[That pellet gun is a multi pumper capable of 800 fps.]
800 fps is nothing to sniff at. Bodkin arrows traveling at a quarter of that speed killed plenty of men-at-arms kitted out in chain mail. A steel BB pellet may not be heavy enough to chain mail, but it’s obviously sufficient to penetrate an eyeball and do some neurological damage:
https://en.wikipedia.org/wiki/Bodkin_point#Armour_penetration
https://www.soarvalleyarchers.com/faqs/how-fast-can-an-arrow-travel/
[The speed of arrows depends on the draw weight of the bow, your draw length, limb material, energy profile of the bow, bowstring material, the weight of the arrow, type of fletching on the arrow and the prevailing wind conditions. Humidity and rain also slows arrow flight. The faster an arrow travels, the flatter the flight trajectory and less deviation from wind.
Recurve bow arrows can travel up to 225 feet per second (fps) or 150mph while compound bow arrows can travel up to 300fps (200mph). Longbow arrows travel slower due to the weight of the arrows. Even at 300fps, it takes around a second to reach a 90 metre target. You hear your release first followed by the thud of the arrow hitting the target a second later (you can’t see it unless you use a telescopic sight). If you didn’t hear the thud, you’ve missed the target!]