Calculating stats and their effects

freehugs9 · May 2013

This post is intended to compile the formula behind Neverwinters stats and effects for use in theorycrafting.
Last updated 2013-07-29, may not be updated from this point.

Power
Power Tooltip = Power*0.04
This formula is largely irrelevant, you can convert power directly to ability damage without multiplying it by 0.04 first.
The power coefficient varies per damaging ability (see Abilities Damage) but they all scale in a linear way with one exception that I've found so far: the Control wizards Ice Storm has diminishing returns from power.
Therefore the value of power depends on the abilities you're using and how often you use them.

Critical Strike
Critical Chance Tooltip = 28.8*CriticalStike^1.2/(LevelConstant+CriticalStrike^1.2)
Critical Chance % = 0.05+StatBonus+FeatBonus+0.288*CriticalStike^1.2/(LevelConstant+CriticalStrike^1.2)
...where the level constant for level 60 is between 10185 and 10187.

Armor Penetration
Armor Penetration Tooltip = 35.72*ArmorPenetration^1.88/(LevelConstant+ArmorPenetration^1.88)
Targets Mitigation % = Mitigation-StatBonus-ArmorPenetrationTooltip*(1+FeatBonus)
...where the level constant for level 60 is between 1225377 and 1225660.
Your % of Armor Penetration subtracts directly from the targets mitigation to a minimum of 0 mitigation. Abilities effects stack, are applied after Armor Penetration and can reduce the targets mitigation into negative numbers. See PvE mitigation info in post #2.

Recovery
Recovery Tooltip = 36*Recovery^1.5/(LevelConstant+Recovery^1.5)
Encounter Ability Cooldown Time = InitialCooldownTime/(1+StatBonus+FeatBonus+0.36*Recovery^1.5/(LevelConstant+Recovery^1.5))
Action Point Gain % = 1+StatBonus+FeatBonus+0.36*Recovery^1.5/(LevelConstant+Recovery^1.5)
...where the level constant for level 60 is between 102309 and 102311.

Defense
Defense Tooltip = 49.99*Defense/(LevelConstant+Defense)
Damage Resistance % = (0.005*(ArmorClass-10)+0.4999*Defense/(LevelConstant+Defense)*(1+FeatBonus))+AbilityBonus
...where level constant for level 60 is 1643.6.
The combined Damage Resistance from AC, Defense and abilities cap at 80% mitigation, with the exception of those abilities that always mitigate 100% of the damage.

Deflect
Deflect Tooltip = 30.8*Deflect^1.4/(LevelConstant+Deflect^1.4)
Deflect Chance % = StatBonus+0.308*Deflect^1.4/(LevelConstant+Deflect^1.4)
Deflected Amount = 50% of damage remaining after Damage Resistance is applied.
...where level constant for level 60 is between 41957 and 41977.
Deflection is not affected by the 80% Damage Resistance cap mentioned above and as such can increase total mitigation to 90% on deflected attacks.

Regeneration
Regeneration Tooltip = 20.77*Regeneration^1.3/(LevelConstant+Regeneration^1.3)
% of Lost Health Regenerated Every 3 Seconds = 0.2077*Regeneration^1.3/(LevelConstant+Regeneration^1.3)
...where the level constant for level 60 is 12938.
Regeneration heals a % of the health you have lost, not your total health. It is also capped at 50% health lost, so you will never gain more than half the amount on the tooltip.

Life Steal
Life Steal Tooltip = 20.5*LifeSteal^1.3/(LevelConstant+LifeSteal^1.3)
% Of Damage Gained As Hit Points = 0.205*LifeSteal^1.3/(LevelConstant+LifeSteal^1.3)
...where the level constant for level 60 is between 12710 and 12713.

Movement
Movement Tooltip = 31*Movement^1.4/(LevelConstant+Movement^1.4)
Run Speed % = 1 + 0.31*Movement^1.4/(LevelConstant+Movement^1.4)
...where the level constant for level 60 is between 42286 and 42340.

Ability Damage
Abilities Damage Tooltip Minimum = (BaseDamage+Power*PowerCoefficient+MinWeaponDamage*WeaponCoefficient)*(1+StatBonus)*(1+FeatBonus)*(1+BonusFrom#OfPoints)
Abilities Damage Tooltip Maximum = (BaseDamage+Power*PowerCoefficient+MaxWeaponDamage*WeaponCoefficient)*(1+StatBonus)*(1+FeatBonus)*(1+BonusFrom#OfPoints)
Abilities Minimum Damage = (BaseDamage+Power*PowerCoefficient+MinWeaponDamage*WeaponCoefficient)*(1+StatBonus)*(1+FeatBonus)*(1+BonusFrom#OfPoints)*(1-TargetsMitigation)
Abilities Maximum Damage = (BaseDamage+Power*PowerCoefficient+MaxWeaponDamage*WeaponCoefficient)*(1+StatBonus)*(1+FeatBonus)*(1+BonusFrom#OfPoints)*(1-TargetsMitigation)
The BaseDamage, PowerCofficient and WeaponCoefficient varies per damaging ability, and there are some rare exceptions where the scaling in non-linear (just Ice Storm so far).

Critical Severity and Combat Advantage
Critical Severity = 0.75 + RaceBonus + FeatBonus + AbilityBonus
Critical Strike Damage = AbilitiesDamage*CriticalSeverity
Combat Advantage Damage = AbilitiesDamage*(1+0.15*(1+StatBonus))
Critical and Combat Advantage Damage = AbilitiesDamage*((1+0.15*(1+StatBonus))+CriticalSeverity)

The information above is a work in progress. You can help with this project by:
1) Posting your tooltip information if you have large amounts of Life Steal or Movement.
2) Posting your tooltip information of any stat that does not fit a formula.
3) If you're not a Control Wizard, see if you can fit a Power Coefficient and Weapon Damage Coefficient to all your abilities.

There is a combat log parsing program here:
http://www.reignofelysian.com/forum/showthread.php?105-Neverwinter-Combat-Log-Parser

freehugs9 · May 2013

Mitigation and Armor Penetration in Tier 1 and Tier 2:
Enemies are Level 62 in Tier 1 and level 65 in Tier 2. This does not affect their mitigation.
(Have not yet tested Castle Never)

Bosses 24% mitigation
Brutes 20% or 22% mitigation
Strikers and Leaders 16.2% or 18% mitigation
Minions 14.4% mitigation
Controllers and Ranged Strikers 12.8% or 14% mitigation

So in PvE Armor Penetration starts to soft cap at 12.8% and hard caps at 24%. Other effects that reduce the targets mitigation don't seem to have a cap, I've so far seen enemies go as low as -132% defenses (2.32 times base damage).

Some ability scores are additive to you Armor Penetration %, for Great Weapon Fighters it's Con and for Guardian Fighters it's Dex. They reduce an enemies mitigation by an additional 1% per point of Con (GWF) or Dex (GF) over 10.

Example:
Tier 2 boss, 24% mitigation. You have 15 Constitution on your Great Weapon Fighter so that reduces his mitigation to 19%.
=24-(15-10)

You also have 1853 Armor Penetration? Great, that's another 19% reducing the bosses mitigation to 0.
=24-(15-10)-35.72*ArmorPenetration^1.88/(1225520+ArmorPenetration^1.88)

Your enemies in PvE have mitigation ranging from 12.8% (e.g. archer trash mobs) to 24% (e.g. all bosses), so how much Armor Penetration do you need?

For every class except GWF and GF, between 1271 and 2536 for 12.8% to 24%
Con (GWF) or Dex (GF) of 15, between 879 and 1854 for 12.8% to 24%
Con (GWF) or Dex (GF) of 16, between 802 and 1747 for 12.8% to 24%
Con (GWF) or Dex (GF) of 17, between 724 and 1646 for 12.8% to 24%
Con (GWF) or Dex (GF) of 18, between 643 and 1550 for 12.8% to 24%
Con (GWF) or Dex (GF) of 19, between 559 and 1459 for 12.8% to 24%
Con (GWF) or Dex (GF) of 20, between 467 and 1371 for 12.8% to 24%
Con (GWF) or Dex (GF) of 21, between 364 and 1287 for 12.8% to 24%
Con (GWF) or Dex (GF) of 22, between 233 and 1206 for 12.8% to 24%
Con (GWF) or Dex (GF) of 23, between 0 and 1126 for 12.8% to 24%
Con (GWF) or Dex (GF) of 24, between 0 and 1048 for 12.8% to 24%
Con (GWF) or Dex (GF) of 25, between 0 and 971 for 12.8% to 24%

Additionally the Great Weapon Fighter Heroic Feat called Constitution Focus gives a 15% bonus to their Armor Penetration bonus from Constitution. e.g. 15 Con gives 5.75% Armor Penetration instead of 5%.

Block Mechanics for Guardian Fighter

Holding the Shift key raises your shield to protect your Guardian Fighter in a 180 degree arc centered slightly forward from the center of the character.
You need to face the point of origin of an attack to block it, which will be the center point of some AoE attacks.
While blocking you can only attack with left click (Stab) and right click (Shield Slam).
The Guard Meter to the left of your character indicates how much damage you can block, an amount roughly equal to a quarter of your unmodified health, plus any bonuses to your Guard Meter.
Increasing your health does not increase the amount you can block.
If the Guard Meter is reduced to empty you take any excess unblocked damage and can no longer block.
The Guard Meter starts to recharge after 3.5 seconds of not blocking an attack, unless the Guard Meter is broken in which case it takes 6.5 seconds.
Once it starts recharging the Guard Meter recharges from empty to full in 16 seconds.
Your Damage Reduction is applied before the blocked amount is subtracted from the Guard Meter.
Blocked attacks can Crit but are never Deflected.
Attacks with a red indicator are blocked with an additive 50% bonus to damage reduction, up to the 80% damage reduction cap.
Very large attacks can remove at most 18% of your Guard Bar, giving you the capacity to block about five and a half very large attacks regardless of how big they are.
Blocking an attack prevents that attacks effects (e.g. stun) from affecting you. There are some exceptions though like the Wright Commanders life steal.
The Iron Warrior ability recharges the Guard Meter in 3.5 seconds from 1% to 100%, or if the Guard Meter is broken, from 0% to 50%.
The Enforced Threat ability regenerates 20% of your Guard Meter over 8 seconds.

Block is not reported accurately in the Combat Log which makes it difficult to test so some of the numbers above are approximate rather than exact, although they are still accurate enough to be useful.
Lord Gallen the combat designer has reported that both Shield Talent and Sheildmaster are working correctly, with the following quirks:
Since the amount of the Guard Meter removed from blocking very large attacks is a capped percentage (~18%), increasing the size of the Guard Meter does not improve the number of very large attacks you can block. They will still cap at 18% of the new total.
While Shieldmaster does work, it in not actually bound to Shield Talent. You do not need Shield Talent to gain this bonus.

Stealth Mechanics for Trickster Rogue
(Mostly stolen without permission from l0th4ri0 HERE)

The Stealth Bar to the left of your character indicates how long you can Stealth and when Stealth can be used.
Pressing Tab activates Stealth if the Stealth Bar is full.
Activating Stealth will make you invisible to most enemies in PvE, invisible at range in PvP, and you will show as a silhouette to any player facing you at close range.
Once Stealth is activated it will drain your Stealth Bar over 5 seconds (6 seconds with the Improved Cunning Sneak feat).
While stealth is active taking damage and activating most Encounter or Daily powers will drain a portion of your Stealth Bar (see exceptions below).
At-Will powers can be used freely while Stealthed.
Once drained your Stealth Bar takes 5 to 6 seconds to recharge.
While Stealth is recharging taking damage will drain a portion of your Stealth Bar.
The Stealth Bar cannot be diminished by damage once it is full.
The Twilight Adept feat restores 10% of your Stealth Bar when you dodge.
The Class Feature Tenacious Concealment reduces the loss of Stealth from incoming damage by up to 90%.
The Class Feature Invisible Infiltrator refills your Stealth Bar when you activate a Daily power.
The At-Will power Gloaming Cut restores 25% of your Stealth Bar when you kill an enemy with it, and restores 10% per hit with the Sneaky Stabber feat.
The Encounter power Bait and Switch can be used during Stealth to refill your Stealth Bar.
The Encounter power Shadow Strike refills your Stealth Bar.
The Daily power Lurker's Assault causes your Stealth Bar to rapidly recharge for 10 seconds, often allowing you to take damage and/or use Encounter powers without draining your Stealth Bar.

freehugs9 · May 2013

Reserved for possible future expansion into abilities power and weapon coefficients.

onodrak · May 2013

Nice work, I was going to start a thread like this eventually if someone else didn't. I think I have all of the CW base damage, and I also found out the weapon you start level 1 with seems to be the weapon without power, if you want to get accurate coefficients. I can't be arsed to level another wizard though...

If you want some raw data, Level 60 Human Wizard, 'un-specd'. Tooltip data only. (Ray of Frost tooltip is 'power bugged')

STR	CON	DEX	INT	WIS	CHA		Wpn Min	Wpn Max	Gear Score	Armor Class		Power	p+	Crit Strike	ArmorPen	Recovery	Defense	Deflect	Regen	Life Steal	Move		Atk/Heal	Crit Chance%	Crit Sev%	ArP%	Recharge%	Action Point%		Protection	DR%	Deflect%	Deflect Sev%	Hp Regen%	Leach%		Run%	Mount		MM Min	MM Max	RoF Min	RoF Max	ChillS Min	ChillS Max	ChillS CD	IceS Min	IceS Max	CoI Min	CoI Max	CoI CD	Entangle Min	Entangle Max	Entangle CD	AS Min	AS Max	OpF Min	OpF Max	Repel Min	Repel Max	Repel CD	Cloud Min	Cloud Max	Shield CD	Terrain Min	Terrain Max	Terrain CD	Storm Min	Storm Max	Storm CD	Pilar Min	 Pilar Max	RoE Min	RoE Max	RoE CD	Knife Min	Knife Max	Rays Min	Rays Max	Rays CD	Time Min	Time Max	Time CD	Avalanche Min	Avalanche Max	Avalanche CD	Chaos Min	Chaos Max
9	11	11	16	13	17		0	0	0	10		0	0	0	0	0	0	0	0	0	0		0	12	75		9	3		0	0	0.5	50	0	0		0	0		50	50	37	37	263	263	11.9	502	502	48	48	16.5	169	169	18.3	346	346	338	338	135	135	10	36	36	18.3	27	27	17.4	406	406	9.1	7	7	271	271	12.8	677	677	135	135	18.3	135	135	20.1	203	203	18.3	503	503
12	14	14	23	19	21		0	0	0	10		0	0	0	0	0	0	0	0	0	0		0	16	75		22	9		0	0	2	50	0	0		0	0		53	53	40	40	281	281	10.6	535	535	51	51	14.7	180	180	16.3	369	369	361	361	144	144	9	38	38	16.3	28	28	15.5	433	433	8.1	7	7	289	289	11.4	722	722	144	144	16.3	144	144	18	216	216	16.3	503	503
9	11	11	16	13	17		0	0	389	14		158	6.3	0	0	0	73	158	0	0	0		158	12	75		9	3		231	4.1	1.4	50	0	0		0	0		52	52	37	37	277	277		528	528	50	50		179	179		346	346	359	359	143	143		38	38		28	28		430	430		7	7	287	287		718	718	143	143		143	143		209	209		503	503
9	11	11	16	13	17		0	0	2298	14		579	23.2	237	0	665	421	158	0	238	137		1481	13.9	75		14.2	8.3		817	12.2	1.4	50	0	1.8		0.7	0		60	60	37	37	315	315		600	600	57	57		206	206		346	346	412	412	165	165		44	44		33	33		495	495		7	7	330	330		825	825	165	165		165	165		225	225		503	503
9	11	11	16	13	17		338	413	1123	10		968		0	0	349	0	0	0	0	0		1123	12	75		11.2	5.2		0	0	0.5	50	0	0		0	0		209	241	145	169	1102	1269		2099	2418	201	232		714	822		1314	1529	1429	1644	571	657		152	175		114	131		1715	1973		30	35	1143	1315		2859	3289	571	657		571	657		820	949		1940	2259
9	11	11	16	13	17		188	230	634	10		564		183	0	0	0	0	0	0	0		634	13.4	75		9	3		0	0	0.5	50	0	0		0	0		139	157	97	111	733	827		1397	1575	134	151		475	535		886	1007	950	1070	380	428		101	114		76	85		1140	1284		20	23	760	856		1901	2141	380	428		380	428		548	620		1305	1483
9	11	11	16	13	17		216	264	741	10		659		0	0	0	0	214	0	0	0		527	12	75		9	3		214	0	1.8	50	0	0		0	0		153	173	106	121	803	910		1530	1733	146	166		520	589		965	1102	1041	1178	416	471		111	125		83	94		1249	1414		22	25	833	942		2082	2357	416	471		416	471		599	682		1421	1625
9	11	11	16	13	17		626	765	1767	10		1312		252	108	252	0	0	0	0	0		1662	14	75		10.4	4.4		106	0	0.5	50	0	0		0	0		338	397	236	281	1775	2085		3381	3972	324	381		1149	1349		2140	2539	2299	2698	919	1079		245	287		183	215		2759	3237		50	59	1839	2158		4598	5396	919	1079		919	1079		1329	1568		3166	3758
9	11	11	16	13	17		626	765	4066	14		1891	75.6	489	108	917	421	158	0	238	137		3143	16.1	75		16.7	10.9		923	12.2	1.4	50	0	1.8		0.7	0		348	407	236	281	1827	2137		3480	4070	333	390		1186	1385		2140	2539	2373	2771	949	1108		253	295		189	221		2847	3326		50	59	1898	2217		4746	5543	949	1108		949	1108		1351	1590		3166	3758
9	11	11	16	13	17		626	765	4963	16		2125	85	489	276	1309	518	0	0	238	137		3937	16.1	75		20.4	14.7		1027	15	0.5	50	0	1.8		0.7	0		351	411	236	281	1847	2157		3519	4110	337	394		1201	1400		2140	2539	2402	2801	961	1120		256	298		192	224		2883	3361		50	59	1922	2241		4805	5602	961	1120		961	1120		1360	1599		3166	3758
9	11	11	16	13	17		626	765	5884	16		2241	89.6	489	276	1961	565	0	0	238	108		4705	16.1	75		25.5	20		1180	15.8	0.5	50	0	1.8		0.5	0		353	412	236	281	1858	2168		3539	4129	339	396		1208	1408		2140	2539	2417	2816	967	1126		257	300		193	225		2901	3379		50	59	1934	2252		4835	5632	967	1126		967	1126		1365	1604		3166	3758
9	11	11	16	13	17		626	765	6354	16		2347	93.9	489	384	2067	609	0	0	238	108		5025	16.1	75		26.2	20.8		1329	16.5	0.5	50	0	1.8		0.5	0		355	414	236	281	1867	2177	10.2	3557	4147	341	398	14.2	1215	1414	15.8	2140	2539	2431	2829	972	1131	8.7	259	301	15.8	194	226	15	2917	3395	7.9	50	59	1944	2263	11	4862	5659	972	1131	15.8	972	1131	17.4	1369	1608	15.8	3166	3758
11	13	13	22	18	20		626	765	6335	16		2347	93.9	489	384	2067	609	0	0	238	108		5025	19.1	75		37.2	26.6		1311	16.5	1.5	50	0	1.8		0.5	0		375	438	250	297	1973	2300	9.4	3758	4382	360	420	13.1	1284	1494	14.5	2261	2682	2568	2989	1027	1195	8	273	318	14.5	205	239	13.8	3082	3587	7.2	50	59	2054	2391	10.2	5137	5979	1027	1195	14.5	1027	1195	16	1446	1699	14.5	3166	3758
12	14	14	23	19	21		626	765	6327	16		2497	99.9	489	384	2067	759	0	0	238	108		5025	20.1	75		39.2	27.8		1302	18.8	2	50	0	1.8		50.5	50		381	444	252	299	2005	2335	9.3	3819	4448	366	426	12.9	1306	1518	14.3	2281	2706	2612	3036	1044	1214	7.9	278	323	14.3	208	242	13.6	3134	3644	7.1	50	59	2089	2429	10	5224	6073	1044	1214	14.3	1044	1214	15.8	1465	1720	14.3	3166	3758

If that doesn't copy/paste well, let me know.

sanctumlol · May 2013

Great, I've been using %s on my dps spreadsheet because I was too lazy to get the equations for stat to % conversion. https://docs.google.com/spreadsheet/pub?key=0Ar5bzJruCOoOdC11aG5nNnRDdE8xaEdhSVhLMHB0Nmc&output=xls

sanctumlol · May 2013

Are the level constants a range of values because the tooltip only displays one decimal?

starman1111 · May 2013

I love the work you have done here.

What method did you use to ascertain the values above? For example discovering that most of the stat percentages like Critical Strike, Armour Penetration, etc rely on Level Constants and stats raised to a power. I'm impressed.

xilinear · May 2013

Would be good if you can provide the errors on those equations.

theblitzwing00 · May 2013

They stealth nerfed the gear stats at some point from open beta to now. I was keeping a log of the stat numbers in an excel sheet when I started playing so that I could eventually figure how to optimize my gear when I got to level 60. Yesterday I bought a load of uncommon gear from the AH to compile numbers and noticed the discrepancy with my older numbers. From what I can tell Critical Strike, Armor Penetration, Deflection, and Regeneration got nerfed. Some others may have too, but I wasn't keeping track of them that well. Power seems to have stayed the same though.

Here's my current new numbers for your research:
*Per point calculation is just the boost (bonus) amount divided by the points.
** I'm a level 60 Trickster Rogue.

Power	Boost	Per Point
125	5	0.04
250	10	0.04
375	15	0.04
500	20	0.04
1125	45	0.04
1750	70	0.04
2372	94.9	0.040008432
		
		
Crit Strike	Boost	Per Point
225	1.8	0.008
450	3.8	0.008444444
800	6.6	0.00825
1025	8.3	0.008097561
1200	9.4	0.007833333
1375	10.5	0.007636364
1404	10.7	0.007621083
1529	11.4	0.007455853
1654	12	0.007255139
1779	12.6	0.007082631
1904	13.2	0.006932773
		
		
AC Pen	Boost	Per Point
125	0.3	0.0024
250	0.9	0.0036
375	1.9	0.005066667
500	3.2	0.0064
675	5.2	0.007703704
850	7.4	0.008705882
1065	10.2	0.009577465
1290	13	0.010077519
1640	16.9	0.010304878
1865	19.1	0.010241287
		
		
Recovery	Boost	Per Point
125	0.5	0.004
250	1.3	0.0052
375	2.4	0.0064
500	3.5	0.007
675	5.3	0.007851852
850	7	0.008235294
1075	9.2	0.00855814
1300	11.3	0.008692308
1650	14.2	0.008606061
1865	15.9	0.008525469
		
		
Defense	Boost	Per Point
134	3.8	0.028358209
268	7	0.026119403
469	11.1	0.023667377
603	13.4	0.022222222
640	14	0.021875
768	15.9	0.020703125
897	17.6	0.019620959
1026	19.2	0.01871345
1155	20.6	0.017835498
1335	22.4	0.016779026
1515	24	0.015841584
		
		
Deflect	Boost	Per Point
125	0.3	0.0024
250	0.9	0.0036
375	2.7	0.0072
600	4.8	0.008
815	6.8	0.008343558
1165	9.8	0.008412017
1390	11.5	0.008273381
1565	12.8	0.008178914
1740	13.9	0.007988506
1865	14.6	0.007828418
		
		
Regen	Boost	Per Point
175	1.2	0.006857143
350	2.8	0.008
475	3.9	0.008210526
600	5	0.008333333
825	6.7	0.008121212
1175	8.9	0.007574468
1400	10.1	0.007214286
1625	11.1	0.006830769
1750	11.6	0.006628571
1875	12.1	0.006453333
1975	12.4	0.006278481
		
		
L. Steal	Boost	Per Point
204	1.5	0.007352941
554	4.6	0.008303249
779	6.4	0.008215661
1004	7.9	0.007868526
1129	8.7	0.007705934
1254	9.4	0.007496013
1404	10.1	0.007193732
1554	10.8	0.006949807

Here's a comparison of my new and old numbers for Critical Strike, Armor Penetration, Deflection, and Rengeration:

OLD		
Crit Strike	Boost	Per Point
55	0.7	0.012727273
196	2.8	0.014285714
306	4.4	0.014379085
416	6	0.014423077
477	6.8	0.014255765
522	6.9	0.013218391
542	6.8	0.012546125
702	7.3	0.01039886
864	8.1	0.009375
		
NEW		
Crit Strike	Boost	Per Point
225	1.8	0.008
450	3.8	0.008444444
800	6.6	0.00825
1025	8.3	0.008097561
1200	9.4	0.007833333
1375	10.5	0.007636364
1404	10.7	0.007621083
1529	11.4	0.007455853
1654	12	0.007255139
1779	12.6	0.007082631
1904	13.2	0.006932773
		
===========================		
		
OLD		
AC Pen	Boost	Per Point
70	0.2	0.002857143
179	1.4	0.007821229
200	1.4	0.007
		
NEW		
AC Pen	Boost	Per Point
125	0.3	0.0024
250	0.9	0.0036
375	1.9	0.005066667
500	3.2	0.0064
675	5.2	0.007703704
850	7.4	0.008705882
1065	10.2	0.009577465
1290	13	0.010077519
1640	16.9	0.010304878
1865	19.1	0.010241287
		
===========================		
		
OLD		
Deflect	Boost	Per Point
39	0.3	0.007692308
54	0.4	0.007407407
94	0.9	0.009574468
148	1.6	0.010810811
163	1.7	0.010429448
		
NEW		
Deflect	Boost	Per Point
125	0.3	0.0024
250	0.9	0.0036
375	2.7	0.0072
600	4.8	0.008
815	6.8	0.008343558
1165	9.8	0.008412017
1390	11.5	0.008273381
1565	12.8	0.008178914
1740	13.9	0.007988506
1865	14.6	0.007828418
		
===========================		
		
OLD		
Regen	Boost	Per Point
31	0.3	0.009677419
79	0.9	0.011392405
141	1.9	0.013475177
149	1.8	0.012080537
523	6.8	0.013001912
560	6.8	0.012142857
917	8.9	0.009705562
996	9.3	0.009337349
1139	9.7	0.008516242
		
NEW		
Regen	Boost	Per Point
175	1.2	0.006857143
350	2.8	0.008
475	3.9	0.008210526
600	5	0.008333333
825	6.7	0.008121212
1175	8.9	0.007574468
1400	10.1	0.007214286
1625	11.1	0.006830769
1750	11.6	0.006628571
1875	12.1	0.006453333
1975	12.4	0.006278481

violated87 · May 2013

@theblitzwing00, ratings scale from your level too. It costs more rating to get +1% of a given stat as your level up. It sounds like you were grabbing data points as you were leveling and then compared them to datapoints at level 60, which is why you see differences.

violated87 · May 2013

freehugs9 wrote: »

Critical Severity and Combat Advantage
Critical Strike Damage = AbilitiesDamage*CriticalSeverity
Flanking Damage = AbilitiesDamage*(1+0.15*StatBonus)
Critical and Flanking Damage = AbilitiesDamage*((1+0.15*StatBonus)+CriticalSeverity)

Could you elaborate on Flanking Damage? What is the StatBonus it's being multiplied by? Where does Charisma's bonus come in? I have 21 Charisma which gives +11% Combat Advantage damage. I assumed that meant I would deal an extra 11% damage during combat advantage, but if that formula is correct (assuming "StatBonus" is this bonus from Charisma) then Combat Advantage is completely worthless.

dkcandy · May 2013

If the stats bonus from Combat Advantate & Strength, etc... are doing the same thing as damage resistance, then they would all be worthless.

Someone would just need to test how the stat bonuses are working. If they are a flat +Bonus or if they are a % of the base value. Meaning 10% of 10 = 1 vs. 10% + 10% = 20%

theblitzwing00 · May 2013

violated87 wrote: »

@theblitzwing00, ratings scale from your level too. It costs more rating to get +1% of a given stat as your level up. It sounds like you were grabbing data points as you were leveling and then compared them to datapoints at level 60, which is why you see differences.

If the rating does scale with your level, yeah my old data was taken while I was leveling up. I wasn't aware of that.

freehugs9 · May 2013

Ahhh so much to respond to!

sanctumlol wrote: »

Are the level constants a range of values because the tooltip only displays one decimal?

Yes exactly, and the more data points I get for a given stat the smaller I can make that range. I've tried working out a formula for the level constant but I can never get something that's exact. I believe the true formula may include a small increase at the start of the equation in the format:
Critical Chance Tooltip = (A + level*B)*CriticalStike^1.2/((C+level^D)+CriticalStrike^1.2)
Which makes it brutal to work out, especially when you consider......

starman1111 wrote: »

What method did you use to ascertain the values above?

Trial and error. Seriously it was painful finding formulas that fit. The level constant is apparent when you level up and find that your gear now gives you less benefit (only apparent sometimes because of the rounding). I figured out the basic design of the fomula from the unusual shape of the curve, stats increase in value initially before diminishing.
Y = X^A/(B+X^A).
Other than that, collecting lots of data and plugging in numbers until they worked. I tried doing the same with the level constant but it's super hard and not important enough for the effort. You don't need to min/max your level 10 GWF.

xilinear wrote: »

Would be good if you can provide the errors on those equations.

If you mean data points that don't match the fomulas I don't have any, because when I find one I fix the formula (please send me data points that don't work!). If you mean the tolerances for the constants, I haven't worked them out exactly except for the working range of level constants. Regen, Movement and Life Steal will need a tweak for high amounts if I can get that data, and the exact damage bonus of Combat Advantage is probably within 1% (15% +/- 1%).

freehugs9 · May 2013

violated87 wrote: »

Could you elaborate on Flanking Damage? What is the StatBonus it's being multiplied by? Where does Charisma's bonus come in? I have 21 Charisma which gives +11% Combat Advantage damage. I assumed that meant I would deal an extra 11% damage during combat advantage, but if that formula is correct (assuming "StatBonus" is this bonus from Charisma) then Combat Advantage is completely worthless.

Sorry I should have written Combat Advantage Damage there, Flanking is what the combat log calls it. Fixed!

Combat Advantage Damage = AbilitiesDamage*(1+0.15*StatBonus)

I have 21 Charisma and I'm getting maybe 1% extra DPS from that supposed 11% bonus to Combat Advantage damage. Disappointing isn't it? CA is not useless, it's about 15% more damage, but the CA boost from Charisma sucks e.g. 15% x 11% = 16.65%

xilinear · May 2013

freehugs9 wrote: »

If you mean data points that don't match the fomulas I don't have any, because when I find one I fix the formula (please send me data points that don't work!). If you mean the tolerances for the constants, I haven't worked them out exactly except for the working range of level constants. Regen, Movement and Life Steal will need a tweak for high amounts if I can get that data, and the exact damage bonus of Combat Advantage is probably within 1% (15% +/- 1%).

For Defense I have the same equation, and that fit is so nice, one could consider it the exact formula used by the devs.
For Crit, I have had quite some issues both with my Formula and also with yours. Don't get me wrong, you can fit any equation to any data and that is not the problem. My problem is that there seem to be a cap for crit with your formula at 28.8 which is such a random value that I do not believe this formula to be the actual one used. In my regression, which uses a different equation, I get a nice value of 25%, however, some data points are missed by an error of up to 0.3%. I think some of these need to be revisited with better modelling than what we have got here.

brantson · May 2013

Thanks for listing this.

I'm punching random numbers with your formula, and it's pretty fun. All of the formula looks similar in diminishing values except Power and Armor Penetration. Power is straight forward but Armor penetration is more enigmatic and complex then the other stats.

For starters, armor penetrations seems to become more efficient as you gain more stats due to having (1.225 million level constant) which your math and theblitzwing00's numbers indicate.

theblitzwing00 wrote:

AC Pen Boost Per Point
125 0.3 0.0024
250 0.9 0.0036
375 1.9 0.005066667
500 3.2 0.0064
675 5.2 0.007703704
850 7.4 0.008705882
1065 10.2 0.009577465
1290 13 0.010077519
1640 16.9 0.010304878
1865 19.1 0.010241287

Then I read Trickshaw's post about resistance ignored and how it's suppose to multiply GF and GWF's total armor penetration.

So what he's stating is if you have "10% resistance ignored from Dex or Con" and "20% armor penetration" you end up with approximately of 22% armor penetration or "Armor Penetration+(Armor Penetration*Resistance ignored)"

So presuming both of you guys are right, and I have 6% resistance ignored for my Guardian Fighter. Does this mean I should aim for a total amount of 2070 armor penetration to reach 22% armor penetration, or did I failed middle-school level math?

sanctumlol · May 2013

ArP is S shaped (I forgot what these are called); It has two horizontal asymptotes. To the guy above me: yes, you're correct if 2070 = 20%.

violated87 · May 2013

freehugs9 wrote: »

Sorry I should have written Combat Advantage Damage there, Flanking is what the combat log calls it. Fixed!

Combat Advantage Damage = AbilitiesDamage*(1+0.15*StatBonus)

I have 21 Charisma and I'm getting maybe 1% extra DPS from that supposed 11% bonus to Combat Advantage damage. Disappointing isn't it? CA is not useless, it's about 15% more damage, but the CA boost from Charisma sucks e.g. 15% x 11% = 16.65%

OK I see what you are aiming for here, but that formula isn't actually accurate. 15% x 11% => 0.15 x 0.11 = 0.0165 => 1.65%. You're just taking 11% of 15%. What you are looking for is +11% of 15%, which should be written as 0.15 x (1 + StatBonus). This gives you 0.15 x 1.11 = 0.1665 => 16.65% that you are looking for. The formula should read:

Combat Advantage Damage = AbilitiesDamage*(1+0.15*(1+StatBonus))

freehugs9 · May 2013

xilinear wrote: »

My problem is that there seem to be a cap for crit with your formula at 28.8 which is such a random value that I do not believe this formula to be the actual one used. In my regression, which uses a different equation, I get a nice value of 25%, however, some data points are missed by an error of up to 0.3%. I think some of these need to be revisited with better modelling than what we have got here.

I understand that, but the formula's not wrong just because it's not neat any more than it's correct because it fits the points I have. The important thing is that's working, and the best we have.
That crit formula fits all 23 points I have from level 60, and another 151 points I collected at different levels from 5 to 59. If I find a single point that doesn't fit (after narrowing the level constant), that's when I'll know my formula is wrong and find a better one.

violated87 wrote: »

The formula should read:
Combat Advantage Damage = AbilitiesDamage*(1+0.15*(1+StatBonus))

Yes! Fixed, and thanks.

starman1111 · May 2013

freehugs9 wrote: »

I understand that, but the formula's not wrong just because it's not neat any more than it's correct because it fits the points I have. The important thing is that's working, and the best we have.
That crit formula fits all 23 points I have from level 60, and another 151 points I collected at different levels from 5 to 59. If I find a single point that doesn't fit (after narrowing the level constant), that's when I'll know my formula is wrong and find a better one.

I agree with 'freehugs9' on this one, I have collated from different sources 40 data points for Crit and when I use his formula for level 60 every point faills within +/- 0.05 which is what the tooltip would round to.

It might not look pretty and rounded but it works and actually could be the exact formula that the devs use also. It may be that someone with some math knowledge came up with the basic formula for Diminishing Returns on Stats [Coefficient*StatRating^Power/(LevelConstant+StatRating^Power)] and the devs just change the 3 constants of LevelConstant, the stat coefficient [28.8 for Crit] and the power[1.2 for crit] to balance the stats as they see fit.

freehugs9 · May 2013

Update 2013-05-31: I have just refined the Regeneration formula thanks to some data from Unspecifiederror. Changed the cap from 20 to 21 and adjusted level constant accordingly.
The movement formula still needs data as does the life steal formula for amounts over 1000 but the rest are reasonably refined.

freehugs9 · May 2013

theblitzwing00 wrote: »

Here's my current new numbers for your research...

TheBlitzWing00! I can't believe I didn't look at your numbers sooner. I've just entered them in and thanks to you, refined the level constants for crit, armor penetration, defense, deflect and life steal.
There are two numbers though that don't seem to fit, are you able to double check these two for me?

Deflect Boost
125 0.3
250 0.9

They're both way less than smaller amounts I had already recorded e.g. 116 = 0.6% and 245 = 1.5%.
Yet all your other Deflect numbers fit very neatly.

onodrak wrote: »

If you want some raw data, Level 60 Human Wizard, 'un-specd'....

Onodrak, yes I really do want some raw data and just figured out how to get it usefully into Excel. It will take me some time to go through but thanks.

freehugs9 · June 2013

Update 2013-06-01: Refined the level constant for Movement. It's not pretty accurate up to at least 670 Movement.

starman1111 · June 2013

I have asked anybody who was contributing to a thread I had started about Crit vs Power (http://nw-forum.perfectworld.com/showthread.php?302762-Crit-vs-Power-%28Maths-inside%29) to come and look at your thread and contribute where possible. I think this thread deserves a lot of attention as your work has borne excellent results so far. I am getting a bit busy myself but good luck with it.

starman1111 · June 2013

Hello freehugs9, I have a request of you if you have the time. Of major interest to me are how offensive stats compare to each other in usefulness and how defensive stats compare to each other in usefulness.

Offensively, I have heard that Armor Penetration basically has a hard cap which depends on the specific mob you are facing and as such it is good to get it up to the hard cap and then leave it alone. This leaves Power, Critical and Recovery. Could you please meld the formulas you have developed to show average damage per second as a function of Power, Critical, Recovery, Power Ability Score (changes with class I think), Crit Ability Score (Str I think), Recovery Ability Score (Cha and Int?), Feat Bonuses, Ability Base Damage, Ability Power Coefficient and Ability Weapon Coefficient?

I was planning to do this myself but you have developed such a good model I thought you may want to take it further. From there if you take the derivative of this function with respect to Power, Critical and Recovery you will respectively get the formula of rate of change of average DPS with respect to Power, Critical and Recovery. If you need help with this I am happy to do so.

With these three formula a spreadsheet or webapp can easily be made which will take the player's ability scores and stats as input and produce three numbers (per ability used) indicating how much DPS will be gained for an increase of one point of Power, Crit or Recovery. This would of course need to be in a table of the class's abilities. I am happy to help develop this as a spreadsheet. This would answer the simple (but hard to answer) question that everyone keeps asking, how much power, crit and recovery should I stack?

Similarly, for defensive skills we have defense, deflect and health. From these three terms perhaps you would find the formula which describes effective health (EH) which is basically EH = Displayed Health / (1 - Damage Resistance) / (1 - Deflect Chance * Deflect Amount). From there taking the derivative with respect to Defense, Deflect Chance and Health will give the formulas we need to directly compare these three stats effectively.

Food for thought if you have the time which unfortunately I do not. Also you have done such an excellent job I thought the credit for developing these formula should be yours. Happy to assist at any point though.

freehugs9 · June 2013

Update 2013-06-03: Tested the damage bonus from a feat and found it was multiplicative with the damage bonus from stats. i.e. my 30% bonus to At-Will powers at close range gave me 30% more damage.

Starman, I suppose a full damage/healing/tanking calculator for every class is the ultimate goal but we've still got a way to go before it's viable. I (or someone) still need to test and determine:
1) How different damage boosting feats stack with each other.
2) How the damage bonus from Ranking up an ability stacks with the attribute damage bonus.
3) How much mitigation targets have in different Tiers of PvE and for different classes in PvP
4) Does Armor Penetration apply separately to effects that lower the targets defense? (the hypothesis is that it does but I'm yet to see good testing)
5) How PvE targets greater level interacts with your stats (e.g. is it calculating your crit rate at your level or at the targets level?)
6) Depending the answer to #5 we may need to determine to way stats scale for levels
7) The base damage plus power and weapon damage/healing coefficients for every ability
8) The cast/animation time and base cooldown before Recovery for each ability
9) The Action point gain system for each class
10) The Determination gain for Great Weapon Fighters (I think Trickshaw may have already done this)
11) The Divinity gain for Divine Clerics
12) The way block is built and diminished for Guardian Fighters
13) God knows what else I haven't thought of
(Note: Before anyone starts responding to the things on this list, I'm not interested in opinions only tests and data).

Then if we want to be really clever we'll figure out how threat works and build a database of level 60 gear.

Anyone can build a rough DPS calculator without all of this but it wont be me. I'll be busy slowly ticking things off my list so that other people can make more and more accurate calculators. That's actually my intention here, to enable other people to build better characters and hopefully share their knowledge.

starman1111 · June 2013

freehugs9, I respect the legwork you are doing here and fully understand that you won't take on what i suggested above, I will do it when I get the time.

If you don't mind though, I will most likely come back here when I have done so to ask your opinion and to error-check it, I hope you won't mind. Simply put, I respect your grasp of the game's mechanics that has come from observation, data-collection and model-testing. A sound approach.

freehugs9 · June 2013

Update 2013-06-07: On the second post I've put mitigation info for T1 and T2 dungeons.

Sounds good Starman, but don't get too stuck into it until after the game goes live because there's a class patch/update coming.

o0k1a7h3m0k · June 2013

Just a bump. Good work!

tcorneliu01 · June 2013

regarding stats the most problematic imo to assess is power.
crt and arp is easy because we have a clear relationship between input (points) and output (dmg). But power is still a mystery...

in spite the fact that has the simplest tooltip formula of all.

Calculating stats and their effects

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