The longbows killed 10,000 men alone (2/3 of the enemy's casualties) and routed the entire enemy army after a week and a half of battle, taking only 400 casualties. So to test it out, I took 10,000 troops (3,000 longbowmen, 18 knights, 1,000 light foot, 1,000 light horse, 500 heavy horse, and 5,000 levies) into battle against 40,000 Holy Roman troops (25,000 levies, 90 knights, 15,000 men-at-arms, mostly light cavalry, crossbowmen, pikemen, and heavy infantry). Specializing in them means that even if the enemy army has lots of counters for them, they have higher stats than the base stats for any other retinue in the game except for armored lancers. Longbowmen can operate in any terrain, counter both heavy cavalry and light infantry, and are cheap, and the same size as any standard retinue. For comparison, armored lancers have an attack stat of 100 and a toughness stat of 39 but lancers suffer penalties in anything that's not open terrain, are half the size of a longbow retinue but cost three times as much, and only counter archers. My longbowmen have an attack stat of 197 (45 + 3 + 56 *1.9) and a toughness stat of 42. Their base stat is 25, advanced bowmaking adds 3, and then I was able to add 56 from my domain, and 90% from my archery ranges).
(Incidentally, even before I was able to recruit longbowmen, this meant my bowmen had attack stats of 159. I built Regimental Grounds in every single castle, as well as archery grounds for all three ducal buildings, and economic buildings for everything else. Starting in 1066, I took England and made Middlesex, Anjou, and Aquitaine into the royal duchies, holding the entirety of Middlesex personally as well as Angers and Angouleme.
This may actually apply to every retinue type if you specialize in them hard enough, but I did it with longbowmen.
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