Combat stat changes on Isengard release. Mitigation and Offence.

Oct 04 2011 12:10 AM

Below are the changes to stats as far as I can tell, with the launch of Isengard.

Note: This post has been updated to reflect the changes to stats which occured with Update 5 (Dec. 2011).

First a short look at the parts of the Isengard Release Notes (Sept. 2011) where stats are affected:

The caps on the base stats: Might, Agility, Vitality, Will and Fate have been completely removed (were 650).
The caps on Block, Parry, Evade, Incoming Healing and Critical Hit % chance have been increased to 25% (were 15%).
The caps on Outgoing Healing % and Resistance % chance have been increased to 50% (were 30%).
The caps on Offence % have been removed. The offence rating to % conversion has been enhanced (more below).
The caps on Mitigation % have been increased or removed (my own observation) (from 30% for Light Armour, 40% for Medium, 50% for Heavy).

The Mitigation rating to % conversion has been changed from a unique curve to 2: one for heavy armour and one for Medium and Light armour (more below).
Common Damage Mitigation is now built upon a new stat called Physical Mitigation (which is mitigation to player weapon type damage: Beleriand, Westernesse, and Ancient Dwarf).
Shadow, Lightning, Acid, Fire and Frost mitigations now build upon a new stat called Tactical Mitigation (more exactly: Non-Physical Damage Mitgation). Note that Light damage isn't listed, and some people have observed that they don't seem to have much mitigation, if any, to Light damage during the fight with Saruman. This may be a bug.
Mitigation by Source (reducing the incoming damage depending on the type of skill which caused it, irrespective of the type of damage itself), is all but phased out of the game. All pocket items and Virtues which had Melee Defence Rating and Ranged Defence Rating have been converted to Physical Mitigation (which is reduction of damage by type of damage). Similarly, all pocket items and Virtues which had Tactical Defence Rating have been converted to Tactical Mitigation (again, reduction of damage by type of damage). Very few items remain with the old bonuses:
- The Legendary Class Item scrolls which added Melee/ranged/tactical defence rating, are still there.
- The old, now unobtainable, gems and runes (relics) which had those defence ratings, are still there.
- Heavy Shields still have the +10% Ranged Defence bonus (only Guardians can use these now; so basically a Guardian will get 10% less acid damage from an arrow that punctures his neck from the back because he's carrying a heavy shield.)
- Update 5 (Dec. 2011) transformed the LI scroll Defence Ratings to Physical and Tactical Mitigation, as well as Defence Ratings on the old relics. Say bye-bye to Mitigation by Source (only mobs probably have this now).

The game should take into account whatever defence rating you still have from these items.

A new stat was introduced, or rather a counter-stat, called Finesse. It allows the owner to lower the avoidance chances of his enemy. So it will lower your opponent's block, parry, evade (in the case of a melee attack) and resist (in case of a tactical attack) chances. It will also serve mobs and bosses that have Finesse to lower your own avoidances and resistances.

Almost all item bonuses that gave a bonus to a specific resistance type have been changed to give a single bonus to Resistance, a new stat. Wound, Poison, Fear and Disease Resistance Ratings all use the new Resistance Rating stat as their starting value. Class skills or pots can still increase a specific resistance type further.

Almost all item bonuses that gave a bonus to a specific Critical Hit Rating type (melee/ranged/tactical) have been changed to give a single bonus to Critical Rating, a new stat. Melee, Ranged and Tactical Critical Ratings all use the new Critical Rating stat as their starting value. Class skills or traits can still increase a specific Critical rating type further.

Update 5 (Dec. 2011) introduced 2 new stat consolidations: Physical Mastery is a stat which feeds both Melee Offence and Ranged Offence. Tactical Mastery is a stat which feeds both Tactical Offence and Outgoing Healing. All bonuses which used to give Melee or Ranged offence were changed to give both (Physical Mastery). All bonuses which used to give Tactical offence or Outgoing healing were changed to give both (Tactical Mastery), those found on many settings and other relics, to name one example.

All Racial passive traits which used to deduct -8 from a base stat (for example -8 Might for hobbits) now deduct -7 only.
The Elf's total immunities to poison and disease are now a flat 1% rather than a rating of 4 per level. (Iluvatar assures me this was not his will, and that He has commissioned a -20 nerf to Turbine devs which Melchor announces will be coming Soon after beta testing. An enthusiast named JRR insisted on testing the beta).
The Dwarf's Endurance of Stone skill was changed from +75% Common, Shadow and Fire Mitigation to -50% Incoming Melee, Ranged and Tactical Damage. While this, in theory, covers all possible types of damage, it lets in double the damage that the old skill let through for the types of damage it covered. Clearly a nerf in most cases and perhaps no longer a true life-saving emergency skill.

All Passive skills (class enhancements) which you used to buy every odd-numbered level from your trainer (parry, evade, accuracy, etc..) have been removed from the game. To compensate, the base stats now contribute more than they did to parry, evade, etc... (more below). This results in the following changes to a non-equipped (naked, with no traits slotted) level 65 burglar (they depend on class):

Block, Evade, Parry ratings decreased by about 1000-1700
Wound, Fear, Poison, Disease resistances ratings increased by about 150-200 (Yay, now we're all as immune as Elves!)
Common and Tactical Mitigation ratings increased by about 100-200
Outgoing healing rating increased by about 0-350
Critcal Rating (depending on class) decreased by about 500-700
Offence Rating (depending on class) increased by around 0-450
Accuracy, which reduces your chance to miss an attack, decreased to 0 (or whatever accuracy your Agility secretly provides). Note that, while Agility will reduce your chance to miss an attack against an on-level or lower opponent, it will not reduce your chance to miss against higher level opponents. You can, however, still kill a mob that is 7 levels higher than you. But not 8 levels, due to excessive misses.

(Rant time: What is unfortunate is that this is yet another move to make us more dependent on gear bonuses. Don't you miss the base stat bonuses we got on level-up? A bit more morale, might, will, fate, and skill damage? Did anyone ever explain why they stopped giving us those at level 50? I mean, you level up to get better and stronger automatically. That's the reward for levelling up (aside from the pleasure of the process itself). Did they clearly say we'll be getting legendary item improvements instead of character improvements? And that we'll have to destroy our item advancement and start over whereas character stat bonuses would have stayed with us? Levelling feels diminished without those bonuses and fresh new skills. It seems the only purpose of levelling now is getting to the new cap so you can grind for the better gear. It would be interesting to see what base stats we would have had by 75, had those little bonuses continued for the past 25 levels (yes, it'll be 25 whole levels without a single stat improvement!). Then deduct those bonuses we would have gotten in 25 levels from the super-duper armour bonus to see what it's really worth. Or are these the 60 points of base stats being sold in the store now? /Rant off.)

Minstrels cannot wear medium armour any more.

Champions cannot use Heavy Shields any more (but can still use Light ones). They got Bubbles instead. ("Orion nerfed CB!") Edit: Light Shield use was stealthily disabled after a server restart. It's uncertain whether this is final or not.

Runekeepers cannot heal any more. (Just kidding).

Captain's buff IDOME (+50 to all stats) is now a toggle. And they can "block" with a 2-handed weapon (as well as parry).

Loremaster's Ancient Wisdom (+60 Will) self-buff is now permanent (get it from the trainer). Their cure wounds and disease skill no longer gives the group a Resistance buff.

Most Uncommon Armour (green background) has had its armour value increased (apparently by around 20%).

Damage and Healing by class will be affected by the following base stats (more below):

Minstrel: Will for Healing, Tactical and Melee offence
Loremaster: Will for Healing, Tactical and Melee offence
Runekeeper: Will for Healing, Tactical and Melee offence
Captain: Might for Healing, Melee and Tactical offence
Guardian: Might for Melee and Ranged offence, Will for a bit of Healing
Champion: Might for Melee and Ranged offence, Will for a bit of Healing
Warden: Might for Melee and Ranged offence, Will for a bit of Healing and Tactical offence.
Hunter: Agility for Ranged and Melee offence, Will for a bit of Healing
Burglar: Agility for Melee and Ranged offence, Will for a bit of Healing
--- Modifications with Update 5 (Dec. 2011):
Minstrel: Will for Healing, Melee, Ranged and Tactical offence
Loremaster: Will for Healing, Melee, Ranged and Tactical offence
Runekeeper: Will for Healing, Melee, Ranged and Tactical offence
Captain: Might for Healing, Melee, Ranged and Tactical offence
Guardian: Might for Melee and Ranged offence, Will for some Healing and Tactical offence
Champion: Might for Melee and Ranged offence, Will for some Healing and Tactical offence
Warden: Might for Melee and Ranged offence, and for some Healing and Tactical offence
Hunter: Agility for Ranged and Melee offence, Will for some Healing and Tactical offence
Burglar: Agility for Melee and Ranged offence, Will for some Healing and Tactical offence

All base stats and virtues can now be increased through purchases in the in-game store. You can also buy magical scrolls which can summon a relic master, vault-keeper, bard, etc... to keep you company in the wilderness. Tom Bombadil refuses to come and dance for you, for the moment.

Other trivia

A Scroll of Greater Empowerment costs 14,100 shards to make. Or you can buy it from the store (you can also get it using some 6k old skirmish marks, about 840 marks and 65 medallions since Update 5). Now we'll know who the skirmish mark millionaires are. Or just the usual type of millionaires. The new fashionable grind is 12-man skirmishes for Superior 4th marks ("Seals" since the skirmish mark re-hash of Update 5).

Loremasters can rez from a distance of 25m now, and don't need the silly shire tobacco any more. Those using the Cure Resistance Duration legacy are kindly asked to replace this deprecated legacy at their own expense (scrolls of empowerment and all), "at their earliest convenience".

Burglars and Loremasters can daze any and all creatures now.

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OK, now that we're over the stuff which you probably already knew about (not all, I hope), let's go on to some (more) undocumented changes:

Stats and How they are Derived

Code:

Stat Rating            BRG        CPT        CHM        GRD        HNT        LM         MIN        RK         WRD
------------------  ---------  ---------  ---------  ---------  ---------  ---------  ---------  ---------  ---------
- After Update 5 (Dec. 2011):
Melee Offence         10*A       10*M       10*M       10*M       10*A       10*W       10*W       10*W       10*M
Ranged Offence        10*A       10*M       10*M       10*M       10*A       10*W       10*W       10*W       10*M
Tactical Offence       5*W       10*M        5*W        5*W        5*W       10*W       10*W       10*W        5*M
Outgoing Healing       5*W       10*M        5*W        5*W        5*W       10*W       10*W       10*W        5*M
- Before Update 5:
Melee Offence         10*A       10*M       10*M       10*M       10*A       10*W       10*W       10*W       10*M
Ranged Offence        10*A        1*A       10*M       10*M       10*A        1*A        2*A        1*A       10*M
Tactical Offence       1*W       10*M        1*W        1*W        1*W       10*W       10*W       10*W        4*W
Outgoing Healing       5*W       10*M        5*W        5*W        5*W       10*W       10*W       10*W        4*W


Morale                 3*V        3*V        3*V        5*V        3*V        3*V        3*V       3*V         5*V 
ICMR                  1.5*F                        >>
NCMR                  7.2*V                        >>

Power                  3*W                         >> 
ICPR                30*SQRT(F)                     >>
NCPR                  12*W                         >>

Critical Rating     1.75*(A+F)                     >> 
 Melee Critical        CR                          >>
 Ranged Critical       CR                          >>
 Tactical Critical     CR                          >>

Block                  4*M                         >> 
Parry                2*(M+A)                       >>
Evade                  4*A                         >>  (same for all classes)

Resistance           2*(V+W)                       >> 
 Wound Resist.         Res.                        >>
 Disease Resist.       Res.                        >>
 Fear Resist.          Res.                        >>
 Poison Resist.        Res.                        >>

Physical Mitigation  2*(M+V) + 0.2*Armour          >> 
 Common Mitigation     PM + 0.8*Armour             >>
 West/AnDwarf/Beler.   PM                          >>

Tactical Mitigation  4*V + 0.2*Armour              >> 
 SLLAFF Mitigation     TM                          >>

Not dependent on Base Stats:  

Critical Defence       n/a                         >> 
Incoming Healing       n/a                         >>
Finesse                n/a                         >>

Melee Defence          n/a                         >> 
Ranged Defence         n/a                         >>
Tactical Defence       n/a                         >>

Mysterious, secret stats:  

Miss Chance            (A?) 
Tact. Crit Multiplier  (F?)
Melee Crit Multiplier  (?)
Ranged Crit Multiplier (?)
Tact. DevCrit Mult.    (F?)
Melee DevCrit Mult.    (?)
Ranged DevCrit Mult.   (?)

Key: M=Might, A=Agility, V=Vitality, W=Will, F=Fate, CR=Critical Rating, Res.=Resistance Rating, PM=Physical Mitigation Rating, TM=Tactical Mitigation Rating, SLLAFF=Shadow/Light/Lightning/Acid/Fire/Frost, n/a=not dependent on other stats.

Conversion of Ratings to %

Except for Offence Ratings where big changes were made, all previous conversion formulas still hold but only to the old caps. Percent stats which have had their caps increased now use another formula when going beyond the previous cap (read: more rating per % is required beyond the old cap).
Finesse uses the same formula as well, and it seems that it has a cap of 50%.

The conversion of rating to % after Isengard uses this general formula:

% = Yo + 1/[1 + K/(R/L - Xo)]

When Xo=0 and Yo=0, it becomes the old formula:
% = 1 / [1 + K/(R/L)] or % = R / (R + KL)
It is of the form: 1 / (1 + K/x)

Where:

R is the Rating to convert
L is the level (generally the opponent's level, except for counter-stats like Critical Defence and Finesse, where I would expect it to be the player's level since it is your opponent who's supposed to convert his ratings after your counter-stat reduces them)
K is a constant which defines the slope of the curve.
Xo is an offset to R/L
Yo is an offset in %

Food for Thought:
It is possible that the ratio R/L in the formula isn't so simplistic. Indeed, if it were so, it would mean you get an advantage or a penalty based on the mob's level alone, independently of your own level. One other possibility is for the R/L ratio to in fact be: R*L1/(L2*L2), where L1 is your level and L2 is the opponents level. I have not made any tests in that direction.
Another possibility is that, at least for some stats, the whole % result is multiplied by L1/L2 to take player level into consideration. For example: % = L1/L2 * 1 / [1 + K/(R/L2)]. This would be transparent to us while looking at the stat tooltips since the opponent level stated there is always equal to our own level.

Important:
The results you calculate with the formulas I list here are in decimal form. I.e. 15.8% will come out as 0.158. If you want the "percentage" value, multiply the result by 100.

Oct 04 2011 12:11 AM

New Mitigation Conversions

Big changes were made to damage Mitigation (reduction):

There is no longer just one formula for all types of mitigations, but 2 curves: One for Heavy Armour classes, and one for Medium and Light Armour classes.
The heavy armour mitigation curve starts off at the old levels, until it reaches 10%, when it switches to a new curve. The new curve is steeper than the old one, producing higher mitigation % per rating for heavy armour classes.
The Medium and Light armour mitigation curve starts off at the old levels as well, until it reaches 20%, when it switches to a new curve. The new curve is less steep than the old one, producing lower mitigation % per rating for medium and light armour classes.
The mitigation curves are valid for all types of damage mitigations: Physical, Common, Tactical, Fire, Lightning, etc...
Although I haven't seen any statements on new Mitigation caps per Armour type, they have certainly been increased, if not removed. (Some people have reported new caps, listed below).
My comments on these changes:

Heavy Armour has more armour value than medium, which has more than light. More armour value equals more mitigation. Putting heavy armour on a separate higher curve gives a double disadvantage to light armour especially, and to medium armour as well. Supposing that they had to raise the curve for heavy armour, why did they have to lower the one for medium and light? This ends up being a triple disadvantage.
Armour is some barrier that stops weapons more or less effectively, i.e. physical hits. Tactical hits (i.e. elemental and magical damage) should not be stopped by heavy armour more than leather or cloth. I would even argue to the contrary in some cases such as heat or electricity in the case of metal. So why are the Tactical mitigation curves being changed this way as well? How does the armour value of armour protect you better from being demoralised by fear of the shadow, for example? And since Tactical Mitigation comes primarily from Vitality and Will, does this change not imply that heavy armour classes have an inherent, hidden, and very substantial, advantage to Vitality and Will as well? If they wanted to include in "heavy armour" an inherent magical shield as well as higher armour value, they could have added a Tactical Mitigation% attribute to armour gear, just as they added Critical Defence to shields at some point. It would have made it clearer to everyone, and would have raised the protests this change deserves.

Here are some graphs that illustrate the differences.

(download)

(download)

Reminder:
All Ratings to % conversions use this general formula:

% = Yo + 1 / [1 + K/(R/L - Xo)]

Light and Medium Armour Mitigation

This is used by Light and Medium armour classes, no matter their level or what armour they're actually wearing, to convert any damage type Mitigation Rating to % (common, fire, shadow, etc...)

There seems to be a cap of 40% for Light Armour mitigation, and 50% for Medium Armour mitigation.

Determine your R/L, then use the values of K, Xo and Yo from the following table:

R/L	K	Xo	Yo	Result Range	Formula
0 - 37.5	150	0	0	0% - 20%	Old
> 37.5	350	37.5	0.20	> 20%	New

If you do not wish to test for R/L and then choose the right formula, the formula to use for L&M Mitigation should be Min(Old formula, New Formula).

Heavy Armour Mitigation

This is used by Heavy Armour classes, no matter their level or what armour they're actually wearing, to convert any damage type Mitigation Rating to % (common, lightning, acid, etc...)

There seems to be a cap of 70% to Heavy armour Mitigations.

Determine your R/L, then use the values of K, Xo and Yo from the following table:

R/L	K	Xo	Yo	Result Range	Formula
0 - 16.667	150	0	0	0% - 10%	Old
> 16.667	150	16.667	0.10	> 10%	New

To calculate the % mitigation in one step without first evaluating R/L, use Max(Old formula, New formula).

An equivalent formula for the new Heavy Mitigation segement (>10%) is: %HMit = 1.125/[1 + 133.333/(R/L)] - 0.025

New Offence Conversions

Equally big changes were made to Offence (% increase in damage) formulas.

All offence sources use the same new curve: Melee, Ranged and Tactical offence.
The "curve" is almost linear. But it isn't. It is composed of 5 segments (at least), each transposed such as to continue the curve in a linear fashion. Each segment covers a range of 20%: 0-20%, 20-40%, 40-60%, etc...
The offence caps have been removed.
I have to wonder why they didn't simply make it linear w.r.t. R/L. Perhaps the bumps make it more exciting.

Here is a graph to illustrate the difference.

(download)

Offence

The formula for offence is the good old rating to % conversion formula, repeated and shifted, with K = 300. It gives 1 error of +/- 0.1 on my data of 153 samples. I have identified five segments but there can be even more. Each segment covers a further climb up the curve of 20% using an R/L range of K/4 (75). Hence, Yo increments by 0.2 and Xo by 75 with each further segment. The 5th and last segment continues the curve beyond 100%.

Determine your R/L, then use the values of K, Xo and Yo from the following table in the general formula:

% = Yo + 1 / [1 + K/(R/L - Xo)]

R/L	K	Xo	Yo	Result Range	Segment
0 - 75	300	0	0	0 - 20%	1
75 - 150	300	75	0.20	20% - 40%	2
150 - 225	300	150	0.40	40% - 60%	3
225 - 300	300	225	0.60	60% - 80%	4
>300	300	300	0.80	>80%	5

You can calculate this in one go without evaluating R/L first, like so: Max(Seg1, Seg2, Seg3, Seg4, Seg5).

A quick and dirty straight line which approximates a large portion of the above bumpy curve (from 0% to 100%) pretty closely is (expect small errors!):

%Offence = 0.002667*R/L + 0.0074

This says that to add 1% to your base damage, you need to increase your Offence Rating by L/0.2667 or 3.75*L, which means increasing your Might (or Agility, or Will, depending on your class) by 0.375*L. For level 75, the required increase in rating is therefore around 281 per %, or 28.1 Might/Agility/Will per %. This applies whatever offence rating (up to 100%) you currently have, since the "curve" is linear. Beyond 100% the curve is non-linear and the segment 5 formula should be used.
(At level 85 you'll need around 31.9 Might/Agility/Will per extra % of Offence below 100%).

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Oct 04 2011 12:12 AM

New BPE % Chance, Critical Hit % Chance, and Incoming Healing % bonus

The previous caps for these was 15%. It was raised to 25%. For a rating which results in less than 15%, the old formulas still hold. For ratings which result in more than 15%, a new formula with a lower slope (needs more rating per percent) must be used. Until you reach the 25% cap where increasing the rating will not increase the %.

Melee, Ranged, Tactical Defence (Mitigation by Source) uses the same conversion formula as BPE%.

Here is a graph showing the new BPE, Crit and Incoming Healing rating conversion functions:

(download)

Reminder:
The general formula for converting Ratings to % after Isengard is:

% = Yo + 1/[1 + K/(R/L - Xo)]

BPE % Chance, Critical Hit % Chance, Melee/Ranged/Tactical Defence, +Incoming Healing % Bonus

As usual, you should calculate your R/L first (your rating divided by the opponent's level), then look up the values of K, Xo and Yo in the following table:

R/L	K	Xo	Yo	Result Range	Formula
0 - 70	396.667	0	0	0% - 15%	Old
70 - 158.15	793.333	70	0.15	15% - 25%	New
> 158.15	---	--	--	= 25%	Cap

*396.667=1190/3; 793.333=2380/3

To calculate this in one go, use: Min(Old formula, New formula, Cap)

You can go above the 25% by getting direct % bonuses, i.e. a bonus which does not add rating, but %.

Critical Defence, the stat which reduces an opponent's chance to critically hit you, gets deducted from the opponent as a rating, before the opponent's Crit rating is converted to a %. The % value displayed in your character panel for Critical Defence is thus exaggerated, as it assumes that *all* of your opponent's crit chances will be negated, and it assumes that your opponent will be of your own level. (It makes sense that your opponent will use your level in the formula when converting his rating to %).

Mitigation by Source (Melee, Ranged, Tactical Defence) found on some older items uses the same formula. This type of mitigation is used by mobs, and is sadly being removed from player equipment and traits.

Partial BPE % Chance, Devastate Critical Hit % Chance

There is a cap of 10%. The conversion rate here has not changed with the expansion.

R/L	K	Xo	Yo	Result Range	Formula
0 - 147.78	1330	0	0	0% - 10%	Old
> 147.78	---	--	--	= 10%	Cap

You can go above the 10% by getting direct % bonuses, i.e. a bonus which does not add rating, but %.
To calculate this in one go, use: Min(Old formula, Cap)

For a comparison of BPE% and Partial BPE% (or Crit% and DevCrit%) on one graph, see here.

Critical Defence also gets deducted as a rating from the opponent's rating, to reduce his chances of landing a devastating crit on you.

(download)

Partial BPE % Mitigation

There is no rating to % conversion for Partial BPE Mitigation.

Partial BPE Mitigation % = Corresponding BPE% chance + 20%

When you partially block, parry or evade, you reduce (mitigate) the damage partially (not totally as in a full BPE). The % of damage mitigated in such cases is equal to your full Block or Parry or Evade % Chance, plus 20%. For example, if you partially evade a hit, and your Evade % Chance is 12%, you will reduce the damage of that hit by 12+20= 32%. But that's not all. You will also reduce that damage by your normal damage mitigation, depending on the damage type. Assume you're hit by a Fire sword in the above example, and that your Fire Mitigation is 25%. After having reduced the damage by 32% due to the partial Evade, you will then further reduce the result by 25%. If the initial damage were 100, your net damage received would be 100*(1-0.32)*(1-0.25) = 51.0; i.e. a net mitigation of 49.0%.
Note: Before Isengard, the two mitigations were added together. This is no longer the case.

There is a cap of 35% to each partial BPE Mitigation (i.e. the game still caps your B/P/E to 15% for the purpose of calculating partial mitigations). This could be a bug, or it could be intentional given that mitigations by damage type seem to have increased. You can go above the 35% by getting direct % bonuses to partial BPE Mitigations (from stances, traits, skills/buffs, relics, etc... depending on your class.)

(download)

Resistance % Chance, +Outgoing Healing % Bonus, Finesse % Chance

There is a cap of 50% on these (was 30%).

As always, determine your R/L then look up your K, Xo and Yo from the following table and use them in the general formula:
% = Yo + 1/[1 + K/(R/L - Xo)]

R/L	K	Xo	Yo	Result Range	Formula
0 - 170	396.667	0	0	0% - 30%	Old
170 - 368.33	793.333	170	0.30	30% - 50%	New
> 368.33	---	--	--	= 50%	Cap

*396.667=1190/3; 793.333=2380/3

You can go above the 50% by getting direct % bonuses, i.e. a bonus which does not add rating, but %.
(I can't think of a way to calculate this in one statement without first evaluating R/L.)

Finesse Rating gets converted to % before being deducted from the opponent's % BPE. I did not see a clear statement that this is also how Finesse affects opponent Resistance, so it may be deducted as a Rating.

Of note is that Resistance and Outgoing Healing got a small boost when being converted from rating to %. But it is nowhere near as high as the boost to Offence. For comparison, here is a graph showing the new Outgoing Healing versus the new Offence conversion curves (bear in mind that they used the same dark blue curve segment before the expansion).

(download)

That's it!

I hope some people will post data points for things not mentioned here so I can update and complete this topic.

If you were interested in this post, then perhaps the subject of Comparing Damage Bonuses reliably will interest you too.

Thanks for reading!

Credits:
I first saw a form of the R/(R+KL) formula posted here by moebius92 and immediately dropped the ones I'd been using. Thanks for that great find moebius!
Many thanks to all the nice people who contributed data in this thread!

Oct 04 2011 09:45 AM

Epic post Alad! This is most helpful, thanks for your efforts, and +rep to you.

Oct 04 2011 09:53 AM

Awesome!

I'm kind of upset Turbine decided to change the curve for different intervals for offence

Oct 04 2011 09:58 AM

Reading this just upgrades my displeasure with the changes, thanks for the info !

Oct 04 2011 10:09 AM

Thanks for the post.

One question:

Originally Posted by Alad.

Mitigation by Source (reducing the incoming damage depending on the type of skill which caused it, irrespective of the type of damage itself), is all but phased out of the game.

Does this work for mobs too?

Oct 04 2011 10:57 AM

Excellent post, OP. This will help jump-start the update of my own charts &etc. Thank you!

Oct 04 2011 03:08 PM

Originally Posted by Alad.

[*] L is the level (generally the opponent's level, except for counter-stats like Critical Defence and Finesse, where I would expect it to be the player's level since it is the mob that converts it.)

This is not correct. L is your level, and not your opponent's level. How your opponent's level figures in is not, as far as I am aware, known, but it is not utilized by using your opponent's level as the level value in the ratings formula.

Test was using heartseeker crits - with all damage buffs running (burn hot + cool burn and strength stance) and with no stance. Since crits are fixed amounts, you can use a small sample to determine the actual damage bonus being used, via, since...

no stance damage number (L) = (1 + damage bonus) * base damage (B)
SS+CB damage number (H) = (1 + damage bonus + 0.6) * B
(H - L) / (0.6) = B
L / B = (1 + damage bonus)

Testing against an on-level 65 wolf confirmed that it successfully recovered my hunter's ranged damage bonus. Testing against a level 65 wolf confirmed that the ratings formula could not be using 66 as the level (even accounting for rounding errors precluded the ratings formula with a level of 66 from being correct).

Note: I really wish people would stop assuming that L was your opponent's level. The ratings formula was derived from looking at the character panel tooltips, and was always your character's level. Assuming that it magically turns into your opponent's level just because it'd be convenient without doing any testing to back it up is just shoddy work.

Oct 04 2011 04:10 PM

For Partial BPE % Chance, and Devastate Critical % Chance, K = 1329.718 ~ 1330?
For everything else (except new Offence and Mitigation), K = 396.643 ~ 1190/3?

Oct 04 2011 04:28 PM

Originally Posted by moebius92

I really wish people would stop assuming that L was your opponent's level. The ratings formula was derived from looking at the character panel tooltips, and was always your character's level. Assuming that it magically turns into your opponent's level just because it'd be convenient without doing any testing to back it up is just shoddy work.

You're right meobius, it is an assumption which I have held for so long, I can't remember if I tested it. It is my own assumption though, irrespective of whether or how others may have reached that same conclusion. I don't take statements posted here for granted and you don't either, I see.

The assumption is based on the fact that L is in the denominator. If it were your own level, it would illogically mean that the higher you are, the lower your damage, the lower your avoidance, the lower your resistance, etc... It doesn't make sense. Assuming the L is your opponent's level make a lot more sense. Even the character panel states something in those lines... "...against level 65 enemies..." your % will be x%. Meaning that at your same level, with your same rating, you will have a different % against enemies of a different level. The formula, and logic, indicate that you will have a lower percent against higher level enemies.

However, if you have tested and come to the conclusion that it's your own level, for all the stats this formula is used in, then I cannot contradict you since I haven't kept any records of whether I've done such tests myself. All I can say then would be the devs have strange logic.

If you can find good arguments why it would make sense for your effectiveness to intrinsically drop as you advance in levels, irrespective of what level mob you're fighting, I would be interested in hearing them.

The formula could contain a term which simply gets eliminated when your level is equal to the opponent's, resulting in R/(R+KL) which, as you say, holds for the numbers displayed in the character panel against enemies of your own level. The new formulas I derived here do only that: they predict with good accuracy the numbers you would see in the character panel for different Ratings, against enemies of your own level.

As to the testing you mention in your post, could there be a typo in what you wrote? Do you mean the second wolf was level 66? I frankly didn't understand what you meant there, nor the proof of it. Your post seems to be missing some words or sentences.

Are you saying your crits on a level 66 were different (probably smaller?) than on the level 65, but that the difference could not be explained by using 66 instead of 65 for L in the offence formula, and in your specific damage calculations?

I don't know if this has any impact on your tests, but the little you wrote suggests that you assume the bonus of 0.6 is added to the offence bonus. I have noticed from very recent testing that this is not the case for RK damage bonuses, where it is (1+offence)*(1+bonus) rather than (1+offence+bonus), at least for the RK skill damage bonuses awarded from traits. However, I know that this is not always the case, since for RK healing, the bonus is added to Outgoing Healing%, which I claim is a bug. Bug or not, the fact is that it could well be that Turbine has not standardised how they accumulate bonuses together. Would your test's conclusions change if the bonuses were accumulated as I suggest instead?

Here's one other recent puzzle I've been seeing on my Burglar's bleeds: The higher the mob's level, the higher the DoT. I'm pretty sure that's something I have never noticed before. What it suggests is that this damage is dependent on the mob's level. And R/(R+KL) wouldn't be able to predict that no matter whose level L is. There is no mention on the bleed skill tooltips either that would make one expect that result.

To conclude, I can't say for certain whose level the L in the R/L ratio is, apart from the fact that it makes sense for it to be your opponent's level, and the tooltip talks about opponent's level. And I'd like to thank you for posting the R/(R+KL) formula on these forums in the first place.

That was most certainly not shoddy work.

Oct 04 2011 04:33 PM

Originally Posted by RtrnofdMax

For Partial BPE % Chance, and Devastate Critical % Chance, K = 1329.718 ~ 1330?
For everything else (except new Offence and Mitigation), K = 396.643 ~ 1190/3?

You should try it yourself and use whatever works for you.

The numbers I list are those that gave the least errors with the hoard of data that I collected over time, and using several classes and levels. They of course assume the Rating is that which is displayed in the character panel, i.e. the rounded numbers. The numbers you mention may be the ones the devs use (I have no idea where they came from), but they know the precise, unrounded, rating values, while we don't.

Oct 04 2011 04:48 PM

Understood. It just doesn't seem game-breaking to have whole numbers. I would imagine they would be able to adjust for this.

Oct 04 2011 05:57 PM

Originally Posted by Fin.

Thanks for the post.

One question:

Does this work for mobs too?

Re: Mitigation by Source (i.e. Melee Defence, Ranged Defence, Tactical Defence)

Edit: Mobs do seem to have Melee Defence, Ranged Defence and Tactical Defence (just rechecked with my Loremaster's "Knowledge of the Loremaster" skill.) No idea if they're being phased out from their stats as well, or they want those nice mitigations to only be available to mobs.

Oct 05 2011 09:44 PM

Added:

Comments on the changes to Mitigation, and especially Tactical Mitigation.
A reminder that you should multiply the formula's output by 100 to get a "percentage"
A linear approximation for the offence conversion formula
A Credits section
Other small details.

Oct 07 2011 04:36 AM

Originally Posted by Starrywisdom

Reading this just upgrades my displeasure with the changes, thanks for the info !

I agree.. Turbine made some bad mistakes with what they did to all of us in this "Expansion"..

Heck, complete re-write!

oh and Like RAD, sorry Character (A) you can't raid with us because your finesse is too low!

Oct 07 2011 05:30 AM

Originally Posted by Alad.

Are you saying your crits on a level 66 were different (probably smaller?) than on the level 65, but that the difference could not be explained by using 66 instead of 65 for L in the offence formula, and in your specific damage calculations?

I don't know if this has any impact on your tests, but the little you wrote suggests that you assume the bonus of 0.6 is added to the offence bonus. I have noticed from very recent testing that this is not the case for RK damage bonuses, where it is (1+offence)*(1+bonus) rather than (1+offence+bonus), at least for the RK skill damage bonuses awarded from traits. However, I know that this is not always the case, since for RK healing, the bonus is added to Outgoing Healing%, which I claim is a bug. Bug or not, the fact is that it could well be that Turbine has not standardised how they accumulate bonuses together. Would your test's conclusions change if the bonuses were accumulated as I suggest instead?

Tactical damage is *weird*. It is, as far as I know, the only type of damage that uses a damage formula of (base damage) * (1 + tactical damage bonus) * (1 + sum of every other damage bonus). The rest of the damage formulas seem to directly add onto the typed damage bonus. Although this wasn't a big deal in the case of my test because everything there was a melee or ranged damage bonus.

What I was doing was measuring my base damage bonus by measuring how much my crits increased when I added a known amount of damage bonus. So, throwing in some actual numbers (and it looks like I've got more complete data for champion using remorseless strikes) - this is pre-RoI, so... 9620 melee offense rating. That gives us 27.2% with a level of 65, and 26.9% with a level of 66. Against a level 65 wolf, in glory (-15%), a crit did 1536, in fervour (+20%) it did 2015, and in no stance, it did 1742. We have a swing of 479 damage over a 35% change in damage bonus - giving us a base damage of 1369 or so. 1742 / 1369 gives us +27.2% which is what the tooltip says we should be getting. In actual practice, due to rounding errors the actual damage bonus could've been anywhere from 26.2% to 28.1% Which unfortunately doesn't make this test good enough to distinguish between 27.2% and 26.9%.

So, now on to the hunter 8580 ranged offense rating - heartseeker crit against a level 66 wolf does 2064, without any damage bonuses. With burn hot and strength stance (+60%), it does 3054 - this gives us a swing of 1650 over a 60% damage bonus, for a base damage of 1650. 2064 / 1650 gives us +25.1%. Again, rounding errors mean this could actually be anywhere from +24.9% to +25.2%. But, a rating of 8580 with a level of 66 gives a damage bonus of +24.6% - just outside of the range. I was actually hoping to use dev crits, because a larger change in damage means a more accurate measurement of the damage bonus, but ... heart seeker wasn't dev critting enough.

I don't think it's fully conclusive, but the level 65 damage bonus was within +24.9% and 25.2% (it was actually +25.0%), while the level 66 damage bonus was not inside the range. It could use a lot more testing, quite frankly (I was in a bored while waiting for RoI phase at that time), which I may or may not do sometime in the future, assuming I can think of a good way to test it in RoI.

Also - are you using curve fitting to figure out the constants? I've always preferred to treat it as a constraint satisfaction problem - i.e., if I have, say, a rating of 402 at level 67, and a percentage of 3.8%, then that percentage can be anywhere from 3.75% to 3.85% depending on rounding, which means the constant is anywhere from 149.8442 to 154. Gather up enough of these intervals, and eventually you've got a very small interval in which the constant can exist - it doesn't get you a single number, necessarily (although I have a tendency to choose the nearest rational on the assumption that the devs are well, choosing rational numbers), but it also guarantees that your constant correctly predicts all of your observed data.

Anyways, a couple other notes you might be able to use - at level 1, ranged offense (and presumably all offenses) has a cap of 20%. Just make an elven hunter. I find this somewhat suggestive given the 20% intervals you've noticed in the offense rating.

Second, both intervals of the armor ratings are actually using the formula of the form r / (r + c * l). (Although for the second interval, you subtract off a fixed amount (based on level) from the rating, and add an equivalent amount to the percentage.)

For heavy armor, the intersection point is 10%, which occurs at a rating of (50 / 3) * level. For some reason the rating is rounded off to the nearest multiple of 5. And then the constant for the second interval is still 150.

As an example, take a level 67 champion, with 11725 common mitigation rating. 50 / 3 * 67 = 1116 2/3, round to the nearest multiple of 5, gives us 1115. 11725 - 1115 = 10610. 10610 / (10610 + 150 * 67) = 51.4% (rounding off), and add the initial 10% intersection point, and we get 61.4% Which exactly matches my recorded tool tip, so that's nice.

For medium and light armor, the intersection point is 20%, which occurs at a rating of 37.5 * level, and again, you round off to the nearest multiple of 5, and this time the constant is 350.

Your heavy armor formula is actually describing this - if you read it as (9 / 8) * rating / (rating + 150 * level / (9 / 8)) - (1 / 8) + 0.10. If you do decent amount of algebra, you can determine that this is equivalent to (rating - (1 / 9) * 150 * level) / (rating - (1 / 9) * 150 * level + 150 * level) + 0.1 - which basically says subtract off (1 / 9) * 150 * level (or (50 / 3) * level) from your ratings, calculate the formula as normal, and then add 10% - which is exactly what you'd do if you had two intervals that met at the 10% point.

I'm beginning to think they used the multi-interval function thing everywhere.

Edit: For completeness' sake, I did test the champion's remorseless strike crit against a level 66 wolf, and that gave me a damage range of +26.6% to +27.8% - which told me that my test wasn't accurate enough to distinguish between level 66 and level 65. Hence, the hunter test.

Further edit: Just checked, because I thought the round to the nearest multiple of 5 thing could have odd effects at lower level, and it doesn't appear to be in play at level 1 (okay, that was capped at 10%), 2, or 10. Also, it appears that you use the function of the armor type that you can potentially wear - captain and guardian were using the heavy armor function, even though they were limited to medium armor.

Further, further edit: Something just occurred to me - my level 1 captain was capped at 10% physical mitigation, which is the intersection point of the two regimes for the heavy armor function. My level 1 hunter was capped at 20% ranged offense, which is the intersection point of the first two regimes of the offense function. So I checked a level 1 minstrel, and his physical mitigation is capped at 20%, which is the intersection point of the two regimes for the light/medium armor function. (On a weird side note, a level 1 dwarf minstrel has a physical mitigation of 20% as well - apparently the racial +1% isn't kicking in?) And just to be complete about things - level 1 hunter's evade caps at 15%. No way to test if the caps for a level 1 for critical hit, outgoing healing, and resistance cap at the end of the first interval of those functions. Still, I'll be entirely unsurprised if they do.

Hopefully a last edit: Light/medium armor intersection point is 20%, not 10%.

Oct 07 2011 03:18 PM

Just wanted to say : wow and thank you for the amazing information!

Oct 08 2011 09:25 PM

Been swamped irl and just getting to the RoI changes. Many thanks to Alad. for this thread and moebius92 for his work as well.

Question/clarification: So now the mechanism of certain mobs being 'weak' to different damage types has been removed? If we assume that mobs/NPC's use the same new combat system that player characters use (I can't imagine it would be different, but one never knows) there is no difference between hitting a mob with the different damage types (i.e. Beleriand/Westernesse/Ancient-dwarf). If this is correct, how sad to lose that bit of 'flavor' and detail. Turbine/WB, please don't dial the dumb-meter all the way to zero!

Comment: I totally agree with Alad. and his rant regarding the removal of level-related passive bonuses. This is obviously a move to make us more dependent on purchased items (stats virtues potions &etc.). But it is what it is, LOTRO has moved to the F2P business model and it's either pay up or leave the game.

Comment 02: Regarding the new armour mitigation system comments by Alad., I agree that this does give heavy armour classes a triple arbitrary advantage. This is not intuitive at all, heavy armour should protect better than medium and light against physical damage, no one would argue that point, but tactical damage should ignore all armour.

Alad. in his comment alluded to the following as well - I used to play a wonderful first-generation MMO named Asheron's Call. By Turbine. In that game, in addition to armour level or rating, different types of armour protected your character against different types of attacks. I can't remeber all the interactions, but for example, Plate armour was great protection against Slashing or Bludgeoning (physical) attacks but not so much vs. Piercing (physical) attacks. And it was weak to Fire or Lightning (tactical) attacks. Chain mail had similar properties but was weaker to Bludgeoning (physical) attacks. Various types of Leather armour (which you would classify as Medium in LOTRO) had better protection vs. Lightning, etc etc. A more detailed combat system along these lines would be welcome and add greatly to the game.

In science fiction writing, there is a saying, there can be no fiction without the science. The same principle applies to LOTRO to any MMO, or indeed to any game; there must be an intuitive, or common sense reason for how the game mechanics work. Outcomes should meet expectations. This increases both immersion and suspension of disbelief, and is what creates hooks for players. More detail makes the game feel more realistic, and attracts the serious player who tends to choose and stay with a game for a longer period of time. Less detail feels simplistic and attracts the more casual player, who will swing in and out of the game. It's a quantity vs. quality issue. OK now /my rant off.

Again, thanks to Alad. for this most excellent post, I look forward to plugging these formulas into my Guardian Gear Grinder and having at it.

Oct 09 2011 08:15 AM

Originally Posted by chazcon3

Alad. in his comment alluded to the following as well - I used to play a wonderful first-generation MMO named Asheron's Call. By Turbine. In that game, in addition to armour level or rating, different types of armour protected your character against different types of attacks. I can't remeber all the interactions, but for example, Plate armour was great protection against Slashing or Bludgeoning (physical) attacks but not so much vs. Piercing (physical) attacks. And it was weak to Fire or Lightning (tactical) attacks. Chain mail had similar properties but was weaker to Bludgeoning (physical) attacks. Various types of Leather armour (which you would classify as Medium in LOTRO) had better protection vs. Lightning, etc etc. A more detailed combat system along these lines would be welcome and add greatly to the game.

The system you've described sounds like it's dependent on the armor makers being too dumb to incorporate leather into plate armor. Or utilizing some sort of non-conductive under layer. Or a non-conductive outer coating.

Oct 09 2011 11:37 AM

I'm looking for some clarification on incoming damage types since I'm trying to decide between several virtues for my characters...

Now, since mobs do not have access to special racial damage types, should it not mean that all incoming physical damage we will ever face is of the common type? As melee/ranged/tactical (by source-damage) is phased out, it means an incoming melee or ranged attack with shadow or fire would go against tactical instead?

This would mean when considering physical mitigation, virtue values of armor and physical mitigation are on equal footing, because they only ever need to work against common damage. Armor is only 20% effective against non-common sources, but there is no physical, non-common source in game. Not even PvMP creeps have beleriand / westernesse / ancient dwarf weapons.

And ultimately, when choosing between physical and armor, if values are equal, armor will trump physical mitigation because it will additionally offer 20% of its value to tactical mitigation.

Am I on the right path here?

Oct 09 2011 02:53 PM

Originally Posted by moebius92

The system you've described sounds like it's dependent on the armor makers being too dumb to incorporate leather into plate armor. Or utilizing some sort of non-conductive under layer. Or a non-conductive outer coating.

Moe, everyone is so gracious to you for your hard numbers work, but you are so harsh on the very people who appreciate you. Perhaps some self-reflection time would be a good thing to mix into your schedule?

More to the point, Middle-earth armourers do not have undergraduate degrees in ceramic-ferrous coatings or electromagnetic conductivity. These are simple medieval craftsmen. Refer back to my rant on common sense.

Oct 10 2011 08:10 AM

Hi!

I have a specific question concerning Mitigation and Resistances with the various damage types. I will use an example:

I have a bow that does 250 Beleriand damage. Now I face an Ancient Evil (susceptible to Beleriand damage type).

That Ancient Evil foe now uses his Common Mitigation to reduce my bow's damage as Beleriand is still considered Common, right?

Now, I put Hunter's Fire Oil on that same bow and use it again against that Ancient Evil. To my best understanding that foe now should use its Tactical Mitigation as Fire is not a Common but Tactical damage type, right?

And what becomes of the Beleriand damage type and the foe's vulnerability against it once the bow is prepared with Fire Oil? Does that Ancient Evil effectively mitigate two types of damage differently but at the same time?

I am a little bit confused. Maybe you could help me out there.

Oct 10 2011 10:04 AM

When you use your Beleriand bow, the mob checks against Physical mitigation, as racial damage is physical, non-common damage. I believe mobs do not have separate armour values, only mitigations, so the rule that armour is only 20% effective on non-common damage is moot here.

Fire is Tactical damage instead of Physical, so if you apply fire- or light-oil, the mob checks against Tactical mitigation.

As far as I get it the summary is:

Physical: Common, non-commons: Ancient Dwarf, Beleriand, Westernesse
Tactical: Fire, Frost, Lightning, Light.

Note that since there are damage types for players only and mobs only, the mitigation lists for us and them (including PvMP creeps) are different. Ie, shadow.

edit - no wait, of course mobs have armour values, since we have skills to reduce that. Unless it simply works as a negative mitigation rating modifier.

Oct 10 2011 10:07 AM

Originally Posted by Maethred

Hi!

I have a specific question concerning Mitigation and Resistances with the various damage types. I will use an example:

I have a bow that does 250 Beleriand damage. Now I face an Ancient Evil (susceptible to Beleriand damage type).

That Ancient Evil foe now uses his Common Mitigation to reduce my bow's damage as Beleriand is still considered Common, right?

Now, I put Hunter's Fire Oil on that same bow and use it again against that Ancient Evil. To my best understanding that foe now should use its Tactical Mitigation as Fire is not a Common but Tactical damage type, right?

And what becomes of the Beleriand damage type and the foe's vulnerability against it once the bow is prepared with Fire Oil? Does that Ancient Evil effectively mitigate two types of damage differently but at the same time?

I am a little bit confused. Maybe you could help me out there.

I'll try to clarify it for you. Anyone correct me if I get some of this wrong.

1 - The effectiveness of common damage types (Beleriand, Westernesse, etc.) is no longer clear in the new post-ROI combat scheme.

The only possibility I can come up with is that Common Damage goes against the Common Damage Mitigation (which is usually the highest Mitigation a mob can have) and Beleriand/Westernesse etc. go against the Physical Mitigation (which is usually the second highest mitigation mobs have).

One would hope that the specific bonuses vs certain mobs are still in effect, but with the changes surrounding common damage/tactical damage mitigations trumping all the previous damage types, I honestly don't think there is any added bonus for using Beleriand damage vs spiders over say Ancient-Dwarf damage.

2 - Adding Fire Oil/Light Oil to your bow transfers your attack skills (not auto-attacks) into Fire or Oil damage. With the new Phys/Tac Mitigations in place, it means your bow is now going against a mob's tactical mitigation. IE, you're doing a lot more damage, since most mobs have lower Tac Mit than PhysMitt

Oct 10 2011 10:55 AM

Originally Posted by Aerundael

2 - Adding Fire Oil/Light Oil to your bow transfers your attack skills (not auto-attacks) into Fire or Oil damage. With the new Phys/Tac Mitigations in place, it means your bow is now going against a mob's tactical mitigation. IE, you're doing a lot more damage, since most mobs have lower Tac Mit than PhysMitt

That was indeed what I was aiming at and what I hoped. To use Fire/Light Oil as a damage enhancer, because of Tactical being the lower Mitigation value of most mobs.

Alas, I fear for Beleriand, Ancient-dwarf and Westernesse. If that be true what Thou sayest the last remnants of those lands and kingdoms long forgotten have now utterly vanished and the Age of Unified Common Damage is dawning fast upon us.

Oct 10 2011 05:46 PM

How is common damage factored against me as a tank?

If some "boss", hits me with "big swipe", for 5000 common damage, what part of my mitigation is doing it's job? My physical mitigation is 41.4%, but my common damage mitigation is 50%. Do I just not pay attention to physical mit if my common is capped at 50%?

Oct 10 2011 06:04 PM

Basically the combat progression is as follows:

1) Miss Chance
2) Resistance (if applicable)
3) BPE (if applicable)
4) Partial BPE and reduction
5) Source-based reduction (Melee, Ranged, Tactical)
6) Damage Type Mitigation

For your example, assuming the boss doesn't miss and his attack can't be resisted, you'd confirm that it hit by checking BPE. After that, it comes down to damage reductions. You would reduce the bosses attack by your melee defence (comes from Class Item scrolls and old relics [e.g. Ancient Rune of Thunder]) and then by your common mitigation. If the damage type was Beleriand, you would use your physical mitigation instead of common. If the damage was from a flaming sword, you will still use your melee defence, but then your tactical mitigation.

The moral of this story is that common and tactical mitigation are extremely important these days.

Oct 10 2011 10:56 PM

Originally Posted by moebius92

[The calculated offence bonus versus level 66] was +25.1%. Again, rounding errors mean this could actually be anywhere from +24.9% to +25.2%. But, a [offence] rating of 8580 with a level of 66 gives a damage bonus of +24.6% - just outside of the range. [The] level 65 damage bonus was [...] +25.0%.

[Reminder: We were discussing whether the L in R/(R+KL) is your level or the opponent's level. You seemed to claim it's your own level. I argued it cannot be. You're relating a test to prove that it can't be the opponent's level.]

What you're basically saying here is that you hit a level 66 with more damage than expected from looking at the Offence% alone (and taking L as the opponent's level). Which would mean it can't be the opponent's level. And that you hit the level 66 wolf with more damage than the level 65 (Which would mean that it can't be your level either

). Or that the damage didn't change between the 65 and the 66 wolf (with you being 65). But it doesn't seem like you to use approximate numbers, so I guess you're not trying to say that (I'm sure you did get different numbers).

This sounds like you may need to try hitting a higher level mob (bigger level difference) to get some more differences to appear, if any. But it also reminds me of what I mentioned in my last post about burg bleed being higher with higher level mobs. Either this is a bug, or there is actually a term in the offence bonus formula which cancels out when you assume your level is the same as the mob's, and which actually tries to compensate for you doing less damage on higher level mobs. For example:

%offence = L/L1 * R/(R+KL), where L1 is your own level and L is the mob's level.
This can also be written as: R/L1 / (R/L + K)

Any formula which resolves to R/(R+KL) when L=L1 could work. Let's try to apply the above suggestion to your test:

Based on crit measurements versus a level 66 mob, you calculated that your offence rating versus that mob should be 25.1%. But your offence rating of 8580 gives 24.7% (not 24.6% btw, unless that's what the actual character panel showed) versus level 66 when using the R/(R+KL) formula for offence with L being the mob's level. The 24.7% doesn't fit in the possible offence range of 24.9% to 25.2%, which takes into account rounding of observed damage numbers (assuming the 60% is a precise number).

If you multiply the 24.7% by 66/65, you'll get 25.1% (or 25.0% if it's 24.6%), exactly what you calculated, and fits nicely within the constraints you found.

This seems to imply that the example formula I wrote above may be what the real offence formula is. But further testing is naturally required, preferably versus even higher level mobs than you, to try and force out bigger differences.

Another one could be: (L+N)/(L1+N) * R/(R+KL)
or (1 + (L-L1)/N)) * R/(R+KL)
or (2 - e^-N(L-L1)) * R/(R+KL) (ridiculous, I know)
or 1/(0.5+0.5/(L/L1)) * R/(R+KL) (hehe)
etc...

Also - are you using curve fitting to figure out the constants?

I look at the pattern and try out different curve forms, let Excel do the curve fitting, and then fine tune it by hand to minimize errors against observed data. The difficulty is in finding the correct form or formula. R/R+KL (which is actually y=1/(1+k/x) ) wasn't that obvious for me. I'm curious to know how you stumbled upon it.

Of course if you know the equations of many different curve forms, it should be easy to recognise it, but this one wasn't part of my repertoire.

For medium and light armor, the intersection point is 20%, which occurs at a rating of 37.5 * level, and again, you round off to the nearest multiple of 5, and this time the constant is 350.

Good catch! I wasn't very satisfied with my power formula, even though it gave very decent results. It was the first one I tackled and so hadn't discovered the repetitive nature of the curves elsewhere, and forgot to go back and visit it. I'll update my post. Thanks.

My heavy armour formula is indeed a shift in both y and x of the same old mitigation formula

You're good at juggling numbers.

The intermediate rounding to the nearest multiple of 5 which you describe can just be an artifact. I think you can ignore it. It could mean they're using numbers which are 5 times smaller, in reality, then multiplying them by 5 to display them to us as ratings. Try to divide the K's and the ratings by 5.

Instead of y = 1 / [1 + K/(R/L)], the second segment equation is: y-Yo = 1 / [1 + K/( R/L - Xo)]. This shifts the curve both to the right by Xo (the R/L where the intersection occurs), and to the top by Yo (the % where the intersection occurs). For Offence, the 3rd and following segments can be built in a similar way. I think you'll find accurate results if you use it as such, without doing intermediate rounding.

So, with your numbers, you also get 61.4% for your level 67 char with 11725 common mitigation (without rounding to the nearest multiple of 5) as follows:
% = 1 / (1 + 150 / (11725/67 - 50/3)) + 0.1 = 61.351% = 61.4%

Also don't forget that those ratings in the character panel are rounded too. For example, Physical and Tactical Mitigation receive 0.2*Armour (there's another multiple of 5 for you

). It's perhaps best to play with common mitigation to hopefully encounter less rounding, since it includes all the armour (even though I doubt ANY number in this game is an integer, even armour.)

I'm beginning to think they used the multi-interval function thing everywhere.

I'm quite certain other formulas haven't changed (ovoidances, resistances, crits, etc...). It's enough to test just 1 point at a high enough level to realise this. (Edit: They seem to have changed as well, but only when you go above the previous % caps).

And yes, I noticed as well that the Heavy armour mitigation curve applies by class, irrespective of level (i.e. even if they can't wear heavy armour yet, which generally comes at level 20). Which makes sense in a way. It avoids them reaching level 20 and suddenly wearing heavy armour (higher armour value) AND being lifted up to the higher curve at the same time. You'd see level 20's running around feeling like supermen! Better tell them the truth starting at level 1! LOL

Thanks for your input, moebious.

Oct 10 2011 11:53 PM

Originally Posted by Maethred

Hi!

I have a specific question concerning Mitigation and Resistances with the various damage types. I will use an example:

I have a bow that does 250 Beleriand damage. Now I face an Ancient Evil (susceptible to Beleriand damage type).

That Ancient Evil foe now uses his Common Mitigation to reduce my bow's damage as Beleriand is still considered Common, right?

Now, I put Hunter's Fire Oil on that same bow and use it again against that Ancient Evil. To my best understanding that foe now should use its Tactical Mitigation as Fire is not a Common but Tactical damage type, right?

And what becomes of the Beleriand damage type and the foe's vulnerability against it once the bow is prepared with Fire Oil? Does that Ancient Evil effectively mitigate two types of damage differently but at the same time?

I am a little bit confused. Maybe you could help me out there.

I think it's quite straightforward: The mob has mitigations against every kind of damage type. Physical Mitigation and Tactical Mitigation don't matter. They're just used by the real damage mitigations, and those do matter.

So against common damage, use common mitigation.
Againt Beleriand, use Beleriand mitigation (which I assume is just equal to the physical mitigation of which it is composed, for players. For mobs, they still should have separate mitigations for all the damage types)
Against fire, use fire mitigation, etc...

To get a hint at what mob stats are like, replay the session-play instance in vol1 where you play as an angmarim and look at the character panel. Or any session play instance, in fact.

Some stats aren't used at all in the final combat calculations as far as I can guess. They're only used to build up the stats that do count. Stats that count (whether for players or for mobs):

Miss % chance, and level-difference miss
Block, Evade, Parry % chances, and their partials % chances and Partial mitigations %
Wound, Fear, Poison, Disease, Cry, Song, Physical, Tactical resist % chances
Finesse % and Finesse Rating
Melee, ranged, tactical crit % chances, dev crit % chances, critical multipliers, devastating critical multipliers
Critical defence Rating (not sure if the % is used)
Offence % bonus, Outgoing healing % bonus, Incoming healing % bonus
Morale, power, and their In-combat regenerations
Common, Beleriand, Westernesse, Ancient Dwarf, Shadow, Light, Lightning, Acid, Fire, Frost % mitigations (mitigation by type)
Melee, Ranged, Tactical defence % mitigations (mitigation by source)

Everything else doesn't matter, including all ratings (except for Finesse Rating and Critical Defence Rating); Might, Agility, Vitality, Will and Fate

; Physical Mitigation and Tactical Mitigation ratings and % (they don't matter, it's the particular damage mitigation which they contribute to, that matters); Resistance rating and % (same here); Critical Rating and % (and same here).

I know, the above is a bit extreme. "Of course ratings do count! How would you get the % otherwise?". I agree

. It's just to stress the fact that, in the very very end, only the % counts. And some skills/traits/equipment do give a direct % bonus. Those are the little gems in the game.

Oct 11 2011 01:57 AM

Originally Posted by chazcon3

Been swamped irl and just getting to the RoI changes. Many thanks to Alad. for this thread and moebius92 for his work as well.

Question/clarification: So now the mechanism of certain mobs being 'weak' to different damage types has been removed? If we assume that mobs/NPC's use the same new combat system that player characters use (I can't imagine it would be different, but one never knows) there is no difference between hitting a mob with the different damage types (i.e. Beleriand/Westernesse/Ancient-dwarf). If this is correct, how sad to lose that bit of 'flavor' and detail. Turbine/WB, please don't dial the dumb-meter all the way to zero!

There should be no change to mobs except the usual: hit more, crit more

And they have finesse now (the better mobs) so you can avoid them less. But they should still have their vulnerabilities, as before. Our (the players') vulnerabilities to Beleriand/Westernesse/Ancient Dwarf damage are the same, and we never knew those before RoI anyway. Strictly speaking, we don't even know them now, since the tooltip doesn't detail their values. But it does say that the new thing called "Physical Mitigation" is the base for those 3 mitigation types, just as it is for common damage mitigation. So it's sane to assume that although not detailed in the tooltip, their values are the same as the base Physical Mitigation. That's not the case for mobs though. They're still more sensitive to certain damage types as you can check with a LM.

Again, thanks to Alad. for this most excellent post, I look forward to plugging these formulas into my Guardian Gear Grinder and having at it.

You're most welcome.

Oct 11 2011 02:13 AM

Originally Posted by Zetsubousensei

I'm looking for some clarification on incoming damage types since I'm trying to decide between several virtues for my characters...

Now, since mobs do not have access to special racial damage types, should it not mean that all incoming physical damage we will ever face is of the common type?

Yes. Damage from mobs. But if you spar, you'll get racial damage (ie Westernesse/Beleriand/Ancient Dwarf). If you're a creep, you will get some too.

As melee/ranged/tactical (by source-damage [mitigation]) is phased out, it means an incoming melee or ranged attack with shadow or fire would go against tactical instead?

More precisely: A melee hit that does fire damage will be mitigated by fire mitigation, just as a tactical spell that does fire damage, or an arrow that does same. And by-source damage mitigation still exists. It's the items and traits that give it that have disappeared, except for a few remaining (the legendary item scroll title, a couple of old runes and old gems). Mobs still have mitigation by source (at least that's what the "Knowledge of the Loremaster" skill reveals.

This would mean when considering physical mitigation, virtue values of armor and physical mitigation are on equal footing, because they only ever need to work against common damage. Armor is only 20% effective against non-common sources, but there is no physical, non-common source in game. Not even PvMP creeps have beleriand / westernesse / ancient dwarf weapons.

Again, yes. If you don't spar you'll probably never get Bel/West/AD damage (unless an orc finds a fancy sword and actually uses it, you never know

). So physical mitigation will serve only for Common mitigation, and Armour (100% of it) will go towards Common, and 20% of it will also go towards tactical damage types (SLLAFF).

And ultimately, when choosing between physical and armor, if values are equal, armor will trump physical mitigation because it will additionally offer 20% of its value to tactical mitigation.

Am I on the right path here?

You are.

Oct 11 2011 02:23 AM

Originally Posted by chazcon3

Moe, everyone is so gracious to you for your hard numbers work, but you are so harsh on the very people who appreciate you. Perhaps some self-reflection time would be a good thing to mix into your schedule?

More to the point, Middle-earth armourers do not have undergraduate degrees in ceramic-ferrous coatings or electromagnetic conductivity. These are simple medieval craftsmen. Refer back to my rant on common sense.

Well, I was thinking either rivet leather armor to plate (which would look ridiculous, but if leather's got better anti-lightning properties than plate, than layering it might help), or use a silk under layer - silk should have a fairly low conductivity, and taut silk apparently makes semi-decent non-rigid anti-arrow armor. (I think there's actually a set of rules in GURPS vehicles about using stretched/taut non-rigid armor as light weight rigid armor. Weird tangent, sorry.)

But what I was really thinking of was the development of the arquebus and plate armor (note, not even an amateur historian, much less an amateur military historian, so it's liable that I've got any number of details wrong). As arquebuses more and more prevalent (and better and better at penetrating plate armor at longer ranges), you see plate armor start to disappear from the battlefield. A lot of this is economics - plate armor is a massive economic investment, but it was used because it provided excellent protection against pretty much any threat the wearer would encounter on the battlefield while still allowing the wearer to present a credible threat. As methods of penetrating plate armor became more and more effective and cheaper (and thus more prevalent), plate armor's usage started to diminish.

Giving heavy armor a similar weakness would imply to me that a similar development would occur - methods that exploit the weak point get weaponized (say fire - and hunters with fire oil), and become more and more prevalent on the battlefield, because heavy armor wearers need to be taken down. As that happens, heavy armor becomes less and less prevalent, because the wearers aren't that much tougher - they just get targeted by the anti-heavy armor weapons, and taken down. One thing that might prevent heavy armor from disappearing from the field (and this gets into simulationist versus gamist things) is that in game heavy armor isn't that much more expensive/hard to produce than lighter armors, so it might stick around. If heavy armor had similar economic costs to plate armor in the middle ages, then I'd expect to see heavy armor disappear from the battlefield, just like plate armor did with the development of gunpowder weapons.

Or, short version - if heavy armor has a weak point, expect weapons development to target it and exploit it - once weapons exploiting the weak point become prevalent, expect heavy armor to disappear, as it effectively provides no additional protection. (Actually, if all armors have the same weak point (tactical damage) - I'd expect all armor based armors to disappear, and we start using the armor slots as ... well, pretty much more jewelery - ignore the armor values, pick the stats.)

Edit: Or another response is armor layering - didn't happen in the case of arquebuses I suspect because "layering" would've been adding more steel.

Oct 11 2011 02:36 AM

Originally Posted by Aerundael

I'll try to clarify it for you. Anyone correct me if I get some of this wrong.

1 - The effectiveness of common damage types (Beleriand, Westernesse, etc.) is no longer clear in the new post-ROI combat scheme.

The only possibility I can come up with is that Common Damage goes against the Common Damage Mitigation (which is usually the highest Mitigation a mob can have) and Beleriand/Westernesse etc. go against the Physical Mitigation (which is usually the second highest mitigation mobs have).

I think you may be mixing things up a bit. Your third paragraph is correct. The second one is not, since there is only 1 type of Common Damage, and that is Common Damage itself. And common damage is a physical type of damage. The other types, Beleriand, etc... are Physical damage types too, but are not of the Common type. (Physical = common, beleriand, westernesse, ancient dwarf, i.e. 4 different damage types). All of the physical damage types will be getting, as their base rating value, the number called "Physical Mitigation". And then each individual damage mitigation will be able to get extra mitigation on top of that base. This is how Armour comes in to add up fully to Common damage mitigation, whereas only 20% of it contributes to Physical mitigation base, and hence to Beleriand/Westernesee/Anc.Dwarf. This is my understanding of it.

One would hope that the specific bonuses vs certain mobs are still in effect, but with the changes surrounding common damage/tactical damage mitigations trumping all the previous damage types, I honestly don't think there is any added bonus for using Beleriand damage vs spiders over say Ancient-Dwarf damage.

I hope the above answer clarifies this point for you too. Mobs that are vulnerable to Beleriand should still be so. And hitting them with Common damage will not be as effective. Get your hands on a couple of cheap legendary swords, and one Beleriand scroll. Hit the spider with common and watch the crit values. Then repeat with Beleriand. That's the only test that would reveal whether the spiders are still vulnerable to beleriand or not.

2 - Adding Fire Oil/Light Oil to your bow transfers your attack skills (not auto-attacks) into Fire or Oil damage. With the new Phys/Tac Mitigations in place, it means your bow is now going against a mob's tactical mitigation. IE, you're doing a lot more damage, since most mobs have lower Tac Mit than PhysMitt

The fire damage will go against the mob's Fire mitigation, not tactical mitigation. Tactical Mitigation is just a base number used by all the 6 tactical damage types: Acid, Fire, frost, shadow, light and lightning. If the mob previously had a lot of fire mitigation, I suspect it will still have a lot of it now. The introduction of 2 base values (tactical and physical mitigation) need not alter any of the mob's effective mitigations to a particular type of damage, that is if the devs implemented those 2 bases for mobs too.

Oct 11 2011 02:49 AM

Updated formulas and graphs in OP.

Oct 11 2011 03:08 AM

Argh. Timeout ate my last post. Okay, time to retype.

Originally Posted by Alad.

If you multiply the 24.7% by 66/65, you'll get 25.1% (or 25.0% if it's 24.6%), exactly what you calculated, and fits nicely within the constraints you found.

This seems to imply that the example formula I wrote above may be what the real offence formula is. But further testing is naturally required, preferably versus even higher level mobs than you, to try and force out bigger differences.

It could be - honestly, I want some larger numbers so the rounding errors aren't making the error bars so wide that actually figuring the actual damage bonus (to say nothing of trying to write a formula for it across multiple levels) is any worse than reading it off a tooltip. Also, it takes a while to collect a good set of crits.

Originally Posted by Alad.

I look at the pattern and try out different curve forms, let Excel do the curve fitting, and then fine tune it by hand to minimize errors against observed data. The difficulty is in finding the correct form or formula. R/R+KL (which is actually y=1/(1+k/x) ) wasn't that obvious for me. I'm curious to know how you stumbled upon it.

Of course if you know the equations of many different curve forms, it should be easy to recognise it, but this one wasn't part of my repertoire.

Actually, this was due to LagunaD's work - if you look at the original set of formulas they produced, it looks awfully like a power series - in this case -1 * (kx)^1 + -1 * (kx)^2 + -1 * (kx)^3. Solving for the power series gives you x / (x - (1 / k)) - we know k is negative, since the sign switches in each term, so set c = - 1 / k, and you get x / (x + c).

Originally Posted by Alad.

Also don't forget that those ratings in the character panel are rounded too. For example, Physical and Tactical Mitigation receive 0.2*Armour (there's another multiple of 5 for you

). It's perhaps best to play with common mitigation to hopefully encounter less rounding, since it includes all the armour (even though I doubt ANY number in this game is an integer, even armour.)

Yeah, this was all with common damage. I'm never certain when a rounded value is used and when it isn't. For example, I've played around with power costs (and how power cost modifications apply to them) and I know some of the base power costs for hunter skills are non-integer values (based on the way various bonuses/penalties modified the cost, the base power cost could not have been an integer) - but, working with the lua side to watch power decreases, I also know that the actual power cost applied is always an integer. (Power itself isn't necessarily an integer - the ICPR tick isn't, for example.)

Originally Posted by Alad.

I'm quite certain other formulas haven't changed (ovoidances, resistances, crits, etc...). It's enough to test just 1 point at a high enough level to realise this.

Actually, I just checked block ratings on my warden (since wardens have a number of buffs that boost block rating), and it looks like a multi-interval function again. In this case, the switch over point is 70 * level at 15% (not surprisingly, the old cap), and the constant in the second half of the interval is 2380 / 3 (technically it's somewhere 793.2 and 793.5 - I chose 2380 / 3 because it's double the constant I was using for the first half - no other reason).

This should apply to parry and evade - it probably also applies to crit.

For resistance and outgoing healing, I've got no data, but it wouldn't surprise me if it turned out that the switch over point there was 170 * level at 30% (again, the old cap), and the constant for the second half was 2380 / 3, again.

(level 67 warden block rating/percentage)

Code:

5432	0.164
5436	0.164
5440	0.164
6808	0.188
6964	0.191
7044	0.192
7048	0.192
8332	0.214
8412	0.215
8416	0.216
8476	0.216
8492	0.217
8572	0.218
8652	0.219
8656	0.219
9756	0.237
9940	0.24
10020	0.241
10100	0.242
10180	0.244
10260	0.245

Edit: Proposed constant is 2380 / 3, not 2280 / 3.

Oct 11 2011 03:42 AM

I'm astonished because I'm certain I verified all the formulas and found only mitigation and offence had changed (as announced). But I did this on a level 65. I don't suppose you still have a level 65 to check on, do you? Mine are all still at 65. I'll take a look at your data, though you seem to have figured it out already. And maybe also healing. Damn, I won't get to see Dunland for a few more days.

Solving a Power series? lol. I vaguely remember that from high school. My studies and work didn't require me to use some math concepts, and so pooof!

It's actually a very good thing that lotro doesn't really round numbers inside. It's a shame it just rounds them for us.

Any idea where that rounding to nearest multiple of 5 came from?

You mean 2380/3.

A big difference in mob level compared to you will also show if that L is your level or his. Do you still think it's your own level?

Edit: I checked your warden data. Your conclusions are correct for this data. And the second segment has a lower slope than the first (old BPE curve), which means that going above 15% is going to be more difficult for wardens? Or did they do that for everyone? The fact that the curve resembles the light/medium armour one, could mean they made it easier for heavy armours to block? LOL, that would be funny. I'll have to check that. I remember reading something in the stat dev diary, then doing some calculations and coming to the conclusions that the announced numbers are wrong, and didn't think about it again until now:

One thing to be aware of though, is that the diminishing returns built into the formula the converts ratings to percentage will start to be much more noticeable as the ratings increase. While it takes 4550 ratings to reach +15% at level 65 it will take 8850 to reach 25%.

To reach 25% with the old formula you'd have needed a rating of: 396.643*65/(1/0.25 - 1) = 8594 at level 65, and 9916 at level 75.
This new formula requires: 65*(70 + 793.33/(1/(0.25-0.15) - 1)) = 10,280 at level 65, and 11,861 at level 75.

It seems a warden can get there though, according to your data, even at level 67. Can a guardian get there too?

I'm wondering why not just make one new curve for the whole range? But I think I know the answer. Such a curve would raise the block ratings at the low end. Or not be harsh enough on the high end.

And now it's clear why I didn't catch that change when I checked: the change is only visible beyond the old level cap, and my char must not have any stats in that region.

That's yet another nice catch, moebius! Keep it up!

Oct 11 2011 08:58 AM

You know, it was nice Turbine raised the cap for crit but how the hell do you get anywhere near 11k crit rating? I'm not even sure I get near half that number with buffs...

Oct 11 2011 09:46 AM

ok, so if I plan on spending most of my time in skirmishes, raids and the moors (where most monsters are going to do fire, lightning, acid, etc... damage, my best bet is to:

A. Raise my armor value as high as possible.
B. Then increase my tactical defense as high as possible.
C. Then worry about physical mitigations.

I have heard that resistance values really arent worth it because even with super high resistance, at most you might resist ~10% of the time.

I am trying to rethink my "well rounded" build and have noticed while leveling that even landscape mobs are tearning me open a lot more than they used to. I play a burg and have always stacked evade then morale and then melee defense in the past.

There was a lot of math on the last few pages and I'm not going to say I understood it all, lol.

Oct 11 2011 12:32 PM

Originally Posted by moebius92

Well, I was thinking either rivet leather armor... et al

Excellent points, especially the fact that plate armour was difficult and expensive to make, (talking about medieval Earth real life, not Middle-earth lol) and very few people wore full suits of plate. Everyone was after all the protection they could get, human nature doesn't change, so you'd often see bits of leather, mail, and plate mixed together. Too bad we don't have that economic dynamic in LOTRO, would be very cool and interesting.

Thumbnail development history of personal armour irl: Leather clothing, made from the tanned hides of whatever we killed for food, was naturally discovered to have protective properties, and that was the first 'armour'. Later, hardened leather armour and leather with scales sewn on or rivets added became the first clothing specifically designed for protection in a fight.

When mail (chain-mail) came about, it was the cat's meow for protection against bladed weapons, and quickly became the preferred armour if you could get your hands on it. And again, not everyone could obtain a full hauberk, but many people could get a mail vest or bits and pieces. One weakness of mail is that a heavy blow can still break your bones under the mail even though it doesn't penetrate the armour. Still, much preferable to having a sword or axe stuck in you.

The real weakness of mail is protecting against arrows and crossbow bolts. Dang English and their cowardly longbows, &etc. Plate armour was developed as a solution to protection against missile weapons. And of course it was just as good vs. slashing attacks from bladed weapons. A man wearing plate armour only gets nervous when his opponent uses piercing attacks with a sword or spear against him, that is how you defeat plate.

And plate actually was very good protection against the current technology in firearms (arequebus, muskets, the early rifles) right up until the middle of the 19th century. Pikemen wore helmets and breastplates of plate, and so did various heavy cavalry (Cuirassiers, Carabiniers) in Napoleonic times. A direct close-range hit from a musket would penetrate this armour, but during the charge a longer-range shot would be deflected. However, it was not proof against a cannon shot:

Back to the topic, of course we play LOTRO in a fantasy world albeit one roughly based on real life history and technology. We don't have any data on how lightning or fire spells fired from a Rune-keeper's fingernails affect us through our armour. But I think we both agree that it would be a very nice addition to add that dynamic to the combat system at some point.

** waiting to get back home and level my Guardian to 75 **

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