Some Math for Armor (Updated2)

You need to account for dodge and accuracy. But you are right about needing some changes to weapons. I suggest you take a look at the expanded weapons mod. It provides some much needed balance and very good tactical strategy. The AI can even use the special abilities it adds. Also, with higher logistics these numbers tend to balance better. And for that matter, armor has a complex equation that I don't have near me to decide how much damage it absorbs. So a spear can still take a chunk out of plate if it rolls well, especially if you can get a logistical advantage. 

I would love to see something like a reason to use smaller weapons than two handed blades, one of the great things about the Gladius or even a dagger is that there are always tiny exposed bits, for example, between the joints of armor.

Most games take this into account, with a rogue with a dagger and high dexterity can often score hits that ignore armor or critical hits etc. As the game stands however, there's no stealth mechanic, no way to account for any sort of "backstab" beyond the assassin trait. There aren't even blunt weapons which do crushing damage that harms armored units.

I suppose this might not be exactly on the topic of armor, but I'd love to see the ability to prepare your own battlefield, if you're the defender. For example when you build a hedge row, you're able to lay it out on a strategic map after you finish the construction (or as you begin it). Then it would be awesome if you could do things such as position troops for an ambush before battle begins, lay out traps on the field of battle, or in any other way prepare your cities or defensive strong points for the enemy. And, to tie that concept back to the armor discussion, I would imagine that steel plate is of little use against a pot of boiling oil dumped on you from atop a wall.

I looked forward to sieging cities, while I wasn't looking for Lords of the Realm 3.5, I was sort of expecting some reason to amass a huge army. While I played a game in 1.1 that did manage to amuse me in much the same way the beta 2 amused me (and no other version between the two had), there was something ludicrous about having my two fully armored knights (husband and wife, rulers of my empire none the less) competely run roughshod over something like 45 units in the final battle against Relias, who always demands money and then attacks me when I refuse him.

There are so many small additions to the tactical combat that would make the entire game more enjoyable, it's a shame to see sieging a city still brings me onto the plains outside the castle walls with no real allowance for more advanced strategies that are usually required for successfully capturing an enemy fortification.

There's also no real provision for any sorts of sieges, I'd love to camp an army atop an enemy stronghold and starve them out, or use a scorched earth technique to deny local crops to the onslaught of besiegers en route to my own stronghold. A game where swords and boiling oil compete with dragons and spellslingers was what I wanted Elemental to be, unfortunately it still lacks the depth I had hoped for when I first imagined the gameplay that went alongside the screenshots that convinced me buying to get in the beta was an excellent idea. While I realize that some of these ideas are much harder to implement than others, I don't see why any of them wouldn't be able to be integrated into future Elemental versions at some point.

Dsraider this is why we are constantly complaining about the AI not using shields or helms. It is essentially stuck on easy-mode.

Edit: I don't think you are calculating average damage correctly. Are you using the method described here: https://forums.elementalgame.com/403879/get;2872856

Edit2: These are the values for attack and armor mitigation averages in 1.11 (rounded to 3 decimals)

edit3: Actually, it will be better to express mitigation as a % of lost damage. I'll do a new table.

These are the numbers I'm getting. Would be cool if someone could check the calcs. This would be for 1.2 (1.19 beta)

Same numbers for 1.11

Ya I got lazy because It was late at night. I meant to come back and do real average this morning. Whats there is just max armor vs max dmg. I thought that would be pretty accurate. I forgot that damage has a %50 min and Armor now doesn't however, so that skews it a bit. I will fix it soon.

We do have an ignore armor function in the abilities xml. It would be so cool if special abilities could be cast on strike instead of click a button.

@HeavenFall: My numbers seem a little different. If you want to compare I added a link to the spreadsheet I used.

I think you are overcalculating the value of armor. In your spreadsheet, you are not correctly taking into consideration that armor that reduces damage to 0 does not get saved for other attacks.

It goes without saying, that when you reach higher than 100% mitigation, your calculations are wrong. In addition, it is easy to further disregard the calculations because you arrive at erroneous results - staffs CAN damage 6-armor targets, as we see in-game. Logically, a staff can roll max attack (5) and armor can roll minimum defense (3). It is therefore impossible to reach your numbers.

In 1.11, for a weapon to have 100% mitigated damage, the attack needs to be half or less of the defense. Any other attack has a chance of dealing damage. In 1.19, any weapon has a chance to deal damage against any armor, unless the attack is 1 and the armor is 1.

Edit: This is the script I used to calculate mitigated damage. http://pastebin.com/raw.php?i=mah4MgpL

As you can see, every possible attack roll must be measured against the average mitigation of every possible defense roll. Only remaining damage is interesting, damage is never negative (armor either reduces an attack to 0, or the attack deals damage).

Well yes, but an average attack roll won't hurt an average roll on full armor.  It's possible to get more then %100 mitigation because average armor in some cases is higher the average damage. It's definitely possible to do damage but most attacks won't do any damage if mitigation equals %100. Mitigation here is for the average roll. Higher then %100 just means that you are even more unlikely to do any damage. You would need a far better then average roll.

I don't understand how that value is in any way interesting to look at, but it's your topic.

It shows you how much dmg on average the armor mitigates?

I'm confused as to what yours does, please explain.

I have no problem believing my math is off, I'm especially worried about all my rounding, which could put me off by 1 here and there. Not usually a big deal but with such small and close numbers even 1 is a significant percentage.

My numbers measure the total amount of damage dealt, vs the total amount of damage mitigated. If you are attacking with 5 attackpower, and the target unit has 6 defense, 87% of all the possible damage you deal will be blocked. The remaining ~13% will deal some damage.

I don't know how rounding works either, I haven't done any of it. Does it round to the nearest integer, or always up? Don't know.

I'm curious how you're doing the math. I did some quick napkin-esque checking of the easiest calculation above, and I got an average of 0.498888.. damage on the staff vs. cloth example (total 449 damage for 900 possible attack vs. armor rolls). Which would be almost exactly 90% mitigation.

My assumptions regarding rounding:

1. All square root results rounded down (based on Kael's post - he does this in his example).

2. Round up the minimum attack roll; 5/2 = 2.5 min becomes 3. Admittedly it would seem more consistent with assumption [1] to round down to 2, but if we do that then some attack rolls (namely, 2) no longer satisfy the "no attack roll can be less than half of maximum" condition, so logically you'd expect them to round up and have a minimum attack roll of 3.

Anyway just curious whether you rounded differently, which would probably explain the small difference in results, or I just screwed up the math. Not that it would change the results much, the +/- 1 rounding error does little enough in this example and would be even less of a difference in all the others.

[Edit: hold that thought, just saw your previous post of your code. I'll take a look at that and see myself where the difference is.]

Ah, I see the big difference - I calculated the final armor-mitigated damage and compared it to the theoretical maximum damage to get mitigation percent, your percent comes from comparing it to the actual attack damage vs. 0 armor, which is definitely a better way to do it. You're also doing the rounding differently, which is debatable since we don't know exactly how Stardock does it - I went by what Kael's post seems to imply, but he doesn't state any rounding rules specifically, so who knows.

If I change the script so that all square roots are rounded down, and all half-damage attacks are rounded up (5/2=3) then the number I get is 85% on 5att vs 6 def (edit: in 1.19).

How did I arrive at this number?

I ran through all the possible attack rolls. For example, for 5 att I would run through 25 attack rolls, each resulting in a certain amount of damage.

Then, for each possible attack roll, I also measured each possible defense roll on that particular attack roll. The defense rolls were then averaged across the attack roll. At this point, I had a number telling me - for that particular attack roll - how much the armor would mitigate on average.

So, if I had 25 attack rolls and 36 defense rolls, I ran through all 900 possible outcomes. Each attack roll had an average remaining damage after armor was removed, and that gives us (in comparison to possible total damage) how much armor did really reduce the attacks.

Maybe this will better visualize how I achieved the numbers. (for 1.19, taking into account rounding from above post) (5 att 6 def)

http://pastebin.com/raw.php?i=eP2yzUv0

Right, I initially did (maximum damage - actual average damage vs. armor)/(maximum damage) to get mitigation percent. If I change it to (actual average damage vs. no armor - actual average damage vs. armor)/(actual average damage vs. no armor) as you did I get 85% (same as your result after rounding changes). Since your original was 87% obviously the rounding is having little effect either way.

Ah! I rounded up here, I will have to recheck my stuff.

I sent a PM to Kael, hopefully he can stop by and shed some light on the rounding issues.

My computer has currently died on me and i am stck with my daughters laptop at the moment - canèt open up the game right now

Is it possible you could you make a quick not of the various armour pieces

ex: cloth chest 2, cloth bracer 1, cloth leggings 1, cloth helmet 1

soldier cloak 2

It would help a lot thank you.

Padded starts at helm and bracers being 1 armor, and chest and legs 2. Every level after gains 1 to each. Master plate is divided into light and heavy. Higher plate has dodge penalties.

Put together a webpage showing all the possible attack/defense combinations. Attack is top row, defense is first column.

http://thedyinggrounds.com/Elemental/patch1.2.htm

new link http://thedyinggrounds.com/Elemental/patch12.htm

Interesting results. Some basic rules of thumb, which could be useful ingame:

If attack is twice defense, expect 45% mitigation

If attack is equal to defense, expect 80% mitigation

If attack is half defense, expect 95% mitigation

(Consistently correct, give or take 1%, for values >2)

Keep in mind that 95% mitigation vs. 80% is a bigger difference than it may seem - you're getting hit for 5% instead of 20% on average, this is 4x the survivability.

Doesn't seem like a bad system, but as the OP pointed out, the actual attack and defense values ingame may need balancing. Right now with attack roughly equal to defense at same tier, you're looking at 80% mitigation when tech is equal, and it's very easy to hit that 95% mitigation mark if you can get your armor a tier or so ahead of enemy weapons. Needless to say, when attack is struggling so much to pierce defense at all, using any weapon except the max damage one is.. a questionable decision.

If attack value was significantly ahead of armor at any given tier (attack being about 1.5x defense would be a good start, I think), we'd be seeing more reasonable numbers like 60% mitigation against same tier armor, and maybe 80% when facing armor of the next tier up.

Also to avoid significantly throwing off the balance of combat, any armor decrease (or damage increase) should be accompanied by a health increase. I really don't want to see more oneshot kills - longer combat is more tactical! You have time to make more choices, and the results are less affected by luck.

As for weapons vs. armor, I think weapons having 175-180% the value of armor would be even more appropriate, to soften the obsolescence curve.

[edit: clarified last sentence]

Oh I agree, hypothetically speaking combat can get too long for a TBS - I'm just saying that right now it tends more towards the "blink and you'll miss it" end of the scale (except when armor is enough to grant nigh-invulnerability), if anything is changed to speed it up further in the name of fixing armor, it should be be balanced by a change to slow things down (more health).

I'm finding the reverse early on - 6/6 vs 6/6 gives a damage range of 0 to 5 with a mean of 1 for both which leads to some long battles with 18 HP