Thread: Combat stat changes on Isengard release. Mitigation and Offence.

Originally Posted by bastiat1

In that same post from Graalx2 they note that Finesse uses the same formulat as BPE. Are you using a different derivation or is it the same?

That's a good point. I couldn't test high ratings of Finesse myself, and someone in this thread (was it moebius92?) told me that Finesse uses the same conversion formula as Outgoing Healing and Resistance ratings. Those conversions are identical to BPE conversions up until an R/L of 70. After 70 they'll start to diverge (finesse rating will produce more % than the same BPE rating).

For example, from looking at the graphs I posted, at R/L=100 (7500 rating for a level 75 character), BPE is a bit more than 19%, while Finesse (if it indeed follows Resistance) would be a bit more than 20%. So if what Graalx wrote about them using the same formula is true, then someone has made a little mistake! Perhaps someone with high Finesse can confirm this.

I'll keep it as it is for now until it's cleared up.
Edit: I've confirmed that Finesse does indeed use the Resistance and Outgoing Healing conversion function, not the BPE%.


@moebius92:
Great data again in your last post. I'll get back to you when my Skyrim stint is over.

Total NCPR = 12*W+n where n = 75 for a level 1 loremaster and 120 for a level 54 loremaster.
Only the total NCPR provided by will is 12*W. This can be verified on the morale and will tooltips.

Please get back to me if I'm wrong.

I am just reposting here an interesting message about Finesse, before it gets lost in the guardians forum:

Originally Posted by Graalx2

Finesse affects the B/P/E percentages proportionally to their values. I made that original post in a hurry so I just used identical values for B/P/E so that they would be 1/3 of Finesse penalties on each.

If block is 20%, Parry 10 % and Evade 5%.
An attacker with 7% Finesse will reduce Block by 4%, Parry by 2% and Evade by 1%.

To answer the question about Finesse and which conversion it uses:

I've just tested it and confirm that Finesse uses the same function as Resistance and Outgoing healing when converted from rating to %.
It does not use the BPE% function as Graalx stated.

Figured I should add a data point I came across with regards to the mastery curves.

LM with 29283 has a +123.2% tactical damage. +15% is due to MoNF traits, +5% is due to a first age LM book. So we've got +103.2% coming from tactical mastery.

If we assume that 80% - 100% is another interval, and there's a 100%+ interval, we get 29283 - (75 * 75 * 5) = 1158, 1158 / (300 * 75 + 1158) = 0.048947502, giving us a total of 104.8947502% - not what was observed.

If we assume that the 80% interval keeps going, we get 29283 - (75 * 75 * 4) = 6783, 6783 / (300 * 75 + 6783) = 0.231636103, giving us a total of 103.1636103%, which after rounding is exactly what was observed.

No idea if there's a hard cap to the 80%+ interval.

Originally Posted by moebius92

Figured I should add a data point I came across with regards to the mastery curves.

LM with 29283 has a +123.2% tactical damage. +15% is due to MoNF traits, +5% is due to a first age LM book. So we've got +103.2% coming from tactical mastery.

If we assume that 80% - 100% is another interval, and there's a 100%+ interval, we get 29283 - (75 * 75 * 5) = 1158, 1158 / (300 * 75 + 1158) = 0.048947502, giving us a total of 104.8947502% - not what was observed.

If we assume that the 80% interval keeps going, we get 29283 - (75 * 75 * 4) = 6783, 6783 / (300 * 75 + 6783) = 0.231636103, giving us a total of 103.1636103%, which after rounding is exactly what was observed.

No idea if there's a hard cap to the 80%+ interval.

Thanks for the info, moebius! I'll update the initial post. And hope some other people will provide more examples of Mastery/Offence Ratings > 29000 at level 75 so we can confirm this.

Lvl 75 Cappy

Phys Mastery - %
30874 - 112.1-5=107.1%
31924 - 114.5-5=109.5%

was taken with war banner so -5% on both

A few questions on overcapping for B/P/E, resistance, and mitigations:

If I have a Block, parry, evade, or resistance rating that takes me over the 25% cap, will this have any additional effect on an on-level mob with finesse?

Over-level mobs: Since the tool-tip for b/p/e, resistance, and mitigations all give you a percentage value "against on level mobs," I assume this means that this percentage is reduced when fighting over-level mobs. Is this true? Also, if this part is true, does having a rating that takes you over the percentage cap (for on-level mobs) have any effect on over-level mobs?

Originally Posted by Sohar

Lvl 75 Cappy

Phys Mastery - %
30874 - 112.1-5=107.1%
31924 - 114.5-5=109.5%

was taken with war banner so -5% on both

Thank you, Sohar! This then confirms that there are only 5 segments on the Offence conversion curves, and that the 5th segment continues the curve beyound 100%.

Originally Posted by spelunker

A few questions on overcapping for B/P/E, resistance, and mitigations:

If I have a Block, parry, evade, or resistance rating that takes me over the 25% cap, will this have any additional effect on an on-level mob with finesse?

Over-level mobs: Since the tool-tip for b/p/e, resistance, and mitigations all give you a percentage value "against on level mobs," I assume this means that this percentage is reduced when fighting over-level mobs. Is this true? Also, if this part is true, does having a rating that takes you over the percentage cap (for on-level mobs) have any effect on over-level mobs?

Here's my opinion (since to give a definitive answer would mean to actually do lengthy testing and provide proof )

No to the first question. Yes, and yes to the second.

I don't know if anyone has actually verified this for BPE with real and rigorous tests (as moebius has been doing with Mitigation and Offence), but theoretically, for a given BPE rating, the higher your opponent's level, the lower your BPE% will be against them. So ratings which are higher than what is required to produce a capped % with on-level mobs, should become useful when fighting higher-level mobs (a small part of the extra useless rating versus on-levels will become useful versus higher-levels).

The BPE rating which caps the BPE% varies with the opponent's level:
BPE R/L Cap = 158.15, where L is the opponent's level.
Rcap = 158.15 * L
= 11861 versus L75 mobs
= 12019 versus L76
= 12178 versus L77, etc...
Note that the useful excess BPE rating is actually quite small as far as extra % is concerned: around 158 rating per mob level.

As for Finesse, it was stated that Finesse is converted to % at the source (owner of the finesse), then deducted as a % from the target's BPE%. Theoretically, the L in the opponent's formula used to convert their finesse to %, is your own level (their opponent, the target), so their % finesse result shouldn't change with their level, only with their finesse rating. Against a given level of opponent, your BPE rating will convert to a certain %. Going above the BPE "cap-rating" for that opponent level (eg. 76) will not improve your % against mobs of that level (76), hence will not protect you more against level 76 mobs whether they have finesse or not. But it will protect you more against mobs of higher levels. So the answer to your first question is no, as far as BPE is concerned.

However, I haven't seen a statement from devs saying that finesse counters Resistance in the same way as BPE (i.e. converted first to % at the source, then deducted as a %). If it is, then going above the Resistance cap-rating versus a certain mob level will not benefit you either against that mob level as far as opponent finesse is concerned. However, if Finesse is deducted as a Rating from the opponent's resistance, then going above the resistance cap-rating should indeed be beneficial.

For the case where finesse is deducted as a %, having excess rating (over-cap) higher than about 450-500 (158 * 3 levels) would probably be useless. If finesse is deducted as a rating, however, larger excess rating values will be useful to directly counter opponent reductions from their finesse. This could be the case for Resistance, and is the case for Critical Rating (since opponent Critical Defence is also a counter-stat that works the same way as Finesse to reduce your crit chance, by deducting their Crit Defence as a rating from your Crit Rating). In such a case having an excess rating as big as the opponent's counter-stat rating would be useful to keep your stat capped.

To summarise, having a higher BPE rating than the %cap-rating for a certain level will benefit you against mobs that are higher than that level, by producing a higher %BPE both before and after deducting opponent %finesse. The higher the mob's level, the bigger the benefit from higher over-capped BPE rating irrespective of the mob's finesse. But the over-cap rating that is useful is small: around 158 rating per extra mob level only, anything higher is wasted. The advantage of over-capping could be even bigger for Resistance, if finesse is deducted from it as a rating rather than as a %.

In you initial post it is stated that agility doesn't lower miss chance against above level mobs. Later it seems there are two types of miss chance, inherent and level difference. Is inherent miss chance still reduced by agility against above level mobs, potentially reducing miss chance to a base of the level difference miss chance?

Originally Posted by Smugo

In you initial post it is stated that agility doesn't lower miss chance against above level mobs. Later it seems there are two types of miss chance, inherent and level difference.

Yes, if that's what you want to call them. I haven't seen any official "name" for them, though.

Is inherent miss chance still reduced by agility against above level mobs, potentially reducing miss chance to a base of the level difference miss chance?

You may be right, if you assume that the miss chance which is reduced by agility also operates on higher level mobs (i.e. that there are 2 miss chances versus higher level mobs). That may not be the case. The first miss chance may, perhaps, only operate on lower level mobs.

All I recall reading from devs is that:
1) Agility improves miss chance. (That was before we discovered there's a second miss chance).
2) There is another type of miss chance which operates when fighting higher level mobs, and which cannot be reduced by higher agility.

Excellent, that seems to make sense. If only more raid bosses were on level some effect of RNG could be reduced.

Nice work OP, thank for you the wonderful post!

Fairly quick test again.

Got my minstrel's common mitigation up to 10141, and then had him get beat up by level 77 Twisted Orcs. (Originally this was going to be Deep-claw haulers, but after doing that it occurred to me that testing incoming damage numbers using a mob with Bloodlust and that had orcs with +damage auras wandering around might not've been the best idea ever.)

10141, at level 77 provides 41.2% mitigation. 9695, at level 77 provides 40.2% mitigation. If the mitigation penalty is applied after the cap, the damage numbers should be the same (41.2%, capped to 40%, -1% penalty to 39% and 40.2%, capped to 40%, -1% penalty to 39%), and if the mitigation penalty is applied before the cap, damage numbers should be different (41.2%, -1% penalty to 40.2%, capped to 40% and 40.2%, -1% penalty to 39.2%, capped to 39.2%).

weak attack did 656 damage in both cases.
Punch did 2538 damage in both cases.

Penalty gets applied after the cap, don't bother going over the regular cap (after adjusting for level).

A quick little oddity that I can't explain....

I was working on tearing apart Hunter skills. I've done most of the testing on the Galtrev dummies. I've removed all traits and meaningful legacies so as to not create confounding variables.

Barbed Arrow has a bleed that is a fixed value. Since it doesn't vary you can easily determine the magnitude of mitigation that the dummy has. It has 15.6% mitigation to common damage.

I then used Bow Chant: Breach Finder which reduces mitigation to ranged attacks by 1,500. I solved for the new mitigation, which was 3.4%. Breach Finder doesn't effect the bleed so I had to solve for the 3.4% using crits, but that doesn't matter.

I plugged the 15.6% and the 3.4% into Alad's equations in the original post. If you assume Light/Medium armour then the dummy's mitigation rating was 2,072 before the Breach Finder and 400 after. That's a reduction of 1,672, which is obviously higher than the 1,500 stated value.

If you assume Heavy Armour then the dummy's mitigation rating was 1,912 before the Breach Finder and 557 after. That's a reduction of 1,355, which is obviously lower than the 1,500 stated value.

Does this imply that there is a different mitigation formula used by the dummy, and presumably mobs and creeps? Given that 1,500 is almost exactly the mid-point between 1,672 and 1,355, does that imply that the mitigation formula is some composite or mid-point between the Light and Heavy?

@bastiat

Just a couple of quick comments and pointers about your above testing of dummy mitigation.

You mention reducing the dummy's Ranged Mitigation (with Breach Finder). This could actually be the old Ranged Defense stat, which IIRC followed another formula than the current Physical Mitigation. They could be 2 different mitigations, cascaded one after the other, is at least what I'm trying to say.

Moebius92 in this post (in this thread) and following posts, tested physical mitigation of mobs as well, and seemed to find that it does not follow the formula I stated in the initial post of this thread. My formula precisely predicts the Mitigation% number which appears on the tooltip, but Moebius seems to say the actual mitigation % does not follow that formula exactly. There's another factor involved. You need to read his posts about this subject.

In any case I'm sure moebius would be better suited to help you out with this one.

Do these formulas plug right in for level 85? Assuming Turbine sticks with the same system, I'm getting something like a 15% increase needed to sustain the same % in offense rating. I would like to say that translates to a 15% increase in stats, but it doesn't seem right given the increment from level 65 to 75. Also, offense rating doesn't suffer from diminishing returns so I would assume that even higher non-offensive stats would be required for say, mitigation. Any input on that?

If you mean the automatic nerf we get with every level up, then yes, going up 10 levels nerfs you by quite a bit, and you need to raise your stats by quite a bit to maintain your net % stats. The mere fact that the level L is in the denominator explains the nerf. The graphs show R/L on the x-axis, so for the same R but a higher L you'll slide to the left and end up with a lower net %. (This is Turbine's way of making your character totally dependent on equipment. You *must* renew your equipment if you don't want to see your combat effectiveness suffer.) Where you now, at level 75 need about 28.1 Might/Agility/Will to gain 1% extra Offence, you'll need about 31.9 Might/Agility/Will to gain that extra % at level 85. This means about 13.3% (85/75) more offence rating at 85 to maintain your current Offence % of 75.

If you're asking me whether those formulas will change with the Rohan expansion, then I don't know.

Note also, wrt Offence, that the fifth and last segment continues beyound 100%, and you start getting diminishing returns beyound 100% Offence. Hopefully you'll be nerfed enough to not go beyound 100%! (Just kidding)

Originally Posted by mootay

Also, offense rating doesn't suffer from diminishing returns so I would assume that even higher non-offensive stats would be required for say, mitigation. Any input on that?

This is going to be a little bit mathy - I've simplified things as much as I can.

The main take away should be that mitigations/defensive stats do not actually suffer from diminishing returns.

In order to demonstrate this, I'm going to make a couple simplifying assumptions - first, that the damage formula is linear - that is, <damage bonus (b)> = <rating (r)> / <constant (c)>, the mitigation formula has only one interval - that is, <mitigation (m)> = <rating (r)> / (<constant (c)> + <rating (r)>), and the actual damage done is <base damage (d)> * (1 + b) * (1 - m).

In some sense, we can view mitigation as being the dual/inverse of the damage bonus - for any given damage bonus, we can find some mitigation that completely counters it.

For example, if you have an 100% damage bonus, you'd need 50% mitigation to counter it (d * (1 + 1) * (1 - .5) = d * 2 * 0.5 = d).
If you have a 200% damage bonus, you'd need 67% mitigation to counter it (d * (1 + 2) * (1 - .67) = d * 3 * .33 = d)
If you have a 300% damage bonus, you'd need a 75% mitigation to counter it (d * (1 + 3) * (1 - . 75) = d * 4 * .25 = d)
If you have a 400% damage bonus, you'd need an 80% mitigation to counter it (d * (1 + 4) * (1 - .8) = d * 5 * .2 = d)

Okay, now let's start with the rating needed to get an 100% damage bonus and 50% mitigation. Due to the way I've setup the formulas, it's c in both cases (b = c / c = 1, m = c / (c + c) = 0.5) - this is mostly notational convenience. Now let's see what happens when I start multiplying that by a constant. Okay, if I set my rating to 2c, my damage bonus is b = 2c / c = 2, and my mitigation is m = 2c / (c + 2c) = 0.67. If I set my rating to 3c, my damage bonus is b = 3c / c = 3, and my mitigation is m = 3c / (c + 3c) = 0.75. If I set my rating to 4c, my damage bonus is b = 4c / c = 4, and my mitigation is m = 4c / (c + 4c) = 0.8.

Hmm, it looks like if I continue to grow both my damage bonus and my mitigation at a linear rate, they continue to cancel each other out. And in fact, that is the case.

Let's say I set both damage bonus and mitigation ratings to x * c, and plug it into the damage formula, and see what happens.

= d * (1 + b) * (1 - m)
= d * (1 + (xc / c)) * (1 - xc / (c + xc))
= d * (1 + x) * (1 - x / (x + 1))
= d * (1 + x) * (1 / (x + 1))
= d

So, yeah. The way the mitigation formula is written, it grows exactly as fast as is needed to counter a linearly growing damage bonus. Which is why I claim that the mitigation and defensive formulas do not actually suffer from diminishing returns.

(If you actually do the math, due to the way that some of the various defensive stats stack additively, it turns out that all of the defensive stats actually suffer from increasing returns, but that's a bit more complex to show.)

Hi Moebius, nice trick you got there

Let's see...

Damage bonus% = linear = Ro/C; where Ro is your Offense Rating. A good enough approximation.
(You wrote it as: b = r/c)

Your Mitigation% = Rm/(Rm + K*L); where Rm is your Mitigation Rating.
(You wrote is as: m = r / (r + c) )
Here you're assuming the mitigation follows the old curve all the way, which of course it doesn't. I'll take it as an approximation, although a bad one.

The rest of your demonstration assumes that the Offense Rating (Ro) of the attacker is equal to the Mitigation Rating (Rm) of the defender. There's practically no chance of that coincidence occurring. And you assume that when you increase one, you increase the other such that they remain identical. Even less probable. You then demonstrate that the net damage is the same if you increase that rating (which is both the offense and the mitigation rating). And yes, you're right, in that simplified mitigation formula. But take a player hitting on a mob. Does mob mitigation work that way? (apart from the fact that the 2 ratings being equal is impossible).

Mob mitigation, if my memory serves me right, and you wrote about it in this thread as well (but I'm too lazy to dig it out), is more like: k*Lev
where k is a constant which depends on the quality of the mob ("eliteness"), and Lev is the mob's level.
And the mob's mitigation rating has no relationship with your offense rating, obviously.

The mob's mitigation rating gets automatically increased with their level, but your offense rating doesn't. It could even be that, versus an on-level player (i.e. if L = Lev), that particular mob's mitigation in % stays the same as their level increases, m% = k/(k+K).

But don't focus too much on the above mob mitigation formula assumption. That's not needed.

You're talking about the player's mitigation, saying that it doesn't suffer from diminishing returns because, if a mob's damage bonus (again, it's mob versus player), increases linearly with their "offence rating" (which most probably only changes with their level... do you know how their damage scales with their level?), and you happen to have a mitigation rating that is equal to the mob's offense rating (!), at every level as you both level up (!!), then the net damage you'll receive from that mob's hit will be the same as you both level up.

Do you see some improbabilities in that sentence?

Yes, of course player mitigation suffers from diminishing returns, my friend M% = R/(R + KL). Take a look at that curve again.


What your demonstration shows is that:
If you simplify the mitigation formula to just one R/(R+KL) segment, and if you took 2 player characters such that the offense rating of the attacker is exactly equal to the mitigation rating of the defender, then a critical hit from skill X by the attacker would produce the same net damage on the defender when you change that unique rating on both, because the change in damage bonus on the attacker would be exactly offset by a change in the defender's mitigation, such as the net damage received is the same.

That's an interesting catch

I think you've misunderstood the argument. The point isn't to demonstrate that if I have this perfect setup, mitigation and damage counter each other.

The argument is:

1) By definition, I state that a linear function does not suffer from diminishing returns.

2) One of the things that defines a linear function is that f(c*x) = c * f(x) - that is to say, if I multiply the input by a constant, I expect the output to be multiplied by the same constant.

3) I assume that we are only interested in mitigation with regards to the actual effect it has - in this case, how does it affect incoming damage.

4) So now I set up a toy example (which is pretty much the majority of my previous post), where I make a bunch of simplifying assumptions, and I demonstrate that if I set both my damage rating and mitigation rating in such a way that they cancel each other out, I can scale them linearly (multiplying by x), and they continue to cancel each other out.

5) Due to the way damage was simplified, it is a linear formula, and does not suffer from diminishing returns.

6) Since mitigation continues to cancel out damage even as we apply an arbitrary scalar, it also, when actually applied to the damage formula, and not just read as a flat percentage, must have a linear effect - it has to be a function of the same order as the damage formula, or else the damage would not remain constant as both functions were scaled.

7) Therefore, mitigation does not, when its actual effects are looked at, suffer from diminishing returns.


Here's another way to think about it - mitigation itself isn't linear. The first percentage point of mitigation is not equal to the last percentage point of mitigation. The first percentage point of mitigation reduces your incoming damage by about 1%. You go from taking 100% damage to taking 99% damage. The last percentage point of mitigation reduces your incoming damage by 100%. You go from taking 1% of damage to take 0% of damage.

One of the standard metrics to deal with this is to look at effective health (well, effective morale in this case). And the way you can look at it is, if I have a 50% mitigation, that's about the equivalent of having +100% morale. I take twice as long to kill as my actual morale suggests. (In actual practice they're not quite equivalent - if you consider healing, mitigation is better, if you consider spike damage, having more morale is better.) Anyways, the typical way to represent this is via toughness (or some equivalent term). Your effective morale = morale * toughness (t). In this case t = 1 / (1 - m). We can check a couple points to see that this make sense. 0% mitigation = +0% toughness, and your effective morale = morale. 50% mitigation = +100% toughness, and your effective morale = morale * 2. 75% mitigation = +300% toughness, and your effective morale = morale * 4.

Okay, now let's plug in the simplified mitigation formula into this. And we find that t = 1 / (1 - r / (c + r)) = 1 / ((c + r - r) / (c + r)) = 1 / (c / (c + r)) = (c + r) / c = 1 + r / c. Which means that toughness is actually scaling linearly with the mitigation formula. Which is why mitigation continues to cancel out the damage bonus no matter how high you scale the ratings.


And, finally, I have simplified the mitigation formula - but if you actually look at the real mitigation formula, it suffers from increasing returns, instead of just being a linear function. Demonstrating this actually takes calculus, which is why I skipped it.

A typical way to check whether a function is linear or not is to look at the derivative - linear functions have a constant derivative. Take the simplified damage bonus formula (r / c), and we can see the d(r / c)/dr = 1 / c. It's constant, therefore it is linear.

So let's look at toughness again. If we're in the first interval, the simplified version is the correct version, and we find that t = 1 + r / c, which we already know has a derivative of 1 / c, so it's linear.

Now let's look at the next interval. m = m0 + (r - r0) / (c + (r - r0)). Applying that to the toughness formula, we get t = 1 / (1 - (m0 + (r - r0) / (c + (r - r0)))) = 1 / ((1 - m0) - (r - r0) / (c + (r - r0))) = 1 / (((1 - m0) * (c + (r - r0)) - (r - r0)) / (c + (r - r0))) = 1 / (((1 - m0) * (c + (r - r0)) - (r - r0)) / (c + r - r0)) = (c + r - r0) / ((1 - m0) * (c + (r - r0)) - (r - r0)) = (c + r - r0) / ((c + (r - r0)) - m0 * (c + (r - r0)) - (r - r0)) = (c + r - r0) / (c - m0 * (c + r - r0)).

Now we take the derivative of that with respect to r.

d ((c + r - r0) * (c - m0 * (c + r - r0))^-1)/dr = 1 * (c - m0 * (c + r - r0))^-1 + -1 * (c + r - r0) * -m0 * (c - m0 * (c + r - r0))^-2 = (c - m0 * (c + r - r0) - -m0 * (c + r - r0)) / (c - m0 * (c + r - r0))^2 = c / (c - m0 * (c + r - r0))^2

Okay, now let's do some simple analysis of the behavior of the derivative. m0 > 0 (well, it can be equal to 0, but then we're in the first interval, and we could've gone with the easier derivative). r - r0 > 0 (if it is less than 0, we're outside the interval we're looking at, and we should probably actually use the interval we're in). So this means that (c - m0 * (c + r - r0)) < c, and in fact it continues to shrink as r increases. And since that's the case, we can take reciprocals to find out that 1 / c < 1 / (c - m0 * (c + r - r0)), and since everything's > 0, we can square, to get (1 / c)^2 < 1 / (c - m0 * (c + r - r0))^2, and therefore 1 / c = c / c^2 < c / (c - m0 * (c + r - r0))^2. So our derivative is actually greater than the constant implies. And then final key is since the denominator is shrinking as r increases, it must be the case that the derivative is increasing as r increases, which means that the toughness is actually suffering from increasing returns. Which is what I said in the beginning.

(And that's why I skipped using the actual formula in my previous post.)

Edit: Sorry if I'm burying you under mathematics, but I find the qualitative analysis of the interval version of the mitigation formula to be even more hand-wavey. The basic intuition is, ignoring the cap, the way the r / (c + r) curve is setup - it starts increasing, and begins tapering off as r increases - that's the apparent diminishing returns. It has a soft cap of 100%, because at 100% mitigation you need an infinite amount of damage bonus to counter that. (Basically, as r approaching infinity, the formula approaches 1.) And it has to do this in order to achieve a linear effect. If you shove the curve up a little, it's going to grow faster than linear, since the actual slope the function is now higher at every point that it was for the original equivalent function.

I really prefer the quantitative analysis.

Nice demonstration, and I fully agree with it. What I disagree with is that you're talking about something other than mitigation, when you say "mitigation doesn't suffer from diminishing returns". When we talk about diminishing returns we're usually talking about the relationship between a Rating and the % it controls. Mitigation Rating controls how Mitigation% behaves. And that's non-linear and has diminishing returns.

You're talking about "toughness" (which you defined as the apparent increase in morale due to your damage mitigation, or how much total unmitigated damage one can take before dying, given their health pool and their damage reduction). Toughness happens to be linear wrt mitigation Rating, while mitigation% isn't.

So, yes, the higher your mitigation Rating, the more incoming unmitigated damage you'll be able to take before dying, and the relationship is linear wrt Mitigation Rating, with no diminishing returns. (Thanks for that insight!).

mitigation%, m = R/(R + KL)

Toughness, as you defined it = 1/(1-m) = 1 + R/KL

It is clear that toughness is directly proportional to the mitigation rating, and that the function is therefore linear, and doesn't suffer from diminishing returns, wrt R. (You wrote that "toughness is actually scaling linearly with the mitigation formula". I think you meant "scaling linearly with the mitigation rating". Toughness does move in the same direction as mitigation%: if you increase m you increase t, and vice versa, but not linearly.)

You then show that, on the larger second segment of the mitigation curve, the toughness would actually have increasing returns wrt R.

They say a picture is worth a thousand words, so here's a graph of "Toughness" which shows its upwards curve on the second segment, just as you proved mathematically


[download]

I'm in no way trying to diminish your intuitive and outstanding analysis because it revealed something new to me, that if you increase your mitigation rating by the same factor at which mobs get their offence rating increased (if they have one), the mob's net damage on you will be the same as you both level up. There isn't always some simple way to look at a relationship and discover a completely new aspect of it, such as this one, and I'd like to thank you for showing this one to me!

It also reveals what the developer at Turbine who devised this elegant relationship had in mind. It reveals one aspect of how the trash mob, PVE part of the game is balanced. The elegance of the %=R/(R+KL) formula, however, doesn't make up for the fact that nerfing your combat performance systematically as you level up, rather than reflecting your continued training and advancement through levelling by actually improving your performance, is... can I say "lame"? To me, that concept is. And it leads to a type of game where you get more and more dependent on better equipment to offset those nerfs. But grind is not the topic of this thread.

Originally Posted by Alad.

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

Quick question on the formulas and statement you made in the above quote, on how the Light/Medium armour and Heavy armour Mitigation formulas are for "common, lightning, acid, etc..." and I noticed on my Guard that he has 10,156 physical mitigation @ 54.2% which matches up perfectly with your formula, but he also has 70.8% common mitigation, and when you look at his tooltip, it says it has a rating of 17,993 which when put into the formula, does not come out to the 70.8% common mit chance. Am I doing something wrong or have they changed this since this thread has been updated or something?

Thanks again for your post, it is very informative and just plain awesome for an amateur number cruncher like me

If your guard is a dwarf they get +1% to common mitigation

Originally Posted by jazzguitarmanic

If your guard is a dwarf they get +1% to common mitigation

Aha! Thats exactly it! Thanks!

Alad, any chance you've confirmed that Rohan preserved all the old equations? Anyone else looked at it in any detail?

Originally Posted by bastiat1

Alad, any chance you've confirmed that Rohan preserved all the old equations? Anyone else looked at it in any detail?

I haven't had the opportunity to play Lotro for some time now. I expect (from the release notes) that the Offence rating has had an extra segment added. That's easy to add as an extra row in the table if you note the segment progression.
I follow the forums and will gladly update the info when people confirm the changes to it and post them in this thread.

Originally Posted by bastiat1

Alad, any chance you've confirmed that Rohan preserved all the old equations? Anyone else looked at it in any detail?

I have not noticed any changes in the formula's in any of the stats I track in my build spreadsheet. Just changing the 75s to 85 and so on. I do think an additional segment was added to the offence curve, but haven't been able to see if more than one was added.

The new critical defence formula (as of update 9) seems to fit with: K = 50, Xo = 0, Yo = 0. Not sure about the maximum. Also, I've only tested with one character so far.

(new) Common dmg mitigation cap is at 71%. At least for my guardian after he got the new BG gear which seems to have twisted armor ratings.

Originally Posted by Schinderhannes

(new) Common dmg mitigation cap is at 71%.

You must be a dorf. They get a 1% Physical Mitigation bonus. All +percentage bonuses allow boosts over cap.

Hi, I'm having difficulty finding the correct partial mitigation values.

My 85 Dwarf Minstrel has (without buffs/virtues):
Physical Mitigation Rating: 5775
Tactical Mitigation Rating: 3530
Block Rating: 1643
Parry Rating: 430
Evade Rating: 1248

On my character sheet this translates into:
Physical %: 29.0%
Tactical %: 21.1%
Partial Block Mitigation %: 24.7%
Partial Parry %: 21.3%
Partial Evade %: 23.6%

I found the Phys/Tact Mitigation values correctly using the formula in the first post, but the partial mitigation formulas I used do not give the correct values. Please help.
EDIT: Ok got it now

That leaves me with the question below, can anyone answer that?
Also how do I calculate which mitigation rating I need for a given %?

Originally Posted by Rhaphael

Also how do I calculate which mitigation rating I need for a given %?

The basic rating equation is:

P = R / (K * L + R), which is calculates P in terms of R, K, and L.

We can solve the equation for R, which gives us:

R = P * K * L / (1 - P)

So, if you wanted to find out how much rating you'd need to get 10% mitigation, you'd set P = 0.10, and use K = 150, which gives you 0.10 * 150 * L / (0.90) = 16 2/3 * L.

It's a bit more complex, because there are intervals, so what you'd do instead would be:

Figure out which interval the percentage you're looking for is in. Let's say we're trying to get 30% - so that's the second interval. X_0 = 37.5 and Y_0 = 20%, which means that the first 37.5 * L points of rating are used to get you to 20% mitigation, and then are discarded.

What you want to do then is, 30% is 10% over Y_0 for the interval in question. Which basically means you need to get enough rating to get into the beginning of the interval (37.5 * L), and then an additional amount of rating to get you 10% of the way into the middle of the interval. We can use the R = P * K * L / (1 - P) formula to calculate how much additional rating you need to get that 10%. P = 10% and K = 350, so R = 0.10 * 350 / 0.90 * L = 38.89 * L. And then we add the initial 37.5 * L rating needed to get into the interval in the first place, and we end up with 76.39 * L rating gives you 30% mitigation.

Thanks a lot for the help moebius92

I couldn't figure out how to solve the % = Yo + 1 / [1 + K/(R/L - Xo)] formula for R, I guess my math just sucks lol.

Thanks for guiding me through it.

Originally Posted by Rhaphael

Thanks a lot for the help moebius92

I couldn't figure out how to solve the % = Yo + 1 / [1 + K/(R/L - Xo)] formula for R, I guess my math just sucks lol.

Thanks for guiding me through it.

Moebius already answered your question. Here's another way to do it:

We wish to find out how much rating will result in a given %.

R/L = Xo + {K / [1/(Y-Yo) - 1]}

where Y is the % you're aiming for.

The tables in my initial post have a column called "Result Range". Look in there for your target %, and use the values of K, Xo and Yo on that row of the table. Plug them all into the formula above and you'll get your R/L. Now depending on your level (L), you can figure out the rating (R) required to get that target %, by multiplying the R/L you found by your level.

For example, you wish to get 50% Offence (extra damage). From the Offence table you see that 50% is on the 3rd row of the table (40%-60%), where K=300, Xo=150 and Yo=0.4. Plug those in:

R/L = 150 + {300 / [1/(0.5-0.4) - 1]}
R/L = 183.333
R = 183.333 * L

(A quick visual verification on the offence graph shows that 50% corresponds indeed to something close to an R/L of 180. Which is a good way to get an approximate answer without going through the calculations.)

If your level is 85, you'll need 183.333 * 85 = 15583 Offence Rating to get 50% offence.
If your level is 50, you'll need 183.333 * 50 = 9167 Offence Rating to get 50% offence.

HTH.

Thanks Alad for maintaining this valuable thread. There are some changes coming for crits, and critical defense changed in U9.1. It now reduces the magnitude of critical hits instead of the occurences. The rating to percentage formula is out of my league, can't help you there.

Two more data points for the outgoing healing %.

32119 is 50.8%
32591 is 51.3%

Transition point at 50% is at 31308.

So, if we assume that k = 1190 for the third interval, we get:

32119 - 31308 = 811, 811 / (1190 * 85 + 811) = 0.8%, exactly as expected
32591 - 31308 = 1283, 1283 / (1190 * 85 + 1283) = 1.3%, exactly as expected

So, assuming there are three intervals, we have:

x_0	y_0	k	range
0	0%	1190 * 1 / 3	0 - 30%
170	30%	1190 * 2 / 3	30% - 50%
368.3	50%	1190 * 3 / 3	50% - ?

If someone gets a tactical mastery past 42548, we can check if the interval actually ends at 60% or not.

Originally Posted by moebius92

If someone gets a tactical mastery past 42548, we can check if the interval actually ends at 60% or not.

Go out to the Ettenmoors, ninja 4 Outposts and revel in 56k Tactical Mastery?

Highly recommend coordinating it first with your creepside so they get back 2 OP's pretty quickly and you don't get an airstrike called in on you.