For the same penetration, a smoothbore matchlock musket have a higher rate of fire than the arbalest. It can take several minutes to wind an arbalest until it can be fired again, while even the earlier arquebuses could be reloaded in a minute or so.

Thhe musket also have other advantages - it can stay loaded for a long time, while a crossbow will eventually lose power if it remaines wind up. The physical strain of loading a musket is also lower than winding or handloading a crossbow, which would tire troops less.

As for sieges, muskets or crossbows were not the problem - it was cannon. The fort would be armed both with heavy cannons to attack enemy siege batteries but also numerous small guns - all of which would have a much longer range than any crossbow. When distance closed, hand grenades would be used and then melee weapons. The point of an assault was not to stop and fire - if the unit did that, it had most likely lost the assault already.

There is one aspect of this that others have not covered yet: combat psychology. Dave Grossman goes into this in his book 'On Combat' my copy of which I have irritatingly misplaced.

However, the gist of the argument is that even though the weapon itself was arguably less combat effective the fear instilled by mass musket fire has a huge psychological impact. The animal kingdom is full of examples of roars being used to scare the enemy away, and humans are no different. When one side has weapons which are totally silent and the other has those which make a lot of noise this can warp the perceptions of combatants, and standing in the face of musket volleys is a terrifying proposition for any solider.

So, whilst combat effectiveness in terms of being able to actually kill the enemy may not have increased, muskets hugely increase the chances of the enemy breaking and running away.

You may be interested in this letter letter from Benjamin Franklin to Major General Lee in 1776 arguing for bows and arrows in favor of muskets. Franklin's proposal seems not to have been implemented though. He seems to have underestimated how hard it is to get troops to fire bows accurately.

One thing which is never, ever brought up in this bow vs. musket thing is the fact that muskets are just much better at killing you.

I'll elaborate more on this later tonight, but here is Samuel Champlain talking about bows and muskets. Note Champlain states that shields of cotton and wood could protect you against arrows, but that they were useless against muskets.

And if training really was the only thing which muskets had over bows, then cultures which had used bows for a long time would hold onto their bow. Outside of England, this didn't happen. The Indians and Japanese among others switched to muskets quickly, so much so among the Japanese that there was one general who participated in the invasion of Korea who wrote back "Give us muskets. Don't give us swords, bows, any of that crap. Give us muskets."

And elaboration: Arrows are actually not that good at killing people, due to the obvious problem that the wound which they leave is sealed up by the arrowhead itself. They really aren't capable of shattering bones and thus penetrating those organs which are protected by said bones in the way that muskets can. Sure, it can kill through infection and all that, but that's not going to do that archer much good when that swordsman he just shot is all hopped up on adrenaline.

The thing when we compare talk about arrow ranges is that the range we use for arrows are not the same as we use for muskets. Yes, arrows can get out to extreme lengths that muskets can't.....but that arrow isn't actually going to kill anyone. Long-range plinking doesn't decide battles even today with modern guns, never mind bows and arrows. What matters is being able to close with something and use overwhelming force like a massed volley of fire, and arrows really couldn't do that. Ever. Even at Agincourt.

The joke I might make is that you don't end up in the city guard if you get a musket ball in the knee. You end up in the invalid hospital.

There is at least one example of it being reintroduced! As described in 'Empires of the Sea' by Roger Crowley, during the Seige of Malta there was one night a tremendous downpour. The Ottomans figured this would be the night they took Malta as the muskets of the time would be nearly inoperable in such constant rain. Little did they know that the Knights Templar had responded to the rain by raiding the fortresses ancient armory. When the Ottomans assaulted the fortress sure of their victory they found themselves torn apart by a rain of anachronistic crossbow bolts.

I think it's been touched on, but it's worth mentioning.

The musket didn't replace the bow and arrow- the cannon replaced the bow and arrow.

Musketry became practical when a massed unit of men could each handle a piece and return fire rapidly enough to keep an enemy at bay. When close-quarters combat was necessary, bayonets could be added, and the very weight of the weapon allowed it to be used for blunt force.

Archers needed to be guarded by infantry- in close combat, they were no match for broadswords. The bow was unwieldy and heavy, limiting its potential for any other form of protection. If archers were able to switch to swords/knives, they would need to protect themselves and their primary weapon. Plus, they weren't trained as swordsmen. They were trained as archers.

Much like later gunpowder artillery, archers needed cover from a different body of troops. Replacing musketeers with archers is not an equal replacement. Eliminating muskets for bows would replace line infantry with artillery- and gunpowder artillery has a much more potential to cause significant damage with one volley than arrows.

Follow-up question: when were crossbows last used by European armies?

Were crossbows actually effective against plate?

I don't have a source (on mobile) but this applies to modern bullets.

The higher speed of bullets allows it to tumble inside your torso, tearing up multiple organs and thus speeding up the death.

What I don't know is whether muskets will provide you the same effect (tumble) , but given the higher speed it'll likely do a lot more damage from shockwaves; compared to a crossbow bolt, which can be pulled out like some others replied.