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Defense, Deflection and Damage reduction (GF)
xilinear
Member Posts: 140 Arc User
Having not seen anything on this topic, I did my maths and so far here is what I come up with. This is valid only for a guardian fighter, as of now I didn't try this on any other class, so if someone could verify these number on their char sheet, I would be glad. Also, GFs are welcome also to check these numbers.
At level 60 (need more feedback from lower levels to verify this).
DR(defense,AC) = (AC -10) * 0.5% + 50% * Defense/(1644+Defense)
A spreadsheet showing how this looks like is here:
https://docs.google.com/spreadsheet/ccc?key=0Aj1iYKPu1WmAdGN2NW1ydzFYdkdwUzE5SmRiNGZLVkE&usp=sharing
Hence, the damage reduction you get from Defense seem to be capped at 50%, overall damage reduction however also uses your AC, so it could in theory be above that (need better gear to be able to verify that),
For deflection, it is not yet clear to me if the deflected damage (already reduced by 50%) still goes through the damage reduction of AC and Defense. My guess is yes for two reasons:
1) If not, then you could in theory (provided the availability of gear of course) have a damage reduction of strictly more than 50% while if deflected it being reduced to 50%...which would make no sense, since having deflection would increase in this case the damage you take :-).
2) The combat log. I went into a zone, agroed one mob and logged the physical damage it did. while the combat log doesn't state at all if that damage was deflected or not, the floating combat text clearly shows crits (the lightning arrow), normal hits and deflections. In this case the combat log show the actual magnitude of the hit and the damage you take. Here is a quick snippet (please don't laugh, I wasn't going to risk this on an epic boss, just some random mob).
[Combat (Self)] Scavenger deals 487 (1036) Physical to you with Claw. normal hit = 53% DR
[Combat (Self)] Scavenger deals 94 (200) Physical to you with Melee Attack. normal hit = 53% DR
[Combat (Self)] Scavenger deals 146 (311) Physical to you with Melee Attack. normal hit = 53% DR
[Combat (Self)] Scavenger deals 487 (1035) Physical to you with Bounding Charge. normal hit = 53% DR
[Combat (Self)] Scavenger deals 48 (206) Physical to you with Melee Attack. deflected hit = 76.7% DR
[Combat (Self)] Critical Hit! Scavenger deals 605 (1287) Physical to you with Claw. normal critical hit = 53% DR
[Combat (Self)] Critical Hit! Scavenger deals 61 (259) Physical to you with Melee Attack. deflected critical hit
[Combat (Self)] Critical Hit! Scavenger deals 92 (393) Physical to you with Melee Attack. deflected critical hit
My overall Damage reduction is currently at (as shown in char sheet) 46.1% this number seem to be incorrect in connection to the actual log since my character seem to consistently shrug more than half the damage. My defense is at 4049, my AC from gear is +20, and I have the shield defense paragon feat (+5) [which seem to be bugged since it display only +1] and the base AC is at (+10), so if my equation is correct :
DR(defense,AC) = (31 -10) * 0.5% + 50% * 4049/(1644+4049) = 46.06% (close enough to the char sheet)
If the Paragon feat was working I should then be at :
DR(defense,AC) = (35 -10) * 0.5% + 50% * 4049/(1644+4049) = 48.06% (too far from char sheet and too far from the log)
But then I remembered that I took a feat which is Armor specialization (maxxed), increases the effectiveness of AC and defense by 5%/10%/15%.
Coincidentally:
1.15 * DR(defense,AC) = [(31 -10) * 0.5% + 50% * 4049/(1644+4049)]*1.15 = 52,97%
I am not claiming this is how Armor specialization works, but the numbers do fit quite nicely. Of course I could respecc and try this out again (but those AD are hard to come by and the cost of a respecc is just out of budget for me right now, If anyone didn't spec into these points, I would gladly want a chat and experiment with them to verify this).
All in all, one can conclude that :
1- Deflection stacks on top of defense
2- Any hit can be deflected (i.e. normal hits and critical hits), which suggests that the combat model is not a combat table, but a double roll. Basically, the mob rolls its damage (hit, crit), you roll your (hit, deflect).
The combination of defense and deflection could lead to very interesting optimizations. I am still working on the deflection rating vs. deflection chance (didn't have much gear with deflection so any input numbers are welcome). One thing is certain, that deflection becomes quite useful per point past a certain point in defense, hence, using deflection runes (which have the same budget per point as defense) could be overall more beneficial in overall damage reduction.
I hope this little analysis could be helpful to others, looking forward to feedback and help on these topics. I may have made some mistakes, in that case I apologize for any misdirection this may cause. I also hope the devs answer my ticket and tweets on the +AC paragon feat if it is a bug or just a display bug in the character sheet (so far I really think it is a bug if my previous analysis turn out correctly).
contact ingame: redgar silverkin@xilinear
At level 60 (need more feedback from lower levels to verify this).
DR(defense,AC) = (AC -10) * 0.5% + 50% * Defense/(1644+Defense)
A spreadsheet showing how this looks like is here:
https://docs.google.com/spreadsheet/ccc?key=0Aj1iYKPu1WmAdGN2NW1ydzFYdkdwUzE5SmRiNGZLVkE&usp=sharing
Hence, the damage reduction you get from Defense seem to be capped at 50%, overall damage reduction however also uses your AC, so it could in theory be above that (need better gear to be able to verify that),
For deflection, it is not yet clear to me if the deflected damage (already reduced by 50%) still goes through the damage reduction of AC and Defense. My guess is yes for two reasons:
1) If not, then you could in theory (provided the availability of gear of course) have a damage reduction of strictly more than 50% while if deflected it being reduced to 50%...which would make no sense, since having deflection would increase in this case the damage you take :-).
2) The combat log. I went into a zone, agroed one mob and logged the physical damage it did. while the combat log doesn't state at all if that damage was deflected or not, the floating combat text clearly shows crits (the lightning arrow), normal hits and deflections. In this case the combat log show the actual magnitude of the hit and the damage you take. Here is a quick snippet (please don't laugh, I wasn't going to risk this on an epic boss, just some random mob).
[Combat (Self)] Scavenger deals 487 (1036) Physical to you with Claw. normal hit = 53% DR
[Combat (Self)] Scavenger deals 94 (200) Physical to you with Melee Attack. normal hit = 53% DR
[Combat (Self)] Scavenger deals 146 (311) Physical to you with Melee Attack. normal hit = 53% DR
[Combat (Self)] Scavenger deals 487 (1035) Physical to you with Bounding Charge. normal hit = 53% DR
[Combat (Self)] Scavenger deals 48 (206) Physical to you with Melee Attack. deflected hit = 76.7% DR
[Combat (Self)] Critical Hit! Scavenger deals 605 (1287) Physical to you with Claw. normal critical hit = 53% DR
[Combat (Self)] Critical Hit! Scavenger deals 61 (259) Physical to you with Melee Attack. deflected critical hit
[Combat (Self)] Critical Hit! Scavenger deals 92 (393) Physical to you with Melee Attack. deflected critical hit
My overall Damage reduction is currently at (as shown in char sheet) 46.1% this number seem to be incorrect in connection to the actual log since my character seem to consistently shrug more than half the damage. My defense is at 4049, my AC from gear is +20, and I have the shield defense paragon feat (+5) [which seem to be bugged since it display only +1] and the base AC is at (+10), so if my equation is correct :
DR(defense,AC) = (31 -10) * 0.5% + 50% * 4049/(1644+4049) = 46.06% (close enough to the char sheet)
If the Paragon feat was working I should then be at :
DR(defense,AC) = (35 -10) * 0.5% + 50% * 4049/(1644+4049) = 48.06% (too far from char sheet and too far from the log)
But then I remembered that I took a feat which is Armor specialization (maxxed), increases the effectiveness of AC and defense by 5%/10%/15%.
Coincidentally:
1.15 * DR(defense,AC) = [(31 -10) * 0.5% + 50% * 4049/(1644+4049)]*1.15 = 52,97%
I am not claiming this is how Armor specialization works, but the numbers do fit quite nicely. Of course I could respecc and try this out again (but those AD are hard to come by and the cost of a respecc is just out of budget for me right now, If anyone didn't spec into these points, I would gladly want a chat and experiment with them to verify this).
All in all, one can conclude that :
1- Deflection stacks on top of defense
2- Any hit can be deflected (i.e. normal hits and critical hits), which suggests that the combat model is not a combat table, but a double roll. Basically, the mob rolls its damage (hit, crit), you roll your (hit, deflect).
The combination of defense and deflection could lead to very interesting optimizations. I am still working on the deflection rating vs. deflection chance (didn't have much gear with deflection so any input numbers are welcome). One thing is certain, that deflection becomes quite useful per point past a certain point in defense, hence, using deflection runes (which have the same budget per point as defense) could be overall more beneficial in overall damage reduction.
I hope this little analysis could be helpful to others, looking forward to feedback and help on these topics. I may have made some mistakes, in that case I apologize for any misdirection this may cause. I also hope the devs answer my ticket and tweets on the +AC paragon feat if it is a bug or just a display bug in the character sheet (so far I really think it is a bug if my previous analysis turn out correctly).
contact ingame: redgar silverkin@xilinear
Post edited by xilinear on
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Damage Resistance = 0.5*(ArmorClass-10)+50*Defense/(Level^0.25*1038-1194+Defense)
So two things:
1) My forumla for the level is close to the constant you've used but not exact so that probably needs a tweak. If you can, check a range of constants to see if more than one works at level 60 (this will almost certainly be the case, i.e. you might fine 1640 to 1650 works for your gear). If you give me those numbers I'll tweak the part of my formula that derives that constant from your level.
2) I've found that Feats affect the formula for Recovery in the same way that you've shown your Mitigation Formula to work with your Mitigation Feat.
I have only one data point for Deflect because it's not a stat I collect as a Control Wizard, so I can't help you there.
I myself specced wholly into Constitution as a dwarf, comin out of the gate with 20 CON, 15 STR and 13 DEX. My basic intent is to concentrate on blocking large damage dealing attacks from either bosses or elites and letting my ridiculous amounts of health take the brunt of the trash. No use wasting guard on an attack that tickles me. lol
Beyond that I'm curious to see what's more worthwhile to put focus on. Defense over Deflection or vice versa?
[SIGPIC][/SIGPIC]
Have a look at Xilinear's link, the stat starts diminishing from the first point. So it's really a matter of when it becomes worse than Deflect...which is far as I can see would take a LOT of Defense.
What %'s are you getting from your Defense and Deflect stats Rokuthy?
In my hybrid gear:
AC - 31 - 10.5%
Defense - 4624 - 36.9%
Damage reduction - 47.4%
Deflect - 2054 - 15.7%
Deflection Chance - 17.7%
Assuming you've got the Armor Specialization Feat you're getting another 15% on your Defense, plus Defense is stacking additively with a larger bonus (10.5% from Armor Class vs. the 2% Deflect you have from Dex). So all up you're getting:
0.0039% damage mitigated per point of Deflect.
0.0104% damage mitigated per point of Defense.
So Defense is 2.67 times more valuable, assuming I haven't screwed up somewhere there.
Defense and Deflect don't even scale well together, if I were a tank I'd dump as much Deflect as possible for whatever gives more threat generation.
1640, 1650 are absolutely fine, the 1 decimal rounding still put the DR percentages right on spot on all but 1 data point. Actually seems that's why my regression gave me something in that range. Here is the numbers I worked with:
150 4,20%
619 13,70%
702 15%
1171 20,80%
2424 29,80%
2976 32,20%
3638 34,40%
3908 35,20%
4017 35,50%
Great to see a fellow theorycrafter investigating too! And yes that feat is absolutely not clear. Effectiveness of AC and Defense, at first I thought It increased the defense and AC by 15% :-) which absolutely didn't fit the numbers.
This seems to be different with different classes, I am not sure yet if this number can be tweaked by gear, it would be great if it did (a set bonus perhaps? wishful thinking). Anyways, I rolled recently an alt rogue (wanted a pvp pwn class, I apologize!), still at low levels and the deflection severity is at 25%.
When it comes to average damage reduction taking into account the RNG, you would get (if i didn't screw up):
DR_average = Deflection_Chance * [50%+ DR(AC,Defense)/2] + (1-Deflection_Chance) * DR(AC,Defense)
Now to really compare point per point the defense rating and deflection rating, we need to know how Deflection_Chance varies as function of Deflection rating. I suspect a similar model as that of Defense, but we have nowhere enough points...(Sad face). Any idea what the cap could be, 50% ?
I am more interested to where to get deflection severity, as GWF I dont have even 1 skill that increase it, didnt see gear that increase it either. But getting deflection severity with high deflect chance should pump defense alot. GWF got lot of deflection chance, i can have up to 50% deflection chance now without bigger problem.
I wonder if the AC is working as it should, why the first 10 points dont give anything, its 10 points still, sems counter intuitive for me. But on other hand it work same for the base stats (str/dex/int) where 10 points dont do anything.
for as much as people hate to hear it, it is a dnd game so the stats starting at 10 but doing nothing represent a normal person, there is nothing special about them, every point after 10 is a representation of how an adventurer is tougher, smarter, stronger, etc.. from the norm. AC starting at 10 represents the base number to hit an unarmored person, so that's supposed to represent just your body. Now in this game AC just calculates to %dam res so you as a person would have none, the armor creates that.
Just my take on why those numbers do nothing in this game but seeing what they drew inspiration from it makes sense to me.
Arktourous, if you can could you write down your
Deflection rating and your deflection change % by swaping pieces of gear, It will be very useful to understand the trade-offs. 3-4 points of different deflection ratings and deflection chance would be great.
I was at 22.4% Deflection (without Ioun Stone stats). 15.4% from 2000 deflection, 2% from 14 dex, 5% from Plate Agility. I stood there naked and added the following amounts/ratings. I tried to aim around a 200 - 250 or so jump in rating each time:
Deflect Rating -- Deflect %
58 -- 0.2%
116 -- 0.6%
245 -- 1.5%
374 -- 2.7%
503 -- 3.9%
755 -- 6.3%
1007 -- 8.5%
1259 -- 10.6%
1539 -- 12.6%
2000 -- 15.4%
2200 -- 16.4% (drank pot)
Graphed:
So you can see diminishing returns start to kick in post 2000. A very tiny amount (couple 100) won't get much out of it but as you get it passively on gear it's not bad. Considering how poorly defense scales past 4000 (which will net you around 45% reduction) going for Deflection or Offensive stats becomes ideal past that point.
Could be wrong, but that's what you math guys are for.
31*Deflect^1.4/(LevelConstant+Deflect^1.4) = % Deflect Chance
where LevelConstant is between 42,276 and 42,346
The same formula fits my lower level Deflect data, although I admit I don't have heaps of it.
As for a formula for the LevelConstant, I've been working on one for Defense and can't for the life of me get anything to fit. I even tried a curve fit program and failed, so their either using a table of values not derived from a formula, or the formula can't be expressed as a polynomial equation (more likely).
Could be wrong, but that's what you math guys are for.[/QUOTE]
I can verify that there is a soft cap around 45% DR from defense. Sadly AC is far less valuable than defense for how hard it is to increase-- although it appears to be calculated separately and not count against the same point of diminishing returns (which is glorious). Another thought in terms of mitigating damage is regen. Granted, lifesteal and regen can both be hard to budget for- but Regen can at least be calculated as a constant. With enough dmg reduction and deflection, it starts to look very tasty in terms of slowing the net loss of hp. (assuming you aren't getting crushed for 16k a pop)
In what way?
I was thinking about Regen too, it scales up faster than Deflect but then diminishes sooner. You can work out it's value vs. Defense and Deflect if you make an estimate of how how much DPS you're taking. The larger the portion of your health bar you lose each second, the worse Regen is vs. Deflect and Defense.
The cut off point for Deflect vs. Regen is about 67% of your health each second. Taking less damage than that? Regen is better.
Defense is much stronger and scales better so it's hard to make a comparison, by the time you've replaced some Deflect with Regen, Regen will have tapered off and wont hold up well vs. Defense.
This is a function of the source material. D&D has always treated 10 as normal no bonus or penalty. Having a state over 10 meant you were better than normal and got a bonus, less than 10 meant you were bad and had a penalty.
Lol, actualy your wrong, it was introduced because D&D uses a d20 die to roll stuff which means a ac of 10 is base, and a +0 to hit netted a 50% chance to hit on each swing, alot is calculated from that formula in D&D, for example base diffuclty of a skill check is 10 ect ect, so in summary its NOT based on body or anything like that its based on the mechanics of rolling a d20 die
Be careful throwing around terms like "always". Before 3E, AC improved downward from 10 (worst) to -10 (best).
lets play a virtual GF with the following stats:
40% Damage Reduce depending to Defense and AC
20% Deflection Chance
This GF is getting 5 Hits. Each hit 100 Damage. 500 Damage in 5 hits.
-> 300 Damage by using the 40% damage reduction.
20% chance = every fifth hit will be deflected (50% damage deflected). 60 damage per hit (after 40% reduction), 5 hits. In this example only one hit will trigger deflec which results in 30 damage instead of 60
-> 270 Damage by using the 40% damage reduction and 20% deflec chance.
well... 20%chance for half damage = 10% less damage. 10% of 60% damage after first reduction = 6%.
40% Damage Reduction +20% Deflec = 46% Damage Reduction
Another example:
GF with high defense. 50% Damage Reduction, 33% deflec. Wow, impressive ... ... no its not impressive: 58% Damage reduction. 33% deflec is hard to get. 8% damage reduction is looking very bad.
Deflec is useless. Its senseless to push Deflec by enchantments.
But well, some people are arguing like this: "omg roflmao lol you deflec the huge attack of the boss!!!! you are godlike!!!!" - well the next X huge attacks will not be deflected at all. Its all about the average damage reduction.
And here is the reason:
+Def!
Why do u think "every fifth hit will be deflected." ?
Its only 20% chance. You can deflect hits 5 times in a row, if you are lucky boy,
or have no deflect from 5 hits at all. Its just a random roll.
And every next roll have no diminishing from previous roll.
It's true, big investment for a small return. I want to add some info:
1) At 4000 Defense it's value drops below the value of Deflect, so you can't just put all those points into Defense and expect it to work out.
2) Damage Reduction caps at 80%, which is an issue when a Cleric is buffing your Damage Reduction (+11% from feated Foresight, +24% from Astral Shield, +30% from Hallowed Ground, +40% from Divine Armor). Deflect exceeds that cap taking you up to 90% damage mitigated.
3) Preliminary testing on the Block mechanics show that your Defense counts for how much you can absorb with Block, but you will never dodge a blocked attack (i.e. Deflect does nothing on Blocks).
4) Life Steal and Regen will both heal you for that 6% for a lot less points.