When Parry is better than Dodge

[shushikiary]

So I was thinking the other day to my self, hmm with the DR curves it might be possible for parry to be better than dodge at some point, so I did some digging and saw that no one did any math on it yet, so here comes...

This is my first ever post so if I mess something up or you think it needs improvement feel free to give feed back!

Based on this article:
http://www.tankspot.com/forums/f63/4...avoidance.html

I simplified the equations for warriors to:
Ad = C*A/(A+K*C)

Ad = (88.129021*A)/(A+84.25134407) dodge
Ad = (47.03525*A)/(A+44.965699) parry

Then graphed these wonderful equations to see what the DR curve actually looks like:



From here I took the derivative of the functions, because once the slopes of the two curves are equal then adding either dodge or parry adds the same percent, however if the slope of the parry curve at a given points is greater than the slope of the dodge curve then parry is better to stack:

d(Ad(A))/dA = K*(C)^2/(A^2+2*A*K*C + (K*C)^2) by quotient rule.


Adding new terminology here we can balance the parry and dodge equations. Ad will be the dodge before DR and Ap will be the parry before DR, Cd will be the C for dodge, and Cp will be the C for parry.

then we have:
K(Cd)^2/((Ad+KCd)^2) = K(Cp)^2/((Ap+KCp)^2)

after some simplification:
sqrt(K(Cd)^2/K(Cp)^2) = (Ad+KCd)/(Ap+KCp)

and again:

sqrt(K(Cd)^2/K(Cp)^2)*KCp - KCd = Ad - sqrt(K(Cd)^2/K(Cp)^2)*Ap

after plugging in all our constants we get:

0 = Ad - 1.874945*Ap

Which means, that if your dodge before DR minus your parry before DR times 1.874945 is equal to 0, then you get the same avoidance from adding parry as dodge. If the number is negative then parry gives you more per point than dodge.

So lets say you're at 15% parry:

Ad = 1.874945*15 = 28.124175

So if you have 15% parry before DR that means that you'd need 28.124175 % dodge before DR before adding parry would give the same as adding dodge.

Edit: it turns out I made a mistake, you cannot simply plug in the rating values as I had before, there is a shift in the 0 point of inflection due to constants that cancel out in the derivative if you do not recalculate the derivative with ratings factored in. The EJ forums realized this and are correct, the end equation including ends up being more complicated, also my above solution only solves for the positive solution of the quadratic (because I square rooted both sides) which is alright because it's the only one we care about (thanks to EJ forums for the equations here).

The real equation after re-calculating the derivative (where rd is the rating for dodge, rp is the rating for parry, P0 is the parry from gear, and D0 is the dodge from gear):



Which simplifies to:


and with numbers:



Which means for my warrior:
The World of Warcraft Armory

at 8.84% dodge, P0 is -0.5269664, which means I shouldnt add any parry at all. However my gear forces me to as it simply comes on it, such is life sometimes.


The graph after accounting for the rating skew ends up being (remember these %'s are before DR):



So simply fallow the X axis for how much dodge from gear you have and see if on the Y axis you have as much parry added from gear as the graph shows, if not, then add more parry to get your best avoidance efficiency.

I'd also like to point out how harsh the parry curve is, it drops of really quick once you get past about 18%


On a side note, after I posed this I found I had been beat to it, but with the same result, and both have pretty graphs lol:

Avoidance Diminishing Returns - Elitist Jerks

[Oghula]

Nice work, shushikiary.
The factor 1.874945 in the formula is the ratio of the avoidence caps. 88.129021 / 47.18499 = 1.874945. You could rearrange your formula a little and would find that parry is better (i.e. 1% parry suffers less diminishing returns than 1% dodge) if Ad/Cd > Ap/Cp.
These are just your findings, but maybe the relation of dodge and parry is more clear.

[shushikiary]

I'd also like to make sure that everyone takes a long hard look at the TTL math:

Combat Ratings at level 80 - Page 13 - Elitist Jerks

Particularly this graph:



This goes a long way to show that defense rating, due to block value and no DR for block rating, has the best TTL even though it isnt the best for overall avoidance. Remember though that TTL is just an idea, and though it's similar to a MTBF (mean time before failure) idea it does not work in exactly the same way, and thus avoidance still has its value.

[Whitetooth]

I'd also like to make sure that everyone takes a long hard look at the TTL math:

Combat Ratings at level 80 - Page 13 - Elitist Jerks

Particularly this graph:



This goes a long way to show that defense rating, due to block value and no DR for block rating, has the best TTL even though it isnt the best for overall avoidance. Remember though that TTL is just an idea, and though it's similar to a MTBF (mean time before failure) idea it does not work in exactly the same way, and thus avoidance still has its value.

Block is not considered at all in my graph, defense is better simply because is gives more avoidance under the same amount of item value.

For example:
2000 Parry rating = 22.32869363% Parry
2000 Dodge rating = 33.16162431% Dodge
2000 Agi (War/DK) = 21.50812438% Dodge + 4000 Armor
2000 Agi (Pal) = 27.59166181% Dodge + 4000 Armor
2000 Defense Rating = 14.26064579% Dodge + 12.49202826% Parry + 5.6% Crit Avoidance + 14.26064579% Miss(Assuming same DR as Dodge) = 46.61331984%

[shushikiary]

So given that, defense combined with SBR (assuming your SBV is some decent proportion of the average boss hit) would be even better then it seems above? Thanks for correcting me, I never realized that it only look into account avoidance until you mentioned it and I took a much closer took at the summation used.

Also, why did you add the chance to not be crit from defense, is it because of combat table mechanics? I guess I'm not seeing why you added the chance to not be crit in the avoidance calculation, though even given that defense still has more avoidance.

Wouldnt it also be possible do you think, that defense may add less TTL than the above shows if you already have too much parry/dodge stacked from other sources such that the values added from defense are subject more to DR than if you had just added defense alone?


It would be interesting to see


modified to give an armor approximation of SBV (based on % dmg reduction of average boss hit) multiplied by SB % in here to see how much your shield block value adds to TTL (which I'm sure would make defense rating look even bigger, but graphing it with changing average boss hit and SBV would make an interesting chalenge). After that maybe add in the effects of your total other added avoidance rather than just looking at 1 stat at a time (a unified theory of TTL if you would?).

[smokeykurt]

i would love to see a simplified version of this...maybe an easy to read chart or something so the person who isnt a math head can grasp it quicker. ~hint hint myself~

[shushikiary]

Essentially if you take how much + dodge you have added from gear (just look at the tool tip on your character sheet when you mouse over your dodge) and pug it in for D0 below:



If the value is negative then stack dodge rating, if the value is positive and your parry added from gear (use the same mouse over method) is less than P0 then you'll get more avoidance by stacking parry rating than by stacking dodge rating.


The 2nd part where we are talking about TTL (time to live) is about stacking what ratings lets you live the longest in a boss fight with no heals. Looking at a single rating at a time, defense rating has the BEST addition to TTL, however that doesnt take into account the existence of already added dodge/parry from other gear, and I believe there may be a point where if you already have too much dodge, or too much parry, from other gear you may get more TTL from stacking dodge or parry than defense alone, and I suggested that maybe we should make a math modle that represents this. (You could pretty much do it with rating buster I think, just by experimenting with gear and seeing what TTL it gives you, I could be wrong).

I also suggested it would be nice to add the SBR added from defense into the TTL calculation as it would make defense look even better, espcially on bosses that have a small (average hit)/(SBV) ratio. (aka if the boss doesnt hit very hard then SBR and SBV add a significant TTL, especially on dual weilding bosses (like perhaps being MT on patchwerk, OT is a different story (in the 10 man version he hits for like 4-5k a hit MT, but around 10k OT, 25 man is a whole different story where he hits for 20k on the OT and 8-9k or so on the MT (aka avoidance is best over SBR/SBV)))). Lotheb is a great example of this, in heroic and non heroic he hits for about 2.5k hit a swing, but the healers can only heal 3 seconds every 20 seconds, and so a warrior is by far the best tank because your shield block is almost a 50% damage reduction on average, combine that with 10 seconds every 40 for the shield block tallent (which is almost 100% reduction due to double SBV) and a psuedo geared warrior can mitigate almost all of the dmg for the fight after armor, SBR, SBV, miss, dodge, and parry.

AKA different gear for different fights, lol.

[Wartorn]

Seems like parry will never realistically catch dodge for point budgeting.

Edit : The more things change, the more they stay the same. :P

[Ion]

So given that, defense combined with SBR (assuming your SBV is some decent proportion of the average boss hit) would be even better then it seems above? Thanks for correcting me, I never realized that it only look into account avoidance until you mentioned it and I took a much closer took at the summation used.

Also, why did you add the chance to not be crit from defense, is it because of combat table mechanics? I guess I'm not seeing why you added the chance to not be crit in the avoidance calculation, though even given that defense still has more avoidance.

Wouldnt it also be possible do you think, that defense may add less TTL than the above shows if you already have too much parry/dodge stacked from other sources such that the values added from defense are subject more to DR than if you had just added defense alone?

Well, I imagine chance to not be crit was added because it acts essentially like being hit twice, by not being crit you're essentially avoiding a second "hit".

It would be interesting to see how dodge/parry rating effect defense's TTL and vice versa. They're definitely not sitting out there in a vacuum.

Unfortunately I'm at work and can't really spend any time on it. Seems like it should be reasonably straightforward to model...obviously Blizz must be doing something similar already.

[shushikiary]

Well, I imagine chance to not be crit was added because it acts essentially like being hit twice, by not being crit you're essentially avoiding a second "hit".
.

I see your logic there, I guess I just wouldnt consider it a "true" avoidance of an attack, but that also explains why he never adds more than 5.6% (once you're crit capped.... you're crit capped, lol), however on a TTL perspective the dmg taken is relivent and therefore chance to be not crit is important until capped. This would also explain why the defense curve falls flat on its face around 687 and then comes back up. (687 = 540 defense = crit capped)


Oh, and wartorn, the whole point here was to show that parry CAN catch dodge if you have enough dodge, you just have to have around +10% dodge from gear alone for it to start happening. However due to the way the gear is currently itemized in game, by the time you get +10% dodge from gear you'll already have a decent amount of + parry % from gear as well, and so yes most likely you'll never end up geming or enchanting for parry (sadly you have to to get the new 2% threat enchant). However if you stack gear that has nothing but dodge rating on it, and gem/enchant for only dodge rating, then it is entirely possible that you may need to swap in some parry rating gear or gem for it to get the best avoidance possible out of your gear.

[Ciderhelm]

Thanks for the work on this. I'm learning quite a bit reading this.

[Blueduck3285]

Wow, this is great infromation especially for DK tanks who are based around avoidance with not having a sheild and all. Great work.

[Giantone]

wow i didn't know how worthless parry was thank you for this info. Now i am off to purge all my gear of this worthless stat.

[Trainwrex]

my head hurts after reading this.

[shushikiary]

my head hurts after reading this.

Goal accomplished!





jk

[lyd]

good lord. i wonder how many math majors blizzard has working for them

[Glomgore]

To sum this up for the non math genius (And I may or may not be right with this summary)

It seems that until we hit insane amounts of Dodge, it's always going to be better than parry.
Defense is always a great stat to stack, and in terms of overall survival and stat balancing, IMO seems better to stack def over dodge, as the diminishing returns do not hit block, and we gain 3 different avoidance stats to spread out the DR.

After seeing this, I would take gear that has dodge over gear that has parry, and gem for defense/stam/str(for block/atk).

What it seems blizzard is trying to do, is make our min/maxing pretty much a cakewalk. Grab all the tank gear you can, build an avoidance set gemmed with def rating, and a block set gemmed with STR.

Red Gems = Expertise or Exp/Hit hybrids.
Yellow Gems = Def gems, (possibly champ gems if you need more threat)
Blue Gems = Stam.

Sounds good. Got it.

[shushikiary]

To sum this up for the non math genius (And I may or may not be right with this summary)

It seems that until we hit insane amounts of Dodge, it's always going to be better than parry.
Defense is always a great stat to stack, and in terms of overall survival and stat balancing, IMO seems better to stack def over dodge, as the diminishing returns do not hit block, and we gain 3 different avoidance stats to spread out the DR.

After seeing this, I would take gear that has dodge over gear that has parry, and gem for defense/stam/str(for block/atk).

What it seems blizzard is trying to do, is make our min/maxing pretty much a cakewalk. Grab all the tank gear you can, build an avoidance set gemmed with def rating, and a block set gemmed with STR.

Red Gems = Expertise or Exp/Hit hybrids.
Yellow Gems = Def gems, (possibly champ gems if you need more threat)
Blue Gems = Stam.

Sounds good. Got it.

I agree, except I'd make sure to put expertese unless capped and not hit, but I'd rather do dodge.

I will say though that with the content so far (uldahar not released) I'd go for expertese over dodge in red slots, as nothing hits hard enough to justify 30% dodge(overall) (except maybe patchwerk). The purple regal gems are favorites of mine in the past for dodge + stam hybrids though it seems not many JC's make them for some reason (at least on my server), but I wouldnt mind swiping them out for expertese/stam for the extra threat (now that the dps in guild is getting geared they are putting out 3-4k tps on a regular basis).

Oh and I would never gem for str. It's just not worth it, the SBV you'll gain and the attack power you'll gain are far out weighted by other stats like expertese/hit, if it comes on the gear, great, but I'd never gem for it.