Reverse engineering the new combat system

[bwoneill]

As a scientist, I'm curious as to how the new combat system really works. I've done what I can with the characters I have on Lamannia and determined how the defense chance (D) varies as a function of AC. It appears to be a logarithmic function with two parameters based on level. From the data I've collected, I've made the following fits resulting in a chi2/dof<0.2 at level 4 and <0.07 at level 19.

D_L(AC)=A_L*(ln(AC-B_L)-1)
D_4(AC)=0.32*(ln(AC-7.76)-1)
D_19(AC)=0.22*(ln(AC-31.63)-1)

As it's much harder to vary level than equipment, there's not much more I can do during the open beta without your help. If you have a toon on Lamannia at a different level and can devote a few minutes to collect some data I'd much appreciate it. Please provide your toon's level and a few examples of D and AC. The more data points I get the more precise my fits will be.
Thanks,
Ben

[Nyvn]

I think I can help you out a bit. Since the NDA is lifted, and old beta posts weren't brought over (And for some reason the formulas weren't released).

Major changes are being made to the hit formulas in Menace of the Underdark to address several Armor Class and mitigation issues that plague the system we currently have on the live servers, and become especially apparent in extreme content. Armor Class is intended to provide indirect damage mitigation over time – it makes sense that the less the monsters hit you, the less damage you take.

We've put this thread together to try to explain what we're doing and why. (Several changes have occurred since earlier beta rounds - if I don't mention something, it's probably been removed.)

The biggest issue that we have is that against any particular monster, there is only a “functional AC band” of 20 points, where each point of Armor Class matters. Let’s look at a mid level example, ignoring critical hits for now, where a monster with +20 to hit is attacking a player:

Figure 1: Mid Level AC – Monster attacking Player
The mitigation curve with the live system looks like this. Against a monster with a +20 to hit, if you have a 21 or lower Armor Class (the first red zone), you are hit 95% of the time, since monsters miss on a roll of a natural 1. It doesn’t really matter if you’re at 10 AC, 15, or 21 – you’re still getting hit 95% of the time. At an Armor Class of 40 or higher, once again, each point of Armor Class is excessive – the monster is only hitting on a roll of a Natural 20, so your Armor Class is “wasted”.

Major problems start arising when character AC’s in a party are 20 or more points apart – monsters can barely touch one character but are almost always hitting the other character. The low AC character is taking an astounding nineteen times as many hits as the high AC character. Meanwhile, to challenge the high AC character, monster to-hit numbers have crept up significantly, until we reach our current epic level content, which has charts like this:

Figure 2: Epic Lord of Blades - Monster attacking Player
The Epic Lord of Blades, without serious debuffs, hits everyone’s Armor Class in the game right now 95% of the time, from the angriest Frenzied Berserker in a loincloth to a Stalwart Defender wearing the best defensive gear in the game.

Since Epic quests, until now, have been designed for a certain extremely hardcore crowd, this was somewhat acceptable, but in Menace of the Underdark we’re opening them up to a wider audience (including Casual, Normal, Hard, and Elite modes).

Players have often told us that the Armor Class system is broken, and the charts above clearly indicate that they’re absolutely right! It’s completely true, especially in high level content. The system functions only in a very narrow band of 20, but player AC ranges wildly from single digits to hovering right around 100. This unsurprisingly leads to characters discarding any attempts to increase their Armor Class, since there’s no way for them to get it to the point where it has any actual effect on gameplay. (Tabletop D&D has a few systems that address the disparity, such as additional attacks per turn at increasing penalties - even if the first attack will hit you 95% of the time, the second or third attack might miss if you have some focus on AC.)

We would like Armor Class to matter to everybody. We would also like everyone to gain some benefit if they acquire an item that increases their Armor Class by another 3 points, regardless of how high their Armor Class already is.

Our solution is to change the way Attack Bonus and Armor Class are compared. Instead of adding 1d20 to a monster’s Attack Bonus and directly comparing the values, we’re calculating a hit chance separately. Each point of Armor Class increases your chance to be missed, while each point of the monster’s Attack Bonus increases their chance to hit you. The tooltip on your Armor Class value of your character sheet will display your chance to be missed by the “average monster” of your level.

Figure 3: Defense Chance in the AC Tooltip
A general rule with the new formula is that every doubling of Armor Class pretty much doubles your mitigation. A character with 30 Armor Class will be hit approximately half as often by a specific monster as one with a 15 Armor Class, and one with a 60 Armor Class will be hit approximately one quarter as often as the 15 Armor Class character.

Players will use the same formula, but will have a 25% bonus to hit if they are proficient with their weapon. Unlike monster attack rolls, player to hit rolls will be mapped to a d20 by rounding to the nearest 5% - if you hit on a 13, you’ll hit on a 13. Players will also graze opponents on a roll of 2 or higher on the d20 instead of a 10 or higher – if you character looks like it hit with your weapon, it should do some damage on anything but a roll of a 1.

Converting to a system like this increases the band of “Effective Armor Class” dramatically, but also results in high Armor Class characters being hit more often. If we did nothing to address that, the mitigation curves for above charts would look like this:

Figure 4: Mid Level AC Comparison of Systems – Monster attacking Player
Values from 17 to 305 Armor Class are supported with this mid-level curve.

Figure 5: Epic Lord of Blades Comparison of Systems – Monster attacking Player
The Epic Lord of Blades now acquires a chance to miss at 66 Armor Class, and the curve doesn’t reach a 95% miss chance until 1244 Armor Class.

While these curves dramatically assist characters with Armor Class lower than the Attack Bonuses of their opponents, this isn’t sufficient to keep high Armor Class characters “tanking” as well as we would like. There are two additional changes that we’re planning to help them out there, and one for the lightly armored dexterous classes out there.
More Armor Class for wearing Armor
We want armor to mean more to your character than it does today. Currently on live, a character with a 90 Armor Class is likely to be getting 16 or fewer points of their Armor Class from the suit of armor they are physically wearing. We’re creating multiple “tiers” of armor that provide increased bonuses, starting around level 7.

Named items will be retroactively upgraded to grant bonuses appropriate for the tier that they drop at. The Epic Red Dragonplate Armor, for example, will provide 27 total points of Armor Bonus instead of 16.

We didn’t forget about the Warforged – Docents will now also grant different amounts of Armor based on your body feats.

Several feats and enhancements have been modified to provide greater amounts of Armor Class or percentage boosts to Armor Class.

Physical Resistance Rating
Heavily armored or defensive characters will be taking decreased damage from physical (bludgeoning, piercing, or slashing) damage due to a Physical Resistance Rating score.

If you are proficient in your armor, you will have a starting Physical Resistance Rating, modified by whether it is light, medium, or heavy armor, that increases as your Base Attack Bonus increases.

Shield Mastery, Improved Shield Mastery, Two Weapon Defense, various Defensive Stances, and the monk’s Earth Stance all provide various amounts of stacking Physical Resistance Rating.

Your Physical Resistance Rating will be visible on your character sheet, and the tooltip will let you know how much it's helping.


Figure 6: Physical Resistance Rating Tooltip

Dodge
Dodge bonuses now give a chance to evade attacks entirely instead of providing Armor Class. Your passive Dodge percentage is capped by the Maximum Dexterity Bonus of your armor, shield, or body feat, but short duration effects can go well beyond it.

Several feats now provide Dodge bonuses that did not have defensive benefits before – Mobility and Spring Attack each grant 2% Dodge, and abilities like Uncanny Dodge and Improved Uncanny Dodge now grant a massive Dodge bonus instead of a small amount of Armor Class.

If we include a 30% Armor Class Boost into our formulas, our Stalwart Defender III tank (wearing heavy armor and a tower shield, with Shield Mastery and Improved Shield Mastery) can expect approximately the following improvement to survivability against the Epic Lord of Blades:

Figure 7: Includes Physical Resistance Rating and AC increases
Our 100 AC tank on live should be going from 5% mitigation to around 64%. The Physical Resistance Rating boosts give a large amount of durability to the character, and very importantly make a healer’s job easier by making the incoming hits smaller.

In our mid level example, we’ll drop our tank down to Stalwart Defender II (reducing their Physical Resistance Rating), but retain heavy armor and a tower shield. Against this opponent, overall mitigation drops some at high AC values (since it’s no longer really possible to get to 95%), our 40 AC tank on live is still at 78% mitigation overall:

Figure 8: Includes Physical Resistance Rating and AC increases
Overall Summary:
With the new combat formulas, we’re hoping to have Armor Class matter at all levels, for every character. Each point of Armor Class that you gain will help you mitigate damage, whether it’s your 17^th point or your 117^th. Armors provide increased Armor Class bonuses as well as Physical Resistance Rating. It’s not really possible to reach the 95% plateau anymore, but a high Armor Class character’s survivability will still be high, and the formula is much more forgiving to middling-AC characters.

We hope that this post helps people understand the scope of and the reasons behind the combat changes, as well as providing clarity to make them easier to understand, and we welcome further questions and feedback here in the forums.

If you're curious, further details on the exact combat formulas are in another post here, containing the deep dive into specific feat and system changes.
"Raar."

This post contains the crunchy formula details, for those that want to know all of the math behind the numbers.

---

Monster’s chance to hit: (Monster’s Attack Bonus + 10.5) / (Target’s Armor Class * 2)

Player’s chance to hit (if proficient in weapon): (Player’s Attack Bonus + 10.5) / (Target’s Armor Class * 2) + 25%, rounded to nearest 5%

Players graze on a 2+ on the attack roll d20.
Monsters graze on a 19+ on Casual or Normal difficulty, 17+ on Hard difficulty, and 15+ on Elite difficulty. Note that at these thresholds, players should only encounter grazing hits when dramatically overleveling content, since it’s fairly difficult to be over a 75% miss rate.

You can calculate how much each point of Physical Resistance Rating is helping using the following formula: (1 – (0.99^Physical Resistance Rating))*0.65
Code:

PPR	Protection		PPR	Protection
0	0.00%			110	43.48%
10	6.22%			120	45.54%
20	11.84%			130	47.40%
30	16.92%			140	49.08%
40	21.52%			150	50.61%
50	25.67%			160	51.98%
60	29.43%			170	53.23%
70	32.84%			180	54.35%
80	35.91%			190	55.37%
90	38.69%			200	56.29%
100	41.21%			210	57.12%

If you are proficient in your armor:
Heavy Armor gives you Physical Resistance Rating equal to your Base Attack Bonus.
Medium Armor gives you Physical Resistance Rating equal to 2/3 of your Base Attack Bonus.
Light Armor gives you Physical Resistance Rating equal to 1/2 of your Base Attack Bonus.

Class Changes:
Barbarians and Rogues gain +1% Dodge at levels 4, 6, 8, 12, 16, and 20.

Monks gain 3 Centered AC instead of 1 at levels 2, 5, 10, 15, and 20.

Feat and Enhancement Changes:
Uncanny Dodge: Activate this ability to gain a temporary 25% Dodge bonus and a +4 reflex save bonus.
Note: Uncanny Dodge is no longer a times-per-day ability, but instead has a cooldown. Temporary Dodge bonuses ignore the Dodge cap normally applied by your armor's Maximum Dexterity Bonus cap.

Improved Uncanny Dodge: Activate this ability to gain a temporary 50% Dodge bonus and +6 reflex save bonus.
Note: Improved Uncanny Dodge is no longer a times-per-day ability, but instead has a cooldown. Temporary Dodge bonuses ignore the Dodge cap normally applied by your armor's Maximum Dexterity Bonus cap.

Defensive Fighting Defensive Stance: While using Defensive Fighting mode, you gain a 5% bonus to AC and a -5% penalty to-hit. Casting a spell ends this mode.

Combat Expertise Defensive Stance: While using Combat Expertise mode, you suffer -5 to your attack rolls but gain +10% feat bonus to Armor Class. Spells have three times their normal cooldown when this mode is active. Combat Expertise dispels and wards against all Rage effects.

Resilience Defensive Stance: While using Resilience mode, you gain a +4 bonus to all saves. Spells have three times their normal cooldown when this mode is active.

Precision Offensive Stance: While using Precision mode, you gain +5% to hit. Spells have three times their normal cooldown when this mode is active.
Note: Damage penalty has been removed.

Dodge Grants you a +1 bonus to your Armor Class that stacks with all other bonuses to AC (this will appear as a feat bonus on your character sheet). You will also gain a 3% Dodge bonus.

Mobility Increases the maximum dexterity bonus permitted by armor and tower shields by 2, and adds a +4 bonus to Armor Class while tumbling. You will also gain a 2% Dodge bonus.

Spring Attack You suffer no penalty to your attack roll when moving and attacking. You will also gain a 2% Dodge bonus.

Two Weapon Defense Grants you a +1 bonus to your AC and 5 physical resistance when you wield two weapons. (This bonus does not apply when fighting unarmed/with handwraps.)

Shield Mastery You are skilled with the use of a shield, and your physical resistance is increased by 3 when using a buckler or small shield, 5 when using a large shield, or 10 when using a tower shield.

Improved Shield Mastery You are exceptionally skilled with the use of a shield, and your physical resistance is increased by 5 when using a buckler or small shield, 10 when using a large shield, or 15 when using a tower shield.

Mithral Body Docents you equip provide armor equivalent to Chainmail. This is treated as metallic light armor. You have a 15% arcane spell failure chance, -1 armor check penalty to certain skills, and a +5 maximum dexterity bonus.

Adamantine Body Docents you equip provide armor equivalent to Full Plate. This is treated as metallic heavy armor. You have damage reduction 2/adamantine, a 35% arcane spell failure chance, -5 armor check penalty to certain skills, and a +1 maximum dexterity bonus.

Lesser Mountain Stance Martial Arts Stance: The unyielding mountain stance focuses on endurance and defense. Lesser Mountain Stance grants +2 Constitution, a 5% boost to AC, 3 physical resistance, and a +25% Insight bonus to melee threat generation, at the cost of -2 Dexterity and -10% movement speed. While in Lesser Mountain Stance, you gain 'Get Hit Effect: Gain 1 ki.'

Mountain Stance Martial Arts Stance: The unyielding mountain stance focuses on endurance and defense. Mountain Stance grants +2 Constitution, a 10% boost to AC, 8 physical resistance, and a +40% Insight bonus to melee threat generation, at the cost of -2 Dexterity and -10% movement speed. While in Mountain Stance, you gain 'Get Hit Effect: Gain 1 ki.'

Greater Mountain Stance Martial Arts Stance: The unyielding mountain focuses on endurance and defense. Greater Mountain Stance grants +3 Constitution, a 15% boost to AC, 12 physical resistance, a +55% Insight bonus to melee threat generation, and the critical multiplier of all weapons you use is increased by 1 on rolls of a natural 19 or 20, at the cost of -2 Dexterity and -10% movement speed. While in Greater Mountain Stance, you gain 'Get Hit Effect: Gain 1 ki.'

Ultimate Mountain Stance Martial Arts Stance: The unyielding mountain focuses on endurance and defense. Ultimate Mountain Stance grants +4 Constitution, a 20% boost to AC, 15 physical resistance, a +70% Insight bonus to melee threat generation, and the critical multiplier of all weapons you use is increased by 1 on rolls of a natural 19 or 20, at the cost of -2 Dexterity and -10% movement speed. While in Ultimate Mountain Stance, you gain 'Get Hit Effect: Gain 1 ki.'

Stalwart Defender: Defensive Stance You may expend a Fighter armor boost to become a bastion of defense, gaining a +2 Competence bonus to Strength and Constitution, +10% maximum hit points, a +1 Competence bonus on all saves, 10 physical resistance, and a 10% bonus to Armor Class from armor and shields. You also gain a 25% Competence bonus to threat generated with your melee attacks. While in this stance, you move 10% slower.

Stalwart Defender II: Improved Defensive Stance You may expend a Fighter armor boost to become a bastion of defense, gaining a +4 Competence bonus to Strength and Constitution, +15% maximum hit points, a +2 Competence bonus on all saves, 25 physical resistance, and a 20% bonus to Armor Class from armor and shields. You also gain a 50% Competence bonus to threat generated with your melee attacks. While in this stance, you move 10% slower.

Stalwart Defender III: Superior Defensive Stance You may expend a Fighter armor boost to become a bastion of defense, gaining a +6 Competence bonus to Strength and Constitution, +20% maximum hit points, a +3 Competence bonus on all saves, 45 physical resistance, and a 40% bonus to Armor Class from armor and shields. You also gain a 75% Competence bonus to threat generated with your melee attacks. While in this stance, you move 10% slower.

Defender of Siberys: Defensive Stance You may expend a Paladin armor boost to become a bastion of defense, gaining a +2 Sacred bonus to Strength and Constitution, +10% maximum hit points, a +1 Sacred bonus on all saves, 10 physical resistance, and a 10% bonus to Armor Class from armor and shields. You also gain a 25% Sacred bonus to threat generated with your melee attacks. While in this stance, you move 10% slower.

Defender of Siberys II: Improved Defensive Stance You may expend a Paladin armor boost to become a bastion of defense, gaining a +4 Sacred bonus to Strength and Constitution, +15% maximum hit points, a +2 Sacred bonus on all saves, 25 physical resistance, and a 20% bonus to Armor Class from armor and shields. You also gain a 50% Sacred bonus to threat generated with your melee attacks. While in this stance, you move 10% slower.

Defender of Siberys III: Superior Defensive Stance You may expend a Paladin armor boost to become a bastion of defense, gaining a +6 Sacred bonus to Strength and Constitution, +20% maximum hit points, a +3 Sacred bonus on all saves, 45 physical resistance, and a 40% bonus to Armor Class from armor and shields. You also gain a 75% Sacred bonus to threat generated with your melee attacks. While in this stance, you move 10% slower.

(Class) Armor Class Boost I Activate this ability to receive a +5 Action Boost bonus to Armor Class for 20 seconds.

(Class) Armor Class Boost II Activate this ability to receive a +10 Action Boost bonus to Armor Class for 20 seconds.

(Class) Armor Class Boost III Activate this ability to receive a +15 Action Boost bonus to Armor Class for 20 seconds.

(Class) Armor Class Boost IV Activate this ability to receive a +20 Action Boost bonus to Armor Class for 20 seconds.

Armor Tiers
Code:

 			AC	Max Dex	Level
HEAVY ARMOR
(Heavy Plates)
Full Plate		8	1	1 to 7
Battle Plate		12	1	8 to 13
Magecraft Plate		16	1	14 to 19
Mountain Plate		20	1	20 to 24
Planeforged Plate	24	1	25
 	 	 	 	 
(Light Plates)
Light Plate		7	2	1 to 7
Light Battle Plate	10	3	8 to 13
Light Magecraft Plate	13	4	14 to 19
Light Mountain Plate	17	5	20 to 24
Light Planeforged Plate	21	6	25
 				
MEDIUM ARMOR
(Breastplates)
Breastplate		6	3	1 to 7
Battle Breastplate	8	4	8 to 13
Magecraft Breastplate	11	5	14 to 19
Mountain Breastplate	14	6	20 to 24
Planeforged Breastplate	18	7	25	
 	 	 	 	 
(Scalemail)				
Scalemail		5	4	1 to 7		
Skirmish Scalemail	6	6	8 to 13	
Feycraft Scalemail	8	8	14 to 19	
Spiritcraft Scalemail	11	10	20 to 24	
Celestial Scalemail	15	12	25		
 	 	 	 	 
LIGHT ARMOR		 	 	 
(Chainmail)				
Chainmail Shirt		4	5	1 to 7
Skirmish Chainmail	5	7	8 to 13		
Feycraft Chainmail	7	9	14 to 19	
Spiritcraft Chainmail	9	11	20 to 24	
Celestial Chainmail	12	13	25		
 	 	 	 	 
(Leathers)				
Leather Armor		3	6	1 to 7
Skirmish Leather	4	8	8 to 13		
Feycraft Leather	5	11	14 to 19	
Spiritcraft Leather	7	14	20 to 24	
Celestial Leather	9	18	25		
 	
(Shields) 	 	 	 
Light Shield		2	-	1 to 7
Light Darkwood		3	-	8 to 13
Light Densewood		4	-	14 to 19
Light Spiritcraft	5	-	20 to 24
Light Celestial Shield	6	-	25

Heavy Shield		3	-	1 to 7
Heavy Darkwood		4	-	8 to 13
Heavy Densewood		5	-	14 to 19
Heavy Spiritcraft	7	-	20 to 24
Heavy Celestial Shield	9	-	25

Tower Shield		4	2	1 to 7
Battle Shield		6	2	8 to 13
Magecraft Shield	8	2	14 to 19
Mountain Shield		10	2	20 to 24
Planeforged Shield	12	2	25

Things we're still watching:
Monks and monk splashes. Further changes may be made to the Monk class to give them a more evasive feel and to improve their defensive ability if it is deemed too weak.

[bwoneill]

Aw man, they just give you the formula. What's the fun in that?
Thanks Nyvn, the second post clears up everything.

[Nyvn]

Well, you could always check it?