Cavalry

[CBR]

At 100 meters a ball from a smoothbore musket will land anywhere {random dispersion} within a {roughly} 20 meter diameter circle reguardless of how good the shooter is.

I have no idea where you got that from but that is definitely not true. Muskets where not very precise weapons but the theoretical performance was a lot better than what you describe. Back in the 18th/early 19th century several tests and calculations were made. You can find out more in the book "Firepower" by Major-General BP Hughes

The mean error at 150 meters, from a musket fired from a rest, is mentioned as 75cm in height and 60cm laterally.

In battles no one came near these results as human error as well as battlefield conditions would reduce it. IIRC US Civil War was about 25% efficiency compared to theoretical performance.

Realistically , a loose ordered troop of genuine Steppe horse archers {which the Tartars would have had} would be vastly superior in a "fire" fight to a typical Napoleonic line regiment . They would have only been hit at 100 meters by pure chance

Well actually the French did encounter Tartars and we can look at their experiences with bow armed loose order cavalry.

Arrows v French cavalry
http://www.napoleonic-literature.com/Book_3/V2C38.html

Their efforts were chiefly directed against Sébastiani's cavalry, and in a moment the barbarians surrounded our squadrons with loud shouts, letting off thousands of arrows. The loss these caused was slight, for the Bashkirs are totally undrilled and have no more notion of any formation than a flock of sheep. Thus they cannot shoot horizontally in front of them without hitting their own comrades, and are obliged to fire their arrows parabolically into the air, with more or less elevation according to the distance at which they judge the enemy to be. As this method does not allow of accurate aiming, nine-tenths of the arrows are lost, while the few that hit are pretty well spent, and only fall with the force of their own weight, which is inconsiderable; so that the wounds they cause are usually trifling. As they have no other weapons, they are certainly the least dangerous troops in the world. However, as they were coming up in myriads, and the more of these wasps one killed the more came on—the vast number of arrows with which they filled the air were bound sooner or later to inflict some severe wounds. Thus one of my non-commissioned officers, named Meslin; was pierced from breast to back by an arrow. Seizing it in both hands he broke it and drew the two portions from his body, but died a few minutes later. I fancy this was the only case of death caused by the Bashkirs' arrows: but I had several men and horses hit, and was myself wounded by the ridiculous weapon.


Muskets v Tartars
http://www.napoleonic-literature.com/Book_3/V2C37.html

During our stay at Pilnitz, the enemy was receiving strong reinforcements, notably 60,000 Russians under Benningsen. These came from beyond Moscow, and included many Tartars and Bashkirs, armed only with bows and arrows. I have never understood with what object the Russian Government brought up from so great a distance these masses of irregular cavalry, who could be of no use against troops armed in the modern fashion, and only made food more scarce for the regular troops. Our soldiers were in no way impressed by the sight of these half-savage Asiatics, whom, from their bows and arrows, they nicknamed ' the Cupids.' The newcomers, however, who had never seen Frenchmen, encouraged by officers nearly as ignorant as themselves, expected to see us fly at their approach. The very day after their arrival they assailed our troops in countless bands, but were received with musketry-fire, and left many of their number dead on the ground. Their losses seemed only to excite them further; and as any ground suited them they began wheeling round us like swarms of wasps, and it was hard to catch them. When our troopers did get at them, the execution was considerable.

Overall they were not that impressed by bow armed cavalry. They might not have had the best discipline but muskets did seem to do the job.

We can also go back to the Crusades and find that crossbowmen could keep enemy horsearchers at a distance and cause big losses too. And crossbows didnt have a high rate of fire or were very accurate.

An archer who spends all day shooting at a target at a certain range will develop a high skill and might end up being able to hit a target with his eyes closed but battlefield conditions will reduce the efficiency considerably.

Long rang shooting is basically plunging area fire which is not very accurate and even at shorter range the archer cant be certain of the precise range which will hurt his accuracy as low velocity arrows are more dependent on knowing the exact range than guns are.


CBR

[Watchman]

Let's remember one thing - it was after the Russians got their mitts on guns that they in time conquered most of Asia right until the border of China. Firearms were more or less what broke the military advantage of the steppe peoples for good - those guys were really good at what they did, and supremely adapted to their environment, but in some rather important ways their culture was a technological dead-end. Once their neighbors got past a certain point they simply had nothing to mobilize in reply...