Why Muskets Supplanted Bows
…[The Native American] self bow and the seventeenth-century musket had comparable effective ranges (50 yards optimum, 100 to 150 yards at the outside)….
…For Amerindians, because the bow or the musket had to serve in both war and the hunt, something in the technology had to satisfy the needs of both pursuits…. A musket ball was less likely than an arrow to be deflected by vegetation, and it also had a greater kinetic impact on the target. A deer hit with an arrow receives a very deep wound…, which, though eventually lethal, might require the hunter to pursue the bleeding deer for some distance. In contrast, a musket penetrates flesh, shatters bone, and creates a larger wound cavity. It “smacks,” whereas an arrow “slices….” A military musketball at 50 yards hits a target with 706 foot pounds of kinetic energy. An arrow from a typical modern bow hits at 50 yards with 50 to 80 foot pounds of energy. This is more than enough to penetrate flesh and tissue and produce a killing wound, but it is much less likely to drop an animal in its tracks.
The musket has similar advantages against humans. Much of a human target is limbs, especially when walls or trees are used to cover the trunk of the body. An arrow wound to the leg or arm is rarely lethal, although it can be debilitating. But a musketball strike to the arm or leg may shatter the bone and is more likely to carry debris into the wound, lead to infection, sepsis, and death.… In the immediate term, a man with a shattered leg or arm, flung to the ground by the weight of a musket shot, also makes a better target for being taken prisoner…. Unable to flee, he becomes vulnerable and may hold up his fellows trying to carry him away from the field…. More obviously, bullets cannot be dodged, whereas arrows in flight over any distance (especially on an arcing trajectory) can be seen and dodged. Modern film footage of the Dani people’s arrow and javelin battles in New Guinea shows this process clearly, and numerous European witnesses commented on the Amerindians’ ability to dodge arrows.
— Empires and Indigenes, pp. 56-58
Players of fantasy RPGs should note the quoted effective range for bows. Many games have much longer distances, but those are derived from battlefields where archers are loosing volleys at large enemy formations. Gamers should further note the ease of dodging an arrow at anything beyond short range.