few notes from my previous game

[crusader.mike]

1. Flame blade does not add 2  ranged attack to my orihalcon high-men magician with focus magic (i.e. ranged attack rating stays at 15). Looks like this is just like with some artefacts -- instead of increasing attack bonus by 2 it sets it to max(current-attack-bonus, 2).

2. Dispelling wave used in the battle (while attacking a city) removes city enchantments. Which is funny, you could remove city enchantment that is totally unrelated to combat. I casted it multiple times on overland map to de-fang AI stack sitting in his fortress and the Stream of Life survived all of them; attacked and casted it in battle -- it got immediately removed. :-) . I wonder if you could remove famine this way...

3. Can someone explain me what is so special about Horde? This unit seem to be not very different from halberdiers, but with few basic buffs (bless, holy armor, endurance, guardian trait) it becomes indestructible (especially to magicians). Is it like combination of factors (extra hit point, + to-defend, + to-attack) that pushes it over some sort of threshold?

[Domon]

1 - because focus magic turne their ranged attack into a magical attack and flame blade doesn't apply to magical attacks

[Nelphine]

1. Flame blade does not apply to magical attacks as Domon mentioned, only missile or rock or thrown attacks.
2. That's a Seravy comment, I can't remember what we ended up doing with dispelling wave and city enchantments.
3. Horde have large shields (+3 defense against any ranged attacks); bless also is counted against magicians. Those 2 things by themselves are therefore +8 defense against magicians. Horde also have 8 figures instead of the 6 that halberdiers usually have, which means they actually have a fair bit more hp than halberdiers. Endurance and guardian mean they have +2 to defend. Assuming they are level 0, that means they end up with 14 armor against magicians, each with a 50% chance of actually blocking damage. That means they block 7 damage from each incoming attack. Assuming you are not high elves, and you haven't got any of the other methods of getting +to hit on your magicians, that means on AVERAGE, you'd need your magicians to have 20+ attack rating in order to hurt those horde units. (Average is not nearly as accurate as EXPECTED though. So, to actually do damage, your magicians probably only need around 15 attack rating. But given the previous mention of horde having more hp than halberdiers, simply doing SOME damage isn't really going to actually do significant damage.)

[crusader.mike]

1. yep, I misread Flame blade description. It clearly states "missile attack" not "ranged attack"

3. I know the math behind all this -- it was surprising how sharp difference was. Even when I was attacked (guardian is not in effect) Horde was almost untoucheable. One dispell wave and magicians wiped out half of attacking units in one turn.


> That means they block 7 damage from each incoming attack.

... block on average up to 7 damage from each incoming attack... :-)


> ... average != EXPECTED ...

It depends on how you define these terms

[Seravy]

2. Dispelling Wave does dispel city enchantments, but if it's done in combat, the effect lasts only for that combat. It only removes the combat copy of the spell.

[Nelphine]

> That means they block 7 damage from each incoming attack.

... block on average up to 7 damage from each incoming attack... :-)

> ... average != EXPECTED ...

It depends on how you define these terms

Average is when you assume the most common result for the attack and armor roll (in our case, if someone has no bonuses to hit, then the average assumes precisely 30% of the attackers attack strength will hit, and similarly for defense.)
Expected is when you consider that although the most common result is the most common, there are other frequent results that will noticeably change the results compared to the average, and so you account for the actual range of rolls that will occur in one attack by a unit.

This is important because even one unit attacking another unit can have literally hundreds of dice rolls. If common results (even if not the most common) noticeably change the results, then the expected can be significantly different than the average. (Such as the case of buffed magicians attacking buffed hordes. If the attack and defense roll were average, the magicians would need attack 22 to do any damage. But they aren't all average, so typically, the expected attack value for the magicians to hurt the horde is around 15 or 16. Big difference.)

[teelaurila]

Or the probability in other words: Average damage can be obtained by the difference of average attack and average defense only when attack values are very high compared to defense. When defense is high, you often end with more defense than attack, which is not negative damage but 0. The probability for at least some attack to be higher than defense can be quite high even when average defense is higher.

The sharp difference with the buffs come mostly from buffing +to-defend -roll. The probability of rolling low for defense decreases quite sharply when the probability of each shield to succesfully block increases. (It's proportional to (1-p)^n, where p is to-defend and n is number of shields)- That's why endurance and prayer are so awesome with high defense units. Example, 8 shields difference between +0 and +2 to-defend, probability to roll 0 defense:

(1-0.3)^8=6%

(1-0.5)^8=0.4%

[crusader.mike]

I see, so you use "average" for this formula:

Code:

average.dam = max(expected(attack.roll) - expected(defense.roll), 0)

naturally it won't give you a correct answer, which is:

Code:

expected.dam = expected( max(attack.roll - defense.roll, 0) )

The thing is I use "expected value" and "average value" as synonyms. Simply because first formula doesn't give you any meaningful answer -- it is simply incorrect, it's result shouldn't be even considered.

It's proportional to (1-p)^n

I know. You should check this post. I'll spend few hours with wolfram -- will try to figure out how to build probability distribution graph/histogram depending on attacker and defender parameters. Will post results to a new thread if I get smth.

[Nelphine]

yeah if you're using wolfram you're probably fine. I'm using those definitions because that is the simplest version of average, meaning, it can be done on a napkin while on the bus - which means some players will use it. the proper expected value is MUCH harder to compute by hand.

[crusader.mike]

Oh, yeah -- I could not do it in Google spreadsheet either. Calcs turned out to be too complex -- I spent quite a lot of time to figure out which public online instrument can do it. Stumbled upon Wolfram and it did the trick.