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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.


Testing Methodology

We made the baseline assumption that the critical damage bonus would only be affected by dLVL and special stats and traits that specifically mention critical damage.  This means that we made no distinct attempt to show that stats (STR, ATK, etc.) play any/no roll in the critical damage bonus.

Because were specifically set out to test the critical hit bonus and not the critical rate, we focused on abilities that attempted to force critical hits to expedite testing.  Various methods were used which are outlined below:

   (1) Low "Base Damage" weapon auto-attack on low rank enemies to test Physical Criticals

The benefit of this data collection strategy is you can directly control the amount of damage you deal based on the weapon's base damage - allowing for control of your precision (low damage has lower precision).  On lower end mobs, you can simply AFK while collecting data and use stoneskin every 5 minutes.  The critical hit rate is much higher on lower rank mobs, so you can reach a sufficient number of critical hit attempts without any special critical hit forcing skills such as Blindside.

   (2) Blindside > Barrage > Light Shot > Return to Territory (high rank mobs, physical criticals)

This was the best way we could find to test physical criticals on high level mobs.  Because these mobs are too dangerous to get in a prolonged fight with in test gear, we had to abuse the return to territory mechanic.  To maximize the most number of attempts and at least guarantee 1 critical, we would open with blindside barrage.  So the general flow is to pre-buff blindside and barrage, light shot, then run away.  Rinse and repeat every 90 seconds.

   (3) Excruciate > AoE Fire (magic criticals)

The only spell that can aid in forcing magic criticals is the THM exclusive Excruciate.  The way this move works is once it is used, the players critical hit rate increases dramatically as the timer counts down.  This means that the critical rate is higher after say 20 seconds into the use as opposed to 5 seconds into the use.  We exploit this by using Excruciate, waiting about 20 seconds (to force a near 100% critical rate), then AoE fire the mobs for multiple critical chances.  The only requirement is that we test on mobs that occur in multiples and at the exact same Enemy Rank.

Raw data was collected using one of these 3 methods and the "MIN/MAX" method outlined in detail in previous posts is used.  Similar to Part III of testing, we did not note the trial number and focused purely on the deviation between the predicted average and the MIN/MAX (noted as "DEV" in raw data tables) to tell us when enough trials were collected.  Of note, the physical damage "DEV" maximum is 8%; the magical damage "DEV" maximum is 5%; the magical cures "DEV" maximum is 3%. These were the cut-offs used in testing.  A summary table of our raw data collection for this testing is shown below.  I had shrink the table to make it more viewable on LJ, so I also gave a thumbnail of an expanded raw data table as well.

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Note that THM has an innate +10 Critical Bonus trait which is included in the "Critical Potency" column

Link to Complete Full-Sized Version

The majority of the post will focus on the Magical Critical Bonus data involving tests using fire.  The physical critical bonus data is used only to make sure that the same formulas and rules that apply to magical damage also apply to physical damage.


Assessing the Critical Damage Bonus Cap and Floor

Taking a glance at the complete data set, we can see that the critical bonus seems to follow a straight percentage increase, which is labeled as "Critical Bonus" in the chart.  Looking closely, particularly at the first 3 data sets shown below:

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We can see that the "critical bonus" is roughly 175% for all 3 of these cases.  This is interesting in that increasing magic critical potency from 10 to 70 did not increase the bonus; increasing dLVL from -49 to -20 also did not decrease the bonus.  This led us to believe that there is a cap on critical damage bonus at 175%.  This leads us to naturally ask if a floor exists (and if so, where?).  Taking a look at the physical critical data...

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We see that the as the dLVL increases, the critical bonus decreases, eventually to around 115% at R54 without any critical potency gear.  This 115% bonus remains even at R58, suggesting that the critical damage bonus has a floor of 115%

Interestingly, if we look closer at this data set, we see that the potency gear increases the bonus above 115% at R54 (dLVL=4); however, at R56 there is almost no increase, and in fact no increase at all by R58 .  This suggests that the 115% floor is applied after potency is factored inTo give a hypothetical situation, if the critical bonus for some dLVL is calculated to be 110%, and one applies enough potency gear to increase this to 114%, there is actually no true increase in the critical damage bonus because both would still be floored at 115%.  This is a concept we will revisit at length when it comes to assessing gear options at the end of this post.


Effect of dLVL on "Critical Potency" Enhancement

We paired out data in groups of two where we took the same enemy (and therefore same dLVL) but varied the amount of critical potency.  This effort is most clearly shown in the full sized version of our raw data set found here.  Taking specifically the magical critical bonus data, we can summarize our findings below:

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The general trend is that adding potency gives some fixed increase to the amount of critical damage bonus for each dLVL.  We only collected two data points for each dLVL, so it is impossible to show what kind of increase this is (linear, or something more complex); however, we went ahead and made the assumption that this increase would be linear.  By doing so, we were able to calculate a "Bonus to Potency Ratio" (shown in the far right column) by taking the gain in critical bonus and dividing it by the amount of potency increase.

We can see that if we exclude the data that involved either the 175% cap or the 115% floor (the remaining data that fits this criteria is highlighted in red), there is a clear trend where the "Critical Bonus to Potency Increase" Ratio decreases as dLVL increases.  We then plotted to see what this trend looked like...

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We find a pretty strong linear (R2=0.99) association between dLVL and the critical bonus to potency increase ratio.  I have cleaned up the formula shown in the graph above as Excel's version of the formula was a pretty big mess. 


Effect of dLVL on Base Critical Bonus

So far, we have talked about the idea of the cap/floor and the increases to the bonus from potency items (Savage Might and Sagacious Might); however, we have neglected to talk about the baseline critical bonus for each dLVL.  This was difficult to assess with our magic critical data because we needed to use THM (which has innate +10 potency) for Excruciate to force criticals on high level targets.  However, now that we have a formula to determine critical bonus to potency ratios for all dLVLs, we can back-calculate the innate critical bonuses for each dLVL (the critical bonus at +0 potency for every dLVL).  Below is a summary calculation table that shows this:

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Again, note that there is a 115% floor that applies for high dLVL, but we go ahead and show the calculated value of the "true bonus" because that is the value that is used when applying critical potency.  We then can graph these values and try to provide a best fit curve...

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The most important feature here is that this association is not linear.  Without even showing you what the best fit linear regression would have looked like, I think you can eye ball that it would not have looked that great.  We instead went with a second order polynomial fit (the line shown in the graph).  While we do not know if the true formula here is actually a second order polynomial fit, this does seem to work out quite well in modeling the data we have available.  The graph below summarizes the baseline critical bonus (the critical bonus for each dLVL at +0 potency)...

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Comparing Physical and Magical Critical Data

So far, the analysis has focused on the magical critical hit data.  This focus was due to the fact that magic damage can produce larger numbers, which give better precision.  However, we also want to make sure that we can apply the formulas and ideas we have discussed regarding magical to physical.  Let's take the physical critical bonus data set shown below.

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The good thing about this data set is that there is no innate bonus to physical critical bonus on the jobs we chose to test on, so we can simply plot the critical bonuses without having to worry about a potency correction.  Below is a plot that contains the polynomial curve modeling the effect of dLVL on the baseline (+0 potency) critical magic damage bonus with overlying data points (shown in red) from the physical damage critical bonus data shown above...

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We find that the when we plot these data points on top of the curve, it fits fairly well despite pretty poor precision in data collection due to low damage.  This gives the impression that magic and physical critical damage bonus follow the same rules.  But to give further verification, we can also plot their critical bonus to potency increases ratios.  This is shown below...

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The R2 for the physical critical is fairly low at 0.7692, but we can still see that the linear curves are roughly the same.  Based on these 2 comparisons, we felt that we could safely make the call that physical and magical critical damage bonuses follow the same set of rules and formulas


Comparing Magic Attack Data to Cure Data

To quickly verify if the formulas that apply to magic and physical critical damage bonus also apply to cures, we revisit our initial cure data set, which is reproduced below.  We will focus on the values on the far right that are bolded in blue.  These values were previously disregarded in Part I, but now that we have more information on critical bonus, we can better assess them.

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These 3 values in blue just happen to represent 3 cases of an R50 curing himself at three different levels of potency.  In this case, we assume that the level of the target (R50) minus the level of the caster (R50) gives us the dLVL (0).  We can then plot our predicted increase in critical cure potency based on the formulas elucidated earlier and compare them to the actual bonuses seen in the cure data set...

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We find that the predicted curve derived for magic attack critical potency fits the data set very well.  This gives us confidence that we can now globally apply the formulas and rules talked about for magic attack critical bonus and potency. 

While I will not specifically show this is the case, I can tell you that if you attempt to cure a lower level target, your critical bonus will actually be higher.  For instance, if you cure an R1 as an R50, your bonus will indeed be very high (nearing 2,000 HP Cura with no Healing Magic Materia).  This gives strong ancedotal evidence that cure critical potency follows the same rules.  Because in the vast majority of cases, the only relevant dLVL is 0 (R50 targets curing other R50 targets), the graph above will also provide a good estimation of the effect of potency on most endgame situations specifically for cure critical bonuses.


Putting It All Together - A Look at Potency Effectiveness

We can summarize the analysis up to this point by providing a table which shows the baseline critical bonuses and critical bonus to potency ratios for reach dLVL.  Values shown in blue indicate that the 175% cap has been applied (meaning the calculated value given is above 175% and that in the actual game, it will be 175%).  Values shown in red indicate that that 115% floor has been applied (meaning that calculated value given is below 115%, but will show as 115%).  The summary table is shown below.

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In this table, I have provided an extra column on the far right called "wasted potency."  This is a calculated value that shows the amount of additional potency required before you will see any increase the critical bonus (another way of saying the amount of potency required to exceed the 115% floor).  For instance, this shows that when fighting an R55 mob at R50, it requires at least +16 potency to see any increase in the critical bonus.

To get an even deeper look at the true effectiveness of adding potency gear (namely from Savage and Sagacious Might), let's apply the formulas derived above to 4 hypothetical situations at +50, +100, +150, and +200 potency and see the overall damage increase relative to having +0 potency expressed as a percent increase in overall damage dealt relative to +0 potency

Below are the raw data charts (with the absolute percentages on the left and the true 0% increases on the right).  On the right, blue values indicate that the 175% cap is in play; whereas red values indicate that the 115% floor is in play. 

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Link to Full-Sized Version

Unfortunately, it is difficult to assess exactly how useful Savage and Sagacious Might are based on this data because it does not consider the critical hit rate or the abilities that alter the critical hit rate.  However, it does show that there are some sizable increases in damage output.  Remember that these are percentage increases and quite sizable.  For instance, if you had a +150 Savage Might body (perfect triple or quad meld - difficult but just to prove a point), a single piece of equipment would increase your damage by 20% on an R52 mob if you could find a way to force the critical


Critical Bonus Enhancement Abilities and Traits

There are a couple traits and actions in the current XIV v1.20 that supposedly provide bonuses to critical hits in some shape or form.  So I wanted to specifically talk about each of these briefly (and the testing involved in necessary).

    (1)  Critical Resilience

There are only 3 ways to obtain the "critical resilience" stat in the current v1.20 - the GLA trait (+10), Plundered Plate Belt (+2), and Sentinel's Celata (+10).  While we did not attempt to test this effect, we can make the reasonable assumption that critical resilience reduces the bonus enemies receive when they critical hit you.  One could make the argument that we could use our dLVL charts to try to find the bonus difference, but we currently do not think the charts apply in reverse.  This is an issue with dLVL itself as it appears to involve the level of the attacker in addition to the actual difference in levels.

    (2)  Rampage Effect (MAR / WAR)

First off, thanks to Miko Neversleeps for this particular test.  Rampage is a non-timered status that grants increased attack speed and an HP return effect on attacks that happen to critical hit.  Our aim here was to test this HP return.  Our results showed that there is a 50% return on the amount of damage dealt (if you deal 100, you get 50 back).  There is a cap to this 50% return though - you cannot recover more than 20% of your maximum HP.  This means if you deal 2000 damage, but your max HP is 2,000, you would be capped at recovering 400 HP instead of getting the full 1,000.  We made no attempt to test the attack speed increase aspect of Rampage.

    (3)  Thundaga (Combo) (THM / BLM)

The description of the Thundaga spell shows "Combo Bonus: Increased Critical Damage."  We tested this using 3 mob sets - R1 Corroded Coblyns, R35 Cursed Eyes, and R50 Zahar'ak Drubbers.  All tests were performed using 256 INT and 435 MATK with no added elemental potency bonuses.  No magic critical bonuses were used except for the innate THM trait.  Data set below.

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The first thing I'll point out here is that for the R1 Corroded Coblyns, the combo bonus hit the damage cap of 9999, so we won't exactly how much damage was supposed to be dealt.  This does tell us, however, that whatever this combo bonus does, it breaks the 175% critical damage bonus cap.  We hypothesized that there are 4 likely possibilities as to what is going on here:

    (1) There is a direct increase in overall damage by X%.
    (2) There is a percent increase in the critical damage bonus (e.g. +X% increase over baseline).

    (3) There is a bulk, static increase in the critical damage (e.g. +25% on top of baseline) that breaks cap.
    (4) There is a set amount of magic critical potency (Sagacious Might) added that breaks cap.

I started 4 columns on the far right to help assess these 4 possibilities.  We are looking for any situation where the R35 and R50 data are the same.  The first labeled "Combo / Normal" is to help assess for a global % increase (#1).  The values for the R35 and R50 data are clearly different, so we can remove this possibilities.  The second labeled "Combo / Critical" assesses for a direct % increase in the critical damage bonus modifier.  This value is closer to being equal but is still fairly off.  The "Bonus Increase" looks for a builk static increase (#3); a clear difference is seen so we can remove this.  Finally, the "Potency Increase" looks to see if there is a simple potency bonus on combo.  This is the possibility we chose to go with eventually given that its the closest of the 4 we looked at.

Although a rough test, I personally felt comfortable in calling the Thundaga combo bonus a simple increase in magic critical potency (the equivalent of adding Sagacious Might).  Given the range between the values and the imprecision in data collection, I decided to just call the Thundaga combo bonus a rough +175 magic critical potency increase on combo.



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.



( 5 comments — Leave a comment )
Mar. 6th, 2012 05:04 pm (UTC)
A single Savage Might does "Zero, Zilch, nada, nothing" on Ifrit?
Mar. 7th, 2012 04:15 am (UTC)
Re: So....
Assuming YG's R58 Ifrit is correct, then yes. You need at least 56 crit+ to see any difference. Single Savage might and nothing both give +15% crit damage.
Mar. 7th, 2012 12:19 pm (UTC)
Conclusions, point #3
I assume this is supposed to read: "The enhancement is applied prior to the bonus floor and cap."

Great work as usual. Interesting read. Thank you!
Mar. 8th, 2012 06:11 pm (UTC)
Re: Conclusions, point #3
Wow what an awful typo. Fixed and thanks!
Mar. 27th, 2012 12:42 am (UTC)
Thinking Ahead
Because you can safely say criticals Globally follow the same formula, would you think that probably all damage follows the same rules?

I've been slowly trying to gather magic damage quantities, in hopes to help narrow down how all the stats fit together, and I've noticed with a warrior friend of mine, our damage range seems to be roughly the same. example: Over the course of 300 thunders on level 50 Drubbers, and 300 swings of his axe, we both see a range of around 50 damage. Even when reducing my INT by 30 points, and doing 200 more, my range of damage was still ~50 damage from Min to Max (excluding resists and Crits naturally).

I'd like to help test more, and compare any notes, if you'd like to feel free to email me at Nkling0@gmail.com
( 5 comments — Leave a comment )