Speed bonus makes it vary a lot, but most of the time it goes down quickly.
@Kulin&Gurni:
Remember speed bonus is a massive factor. I could 1hit arabians with 5pt and franciscas on my 1h/ht when we both rode straight at each other (I was testing it), but I could also need up to 8-9 of them if I was standing still and he was riding away.
For throwing, yes. But my impression in any of these horse ranged related threads is that people overestimate the effects of speed bonus when talking horse archery or crossbowery. Here's why:
I am not sure how it is handled in game, but google tells me longbow arrows can go as fast as 300 km/h or 83 m/s in the real life. Longbow are probably quite powerful in comparison to other ingame bows, so let's say arrows travel between 50-80 m/s. I remember Paul stating that arrow velocity in game was pretty close to real life, can't find the post. Bolts are probably towards the high end of this or maybe even faster. As is reflected in their ingame stats, Longbow has 40 missile speed and the Light Crossbow has 44.
Now a horse, how fast is a horse in game? When talking a full speed courser, probably like 50 km/h or 14 m/s. Which means that if I take the slowest case scenario of an arrow or bolt moving at 50 m/s, which is most likely way too low, and the quite fast speed of the horse at 14 m/s towards the target, the bolt speed is:
50+14 = 64 m/s
Which amounts to (64/50 x 100 = 128% ) a 28% increase in missile speed from moving at full speed towards a target compared to standing still. And this is at the best case scenario with a really fast horse and a really slow projectile.
A more likely calculation in my opinion yields a 17,5% increase in missile speed compared to standing still. (80+14 = 94, 94/80 x 100 = 117,5%)
The speed bonus from a moving horse only has a minor impact on the damage you deal. The varying speed of a horse is simply not that significant compared to the speed of a bolt or arrow. From the looks of it, this is true ingame as well as reality. Different case with throwing, which probably moves at like half or a third of the speed of a bolt and arrow, and therefore the varying speed of a horse is a lot more significant.
tl;dr:You are not going to do twice the damage because you ride towards a person, a quarter or a third increase is about the best you could hope for.