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IT TURNS OUT THAT THE HERO'S INITIAL SPEED IS SIGNIFICANTLY AFFECTED BY THE TYPE OF CASTLE HE WAS PURCHASED IN (HIS NATIVE CASTLE, AN ALLIED CASTLE, OR AN ENEMY CASTLE)! This can be clearly seen in the example described below.
AmberSoler, if this information is not in the reference guide (I didn't see it, at least), please add it.

Excerpt from the physics of the Heroes world:

Terrain penalty does not apply if:
- the hero's army consists entirely of creatures for which this terrain is "native":

Let's consider 3 of the fastest heroes and one cute girl.

Kerr is a Ranger. His native terrain is "grass." His starting army of 1 Centaur gives him a speed of 6 points, which is 1700 movement points (mp). Logistics skill +10% + specialization 5% = 1955 mp!

Dessa is a Combat Mage. Her native terrain is "stone." Her starting army of 1 Goblin gives her a speed of 5 points, which is 1630 mp. Logistics skill +10% + specialization 5% = 1874.5 mp!

Moner is an Elementalist. His native terrain is "grass." His starting army of 1 Small Sprite gives him a speed of 7 points, which is 1936 mp!

Pir is a Demon. His native terrain is "lava." His starting army of 1 Imp gives him a speed of 5 points, which is 1630. Logistics skill +10% = 1793 mp!

Therefore, Kerr should run the farthest! And Dessa and Pir should run the least!

Let's analyze the speed of these three heroes (Pir will be discussed in point 6) based on this tournament.
To do this, I will open the map using nwcwhatisthematrix and take a screenshot to show you the path!

Please also note that Moner and Kerr have an advantage over Dessa; they do NOT have a penalty on their NATIVE TERRAIN – GRASS. And according to the Physics of the World, heroes should not have any penalty on grass at all! And they will all run on grass and roads!

So, let's start the race:

Kerr starts – following the proposed route, and makes his last step on the Mercury Mine (turn 5)!
Dessa starts – following the proposed route, and makes her last step on the chest (turn 6)!
Moner starts – following the proposed route, and has only 1 small last step left after 6 turns!

Does this seem paradoxical to you?
Transferring the poor Goblin didn't lead to anything.

From all this, I can only draw one conclusion:
THE INITIAL SPEED OF A HERO WILL BE HIGHER IF HE WAS PURCHASED IN HIS NATIVE CASTLE, OR NOT!

I think that the initial speed of the army depends on the army (the default army, i.e., the one that would be if he stood first in the tavern (Centaurs + Gnomes + Elves)) of the hero. And with Gnomes, Kerr naturally moves less. (I think AmberSoler wrote about this somewhere)
Moner, by the way, ALWAYS runs the farthest (and on other penalty-free terrains).

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