## Friday, 3 February 2012

### Guides - Shield versus Defense

WARNING MATH !!!

NOTE: This post has been supplemented by: http://www.tankingtor.com/2012/07/swtor-optimal-tanking-gear-guide.html which describes optimal gearing for a tank in more detail and with more real game examples.

For the last few days I've been theorycrafting with Shield chance/absorb and Defense rating to see how the survive-ability works out and with diminishing returns where you're better off spending those points.

For the sake of these calculations both defense and shield proc off the same types of attacks.  They do not proc off all attacks (I'll be writing up a guide for this later) but they do proc off the same attacks so weighting them based on what they effect has no bearing on calculations.

Because of the types of damage they defend against both stats are inherently more useful in PvE than in PvP, but there is no difference between them for how effective they are in either place.  IE: They are both equally effective in PvE and equally ineffective in PvP.

So - premise:
Most of my numbers are based off the Jedi Guardian base defense and shield chances.  Some of my specific numbers will change based off your spec - the actual impact and overall guidelines will be the same no matter what your final numbers are.

For example:  Adding 5% shield change costs ~90 attribute points.  For a JG that will bring my total to 25% shield chance (base 20), for someone else it will bring them to 10% (base 5), or 20% (base 15).  The actual bonus calculation from skill points doesn't change based on what your base is.

Here is the diminishing returns chart for Defense and Shield.

You'll see the chart starts at 20% shield and 5% defense, that's just because that's where my guardian starts.  The chart doesn't alter based on your baseline other than the starting point moves up or down.  So if you have base 0% shield your max will be ~50% instead of ~70% shown.

The bottom is how many skill points it takes to reach that value.  You can see why reaching 50% absorb OR shield requires you to sacrifice in many other areas.

The next graph shows how much return you get for your point value.  You'll see at the beginning that Absorb gives the largest increase per point spent, then slowly falls below shield rating coming more even with Defense rating.

This graph led me to ask the question, How much value does each percentage increase actually net you.  IE: Is it better to stack Absorb for the higher net gain at the start or does Defense provide more mitigation even with a lower value.

Bring on the math!!

First I set up my experiment.
Based on 100 hits doing 100 damage, what is the mitigation gained for each stat.
NOTE: I altered this primary experment in various ways throughout my calculations (1000 hits of 100 damage, or 100 hits of 1000 damage) and it had no effect on the actual 'winners' in the formulas.  The only difference was how much damage was actually mitigated.

Defense was quite linear since I was working with round numbers, 5% defense rating dodges 5 our of 100 attacks - effectively netting 500 damage mitigation.  Easy.

Where things got complicated was with the Shielding formula.  It wasn't good enough to calculate how much gain you got from one stat or the other because they were dependent on each other.  So, to find the sweet spot (best investment for points spent) I set up a matrix of Shield v/s Absorb.  I'm attaching a screenshot for you just so you can see what I was working with.  This is just a small sample of the first series, my chart actually went to 2450 points spent on either talent (~5000 total points spent) just for the sake of correctness.

Using the above chart I determined the best distribution of skill points for absorption and shield rating to get the highest mitigated damage value.

My findings are:
Until you spent 120 points directly in absorption shield gives less of a benefit.
Sweet spot at ~300 total points spent (180 absorption, 120 shield rating)
Sweet spot at ~400 total points spent (230 absorption, 170 shield rating)
Sweet spot at ~500 total points spent (270 absorption, 230 shield rating)

You see the trend, shield rating slowly catches up to absorption rating in terms of effectiveness.
At approximately 680 total points spent shield and absorption should be at a 1:1 ratio.  From here Shield becomes more effective then absorption, so you should stack 10 points of shield for every 8 points of absorption (this ratio is a pure approximation, in fact at 690 total points the ratio is 0.98:1, then at 690 points  it is 0.96:1, then at 700 points it is 0.95:1)

People have asked for Ratios and why they don't match my exact sweet spots, that's because every 10 points you put into shield rating the ratio changes on an exponential curve.  The best I can do is give you a head start with the below image.  Actual Shield and Actual Absorb are the ratings on your tooltips given by the skills you've chosen.  Add these numbers to your base chance for a total number.  So for my JG I add 20 to all numbers to get my actual tooltip total.

Shield Points and Absorb points are the actual amount of points put into the skill to get the outcome percentage.

For completeness sake at ~1590 points total you should have: 710 absorption, 880 shield rating.  You see here how Shield rating gradually overtakes Absorption and then surpasses it.

See chart below for trend lines.  It is jerky because I am counting x,y points in multiples of 10, so it isn't a perfect formula.  If I was doing it in single points used it would be much smoother and take much more time to compile.  The rough numbers I'm giving you should be close enough for your needs.  There isn't any way you'll be getting +1 shield anyway, it'll probably be +25 (minimum) so everything else is just superfluous.

You see the initial spike in Absorb usefulness over Shield usefulness.  After that it rapidly declines until almost coming even, then slowly Shield overtakes Absorb for usefulness.

This chart only goes up to 730 total points spent because I got tired of putting in key points, assume the trend continues so that at ~1590 points the graph line would be at 0.8 (very slowly declining toward the X axis).

What does it all mean?

So, now with a "sweet spot" for shield and absorb usage we can determine if it is more effective to spend 10 points on Defense rating, or 10 points (mixed between shield and absorb to provide optimal performance).

Here are my findings:

 Defence Shield Points Mit Dmg/Points Mit Dmg/Points 10 53.67565 42.21974 20 28.65313 22.1951 30 20.29746 15.50416 40 16.10865 12.14692 50 13.58668 10.12336 60 11.89822 8.76681 70 10.68613 7.791556 80 9.771831 7.054732 90 9.056122 6.476969 100 8.479474 6.010641 110 8.004007 5.62544 120 7.604467 5.631648 130 7.263369 4.604626 140 6.968226 4.830733 150 6.709877 4.508684 160 6.481454 4.465422 170 6.277701 4.202751 180 6.094534 4.18327 190 5.928726 4.064324 200 5.777695 3.956067 210 5.639351 3.767682 220 5.511984 3.687722 230 5.394181 3.698407 240 5.284764 3.544307 250 5.182744 3.56076 260 5.087283 3.423808 270 4.997668 3.444199 280 4.913286 3.392012 290 4.833611 3.275046 300 4.758184 3.299423 310 4.686608 3.19299 320 4.618533 3.218745 330 4.553652 3.121207 340 4.491695 3.14779 350 4.432422 3.115059 360 4.375619 3.028529 370 4.321096 3.055917 380 4.268682 2.975498 390 4.218225 3.002871 400 4.169585 2.927799 410 4.122639 2.954971 420 4.077274 2.932411 430 4.033387 2.864216 440 3.990885 2.891071 450 3.949683 2.826825 460 3.909703 2.853178 470 3.870874 2.792472 480 3.833131 2.818258 490 3.796414 2.801578 500 3.760666 2.745546 510 3.725838 2.770603 520 3.691883 2.717322 530 3.658755 2.741712 540 3.626415 2.69094 550 3.594825 2.714647 560 3.563949 2.701608 570 3.533757 2.654211 580 3.504216 2.677054 590 3.475298 2.631681 600 3.446977 2.653822 610 3.419228 2.642455 620 3.392027 2.599835 630 3.365353 2.621092 640 3.339185 2.580137 650 3.313503 2.6007 660 3.28829 2.59059 670 3.263527 2.551924 680 3.239199 2.571615 690 3.215291 2.534345 700 3.191788 2.553364 710 3.168675 2.517401 720 3.145941 2.535764 730 3.123573 2.527056 740 3.101558 2.492906 750 3.079887 2.510443 760 3.058548 3.225495

The actual values are meaningless.  What you are looking for here, is the larger value is more useful than the smaller value.

Points refers to how many points spent in the talent.
As you can see spending a small amount of points nets a large increase at very low ranks.  Spending at least 40 points on defense and at least 30 points in the shield (less than 120 points so 0 shield and 30 absorb based on previous calculation) nets you huge gains in survive-ability.

Using the above numbers you can easily see where putting points will net you the most survive-ability.  For example, upon reaching 400 points on defense (4.1 usefulness) you should have also spent 190 points into the shield (at optimal distribution this is ~130 absorb and ~60 shield) also 4.1 usefulness.

From that point Defense almost equals shield for a 1:1 point distribution, only slightly favoring Defense.  The trend continues all the way up the point spread, with defense being more useful then shield.

NOTE: As Defense increases the "weight" of shielding stats decreases.  This happens because you will be dodging more attacks, and therefore will see less effect from your overall shield mitigation.  This doesn't mean that your shield is less effective, but you will see less mitigation coming directly from it - which will tend to skew numbers at higher levels.  None of the math here takes that fact in to account since I was only comparing direct mitigation values and not adding the mitigation effect together into an overall formula.

---------------

Everything I've said also has a caveat.  This is overall AVERAGE survive-ability.  Fighting a boss that throws lightning at you that you can't block or dodge but you can shield makes defense useless.  This doesn't happen very often, usually anything that you can't block or dodge you also can't shield.

TL;DR Recap:

• Spend 120 points in absorption before stacking shield rating
• After 120 points see table screenshot for optimal distribution
• Put at least 40 points toward shield and defense to start, ignoring either causes a huge hit in survivability
• Defense is more useful then shield for overall mitigation, stack 2 points of defense : 1 point of shield (split shield optimally between absorption and shield chance according to above calculation)
• At ~400 defense and ~200 shield start stacking at appromxately 1.1 defense : 1 shield ratio

-

1. Can we get screenshots of actual in-game stat percentages to target?

1. I don't have any at this point since I've only just put this up and figure it out, it takes time to max out in end game gear since I have to rely on random drops to change my enhancements more in line with what I want out of my stats. Unfortunately there isn't an easy way to farm mods/enhancements for Rakata level gear.

2. I think I get what your saying, I'm doing my best to follow this post. Right now I have 273 Def, 246 Shield and 164 absorption so, working on it. But ive been trying to figure out what this Skills/Buffs is and if its important. mainly absorption is at 0.00. Anyway a better explanation would be nice. :)

1. The guide is really just theorycrafting, it's quite hard to min/max at this stage with the unavailability of Tiered mods and enhancements for level 50s. You're mostly stuck with whatever bad itemization BW has decided to give you.

I'm not sure what you're asking for Skills/Buffs? Or where you see your absorption at 0.00 - unless you aren't wearing a shield generator you should have a minimum of some absorption. Check your offhand slot and make sure it shows shield/absorb chance and is a shield generator.

3. an easy way to look at it is, def chance is more important (afterall not getting hit means no damage), follow up with closely matched shield chance and sheild damage reduction (since that reduces all damage, including armor penetrating damage).

4. Hey, could you share the tabs, since screenshots end when it starts to get interesting as well as mitigation / point table.

1. Sorry it took me so long Scott, yes I'll put the sheet up so you can take a look at it. Unfortunatley Google couldn't convert the calculations for some reason so you'll have to just look at it in PDF style view. You can find it here:

5. Any chance of getting something similar for Power / Surge / Crit? Should be a bit easier w/o the added dynamic of Shield vs Absorb...

And where did you get the data for all of your charts?

Nice work!

1. I will look at doing something for Power/Surge/Crit - there is still the dynamic between Crit/Surge so it won't be much different, since one depends on the other for maximum effect.

I got the formulas from sithwarrior.com - they have great theorycrafters there and they've dug into the data files to find the actual calculations used. The rest of the data was created by me, based on those calculations.

6. The theorycrafting seems nice. Way to go Richard, really nice job.

But I am missing one really important point. As we all know the defense check is applied before shield check. So it significantly reduces the overall effect of shield/absorption.

e.g.
I have 50% shield and absorp and no defense => I get 25% (0,5*0,5) dmg reduction from shielding.
But when I have 30% in defense with same shield and absorp => I get just 17,5% [0,5*0,5*(1-0,3)]

So from the first look it seems, you havent taken this to an account and the oveall usefullness of shield/absorp is a bit lower.

1. Thanks Hardbringer.

Defense doesn't reduce the effect of shield and absorption, it just makes it occur less frequently because you aren't taking hits as often.

Pretend you're fighting a boss that hits really fast and are getting hit a lot, your shield is proccing a lot because the hits are coming in fast. Then you fight a boss that's slow and the hits are coming in really slowly - your shield doesn't proc much. In both situations the math is the same, just because it occurs more or less frequently has nothing to do with it.

I understand that you're saying because defense causes shield to occur less frequently it therefore makes it less effective overall. To make that kind of determination was beyond the scope of what I was putting together, and will rely as much on the enemy's stats as your own. For example - defense is less useful against an enemy with a higher accuracy, causing it to affect less hits and making shield rating more important for that encounter. An enemy with high crit will make shield next to useless and force you to rely solely on defense rating for that encounter.

Simply to say that shield is less useful than Defense is premature and would require a lot more "unless" put in the calculations.

7. You were the doing math on mitigation dmg / invested point on shiedl/absorp vs. defense. I just said, that with that test and within that comparison you shoud count also that defense lowers the effect on your very own given conditions 100 hits/100 dmg.

Your statement the saying its premature and for no use (=it depends more on the stats of the opponent) undermines your work and the part of comparing mitigation effect in last part of this article.

And I never said shield is less useful than defense (i personaly from certain point favour it a bit cause it has more potential to eliminate the spikes) - you said that (even make a table out of it) I just pointed out that the math in that comparison on the pretended conditions isnt quite accurate.

1. Sorry Hard - apparently I was reading something that you weren't saying.

You are correct - I was not comparing the two mechanics together. I was looking at each one independently against the damage and outputting a modified mitigation number, then comparing those mitigation numbers to properly rank the importance of each stat on a per point basis.

I thought we were getting in to a debate on usefulness of each stat rather than just looking at them outright. Which is probably my fault for looking at this just after I rolled out of bed in the morning.

I won't be going back to redo this math, since I've been working on further calculations that hopefully will make some of this obsolete (since some of it is already). I'll put a note up at the top something along the lines of what you're saying here so people see what you're saying.

2. No hard :)) feelings. Really looking forward to your new calcs to compare it with some of mine. May the Force be with you.

8. How ever, I'm a venguard: I add only Shild-augemnts (700) points and I do not care about def and absorb (200 each)...
1) I have a relict, when I shild I get +400 Absorb
2) When I shild, I can stockstrick
3) When I shild, I receive an Ammo
4) My healers seems to like a tank how do more often shilding rather then to defense an attack (low shild and hight absorbe seems to be the same like defense...)

however shilds and defenses are rare in PvE. Everybody knows it about PvP - knowbody talks about PvE... ;)