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For a start, the tooltip for some reason lists the rank 0 bonus which makes no sense, but never mind that.
Supposedly the way it works is that it gives that amount of xp to every person in your party below your level X by the number of levels higher than the target you are.
So if you're level 10, you've got rank 5 trainer and it gives 36xp, and you're training a level 1 soldier, you'll give them 324 xp a night...
Still not certain if that's right, but it makes a lot more sense than it just giving the base xp per night.
I just give myself and my companions as many points in training as I can because I consider that to be a priority after basic combat skills. Once they are capable of standing in my shieldwall, they all become trainers.
I consider it my mentorship program.
This is given at the end of each day at midnight so if you want to game the system you can swap out your max level troops for recruits at night then swap back after they receive the training xp.
Now there is an extra layer of complexity because trainer in Native is a personal skill and not a party skill. That means that each hero as well as the player's main character will all provide a benefit if they have trainer skill and there are any troops or heroes with a lower level. In other words, the benefit of the trainer skill stacks. Once you and your companions are all at fairly high level and have a bit of trainer skill then you can collectively provide a large amount of xp each day to any low level troops. It is not unusual for this to be several thousand xp each day.
You can see how much xp you are getting each day in the log when it is provided at midnight.
Now to go back to our example, say we have two heroes and they each have 2 in trainer. One of them is Ymira at level 12 and the other is Jeremus at level 18. Your 10 troops will now get 10x10=100 xp from you but also 10x10=100 xp from Jeremus. Ymira however will provide zero xp because she is lower level than the troops are. Also, Jeremus will get 10 xp from you and Ymira will get 10 xp from you and Jeremus for a total of 20 xp. You will get no xp from training because the other trainers are both lower level than you are.
But then you hire 5 more fresh recruits that are each level 4. Now everything else is still the same but these new recruits will be getting 10+10+10 xp each. SInce there are 5 troops that is 30 x 5 = 150 xp for the stack of recruits. This is because you, Jeremus, and Ymira are each providing 10 points from your trainer skills of 2.
They prob use that system (with showing the "bonus" for rank 0) because they also have to use it for the weapon master skill.
The full list is here:
skill rank (xp bonus) 0 (0), 1 (4), 2 (10), 3 (16), 4 (23), 5 (30), 6 (38), 7 (46), 8 (55), 9 (65), 10 (80).
I just checked it in game and copied it. You can do the arithmetic yourself and see : {0,4,10,16,23,30,38,46,55,65,80}
In Viking Conquest the skill limit is 5 for trainer so the sequence is {0,4,10,16,23,30}.
It is possible that it has been changed in some mods as well.