated a small amount, the other arrows did not penetrate. In Bane's view, the plate armour would have kept out all the arrows if thicker or worn with more padding.
So according to this, longbows need a heavy nerf against the armour we have now in game, gotcha...
HEY FASADER! I need you for a second...