Damage Reduction (DR) vs Armor Penalty

[mar3usmc]

How much do you value DR over being able to dodge? i.e. How much dodge are you willing to give up per DR gained.

From some of the lighter armors I have seen, it looks like you get about 1 DR per 5 dodge lost once you are past 3 DR. Does that sound about right? Do other armors have better ratios?

[General Profit]

It sort of depends

A great smith can reduce the armor penalties and increase the AP cap of any said armor this should be kept in mind for such a character

For Crit characters without dodge or block the armor penalties won't do you much harm apart from the thc one on the helmet so a light helmet and heavy armor for an axe beserker could work quite well and focus on alchemy+axe+crit for a potentially very nice combo (prioritise archers with such a build though)

For Dodge characters without smithing Light metal or for a stealth character Strong leather can fit the role nicely
For Block characters without smithing i would suggest something rather light like the arm guard cannot remember its name i think it began with an M, alternatively pay 100-150 or talk the guards (praetor only i think) into letting the refuges in at the gate you will recieve some nice light armor

From enemies killed or aquired for expensive prices from merchants you can get smithing enchanced gear

[mar3usmc]

Yes, we know smithing can adjust an armor's properties. The question is, at what point, what ratio, do you value DR relative to Armor Penalty.

I feel, with my limited experience in this game, if you can get 1 DR per 3 AP that is pretty decent and may be worth it.

I may work up a simple excel sheet to work out some numbers such as average damage taken increase or decrease dependent on incoming damage.

[General Profit]

Originally posted by mar3usmc:

Yes, we know smithing can adjust an armor's properties. The question is, at what point, what ratio, do you value DR relative to Armor Penalty.

I feel, with my limited experience in this game, if you can get 1 DR per 3 AP that is pretty decent and may be worth it.

I may work up a simple excel sheet to work out some numbers such as average damage taken increase or decrease dependent on incoming damage.

For a baseline i would say don't to go above 15 penalty in a block/dodge using build
and try not to go over 6 thc penalty

[mar3usmc]

Ok, I ran some numbers and here is what I came up with:

First let me lay out some independent variables,

Damage Input (Dmg)
Damage Reduction (DR)
Dodge/Block Chance (C) (Decimal Value, greater than or equal to zero, less than or equal to one) Note: This is the chance the enemy has to hit you before taking into account the AP. This is NOT your defense rating!
Armor Penalty (AP) (Decimal Value, less than or equal to Dodge/Block Chance)

and a couple dependent variables,

Effective Damage (ED) = Dmg - DR
Defense (Def) = C - AP (Decimal Value, greater than or equal to zero, less than or equal to one) Note: Again, not your defense rating, just the aggregate chance the opponent has to hit you.

First, the average damage per hit a character will receive can be calculated as,

(1-Def)*ED = AvgDmg

This is a bit simplified because we are assuming criticals are part of the input damage, which is the average damage your opponent is rolling.

This is nice for checking how much damage you should expect every time your opponent attacks you. This is the damage you would receive on average per attack if your opponent attacked you many many times, averaging in the misses.

Now, let's take a look at how much that armor is actually helping you. Relative to if you were naked, the aggregate effective damage reduction (AEDR),

DR*(1-Def) - Dmg*AP = AEDR

Notice a couple things. The first part of the equation is the effective damage reduction (EDR). The higher your dodge or block is the lower the "value" your DR has. Basically, if someone can't hit you, your DR has no value. The second part of the equation is the penalty you receive for wearing the armor. It basically subtracts the average extra damage you will be taking from a reduced dodge/block. Notice that very high damage input values will bring the AEDR into the negative. That is the point we are looking for.

Back to the primary question. For a given dodge/block and given damage input, what is the point at which the DR per AP no longer becomes beneficial. Holding Def and Dmg constant, and setting AEDR to zero we have the following,

DR/AP = Dmg/(1-Def)

With this equation you can determine the minimum ratio of DR/AP for a given damage input and defense chance.

e.g. I am being hit, on average, 10 damage BEFORE damage reductions, and my opponent has a 50% chance of hitting me. So the armor I want to use needs to have a DR/AP ratio of at least 10/(1-0.5) = 20. Anything less means that I am actually gimping my build. Notice how as your Def goes to 1.0 that your ratio becomes infinite. Basically, this means you can just run around naked as that oppenent can't hit you. An example of some acceptable armor would be something with a DR of 6, and an AP of 16. That is a ratio of 37.5. However, if that damage amount was 20 instead of 10, then that armor would actually hurt you as it would be under the ratio of 40.

Questions?

[feliscon]

You shouldn't use AP for Armour Penalty. That is already used in the game for Action Points.

[Sunfire]

What about other armor stats (vsCS, max AP, hardness)? How do you take they into account? They are even much more significant for the dodgers, then DR.

[mar3usmc]

Originally posted by feliscon:

You shouldn't use AP for Armour Penalty. That is already used in the game for Action Points.

I understand how that may cause some confusion, but the discussion isn't about AP. I also defined my variables. So as long as the reader reads that part there should be no confusion.

Originally posted by Sunfire:

What about other armor stats (vsCS, max AP, hardness)? How do you take they into account? They are even much more significant for the dodgers, then DR.

This discussion isn't about your max AP, or whether or not your armor will be damaged. Criticals and side effects are also not up for discussion. This is simply about how to best mitigate any incoming damage. Given a set of options for armor, disregarding all ability point and other limitations, focusing only on the DR and armor penalty, the constructed formulations I gave will tell you which armor will be best for damage mitigation.

The damage input already takes into account any damage from criticals. It is simply the damage you expect an enemy to do on average. Now, if you really want to get into the specifics of that number you would need to know the strength of the enemy, weapon statistics, attack type, and the critical chance for that specific attack type. With those variable defined you could then calculate the average damage an opponent will do when attacking with that specified attack.

As you can see, that is quite a few additional variable to take into account. Given the slew of weapons and attack types I just didn't find it worth while to work out another equation for that. Instead, I think just using a standard 5, 10, 15, and 20 damage amount, and chance to hit to test armor setups is a better way to go. This way, you know what enemies are the biggest threat to your character setup. Those are the enemies to take out first.

[Sunfire]

It seems like artificially simplified approach, good luck in your research then.

[Shining Hector]

Honestly you generally do best to just get the heaviest armor that you can wear with your dex without losing AP (action points). Leather is fine starting out and holds its own against unmodified bronze and maybe iron, but it just flat loses to lootable blue steel armor every time, which is quickly available in Maadoran. If you can craft, awesome, if not, buy or loot specialty armor ASAP once you're out of Teron. For findable armor, Kadmos' blue steel Manica is great for dex 10 and attainable your first minute in Maadoran if you can fight reasonably well, and Darius' armor is great for dex 8 (only available to HA Praetor, though), or Honor Bound from the MG for everyone else. Very late in the game there's also maxed out blue steel Imperial armor perfect for a dex 8 or lower character as the last last fight in the Arena, and power armor best for characters with 9 or 10 dex. It's not a great idea to have a combat chracter with a dex lower than 8, but if you want to loot someone's steel Imperial armor and tank it up nobody will stop you.

Enemies will usually be forced to use power attacks if you're in reasonably heavy armor, and their THC penalty roughtly balances out with your defense penalty as well as their damage vs. your DR, but the upshot is you take less total hits since they're also slower. All a dodger in leather needs is a couple of aimed leg shots and then a bunch of fast attacks to ruin his day, and, yeah, the AI knows to do that.

[mar3usmc]

I think I have already shown that heavier armor is not always better. Once the damage is high enough, those armor penalties will result in higher average damage over time. What is most important on an armor with regards to damage reduction over time is the Damage Reduction per Armor Penalty.

I will agree with you on the point though that if an opponent has to use strong attacks to break your DR then they will get fewer attacks per round, and at a lower chance to hit. It is hard to say at what point an opponent will switch to such an attack. I don't know how the AI code is set up. It could have a 1 damage or greater threshold, or it could be a 3 damage or greater. That is something that would make for a far more complicated but complete equation if I did know that answer. It is a very interesting thing to think about.

Edit: Another thing that comes to mind is piercing damage, such as that from bows and crossbows or other projectiles. The 60% reduction in DR is huge, and painful. I know I use a crossbow instead of daggers from time to time to soften up those heavy armored opponents.

[Shining Hector]

Honestly your equations just don't really come up in the actual game in a meaningful way. Non-crafters are realistically limited to the options available, crafters are limited by the amount of steel/bluesteel/skymetal they can scrounge at a particular time. Kadmos' manica has DR 6 and -4 defense, so if you have 10 dex and no crafting you're crazy not to use it most of the game until you can trade up to power armor. Honor Bound has 10 DR and -20 defense, but opponents would have to take an effective -30 to hit going from fast attack to power attack to get the extra +4 damage to counteract that, compared to the -16 defense hit you take for the +4 DR in relation to Kadmos' manica, so if you have 8 dex and the cash you're better off with Honor Bound, or the even better 11 DR Darius' armor if you're a HA Praetor. The Blue Cuirass from the Arena champion is the other solid contender once you're good enough to beat him, with 9 DR, -15 defense, and 11 max AP. The other good purchasable armor is the Mangudai with 5 DR, 0 defense penalty, and 11 max AP, which is nice, but again the penalty oppenents can and will end up taking to power attack you to punch through the higher defense of the other armors is bigger than the defense penalty you'll take to wear them.

If you can craft, you can get all the steel you need pretty early in Maadoran, all the bluesteel you need once you can conquer the Arena, and have to wait a long time and play your cards right to have skymetal armor. Past that, you really do typically do best crafting the heaviest armor you can without taking an action point penalty, putting priority on masterwork and lightening to get the heaviest armor possible. Just try it and see.

[grraf]

For dodge builds i always have 2 armour sets: best lite i can craft at lvl 8 (reached shortly after entering madoran) so either hardened leather or phrygian(literaly 0 or 2 penalty for more then 40vsCS and 3or4 DR basicaly u are unhitable by all but fast shots and those are rarely crits when they do land) and on the oposite end of the scale is the strongest blue steel lorica musculata in can make... for blocking minimum is lorica hamata and maximum is praetorian armor(made from blue steel and with +1AP tech on it is simply crit proof and can shrug off just about any blow while still alowing for the crucial 10AP a turn(2 aimed arm/leg/torso shots with a medium weapon or 3 fast hits...)