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On a sidenote. If you give horses to your companions they too will count as cavalry for the purpose of calculating whether or not you receive the bonus.
I myself have only a few thousand hours of playtime behind me and have often and happily occupied myself with this very map travel speed, experimenting and testing it endlessly.
But all too often, I don't really understand the system's calculations...
Either I often overlook something, or there's an unfixed bug with a skill or the troop travel speed of foot or cavalry units,
and that's why all my considerations and calculations don't add up in the end...
I can only mention a few pieces of information that are familiar to me and certainly to many others, which you can find out through reading or testing.
For example, the initial character selection of a Battanian culture gives a bonus for foot troops and cavalry. These have a forest travel bonus, which reduces the penalty for traveling through forests.
(I don't really know if this bonus only applies to Battanian units, or also to, for example, hired aserai or Vlandia, etc., applies to troops),
The Khuzai culture selection does give a steppe rider speed boost, as far as I'm concerned.
The Aserai culture, as far as I'm concerned, doesn't give a desert travel penalty.
I'm not even sure anymore if you could drink wine or beer in campaign mode, for example, like in multiplayer, where you wouldn't have a speed penalty when traveling through snow for a certain amount of time...^^
The constant switching between game modes often confuses me if I haven't played a mode for over a week... (I guess it's my age :( ^^ )
For some reason, the travel speed is higher if you don't have the maximum number of cavalry units with you, for example, 230 units, but only 180 units...
You have to figure it out for yourself by opening the exact travel speed info in the bottom right, by moving the units back and forth in the troop window when you're in one of your cities or castles,
for example, if you have fians with you If you want to have the appropriate horses for riding, and have load-bearing animals, camels, or donkeys, you can also get 0.1-0.2 speed by testing around by carrying fewer camels or donkeys and taking riding horses instead, which can carry less load but have a higher speed.
Usually, the penalty for a herd is lower than the bonus you get for riding infantry.
You always have to test it out a bit.
Lugging, for example, 1-2 cows, sheep, or pigs at a time rarely results in a penalty,
but it greatly increases troop morale, especially at the beginning of a game round, by carrying various foodstuffs.
These are only slaughtered in times of famine and are therefore always a welcome reserve food.
A good scout hiker can also bring a bonus through his skills, and you don't have to level up this column yourself, and you have the saved points free for other skills.
Although I think you should have 50 or 75 points in scouting, for example, to be able to... Having a daytime wanderer scout while being a night-hunter scout yourself, and then being able to replace the scout at night or day if necessary to gain another 0.2 speed...
to catch up with fleeing enemies more quickly, for example...
The map travel speed info in the bottom right could, in my opinion, have a slightly larger info image when hovering over it with the mouse,
to provide the player with more and better (more precise) map speed explanations.
Have Fun, a Nice Day and Happy Easter
I can clarify a few things for you.(I only play single player)
1. Each foot troop can allow for 2 total animals(baggage animals, livestock, or riding mounts) without the herding penalty. For example, they can care for either 2 riding mountsincluding the one they ride for the footmen on horses bonus), two non-riding animals, or one riding animal with one no riding animal. Cavalry can handle one animal, not counting the horse that they are riding. You seem to already be aware of the difference between riding and baggage mounts. I think that calvary can be slower than infantry on the map if you have a huge herd penalty. It can slow you down a ton if you have a lot more animals in your inventory than your troops can handle. Sometimes it is helpful to hire any footmen recruits that you can find to speed up your party if you have a herd penalty and don't want to get rid of the extra animals. With huge herd penalties, footmen can potentially speed your part up more than cavalry
2. I'm about 95% sure that the culture of your troops has no effect on map speed. Only the party leader's culture matters. I'm pretty sure khuzaits no longer get any map speed bonuses. I think it was in an old version but taken out for balance purposes or something.
(Battanian culture bonus is awesome. I personally think it would be great if khuzait footmen on horses moved at cavalry speed, and if sturgians had less penalties from the snow compared to other factions)