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Just wanted to add, to do tank duties, you need both layers of defense.  DR and deflection/saves.  Neglecting one or the other leads to terrible situations in practical optimization.

 

The only one that can do "dodge" everything currently is the wizard due to the new arcane veil coming in 1.05 and their spells that beef them up.  Even then, its a resource dump, so can only be considered a per rest thing.  Same for their later Safeguard spell, etc.

Edited by MoxyWoo
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Just wanted to add, to do tank duties, you need both layers of defense.  DR and deflection/saves.  Neglecting one or the other leads to terrible situations in practical optimization.

 

Agree 100%  While one can create an excellent high DEFL frontliner who avoids taking hits rather often, in the long run, unless you've made an extreme min-maxed ober-DEFL character, the character will take hits from time to time.  And having the best DR he can get at the time will help reduce the damage the frontliner takes and increase his long term survivability.

 

High DEFL, but low DR types aren't probably intended to hang on the front line for the long haul.  They're probably a mid or back liner who was forced into melee due to the situation.  Characters who would prefer to kill whatever's in front of them and fall back to the rear to get back to their normal duties.

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Monks benefit from Might more than other damage dealing classes.

Might increases fist damage, just like everyone else. But Might also increases the Transcendent Suffering buff, which buffs fist damage.

So Monk fists double dip from a high Might score.

 

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For any non-tank build... basically every character that isn't a fighter and/or custom companion Paladin (main character Paladin doesn't count because of the reputation bonus, you can pretty much min-max it the same way if it's the main char)

 

Mig: max

Con: min

Dex: max

Per: min

Int: max

Res: whatever's left over. Which equals to 15 in just about any case.

 

Res over per because of concentration.

 

I wouldn't recommend this for a pure tank build though. I am currently running a game though with Paladin as main tank, which is built like this. Only I fiddled a bit with the Int and Res values, knowing all other saves but deflection will get a ridiculous boost by Faith and Conviction, so I opted for a bit more Res. Still maxed out Str and Dex.

 

Every character in the party is built like the above though. Especially looking forward to seeing the Nature Godlike Barbarian Carnage/Vengeful Defeat built to do it's thing. I don't think I've ever made a character in an RPG that I actually wanted to die... revive with the Paladin.. die again.. revive with Priest, die again tongue.png And that sweet synergy with the racial power :D

 

(Oh yeah, they all superior will saves. But that's just an added bonus)

Edited by Psychevore

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I can't help but notice that while everyone here has plenty to say on what's good for a character in combat, everyone is neglecting one fairly important point: How your attributes play into conversation options. The by far most commonly used attribute for conversations is Resolve, with Perception a close second. This is always checked on your main character, not your companions, so if you want to experience lots of different dialogue options you should definitely invest in these two attributes.

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Suppose there is something that will miss you 98% of the time when it has 100 accruacy.  Now suppose we change your defense such that it will miss you 99% of the time.  This effectively doubles your defense simply by adding 1 point of defense.  This is the extreme, but not unattainable case.  Similarly suppose you will be missed 50% of the time by that something, when we add 1 point of defense you are missed 51%.  This is not nearly as big of an increase.  A good way to quantify this is to multiply your mitigation by your health.  At 50% miss rate you, over time, have 2x your health in "effective health".  At 99% miss rate you have 100x.  As you can see going from 50% to 99% is a 50 fold improvement.  But going from 50% to 51% is a very small improvement.

 

This is wrong correct. Here is why:

 

In case of PoE it can be simplified: because it doesn't use percentage-based stats and thus has no diminishing returns on your stat gains. Deflect doesn't say: Negate 80% of all incoming physical damage. Or: Monsters have a 80% reduced chance of hitting you. Nor do the saving throws say: You have a 80% chance of resisting a certain effect. All of PoE's offensive actions are made by using opposing rolls and those work with absolute values. This means that going from 120 deflection to 121 deflection means just as much as going from 1 deflection to 2 deflection. You lowered your enemies chances to hit you by increasing the threshold he has to overcome by exactly 1.

 

IIRC, your train of thought first came up when World of Warcraft hit the mass market and people started to theorycraft around its combat mechanics. In WoW all your defensive stats are percentage-based, i.e. your armor does reduce incoming damage by a certain % and your block does negate a certain % of all incoming physical attacks. This made it necessary to also introduce diminishing returns on your stat points to avoid getting any stat over 100% thus making your character immune to something and trivializing certain encounters in the game. Now the argument went exactly like you said: I'm at 80% in some defensive stat. So if I increase it to 81% (despite it's relatively higher cost due to diminishing returns) , I just reduced my incoming damage by 1/20 (i.e. I turned 20% into 19%), which is significantly higher than what I get if I increase my stat from 40% to 41% which reduces my incoming damage only by 1/60 (i.e. turned 60% into 59%). So clearly the later points in defensive stats have more impact despite their increased cost due to diminishing returns. Except that this isn't how percentages work.

 

You gave the example yourself. Let's assume you're sitting at 80% mitigation. Ignoring diminishing returns, we compare this with sitting at 40%. In both cases we go up by 1% and look at effective health.

 

Precondition

 

I have 1000 HP.

My defenses reduce incoming damage by x%.

Thus my effective HP are at 1000 HP * 1.x.

 

40% to 41%

 

I still have 1000 HP.

 

My defenses reduce incoming damage by 40%.

Thus my effective HP are at 1400 (1000 HP * 1.40).

 

My defenses reduce incoming damage by 41%.

Thus my effective HP are at 1410 (1000 HP * 1.41).

 

A 1% increase in my defensive stat yielded me a net gain of 141/140 (~1.0071%).

 

80% to 81%

 

I still have 1000 HP.

 

My defenses reduce incoming damage by 80%.

Thus my effective HP are at 1800 HP (1000 HP * 1.80).

 

My defenses reduce incoming damage by 81%.

Thus my effective HP are at 1810 HP (1800 HP * 1.81).

 

A 1% increase in my defensive stat yielded me a net gain of 181/180 (~1.0055%).

 

Conclusion

 

Even if we take a %-based system, the effective impact of increased defensive stats isn't growing proportionally or even exponentially towards the end of the curve. Why? Because when you say you go from 98% to 99% you haven't halved your incoming damage. Percentage-wise you have just increased your reduction from 98/100 to 99/100. So the opposite is actually true. Your first point in a defensive stats is the most valuable, as it increases your defenses from 0/100 to 1/100, which is a gain of 1.01 whereas any later gain is always less than 1.01.

 

So kids, stay in school, don't take drugs and stack your defensive stats. Unless you have diminishing returns. Then act smart and look at your overall gain.

Edited by Eos

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Suppose there is something that will miss you 98% of the time when it has 100 accruacy.  Now suppose we change your defense such that it will miss you 99% of the time.  This effectively doubles your defense simply by adding 1 point of defense.  This is the extreme, but not unattainable case.  Similarly suppose you will be missed 50% of the time by that something, when we add 1 point of defense you are missed 51%.  This is not nearly as big of an increase.  A good way to quantify this is to multiply your mitigation by your health.  At 50% miss rate you, over time, have 2x your health in "effective health".  At 99% miss rate you have 100x.  As you can see going from 50% to 99% is a 50 fold improvement.  But going from 50% to 51% is a very small improvement.

 

This is wrong. Here is why:

 

<condescending crap snip>

 

I have 1000 HP.

My defenses reduce incoming damage by x%.

Thus my effective HP are at 1000 HP + 1000 HP * 1.x.

 

<bad maths snip>

 

So kids, stay in school, don't take drugs and stack your defensive stats. Unless you have diminishing returns. Then act smart and look at your overall gain.

 

 

Would you agree that 100% mitigation means the enemy is doing no damage?

If the enemy is doing no damage would you agree that you have infinite effective hit points?

 

Hopefully you answered 'yes' to both of those, because that means that this formula is clearly wrong: 

1000 HP * 1.x.

 

Because that predicts that having 100% mitigation merely doubles your EHP. Rest of your post is garbage since it was based around that.

 

FYI, the correct formula is 1/(1-x), and it's grade school algebra to figure out that result. Stay in school indeed.

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Suppose there is something that will miss you 98% of the time when it has 100 accruacy.  Now suppose we change your defense such that it will miss you 99% of the time.  This effectively doubles your defense simply by adding 1 point of defense.  This is the extreme, but not unattainable case.  Similarly suppose you will be missed 50% of the time by that something, when we add 1 point of defense you are missed 51%.  This is not nearly as big of an increase.  A good way to quantify this is to multiply your mitigation by your health.  At 50% miss rate you, over time, have 2x your health in "effective health".  At 99% miss rate you have 100x.  As you can see going from 50% to 99% is a 50 fold improvement.  But going from 50% to 51% is a very small improvement.

 

This is wrong. Here is why:

 

<condescending crap snip>

 

I have 1000 HP.

My defenses reduce incoming damage by x%.

Thus my effective HP are at 1000 HP + 1000 HP * 1.x.

 

<bad maths snip>

 

So kids, stay in school, don't take drugs and stack your defensive stats. Unless you have diminishing returns. Then act smart and look at your overall gain.

 

 

Would you agree that 100% mitigation means the enemy is doing no damage?

If the enemy is doing no damage would you agree that you have infinite effective hit points?

 

Hopefully you answered 'yes' to both of those, because that means that this formula is clearly wrong: 

1000 HP * 1.x.

 

Because that predicts that having 100% mitigation merely doubles your EHP. Rest of your post is garbage since it was based around that.

 

FYI, the correct formula is 1/(1-x), and it's grade school algebra to figure out that result. Stay in school indeed.

 

 

 

 

PoE is a d100 system.  3rd Ed D&D is a d20 system.  They work essentially the same as far as the math goes.  For one system each point is 1/100 for the other each point is 1/20.  The main trick with these system is that they are a sliding scale due to opposing stats (accuracy versus defense) and are completely dependent on content (monster accuracy).  However while they are dependent on content they are quite simple to plan for, you just need to know the high end of the range of accuracy.  If you are at 80% avoidance against the most accurate monster in the game, then you are at least that good against everything else.  

 

The equation quoted above is the correct equation, there are some important differences between % chance to take no damage and %damage resistance.  Over enough time they will be effectively similar but there are consequences to avoidance on small sample since it is probablistic, i.e. you can get one shotted instantly even with 99% avoidance.   So the "effective health" model has some flaws with avoidance.  In a practical sense, if you are getting hit by smallish amount of damage say 1/5 to 1/4 of you rhealth and have any kind of healing at all then the model works fine.  If you are getting attacked by things with that could one shot you over and over and often its still OK but becomes problematic

 

The damage threshold on armor in POE is not damage resistance and is somewhat different and more of a pain in the ass to express.  However it can still see a similar trend as well, this is plainly seen by comparing extremely high DT where you only do 1 point of damage, use something that penetrates 3 DT and you quadruple your damage.  Yes you still do crap damage, but its still quadruple.  However since most (but not all) games have variable damage it can a gigantic pain in the ass to quantify and is generally kind of eyeballed. 

It is important to note that since you have two defense mechanics that are both exponential in there effects combining the two can be very very powerful.  

 

However DT has little to do with stats.  Additionally you can be hit much much harder by the really big enemies than you would be able to get DT for.  As with most games DT is uber powerful against small hits and can be very low on the curve for large hits.  25 DT is incredibly strong against things hitting for 20, but its only pretty nice against things hitting for 50 and only modestly useful against something hitting for 100.  All of those hit numbers are possible (in a rough sense) at endgame in PoE so the "value" of DT is extremely variable due to content.  You are not likely to get enough DT to get into the powerful or really powerful portion of the exponential curve for 100 damage hits.  This does not mean it should overlooked by any means.

 

Straight up % damage resistance is not content dependent even though it uses the same base equation for establishing a "time to live".

 

Since PoE is a d100 system, when you take any single opponent in isolation for your analysis each point of a defense (any of the 4) is +/- 1% its useless once it is too far above or below the range of contention (this range is massively extended in the case of crits when compared to defenses).  This requires qualifications for PoE in form of additional multipliers since mitigation is not a straight up binary 0% or 100% like AC in 3rd ed D&D due to the Crit/graze mechanics. This is still pretty straightforward but somewhat of a pain in the ass.  It would essenitally be a spreadsheet that calculated the relative mitigation due to graze(50%)/hits(0%)/misses(100%).  Pure binary hit/miss avoidance mitigation is a simpler case as it is equivalent to to miss chance when taken over time.   Crits can be completely nullified, grazes/hit/misses are a straightup range.  At the -50 portion of the curve you are only rolling over whether you miss or graze and can never actually hit.  So one could argue that at this point each point in a defense has become reduced in effectiveness since you never take more than 50% damage etc.  First this does not change the fact that the curve is still exponential.  Second all the the d# systems eventually reach a point where additional points are useless, either because they are 100% or because a 20 is always a hit and you are at 95% or whatever.  The last point is radically powerful and subsequent points are completely useless until you run into something with higher accuracy.  This statement even holds true with the PoE graze system, 50% is not enough to curtail the massive growth of an exponential curve.  That last point is still radically powerful.

 

Over the broad context of the game since the d# systems use opposing checks (in the parlence of 3rd edtition D&D a Difficulty Check) the relative value of the 1% ( or 5% in the case of d20 ) can change quite radically.

 

Now it is not at all necessary to express these things as percents, which is a just way of expressing ratios and therefore lends itself naturally to any d# system, however it is necessary to understand that the closer you are to the maximum end of the avoidance curve the more and more powerful each advancing numeral of the "roll range" becomes.  You can think of it however you like but this is the curve of the graph.   

 

 

This analysis does not come from WoW, although it has been replicated there since the equation for damage resistance is basically the same.  This analysis has been well understood since 3rd ed D&D.  And probably earlier as well since D&D was using d20 thaco rolls etc.  But  3rd ed D&D everything was a DC on opposing stats so trying to figure the relative value of a point in a skill or +to hit become of central importance and this became more well known and rigorous.  For skill checks, of course, this is different as their results are often a binary outcome rather than an outcomes whose result is a countable number ( ie. an integer ), again this is very content dependent.  Many people building for skill check DC just go for 100%.  For example in DDO certain dungeons would have traps that basically one shot most people, thus they want a rogue with a DC that assures 100%, but for dungeons with many less damaging traps they are ok with 90% or 95% and extremely occasionally have to run through a trap, because the dynamic is the same; the trap burden is reduced by a HUGE amount at those DCs.  Generally they won't go much below a certain DC range because in the d20 system the difference between 1/2 and 1/10 things hitting you is 8 points (50% roll versus 90% roll is 8 skill points in the d20 system), so if you accept someone into your party with 8 less skill points you will be rolling bad 5 times as often.  If you accept someone with 4 points less (70% vs 90%) you have 1/10 vs 3/10, so you are still getting bad rolls 3 times as often.  That is a figure of extremely high statisitical significance.  These things are known in games like DDO, that is why people generally tolerate a swing of 2-3 skill points (generally for rogues/traps) when recruiting for various dungeons that they really want to succeed at, if they are just running for fun its different of course.  

 

If one is truly convinced that this is some sort of %damage resistance WoW exclusive type thing I would invite you to read through the D&D Online boards for tanks and rogues or through various Never Winter Nights boards.  It might be hard to find though unless its stickied as its pretty well settled. 

 

Please note that of course x% chance IS always the same probability as x% chance.  This is an obvious identity.  All of these analysis are about quantifying the consequences of this identity.  % damage resistance IS simpler because there is no probability involved in it and it covers burst and it has no content dependence etc etc.  It would be a mistake to assume that a model covers everything.  But in the end the ratio based damage mitigations can be analyzed in this way with a good amount of accuracy.  This does not mean that the outlier cases of avoidance should not be accounted for, games like City of Heroes expressly addressed such things over time in regards to the "large hits makes it all one big casino problem".

 

Po_EDefense.png

 

 

"Mitigation" above corrects for the +/- 50% mechanic of grazes and crits.  So that mitigation curve is, on average, what PoE defense will do for damage.  It is important to note that various afflictions can operate on grazes so this is an important factor for the non-deflection defenses.  So the above graph is mainly for damage based things. 

 

As the graphs above show, while your mitigation does actually slow down in its improvement due to moving into the graze range, your effective health still increase extremely fast.  Note I left off the last 5 points because effective health becomes so much higher (20,000 for base 100 health) that it makes the rest of the curve harder to visiualize.

 

This is the main reason that defensive stats are radically more important than offensive stats for defensive builds.  If you are at, let's say, -60 due to equipment abilities etc. and your stats bump you up to -80 (stats giving this much is reasonable) then you have gone from 800 to 4000 effective health from a base health of 100.  Conversely going from 20 to 0 (acc-defense) is about 110 to 150 effective health, which isn't bad but all in all is not really likely to seriously matter in a tough fight and against heavy hitters will feel extremely spotty and like gambling high stakes.

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cctobias - I was agreeing with you. Disagreeing with Eos. You don't need to convince me :p

 

I just quoted you cuz you had the right formula as conversation sort of thing.

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I can't help but notice that while everyone here has plenty to say on what's good for a character in combat, everyone is neglecting one fairly important point: How your attributes play into conversation options. The by far most commonly used attribute for conversations is Resolve, with Perception a close second. This is always checked on your main character, not your companions, so if you want to experience lots of different dialogue options you should definitely invest in these two attributes.

 

I have some notes from when I had the same question as you.  Assuming you bother to use whores (regular, not fiery) and resting bonuses, Here's what you'd need for 18 checks.  The list of known checks info is based off of wiki, so it's badly outdated and incomplete. Apologies for the roughness, again it's a paste directly from my notes.

 

So, for conversation purposes, you can get the following bonuses:

Might: 2 from Lyriana, 2 from Dyrford for +4 total

Con: 2 From Serel, 2 from Lyr, 1 from salty or 2 from Cyr for +5-6.  

 need 16 AND rope for egg (!) (dyrford)

Dex: 2 from Serel, 2 from Iquali, 2 from Goose for +6.  

 Badly documented in wiki, need a high score to pickpocket key instead of fighting in dozens quest

Per: 2 from Aldwyn, 2 from Cracker Barrel for +4  

 Bunch of checks up to 16 in Dyrford and crossing

Int:  2 from Aldwyn, 4 from Cracker Barrel for +6  

 Needed in Dyrford and Dyford crossing, mostly (18-14)

Res: 2 from Biggo, 2 from Gilded Vale or 1 from Goose for 3-4    

 Used a lot, but wiki out of date.18 needed for early eder

Lore: 1 From Ald, 2 from Goose for 3.

Athletics:  Recommend 3 for everyone. (there are party-wide checks on this stat)

Survive: 1 from Biggo or Orico, 1 from Cracker Barrel for +2

 5 check at dyrford ogre

So for 18's without equipment, you need 14 might, 12-13 con, 12 dex, 12 int, 14 per, 14-15 res (of course getting all this is impossible without cheating or items)

Assuming you keep enough +2 equipment, that'll take you to 20's for extremes

 

 

So you choose which checks you want to pass and make sure you have at least that much.

Edited by Manty5

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Suppose there is something that will miss you 98% of the time when it has 100 accruacy.  Now suppose we change your defense such that it will miss you 99% of the time.  This effectively doubles your defense simply by adding 1 point of defense.  This is the extreme, but not unattainable case.  Similarly suppose you will be missed 50% of the time by that something, when we add 1 point of defense you are missed 51%.  This is not nearly as big of an increase.  A good way to quantify this is to multiply your mitigation by your health.  At 50% miss rate you, over time, have 2x your health in "effective health".  At 99% miss rate you have 100x.  As you can see going from 50% to 99% is a 50 fold improvement.  But going from 50% to 51% is a very small improvement.

 

This is wrong. Here is why:

 

<condescending crap snip>

 

I have 1000 HP.

My defenses reduce incoming damage by x%.

Thus my effective HP are at 1000 HP + 1000 HP * 1.x.

 

<bad maths snip>

 

So kids, stay in school, don't take drugs and stack your defensive stats. Unless you have diminishing returns. Then act smart and look at your overall gain.

 

 

Would you agree that 100% mitigation means the enemy is doing no damage?

If the enemy is doing no damage would you agree that you have infinite effective hit points?

 

Hopefully you answered 'yes' to both of those, because that means that this formula is clearly wrong: 

1000 HP * 1.x.

 

Because that predicts that having 100% mitigation merely doubles your EHP. Rest of your post is garbage since it was based around that.

 

FYI, the correct formula is 1/(1-x), and it's grade school algebra to figure out that result. Stay in school indeed.

 

 

Guess you're right. Shouldn't do math late at night. Also shouldn't act condescending (but hey, at least I made someone new join the forums!). Sorry for both.

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@cctobias:

You are confusing a +1 increase in chance to dodge, and chance to dodge increased by 1%. The latter indeed leads to the exact exponential figures that you showed in your graph, but the former is what actually happens in the game and it is by definition linear, being a flat +1 and all.


The game to-Hit formula is I believe as follows:
Accuracy - Defense + Random[1, 100] = Total
Miss if Total <= 15
Graze if 16 <= Total <= 50
Hit if 51 <= Total <= 100
Crit if Total >= 101

Assuming a foe accuracy of 5, your chance to dodge is 10% at 0 Def, and 90% at 80 Def
Assuming a foe accuracy of 5, your chance to dodge is 11% at 1 Def, and 91% at 81 Def

Assuming a foe accuracy of 50, your chance to dodge is 10% at 45 Def, and 90% at 125 Def
Assuming a foe accuracy of 50, your chance to dodge is 11% at 46 Def, and 91% at 126 Def

As you can see, chance to dodge increases in a perfectly linear way as your Def increases, so long as foe accuracy stays within range.


A quick search just now resulted in this:
AccuracyMinusDefenceChart.jpeg

 

And this, from J.E. Sawyer:

In PE, for any standard attack, every 5 points of defense translates to a 5% shift to miss, graze, hit, and crit (sometimes negating the possibility entirely).


(It's been confirmed that 1 point of defense translates to a 1% shift as well, i.e. it's not per 5 points increments.)
So the effetcs of extra defense to any pre-existing value is confirmed to be always the same in terms of chance to dodge.


Now how does chance to dodge translate in terms of damage reduction ?

Damage reduction can be expressed with the difference in actual damage vs full damage, i.e. if you take 75 damage when you were supposed to take 100 without some bonus stats, you have a 25% damage reduction going on.

If you dodge successfully, you take no damage. If you fail you take anywhere from 50 to 150% of whatever your opponent's damage is supposed to be. Since our purpose is to prove that there is no exponential growth in usefulness to getting +1 Def, we don't need to obfuscate reasoning with variance in damage or armor DR because as you point out, it is going to be negligible in the face of exponential growth. So we can safely consider that we take 100% damage whenever we fail to dodge.

For our purpose we thus have dodge equal 0% damage and no-dodge equal 100% damage: This equivalence shows that you can substitute 1 to 1 damage reduction with chance to dodge, and therefore if +1 Def translates to the same increase in chance to dodge no matter the amount of pre-existing Def, it follows that +1 Def translates to the same amount of damage reduction as well. There is no exponential :)

Edited by Adragan

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Whoopsies, I forgot to cover your last step.

 

How does damage reduction (and thus defence) translate in terms of effective health ?

 

Effective health can be expressed as the amount of starting health that we need to achieve the same end health value at 0% damage reduction than we would at a non-zero damage reduction. If we have 25% damage reduction and 100 starting health, we will fall to 25 end health against a 100 damage attack. With no damage reduction, we need 125 starting health to reach the same end health. 25% damage reduction is thus equivalent to 125 effective health, which is a 25% health increase. Is +1% damage reduction equivalent to a +1% health increase regardless of the amount of pre-existing reduction ?

 

Assuming a base of 100 starting health and an attack of 100 damage:

 

With 10% damage reduction, we get 10 end health, translated to 110 effective health, and thus a 10% health increase

With 11% damage reduction, we get 11 end health, translated to 111 effective health, and thus a 11% health increase

 

With 90% damage reduction, we get 90 end health, translated to 190 effective health, and thus a 90% health increase

With 91% damage reduction, we get 91 end health, translated to 191 effective health, and thus a 91% health increase

 

As you can see, the effective gain in health increases in a perfectly linear way as our damage reduction increases. Since +1% damage reduction is equivalent to +1 Def when foe accuracy is in range, as showed earlier, it follows that +1 Def equals +1% health indeed.

 

When used properly, all indicators should confirm that the benefit from adding +1 Def is identical whether we have 10 or 90 Def -- modulo graze, crit, armor DR and non-exponential stuff like that.

Edited by Adragan

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Lets not forget here that deflection is physical-only but DR reduces ALL attacks except raw.

 

I'm not implying that you folks don't know this, but I feel that in the excitement of proving how great deflection is that we're easily ignoring the fact that it's a one-trick pony.

 

Granted... it is a very NICE trick... =)

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Assuming a base of 100 starting health and an attack of 100 damage:

 

With 10% damage reduction, we get 10 end health, translated to 110 effective health, and thus a 10% health increase

With 11% damage reduction, we get 11 end health, translated to 111 effective health, and thus a 11% health increase

 

With 90% damage reduction, we get 90 end health, translated to 190 effective health, and thus a 90% health increase

With 91% damage reduction, we get 91 end health, translated to 191 effective health, and thus a 91% health increase

 

Seems like you made the same mistake as I did. But your example should look like this:

 

100 Health, 0% Damage Reduction, after 100 points of (unmitigated) Damage I fall over dead resulting in 100 effective health.

100 Health, 90% Damage Reduction, after 1.000 points of unmitigated Damage (1000 * (1.00 - 0.90) = 100) or 100 points of mitigated damage I fall over dead resulting in an effective health of 1.000.

100 Health, 99% Damage Reduction, after 10.000 points of unmitigated Damage (1000 * (1.00 - 0.99) = 100) I fall over dead resulting in an effective health of 10.000.

 

Every attack has it's damage reduced by damage reduction thus resulting indeed in an exponential growth of my effective health.

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Lets not forget here that deflection is physical-only but DR reduces ALL attacks except raw.

 

I'm not implying that you folks don't know this, but I feel that in the excitement of proving how great deflection is that we're easily ignoring the fact that it's a one-trick pony.

 

Granted... it is a very NICE trick... =)

 Yeah but all defenses go against accuracy and the various stats give those as well.

 

This is a reason why a defensive build also has less dump stats than an offensive, however the same math applies to all defenses.  The only sticky point is that grazes affect duration and on some spell a lower duration may still be a very dangerous situation so you may want a higher target number for Fort vs Def.  But stats like PER or RES give deflection and REF or WIL as well.  Defensive builds need to be careful about dumping Con or Mig or Dex so they can get decent non-deflection defenses, but the deflection stats give DEF and the exact same amount of other defeneses as whatever the other stat for that is.  

 

Oddly for defensive build Fort is often the troublesome defense because Con is such a weak stat.  Frankly the stat system in POE is really messed up both thematically and in that it does the exact opposite of what it was supposed to for builds. 

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@Eos: That's right! All of my posts are correct except the last - I was not used to the concept of effective health and had to make a definition up, and failed to calculate properly in the process.

 

Even with the train of thought I picked we do end up with 1000 effective health for 100 actual health with 90% damage reduction. Not 190. That's because health necessary to reach the same HP mark at 0% reduction and a constant incoming damage, is Health + DamageReduction*IncomingDamage, not Health + DamageReduction. (that only works when incoming damage is 100, duh)

 

Indeed, effective health does grow exponentially as damage reduction increases. The rule applies to all sources of multiplicative damage reduction, not just defense, and it does mean that +1 Def is way more useful when you have 90 than when you have 10, assuming other potential damage reduction sources are the same. (As other sources grow the increase is usefulness becomes less drastic, but I don't know if there are other sources in PoE)

 

Thanks for pointing this out to me :)

Edited by Adragan

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@cctobias:

 

You are confusing a +1 increase in chance to dodge, and chance to dodge increased by 1%. The latter indeed leads to the exact exponential figures that you showed in your graph, but the former is what actually happens in the game and it is by definition linear, being a flat +1 and all.

 

 

The game to-Hit formula is I believe as follows:

Accuracy - Defense + Random[1, 100] = Total

Miss if Total <= 15

Graze if 16 <= Total <= 50

Hit if 51 <= Total <= 100

Crit if Total >= 101

 

Assuming a foe accuracy of 5, your chance to dodge is 10% at 0 Def, and 90% at 80 Def

Assuming a foe accuracy of 5, your chance to dodge is 11% at 1 Def, and 91% at 81 Def

 

Assuming a foe accuracy of 50, your chance to dodge is 10% at 45 Def, and 90% at 125 Def

Assuming a foe accuracy of 50, your chance to dodge is 11% at 46 Def, and 91% at 126 Def

 

As you can see, chance to dodge increases in a perfectly linear way as your Def increases, so long as foe accuracy stays within range.

 

 

A quick search just now resulted in this:

AccuracyMinusDefenceChart.jpeg

 

And this, from J.E. Sawyer:

In PE, for any standard attack, every 5 points of defense translates to a 5% shift to miss, graze, hit, and crit (sometimes negating the possibility entirely).

(It's been confirmed that 1 point of defense translates to a 1% shift as well, i.e. it's not per 5 points increments.)

So the effetcs of extra defense to any pre-existing value is confirmed to be always the same in terms of chance to dodge.

 

 

Now how does chance to dodge translate in terms of damage reduction ?

 

Damage reduction can be expressed with the difference in actual damage vs full damage, i.e. if you take 75 damage when you were supposed to take 100 without some bonus stats, you have a 25% damage reduction going on.

 

If you dodge successfully, you take no damage. If you fail you take anywhere from 50 to 150% of whatever your opponent's damage is supposed to be. Since our purpose is to prove that there is no exponential growth in usefulness to getting +1 Def, we don't need to obfuscate reasoning with variance in damage or armor DR because as you point out, it is going to be negligible in the face of exponential growth. So we can safely consider that we take 100% damage whenever we fail to dodge.

 

For our purpose we thus have dodge equal 0% damage and no-dodge equal 100% damage: This equivalence shows that you can substitute 1 to 1 damage reduction with chance to dodge, and therefore if +1 Def translates to the same increase in chance to dodge no matter the amount of pre-existing Def, it follows that +1 Def translates to the same amount of damage reduction as well. There is no exponential :)

 

 

Whoopsies, I forgot to cover your last step.

 

How does damage reduction (and thus defence) translate in terms of effective health ?

 

Effective health can be expressed as the amount of starting health that we need to achieve the same end health value at 0% damage reduction than we would at a non-zero damage reduction. If we have 25% damage reduction and 100 starting health, we will fall to 25 end health against a 100 damage attack. With no damage reduction, we need 125 starting health to reach the same end health. 25% damage reduction is thus equivalent to 125 effective health, which is a 25% health increase. Is +1% damage reduction equivalent to a +1% health increase regardless of the amount of pre-existing reduction ?

 

Assuming a base of 100 starting health and an attack of 100 damage:

 

With 10% damage reduction, we get 10 end health, translated to 110 effective health, and thus a 10% health increase

With 11% damage reduction, we get 11 end health, translated to 111 effective health, and thus a 11% health increase

 

With 90% damage reduction, we get 90 end health, translated to 190 effective health, and thus a 90% health increase

With 91% damage reduction, we get 91 end health, translated to 191 effective health, and thus a 91% health increase

 

As you can see, the effective gain in health increases in a perfectly linear way as our damage reduction increases. Since +1% damage reduction is equivalent to +1 Def when foe accuracy is in range, as showed earlier, it follows that +1 Def equals +1% health indeed.

 

When used properly, all indicators should confirm that the benefit from adding +1 Def is identical whether we have 10 or 90 Def -- modulo graze, crit, armor DR and non-exponential stuff like that.

I graphed out the mitigation above and accounted for both grazes and crits.  Mitigation is not exponential.  In fact it begins to grow slower due to grazes but would otherwise be linear.

 

In your example above you die in less than two hits at 10%, you die in 10 hits at 90%.  The "time to live" is many times larger.  This is why the equation drainbramage posted is more useful.

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Right-o. My last post in page 2 miscalculates effective health. It uses a different viewpoint to get there but the result is the same as yours once corrected. So effective health is a very valid notion that I didn't consider previously, thank you guys ;)

 

It's interesting to know that any effect that is applied multiplicatively to damage reduction will benefit from the exponential growth in usefulness as well. Are there skills like that in the game other than defense-increasing ones ?

Edited by Adragan

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Right-o. My last post in page 2 miscalculates effective health. It uses a different viewpoint to get there but the result is the same as yours once corrected. So effective health is a very valid notion that I didn't consider previously, thank you guys ;)

 

It's interesting to know that any effect that is multiplicative damage reduction will benefit from the exponential growth in usefulness as well. Are there skills like that in the game other than defense-increasing ones ?

 

For the most part just Armor ie. DT, and that is problematic in its variance.  For offense there really isn't, Crit won't work out that way, its at best a straight 50% increase in damage.  All damage stuff adds to the multiplier figure

 

But the other side of the coin of of course is the defense DEBUFFS can be very imporrtant if you are finding yourself having trouble, and of course you want to avoid them like the plague on a tank.

 

Most of my education on this topic comes from posts by Arcanaville on the City of Heroes forums.  Unlike many MMORPGs, City of Heroes allowed an encounraged various defense buffs to be stacked on top of each other to significant maximums.  There were no dedicated "healers".  The various power sets of the Defender Archetype, might buff avoidance or resistance and some had some amount of healing.  You could run an team with two forcefield defenders and only be buffing avoidance with no healing.  The buffs from both those defenders would stack up to an archetype maximum.  

 

Those forums are probably gone, but she made a comprehensive analysis of the various defensive sets in that game.  The power sets involved %dam resistance, avoidance, and healing.  Some being all around one type, some mixing things.  The game could also involves fight with few or very very many opponents, with a very wide range of damage.  To compare things in a way that did not come to down how it "felt" she attempted to be very comprehensive.  Due to her analysis the Devs actually altered certain powersets as she essentially proved mathematically that the avoidance based power set was a) weak in general and b) extremely weak in certain circumstance (alpha strikes of spawns when in a large party).   CoH's content was generated dynamically, the more people in your party the more and tougher things that spawned.  This exposed a weakness of avoidance as even though over time the mitigation may be the same as % damage when 20 things are shooting at you and some of those things can take off half your health or more, well you may have a problem.   Especailly when a full team may 3-4 boss level mobs at +2 or more level.  Having one of the powersets be weaker the more it teamed up in an cooperative game was obviously bad.  

 

Similarly the Willpower set was a combo of all three mitigations and it had modest amount of regen similar to the PoE fighters inherent.  Well how do you rate that healing?  Alone it was fairly poor, but layered on top of both ok avoidance and ok %damager she proved it was actually quite strong.  In a game where your character development involves enahcaning some aspects of your power this is very important, do you enhance the accuracy penalty or the healing effect on your aura power?  At some price point it, since you may have a lot of mitigation already healing becomes stronger and stronger as well.

 

As an off topic aside this is also why CoH was the best party based MMORPG that has ever existed.  Not that it was the best MMORPG, but the majority of its players would play cooperatively and teams would run for hours swapping people in and out, varying how things spawned and what the offensive and defensive make up of the team was.  Unfortauntely it was a bit too generic due to the dynamic content model.

 

It is important to note that while everything above is phrased in terms of effective health, you can put all healing into that equation as well.  So in theory, the Might bonus that applies to healing will be multiplied by the effect of defense as well, so this can be an important factor when considering a defensive fighter build.  Might is possibly considerably stronger than CON.  However that strategy is complicated by endurance vs health as the fighter will eventually die no matter what, given enough time and that dynamic favors Con.

 

Same goes for paladins and lay on hands.

 

This is one of the reasons that later in CoH's career for the eventually fixed Super Reflexes power set the Heal generic power (something any type of character could take) was almost always selected by such builds.  "Time to live" is fine but if you can make damage coming in be eclipsed by health coming in, you are immortal (without the end/health mechanic of PoE).  Super Reflexes was a power set that offered no healing and no extra regen.  If  I remember right all archetypes could, in theory, achieve 95% avoidance (whereas Tank archetype could get 85% res and others were 75%), so the effect of a heal + high avoidance was quite huge, I beleive Arcanaville had that combo rated as one of the most powerful defensive things in the game even though Heal itself was just an ok healing power compared to the 4-5 other major heal powers on some Defenders etc.  

 

People would basically say you ruined your build if you were an SR without Heal power taken.  Of course others would say 95% avoidance was enough and they didn't really need it etc etc and that gets rather subjective and never really resolved beyond personal taste. 

 

Note that a really good group in CoH could have layered defenses of avoidance+%res+healing due to stacked buffs and multiple defenders etc, so offense in that game could get scaled to much higher numbers than might be initially thought.  So getting one shotted or very quickly one-two-three shotted even with really excellent avoidance was something that actually was an important case to handle.  Generally you wouldn't see that with high amounts of all three layers, but there could be a very large varaince in both difficulty and group make up and sometimes you would see a lot of insta-gibs when things didn't line up right or a certain enemy group had certain debuffs.  Which again caused a lot subjective arguing back and forth about what powers to pick, generally people who did PUGs a lot and were SR always took Heal.  And one of the great advantages of Ninjitsu was that it had a heal already and saved you a power slot although it didn't handle debuffs as well etc etc.  

 

One interesting conclusion of this multiple year forum discussion was a general concensus that layered/multi-spectrum defenses were really surprisingly good.  This was mostly due to the Willpower defense set for Scrappers and Tanks being released later in the game.  It had basically a bit of everything and it was surprising good at staying alive even though none of its powers was really on the large up slope of any particular type of defense.  It didn't even have on-demand healing just good regen.  Not that it was the best Defensive power set but it was something that performed better than anticipated.  Of course people knew a Heal with high mitigation was strong.  But Willpower was like 3-4 medium level mechanics and performing as well as sets with high values for one type of mechanic.

 

 

So oddly Might is actually possibly a better defensive stat than Con.  Even though might is linear, the effect will piggy back on the exponential defensive curve.  Its still linear but it will have such a large multiplier with better defensive stats that even really crappy heals become really good.  Making each point in Might go from meh to very interesting for self heals.  However each point of Might is of the same weighting.  But I am not saying that for certain (due to health/end and resting) and that only applies to self heal.  But due to needing Fort you should have the combination of those two stats at a decent level no matter what.  For fighters specifically this should be a real consideration because that heal is always in effect, and while going from 3 to 4 (or whatever close enough) maybe seem small, with the addition of defense and DT and the fact that its not an action its considerably more than it may seem.  For an offensive fighter with no armor and only ok defense, meh whatever maybe ignore it.  Specifically for high defense with significant regen it is hard to get a "feel" for how valuable it is.  I never really quite got a good feel for it until I made a Willpower based scrapper in CoH and pushed it to its limits.  You can fight at medium and low health for far longer than you may think, its a sort of energizer bunny type feel to it, it just keeps going, especially if you play smart and buy yourself some time when in a bad situation. 

 

 

For the most part though such analysis is only necessary in this game for the offtank with good damage sort of build.  The question being something like is really good defenses + might as a fighter enough to make up for, say, not using heavy armor so you can attack fast?  Pure defense just stacks everything.  But very high defense + decent regen could be very tough and being naked is essentially similar to good armor + high dex.

 

So it may be the case that a naked low DEX high MIG high PER/RES fighter build is actually similar in performance damage wise to high migh/high dex with big armor and possibly actually better defensively.  I am not real sure on that though.

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Yeah it needs some hard math or a simulation because there are too many variables interacting at this point.

 

It's an interesting take on the RPG builds issue, anything that challenges the dogma of indestructible but harmless tanks generating unjustified aggro is good in my book. I'll keep my eyes peeled and explore the topic as I play for now ;)

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FWIW, MERP/ROLEMASTER  was probably the first D100 game system that used a D100 roll VS DC. The fact DND 3rd Ed used a D20 still was mitigated in a lot of instances with the new saving throw/one point based skill system. Monte Cooke is Genius :)

 

Note, Role Master still only had about 8 result categories to determine what effect actions had (covering -100 to +100). A good DM/GM will turn a 'one in 5%' into a truly chaotic result.

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