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Overview

In this article, we detail the damage bonus associated with critical hits for physical damage, magic damage, and cures.  In addition, we talk about the gear and trait modifiers which augment this critical damage bonus - specifically critical potency (Savage Might), magic critical potency (Sagacious Might), and very briefly on critical resilience.  I will also briefly talk about class abilities in the current v1.20 that involve critical damage bonuses, namely - Rampage, Thundaga (Combo), and "Enhanced Blindside" Trait.  Due to length restrictions, I have chosen not to talk about critical rate in this post, and instead focus solely on the critical bonus once the critical has occurred.

Similar to previous posts, this testing was a collaborative effort with Seiken Valk.  I would also like to thank Miko Neversleeps for MAR Rampage testing, and Anzu Mazaki and Katsu Kobashi for gear sets.

As with my other math-heavy posts, I have sectioned off the methodology and discussion sections so that you can simply skip down to the "conclusions" section if the math does not interest you.


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Methodology and AnalysisCollapse )




Assessment of Potency"s EffectivenessCollapse )




Testing Abilities and TraitsCollapse )



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Conclusions

I have color coated the conclusions this time.   Red conclusions indicate fundamental ideas and formulas regarding the critical damage bonus.  Blue conclusions indicate that we are talking about efficiency, gear choices, and the all important "is X better than Y."  Purple conclusions indicate we are talking about specific abilities or traits within the game that deal with critical damage bonus (e.g. Rampage).

    (1)  The critical bonus is a straight percentage increase in damage / HP cured.  This percentage increase is
          only affected by "Crit Potency" enhancements, "Crit Resilience" enhancements, and dLVL.


The critical bonus effect follows the same rules regardless of the kind of critical you are attempting to land - whether it is a physical attack, magic attack, or cure spell.  Critical resilience is assumed to be the same as negative critical potency; however, this was never formally tested here.

    (2)  There is a cap on the critical bonus percentage increase at 175%.  There is a floor at 115%.

To clarify, there will be a formula presented further down in the conclusions which may predict a critical bonus percentage of greater than 175% or less than 115%.  The game will simply cap you at one of these 2 values.  The calculated bonus is still important, however, because the + critical potency effects are applied prior to application of the cap and floor.

    (3)  + Crit Potency enhancement increases the the critical bonus by a fixed increase in %.  This fixed bonus
          decreases as dLVL increases.  The enhancement is applied before the bonus floor and cap. 


The key here is that the enhancement is applied prior to application of the cap and floor.  This means that say you have 108% critical bonus at +0 potency.  This is floored to 115%.  Now let's say you add a certain amount of potency that brings your critical bonus to 114%.  This value is still floored again at 115%, meaning your potency increase actually changed nothing.  This is an extremely important concept at higher dLVLs.

    (4)  The baseline critical bonus (the critical bonus at +0 potency) is affected only by dLVL.

The effect of dLVL on the baseline critical bonus can be summarized graphically by the graph below...


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    (5)  The table below summarizes the baseline critical damage bonus and the amount of critical bonus
          added per point in + critical potency for each dLVL (range -30 to +10).


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Blue means that the 175% cap will affect the calculated value.  Red means that the 115% floor will affect the calculated value.  The "Bonus to Potency Ratio" is the amount of critical bonus % you add per point in potency.  As a sample calculation, for dLVL=0, let's say we have +10 potency.  The baseline critical damage bonus is 121.43%.  The additional bonus added by the +10 potency is calculated by 10 x 0.1729% = 1.729%.  This gives a final critical damage bonus of 121.43% + 1.729% = 123.159%.  "Wasted Potency" refers to the amount of + crit potency enhancement one would require to see any difference. 

    (6)  For cure criticals, dLVL is calculated by [Target Rank] - [Caster Rank].  This means that for most endgame
          situations, the only relevant dLVL is 0 (rank 50s curing other rank 50s).


If you take a R50 mage and Cura a R1 target, you actually will see the full 175% cap in play (and see a Cura critical that can exceed 2,000 HP).  However, as stated above, dLVL=0 is really the only relevant endgame situation right now.  The chart below illustrates the effectiveness of adding Magic Critical Potency on cure criticals at dLVL=0.


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    (7)  To attempt to better answer the question "how good is Might materia?", the following graph illustrates
          the overall % increase in damage when you critical hit at varying potency increases.


This graph specifically shows how much increase you get by adding +50, +100, +150, and +200 critical potency (as compared to someone with +0 potency or the baseline).  Because the "return" or "effectiveness" of the potency stat varies significantly with dLVL, this graph charts the effectiveness of each of the 4 cases across the spectrum of "useful" enemy ranks (dLVL=-20 to +10).  To give a sample read of the graph - if fighting an R52 enemy and your critical at +0 potency does 500 damage, it would do +15% or 575 damage if you had had +100 potency (purple line).


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    (8)  The Rampage status gives 50% of the critical damage dealt back to HP.  This HP return is capped at
          20% of your maximum HP.  This means if your max HP is 4,000 the most you can get back is 800.



    (9)  The Thundaga combo bonus grants a rough +175 magic critical potency and allows the critical to
         break and exceed the 175% critical damage bonus cap.


This is the same effect as adding +175 magic critical potency from say Sagacious Might.  It also allows the spell to potentially break the 175% cap.  This was only small test, however, so this value may vary with other variables such as the caster's level. 


That pretty much covers it.  I think we were pretty thorough in covering everything that dealt with critical bonus in this post.  The only two things we missed were specifically testing the effect of critical resilience and PGL trait "enhanced blindside" which adds an INT modifier to blindside criticals.  Again, we intentionally avoided talking about critical hit rates in this post due to length restrictions.

XIV v1.21 is due to come out in a few days, which means the advent of new jobs and 2 new instances.  A couple people have asked why we would go through this much trouble testing when the game is still in such flux.  My personal response to this is that I believe the core mechanics of the game (the fundamental formulas of attack, defense, and resistance) have been implemented already with v1.20.  If future changes are made, they will likely be small tweaks rather than complete overhauls (in which these previous tests may not be valid but still partially correct).  This is of course still a gamble and only my opinion though.  Either way, looking forward to v1.21 and the population increase it brings.


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Overview

This third post focuses on the variables at play in determining the amount of damage taken against physical attacks.  The data collection and analysis in this post was completed through a collaborative effort with Seiken Valk (some of his posts here in the official forums on ARC and LNC testing), who's in the same LS as me.  Building upon the previous 2 posts, the data collection methodology relies heavily on Part I's analysis of MIN and MAX distribution; so I highly encourage you to at least read that section if you're interested in how the conclusions in this post were reached.

Special thanks to of course Seiken Valk, but also Miko Neversleeps and Katsu Kobashi for gear sets.  In addition, a good amount of credit should be given to Grain Malt's initial DEF/VIT testing as well as Stanislaw for his translation of Malt's post.

As with my other math-heavy posts, I have sectioned off the methodology and discussion sections so that you can simply skip down to the "conclusions" section if the math does not interest you.

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Testing Methods and Data AnalysisCollapse )




The Increasing Return of DEFCollapse )




Explaining the "Naked Ifrit Run"Collapse )



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Conclusions

There's a great deal of information in this post, but I will try to keep the conclusions pretty brief.

    (1) The amount of damage one takes can be summarized in the following formula:

   Physical Damage Taken = [ "Damage Taken at 0VIT/0DEF" ] - [dLVL modifier] * { [ DEF ] + 0.67  [ VIT ] }

This formula tells us that for every 1 DEF we add, we get a static amount of damage reduction which is directly related to the dLVL of the mob we are getting hit by.  This relationship between dLVL and the amount of damage reduction per +1 DEF added can be summarized in this graph:

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    (2) VIT and DEF are related in a 2:3 DEF:VIT ratio, meaning adding 3 VIT is like adding 2 DEF.

This is also evident if we look at the formula in conclusion 1.  Testing was done specifically at a range from VIT of 252 to 345, meaning if a "tier" argument is to be made, no such "tier" appears to exist between this range.  Seeing as most R50s will fall at or below this range, we do not find any evidence of a practical VIT "tier".  This is a very interesting conclusion since previous testing in both 1.18 and 1.20 have pointed to a 2:3 ATK:STR ratio as well.

    (3) VIT, in addition to affecting physical damage taken, also decreases magical/elemental attacks.

We chose not to go any deeper into this aspect of VIT since this post focuses on physical damage.

    (4) Damage from different physical attacks (normal, WS, etc.) all carry the same damage reduction per
         adding DEF or VIT.  Meaning DEF and VIT decrease damage taken the same on everything.


This means that if we have a mob with 4 different physical attacks, say Full Thrust, Pierce, Light Thrust, and Leg Sweep - adding a certain amount of defense or VIT will decrease the average amount of damage taken by all of these attacks by the same amount.

    (5) There is a "damage floor" at which adding defense or VIT will no longer decrease damage taken.
         This "damage floor" depends on the dLVL of the enemy attacking.


The damage floor is not affected by mob or player stats and is solely dependent on the attacking enemy's dLVL relationship with the player.  The relationship between dLVL and the damage floor is summarized in the plot shown below.

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    (6) The efficiency of adding more defense increases as one approaches the required defense to reach
         the damage floor for that particular enemy.


I highly recommend reading the section of this post that focuses on efficiency.  This is ultimately what the vast majority of players will care about with respect to defensive stats ("how good is it if I add X amount of defense to my current build?").  Embedded in this analysis is a quantitative explanation as to why the "naked Ifrit run" works.

That concludes the end of part III!  There's a lot to digest here but we've really only explained a small percentage of how things work so far.  The obvious extension to this post on physical damage taken is physical damage dealt.  Being able to connect to two in a formulaic will definitely be the goal in the future.  Til next time.


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Stat Testing - Part II (MEVA)

Overview

In this second post on stat testing, I want to focus on XIV's current concept of magic evasion (MEVA) and a little bit on its counterpart magic accuracy (MACC).  Before starting, I want to state clearly that my intention in this post is not to offer a MEVA (or MACC) formula with regards to resistance rates.  As you'll see later on, the trial sizes in these tests were pretty large, but not near the amount required to reach that level of precision.  To contrast this with the 5,400 trial series of tests I'm presenting in the post, Lodeguy's original MACC testing in XI took about 23,000 trials.  What we can hopefully get out of this preliminary testing, though, is a rough idea of how MEVA and MACC are related to resistance rates, what other factors play a role in resistance rates, and finally, a ball park idea of how useful these stats are.

Special thanks to Miko Neversleeps for helping me with parts of the testing in this post.

As with my other math-heavy posts, I have sectioned off the methodology and discussion sections so that you can simply skip down to the "conclusions" section if the math does not interest you.


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Read more...Collapse )




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Conclusion

Moving straight to the summary of conclusions for this post...

    (1) All magic spells and elemental based normal/TP attacks are subject to a MEVA check.

The in game log currently will only openly notify you if a partial resist for magic spells.  For elemental attacks and TP moves, you will only notice the damage reduction of the resist, but will not be notified of the resist in the log.

    (2) There are 3 "tiers" of resists, labeled in this post as "Single" (-25%), "Double" (-50%), and Triple (-75%)

The game will only give you notice on magic spells that a resist occurs, but you will not be notified of exactly of the strength of the resist.  There is no apparent -100% resistance tier with the exception of using "Decoy" and direct non-damage enfeebling spells like "Bio".

    (3) Elemental Resistances only affect direct damage taken and not MEVA or resist rate.

There is a clear damage decrease when the correct elemental resistance gear is used on particular attacks, but not a change in the resist type rate.  This is a completely seperate kind of testing that I did not really go into in this post beyond the fact that it does not have anything to do with MEVA.

    (4) The resist rates for elemental damage attacks (specifically Seismic Scream) is plotted and shown here.
         This plot can be used to estimate how potential increases and decreases in MEVA will affect resists.

         The plots requires that you have at least 1 data point to be useful on particular mobs.  A brief table
         outlining a couple of mobs tested in this post is shown here as well.


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    (5) There is no pre-mature resist rate floor or cap.  You can potentially resist 100% or 0%.

    (6) "Status Resist" equipment gear like Aurelia's Kiss does not change duration or potency of enfeebles.
         There is a 1:1 ratio where 1 "status resist" gives 1 MEVA for that status ailment.


Just to add clarify and emphasis, yes this does appear make MEVA the better stat since it adds global resistance as opposed to just resistance to a specific element.  The amount of testing done on this is pretty small so I could be easily missing something but based on my tests, I don't see how this is useful, especially on head and feet pieces which can receive Manaflight materia.

    (7) Enfeebling spells (maybe all magic spells) have their own unique land rates for a given MEVA.

This just means that if you resist say 50% of 1 spell at a particular MEVA, you may not resist 50% for all spells.

    (8) Enfeebling spells (e.g. Poison) likely only need to have any resist to fully resist.  There is currently no
         such thing as a "partial resist" for enfeebles right now.


    (9) The "Magic Evasion Down" effect on R50 CNJ's Stone gave -29 MEVA on R40 Lemurs.

This gives a rough estimate of the MEVA down effect for an R50.  This value did not change with a +20 increase in enfeebling skill (+80 PIE).  It could still change based on the mob's statistics or the CNJ's level though.


That just about does it! 

Taking briefly about potential application of these results to in-game scenarios, I feel that stacking Manaflights and MEVA probably won't be too useful for high-end mobs like Ifrit.  We can see that the MEVA to 100% "partial resists" even for the R30 Ifrit is extremely high and near unreachable currently without amazing triple socket gear at least.  The R50 Ifrit would be pretty impossible to reach a decent resist rate on.  However, for normal mobs in general instances like Darkhold, I can see a MEVA set being potentially useful, specifically for stopping enfeebles.

We also talked about in the post turning around the MEVA plot and plotting for the opposite stat in magic accuracy.  If we make the assumption that there is a direct 1 for 1 check between MACC and MEVA, we can get a plot like this:

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Ultimately, this may be the biggest "prize" piece of information coming out of this post due to the importance of avoiding resists for magic combos on mage jobs.  Seeing how most endgame situations have mages fall between the -200 and 0 range on the plot, it shows how potential gear increases in MACC roughly correlate to gains in the land rate of spells.

I'll probably end up coming back to some of the concepts tested in this post later on as I have more time.  For the most part, these are ball-park, qualitative ideas and statements and it would be interesting to try to add more quantitative data to back up the ideas here.  But moving on to what's ahead, there are other big, global concepts on stat increases I'd like to get to first.  Til part III.


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Stat Testing - Part I (Cure Formula)

Overview

The December 1.20 patch fundamentally changed essentially every skill and formula in FFXIV - a much needed rework.  With this, it allows players to, for the first time, test for particular formulas without the inevitability that it will just be changed in a few months.  I know that I had personally been looking forward to testing stats prior to the 1.20 patch, but just found it pointless with 1.20 looming.  It has been roughly 1.5 months since 1.20 came out, and the quality of testing regarding stats out on the official forums has been pretty disappointing for the most part.  I hope that this series of posts will help to lay the foundation for future testing on a number of subjects.

For this first post, I wanted to start with the "cure formula" - specifically for Cure and Cura.  I realize that there is already some preliminary testing out there - specifically my own Cure testing in 1.19 and Deli's testing on the official forums.  I want to explain that before we start, I am not going to "build" upon and previously collected data, but intend to start from scratch. 

As a *disclaimer*, I try to involve statistics where they are helpful and necessary, but the overall understanding of statistics would be best described as novice (AP high-school to undergraduate) at best.  My terminology use is especially poor.  Basically, I am in no way shape or form a Robonosto; however, I also don't think that amount of depth and expertise is necessary for this particular set of data.  I will, however, always appropriately note any lack of expertise when tackling data in the future.

As with my other math-heavy posts, I have sectioned off the methodology and discussion sections so that you can simply skip down to the "conclusions" section if the math does not interest you.

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Conclusions

I will try to summarize the "important" game-application findings found from the discussion of the cure data set; however, be aware that I will be extremely conservative when making calls here since most of the results are at best estimations of what's really going on with the formula.  That being said, I feel like there are still some good things to know even without the true formula.

    (1) Mind itself does not affect the HP gain from Cure when used on classes other than CNJ.

This still means that if you increase the Mind stat on say THM, it will increase your Cures, but it only does this because you also get 1 point of Healing Potency for every 4 Mind you add.  However, you will only get additional bonuses to cures for the mind stat itself if you are on Conjurer.  As a preview to future stat posts, I can go ahead and safely say that this "modifier loss" also applies to other formulas such as Second Wind and attack magic.  For example, if you use Second Wind on PGL, INT is a modifier, but is not for non-PGL classes.  INT is also a modifier for Thunder on THM, but other classes do not get this INT modifier if cross-classing Thunder, etc.

    (2) Adding +1 Healing Magic Potency adds roughly 1.25 HP on Cure and 2.50 HP on Cura when on CNJ. 
          It adds roughly 1.10 HP per potency when on non-CNJ classes.  Be aware this is an oversimpliciation.


I chose to write this in terms of "ratio of increase" despite the fact I kept calling it an oversimplification in the body of the post.  I feel like for the average player, ratios make more sense when it comes to gear choices.  I feel that in the future, a formula estimation will be inevitable and at that point, the true relationship will replace the "ratio explanation."  From the mathematical point of view, it looks like potency is a percentage increase to HP cured, meaning if you increase your potency by 20% keeping everything else the same, your HP cured will go up by 20% as well.

    (3) Vitality is a minor modifier to the Cure formula.

Vitality appears to add roughly 1 point to Cure for every 8-10 points added to it.  It's probably too small to make a difference or make it worth having a "VIT build," but is good to know for the purposes of controlled testing.  I did not test the effects of VIT on Cura, but made the assumption that it would not make a big difference relative to potency and Mind.  It's important to just know this modifier exists.

    (4) For CNJ only, +1 Mind adds roughly +0.25 to HP to Cure and 0.50 to Cura.  Much like my explanation
         for Healing Magic Potency, this is an oversimplification of what's really going on.


To stress, remember that this only applies if you are on the CNJ class.  Other classes do not benefit from a mind modifier on cures.  This "ratio explanation" is an oversimplified version of what's really going on and the ratio will increase as your Healing Magic Potency increases.  When making gear choices, also remember that adding 4 mind grants you 1 potency.  This 0.25 / 0.50 ratio increase described above does not take that into account.  When you do take that into account, the ratios are actually more like 0.5625 for Cure and 1.125 for Cura.  You could summarize stat gain ratios as:

* Cure on CNJ
    1 potency = 1.25
    1 mnd = 0.5625

* Cura on CNJ
    1 potency = 2.50
    1 mnd = 1.125

* Cure on non-CNJ
    1 potency = 1.10
    1 mnd = 0.275


    (5) When the caster and target are both R50 with no critical bonuses, the % bonus on critical cures is roughly
         an increase of 22-23%.  The rate is roughly 7.8%.  Limited testing on critical potency bonus so far.


The amount of testing and discussion for critical was fairly limited in this post because it's a bit more complex than I'm ready to get into at this point.  The best I can offer for this post is that that THM trait that gives +10 critical rate does work for cures and that if you add +58 critical potency, the critical bonus increase jumps from about 22-23% to 34-35%.

Whew!  That's about it for this.  Just a couple notes to end things.  Critique is always welcome; the harsher the better.  The testing and discussion shown here is limited to the point where we can't derive a usable "cure formula" as of yet, but I am confident that with some community help or just pure time to test more, one will be found fairly soon.  Also I'm sorry I didn't get to test Curaga. 

Lastly, for those that don't play XIV but still follow me and want my advice about the game: wait for 2.0 in Q4 2012.  The game is fun right now but that's only because I just played 1.5 years in the train-wreck that was this current game's predecessor.  If you play now, it's paid beta-test.  If you still want to play though, I'm on Figaro!

Til next time.


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XIV Enmity Table v1.18

Enmity TableCollapse )


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