Most actual
used bows seem to have been 80 to 120lb, not 160lb.
For years it was assumed they was 60 to 80lb draw weights as today's hunting bows are, but archealogy showed much heavier bows were used (thought here's still debate, iirc, on whether those super heavy ones are finished bows, or were a bit lighter in actual pull etc).
better recreation work etc and long practice have shown 80 to 120lb bows can certainly be used.
The longbow's great span, requires less complex bow material and doesn't pinch the fingers in the bow string, so it's an efficient weapon. You can also use longer arrows for "shoulder" firing.
Note I'm a big guy (for my part of the world, not America, lol) and a 60lb bow is a bugger to keep drawn, gah!!! Much rather have a 120 or 150lb crossbow anyday of the week. I was pretty good with a bow, but I know I could hit a target far more precisely with a crossbow...and I could keep it cocked as long as I want, hehe.
30 or 40lb draw wight bow is
pleasant to use, for me, and I could cock 120 and 150lb crossbows without a lever no problem.
I can't recall if my crossbow was 120 or 150lb draw weight, now as it was along time ago, but when firing it for a test, it went through an inch thick plank, and through both walls of my Dad's wooden garage, with the point sticking out the back wall...lol.
Also, with bows and sling's too, unless you have innate ability, you're never going to be that great. Practice
is a very large part, but it's also down to innate ability as you aren't aiming like with a rifle.
Since archers had ot have a degree of innate skill and long practice, they were "specialists" and thus, very expensive to pay. Crossbowmen were far cheaper, it was their
weapons that were very expesnive (since they often needed spring steel bow limbs for the crossbows).
Another advantage of the bow, however, is for "clout" shooting, that is, where as a crossbow fires straight, accurate and hard, bows are great for arcing high fire, that plunges down. Thus it's easy to fire like a mortar, over front line allies, and down into enemies, even those behind cover. Striking from above they'd hit thin armour, skull, shoulder etc.
Also, it has to be realized that the impact energies of these high power crossbow and longbow projectiles didn't just cut flesh, they shattered bone and traumatized the victims. Not as bad as heavy lead slugs (shotguns and the like are horrendous manstoppers), but certainly enough to render you
hors de'combat.
Bit off topic, an animation (using the DIVX video codec) I made of Roman light ballista a few years ago, to show another aspect of such things.
http://www.silverblades-suitcase.com/movies/ballista_light.avi