Question regarding commanders

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   the results are in bold and underlined below if you don't care how I got them.  I might be wrong, someone should check.  I checked these results with the combat calculator. 

The attacker casualty formula is Defender Strength (Ds) over Attacker Strength (As) times the number of attackers.  Using the following variables:

Na = number of attack units.
B = Charge Level (not percentage, the Level)
Us = Unit Strength, single unit attack strength (like 65 for a knight)
H = Heroism Level

we can say:
Troop Attack Strength = Us * (1 + B / 100) * Na
Commander Attack Strength = Us * (1 + B / 100) * (1 + 6 * H)
adding them together and re-arranging we can say this about Attack Strength:
As = Us * (1 + B / 100) * (Na + (1 + 6 * H))

This equation is exact making the following assumptions:
Na has a sufficiently high value (to avoid commander attack strength discontinuity, how high is specified below)
commander and troop types are the same
there is only one commander
Putting it together and re-arranging the complete casualty equation looks like this:

Attacker Casualties = 1/((1+B/100)*(Na+1+6*H)) * [Na * Ds / Us]

There is more to the complete combat calculation, but this is exact with the assumptions made.  From this formula, we can see that casualties will vary proportionally with the following formula (dependent on B and H):

f(BH) = 1/((1+B/100)*(Na+1+6*H))

This formula has three variables, two of which we want to compare rates of change against so we need to calculate derivatives and solve for the third variable.  So, we should calculate df(BH)/dB and df(BH)/dH and set them equal.  I didn't do that, it's a pain and I'm too old to remember how.  It will be close if we set the equation equal to itself with B=0,H=1 on one side and B=1,H=0 on the other and solve for Na.  When we do that we see that for Na=599 it doesn't matter if you increase Heroism from 0 to 1 or Charge from 0 to 1.

Even if you have a knight commanders with 9 Heroism and 0 Charge the point at which it doesn't matter if you increase B or H only drops to ~545.

If the number of attackers is greater than 545 then increasing B from 0 to 1 will decrease casualties more.  If the number of attackers is less than 545 then increasing H from 0 to 1 will decrease casualties more.

What changes if you have a knight commander leading men-at-arms?  Parity will be reached at a higher number of troops (probably much higher) because the bonus is less effective as it no longer applies to both the commander and troops.  What happens if you have 5 knight commanders?  Parity between increasing B from 0 to 1 or H from 0 to 1 for all five at once is reached at 2,995 troops.  etc...

If you are sending out more than 545 troops with the goal of leveling commanders then you're taking more casualties per Xp than you need to in order to level your troops (please don't make me show how).  In that scenario, the question is why would you care if increasing B or H is more effective at reducing casualties?

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Salararius Members Profile Send Private Message Find Members Posts Add to Buddy List Postmaster Joined: 26 Sep 2011 Location: USA Status: Offline Points: 519	Topic: Question regarding commanders Posted: 16 Sep 2012 at 00:54
	the results are in bold and underlined below if you don't care how I got them. I might be wrong, someone should check. I checked these results with the combat calculator. The attacker casualty formula is Defender Strength (Ds) over Attacker Strength (As) times the number of attackers. Using the following variables: Na = number of attack units. B = Charge Level (not percentage, the Level) Us = Unit Strength, single unit attack strength (like 65 for a knight) H = Heroism Level we can say: Troop Attack Strength = Us * (1 + B / 100) * Na Commander Attack Strength = Us * (1 + B / 100) * (1 + 6 * H) adding them together and re-arranging we can say this about Attack Strength: As = Us * (1 + B / 100) * (Na + (1 + 6 * H)) This equation is exact making the following assumptions: Na has a sufficiently high value (to avoid commander attack strength discontinuity, how high is specified below) commander and troop types are the same there is only one commander Putting it together and re-arranging the complete casualty equation looks like this: Attacker Casualties = 1/((1+B/100)(Na+1+6H)) * [Na * Ds / Us] There is more to the complete combat calculation, but this is exact with the assumptions made. From this formula, we can see that casualties will vary proportionally with the following formula (dependent on B and H): f(BH) = 1/((1+B/100)(Na+1+6H)) This formula has three variables, two of which we want to compare rates of change against so we need to calculate derivatives and solve for the third variable. So, we should calculate df(BH)/dB and df(BH)/dH and set them equal. I didn't do that, it's a pain and I'm too old to remember how. It will be close if we set the equation equal to itself with B=0,H=1 on one side and B=1,H=0 on the other and solve for Na. When we do that we see that for Na=599 it doesn't matter if you increase Heroism from 0 to 1 or Charge from 0 to 1. Even if you have a knight commanders with 9 Heroism and 0 Charge the point at which it doesn't matter if you increase B or H only drops to ~545. If the number of attackers is greater than 545 then increasing B from 0 to 1 will decrease casualties more. If the number of attackers is less than 545 then increasing H from 0 to 1 will decrease casualties more. What changes if you have a knight commander leading men-at-arms? Parity will be reached at a higher number of troops (probably much higher) because the bonus is less effective as it no longer applies to both the commander and troops. What happens if you have 5 knight commanders? Parity between increasing B from 0 to 1 or H from 0 to 1 for all five at once is reached at 2,995 troops. etc... If you are sending out more than 545 troops with the goal of leveling commanders then you're taking more casualties per Xp than you need to in order to level your troops (please don't make me show how). In that scenario, the question is why would you care if increasing B or H is more effective at reducing casualties?

Rill Members Profile Send Private Message Find Members Posts Add to Buddy List Postmaster General Player Council - Geographer Joined: 17 Jun 2011 Location: California Status: Offline Points: 6903	Posted: 14 Sep 2012 at 19:01
	In leveling my commanders vs. NPCs, I rarely use more than 150 troops to attack. If one uses multiple commanders in one army, the commander bonus can equal up to 5/6 of your total attack power, which substantially limits casualties. If I send 120 t1 cavalry to attack a horde of wild dogs, wolves, etc., I might lose 10 of them with multiple commanders fully leveled in heroism. If I sent the same 120 cav with a single commander not leveled in heroism, I would lose more like 30-50. Just rough estimates since I haven't been leveling commanders lately, too busy attacking elementals.

mizaralcor Members Profile Send Private Message Find Members Posts Add to Buddy List New Poster Joined: 25 Aug 2012 Status: Offline Points: 15	Posted: 14 Sep 2012 at 15:16
	Thank you for the inputs. Also, thanks for confirming that dunnoob, apparently it's clear that divisional skills will not only affect the troops inside the division, but the commanding commander as well.

Captain Ganoes Paran Members Profile Send Private Message Find Members Posts Add to Buddy List Wordsmith Joined: 23 Jan 2012 Status: Offline Points: 158	Posted: 14 Sep 2012 at 13:37
	your commander will level easy at the start ,so until you have a big army you'll already have your commanders much higher than 20 and you'll have both heroism and divisional bonus maxed

dunnoob Members Profile Send Private Message Find Members Posts Add to Buddy List Postmaster Joined: 10 Dec 2011 Location: Elijal Status: Offline Points: 800	Posted: 14 Sep 2012 at 12:35
	The new elite squadrons are smaller, a heroic commander would be fine. In cities with less than 10K pop it would be hard to have 5600=3K troops, and heroism helps to get XP with smaller divisions. In theory you could spend prestige and reassign heroism skills to defensive divisional skills later, when your divisions are big enough. Checking your first question, the values are listed on the military overview page for armies at home: One heroic packsman commander allegedly has an attack value 2147. For 6132=1952 that's about 110%. The divisional skill charge is at 10 and was added, 6132110/100=2147.2.

JimJams Members Profile Send Private Message Find Members Posts Add to Buddy List Forum Warrior Joined: 20 Sep 2011 Location: Italy Status: Offline Points: 496	Posted: 14 Sep 2012 at 12:26
	The quick answer is you need to level your commanders, so you need to make them fight, and you don't want to waste too much units doing that, so the bigger is the personal attack power of the commander the more effective and cheap is leveling. Optimal result can be reached when you have half the power coming from the commander and half from the units, at max Heroism.


mizaralcor Members Profile Send Private Message Find Members Posts Add to Buddy List New Poster Joined: 25 Aug 2012 Status: Offline Points: 15	Posted: 14 Sep 2012 at 11:37
	Fellow Illy players, I got a couple question regarding commander's skills and their influence : 1. Do the divisional bonus skills also take the commander's own stats into calculation, or just the troops within that commander's division? For example, with a single division comprised of 200 infantry and a commander with 10 levels in +divisional infantry attack skill, i.e. Bloodlust, is it going to be a total of 110% attack increase from 200 infantry alone, or from 201 units (including the commander)? 2. Why do many people suggest players to level Heroism first on their commanders rather than the divisional attack skill? Unless I misunderstand the skills' formula, I calculated that for a division consisting of 600 troops or above, divisional attack skill actually yields bigger bonus than Heroism. For example : -> A Human T1 Cavalry troop has 37 attack value. -> A division of 601 T1 cavalries with a T1 cavalry commander with 10 levels of Heroism has a total attack power of : (601)(37) + (61)(37) = 24,494 attack power -> A division of 601 T1 cavalries with a T1 cavalry commander with 10 levels of divisional cavalry attack bonus (i.e. Charge) has a total attack power of : (601)(37)(1.1) + 37 = 24,498 attack power -> This difference is small, but with bigger and bigger divisions, the difference will be more and more pronounced as divisional attack bonus scales with amount of troops present in the division, while Heroism does not. I understand that with small divisions (i.e. less than 600 troops), commander's personal defense skills or Heroism gives higher bonus than divisional attack or defense skills. But won't leveling divisional skills first be a better choice for divisions consisting of 600 troops or more?