Are there multiple levels or tiers of Conserve MP?

I was recently looking into what exactly the proc rate is for the "Augments 'Conserve MP'" property of the full Goetia attire +2 set (5/5), which was estimated indirectly last year (a thorough overview of the set bonus, including the relationship between damage multiplier and the fraction of MP conserved, is presented at The Black Mage's Apprentice in two posts). This was done by estimating the effective rate of observed procs, or the product of the actual augment proc rate (which itself cannot be observed directly when the Conserve MP rate is not 100%) and the proc rate of BLM's Conserve MP trait, which is supposed to be 25%. If you believe the set proc rate is a multiple of 5, then 15% and 20% are plausible estimates.

While some of the reasonable assumptions underlying the analysis caught my interest, such as whether the occurrences of Conserve MP, resists, magic critical hits and the Goetia set bonus are all actually mutually independent (kind of similar to whether the Double Attack trait procs on two hits of a multi-hit WS; no one actively looks for these rare events so you have to use more clever methods of providing evidence of such), of greater interest was the suggestion that there are multiple "tier"s (or "ranks" or "levels") of Conserve MP.

I just checked wiki.ffo.jp for the Conserve MP article and found a claim of at least one more Conserve MP "rank" at level 76 for BLM and level 96 for SCH. The claimed Conserve MP rate was 33%, but I couldn't find any evidence supporting this. (But there must have been some reason for this to be posted?)

I then tried to look for evidence of another tier  on the BG forums. I totally forgot I already looked at the evidence for this last year (posts #154 and #155...), and test 1 showed that the estimated Conserve MP rate for BLM was well below the claimed 33% rate. (Due to the use of a non-MVUE for the conserve MP rate, which is a binomial proportion, for the sake of convenience and sanity, the nominal 95% normal approximation confidence interval based on the binomial proportion but plugging in the non-MVUE actually has a lower coverage probability, or 91% as I claimed previously...).   This was before the September 2011 version update raised the maximum job level to 95, so this doesn't rule out any new levels being introduced since then.

So as long ago as June 2011 there did not appear to be evidence of multiple tiers of Conserve MP. If this is to be checked again in the future, the data collection procedure as described on the BG forums (see the previous link) would be one way to amass evidence for or against multiple tiers.

Some black magic - test server findings

There are at least 20 things I could post about more interesting than my checking parameters for black magic spells (BG forum), but those other things would take too long.

That Breakga appears to last only 30 seconds unresisted is notable since the recast time is 50% longer (45 seconds). Compare this to single-target Break (30 second duration, 30 second recast). Even Horde Lullaby II lasts 60 seconds (with only a 24-second recast).

Comet's direct damage/MP efficiency doesn't compare favorably to Blizzaja and Thunder IV without the usual ice or lightning potency merits.

I also checked the magnitude of Kaustra's direct damage, but surprisingly the direct damage appears to be variable in a way that can't be explained by resists. With 85 INT on SCH95/MNK1 I managed to get 378 damage 3 times and 340 twice.

"Naked" Aspir and Aspir II at 400 dark magic skill

At 400 dark magic skill and with no Aspir-enhancing equipment/traits, unresisted Aspir I appears to have a maximum of 160 MP (actually observed maximum: 160 MP) and minimum of 80 MP. (The two lowest observed values, 74 MP and 76 MP, may reflect a resisted state.)

At 400 dark magic skill and with no Aspir-enhancing equipment/traits, unresisted Aspir II appears to have a maximum of 240 MP (actually observed maximum: 238 MP) and minimum of 120 MP (actually observed minimum: 121 MP).

Consistent with previous results, the variability of MP drained with Aspir II is higher than that with Aspir I, which appears to be a result of the range of possible values increasing as the maximum increases. (The maximum of Aspir II, for a given level of dark magic skill, is higher than that of Aspir I.)

Dot plot

Raw data (first column observed MP drained, second Aspir I or Aspir II, third order of data collection)

107 1 1
184 2 2
118 1 3
121 2 4
120 1 5
238 2 6
127 1 7
172 2 8
141 1 9
142 2 10
159 1 11
149 2 12
155 1 13
227 2 14
106 1 15
190 2 16
87 1 17
191 2 18
101 1 19
209 2 20
114 1 21
144 2 22
93 1 23
166 2 24
132 1 25
165 2 26
136 1 27
161 2 28
74 1 29
228 2 30
155 1 31
178 2 32
156 1 33
174 2 34
97 1 35
192 2 36
111 1 37
126 2 38
132 1 39
211 2 40
126 1 41
213 2 42
145 1 43
137 2 44
95 1 45
176 2 46
118 1 47
127 2 48
147 1 49
227 2 50
108 1 51
141 2 52
133 1 53
121 2 54
126 1 55
129 2 56
140 1 57
124 2 58
106 1 59
141 2 60
160 1 61
157 2 62
84 1 63
162 2 64
138 1 65
179 2 66
143 1 67
168 2 68
121 1 69
122 2 70
87 1 71
199 2 72
156 1 73
211 2 74
112 1 75
127 2 76
156 1 77
122 2 78
132 1 79
212 2 80
76 1 81
157 2 82
100 1 83
198 2 84
101 1 85
201 2 86
107 1 87
144 2 88
93 1 89
160 2 90
103 1 91
162 2 92
118 1 93
215 2 94
159 1 95
137 2 96
89 1 97
205 2 98
133 1 99
131 2 100

Drain, Aspir, and Aspir II after the update.

Previous posts have shown that increasing dark magic skill beyond 300 did not increase Drain potency prior to the September 8, 2010 version update, but the version update details state that "maximum values have been increased for certain enhancing magic, dark magic, and blue magic spells whose potency is commensurate with casting skill." The following summarizes the results of checking the potency of Drain, Aspir, and Aspir II without any equipment or other factors that "enhance" any of these spells other than equipment with dark magic skill bonuses.

Raw data is available upon request or I may just post them in the comments below after a week if there is no feedback.

Drain

The distribution of Drain potency (unresisted Drain values) was checked at both 303 dark magic skill (my current dark magic skill level without any equipment) and 340 dark magic skill (with this equipment) on Zvahl Fortalices in Castle Zvahl Baileys (S). The following dot plots show an obvious increase in the maximum value of Drain. Although I was unable to check the distribution of Drain at 300 dark magic skill, it seems that the change in the maximum Drain was done merely by removing the "cap" on increasing it with dark magic skill beyond the 300 level, holding all other potency-increasing factors (maximum-increasing factors) fixed. (In this case, what was fixed was that there were no other factors "present" to affect my results.)



Previously, I gave a formula for the maximum Drain as a function of dark magic skill (without any other potency-affecting factors) as (skill) + 20. The following summary of the minimum and maximum suggests that this formula does not apply beyond 300 skill.

                        ·--------·---------·--------·------------·
                        |    n   |   Min   |   Max  |   Median   |
·-----------------------·--------·---------·--------·------------·
|   Drain (303 skill)   |   60   |   170   |   321  |    247.5   |
|   Drain (340)         |   60   |   173   |   345  |    248.5   |
·-----------------------·--------·---------·--------·------------·

For now, the maximum observed Drain without any other maximum-increasing factors present (or, for shorthand, "naked") is 345.

I do not have access to Drain II so I cannot check it at this time.

Aspir and Aspir II

I actually checked the distributions of Aspir and Aspir II (not omitting resisted values) before that for Drain, and I collected data at both 300 and 302 dark magic skill (on two separate occasions), thinking I had done so only at 300 without realizing later I had skilled up beyond 300. I was lazy and pooled the data, but it is straightforward to see that, similarly to the Drain maximum, the increase in the Aspir (and Aspir II) maximum was done merely by removing the "cap" on increasing it with dark magic skill beyond the 300 level. I checked at 339 dark magic skill with this equipment set. All data collection was done on Stone Eaters in North Gustaberg (S).



I had no idea what the distribution of Aspir II was like compared to Aspir before the update. The previous image shows that, at least after the September 2010 update, the variability of Aspir II (controlling for resist level) is higher than that of Aspir (no reason to assume anything about this beforehand) even though the maximum Aspir II is higher (as expected) as shown in the above image and following summary statistics table:

                            ·--------·---------·--------·------------·
                            |    n   |   Min   |   Max  |   Median   |
·---------------------------·--------·---------·--------·------------·
|   Aspir (300/302 skill)   |   50   |    60   |   120  |     85.0   |
|   Aspir (339)             |   50   |    50   |   135  |     95.5   |
|   Aspir II (300/302)      |   50   |    83   |   180  |    130.5   |
|   Aspir II (339)          |   50   |    56   |   202  |    152.0   |
·---------------------------·--------·---------·--------·------------·

Previously, I gave a formula for the maximum Aspir as a function of dark magic skill (without any other potency-affecting factors) as (skill/3) + 20 (decimals truncated where necessary). The above data shows that this formula does not really apply above 300 dark magic skill. I make no attempt to suggest a formula for the maximum of Aspir II at this time.

The maximum "naked" Aspir observed is 135, and the maximum observed Aspir II is 202.

Summary

Announced in the September 2010 version update, the increase in the maximum Drain, Aspir, and Aspir II values seems to be the result of allowing their potency to increase by increasing dark magic skill beyond 300, holding all other maximum-increasing factors fixed. Before the update, the Drain and Aspir maximum did not increase beyond 300 dark magic skill.

The variability of Aspir II values (controlling for resist level) is higher than that for Aspir values.

I observed a maximum "naked" Drain of 345 (340 dark magic skill), a maximum "naked" Aspir of 135 (339 skill) and maximum "naked" Aspir II of 202 (339 skill). The actual maxima are likely higher and are likely to be attained only by increasing dark magic skill further (well above 340).

Blitzer's Roll

Blitzer's Roll (COR Lv.83)
Reduces melee attack delay for party members within area of effect. Lucky number: 4. Unlucky number: 9.

Seeing as this is the only interesting thing from the update as far as TP-burning for one-handed melee DD vs. Hasso (you self-identify as WAR/DRK/DRG/SAM? Are you a tool? It's either piercing Hasso or non-piercing Hasso) is concerned (although that supposes anyone still cares about FFXI), let's anticipate what the effect might actually be.

Thoughts:

• If this really reduces melee attack delay a la Sword Strap, maybe it will be exactly the same form of delay reduction as that from dual wield. (Why not?) If Blitzer's Roll actually stacks with dual wield and the bonuses are good, this would benefit dancer and ninja the most.
• One-handed melee jobs get more from Blitzer's Roll even if it reduces weapon delay separately from dual wield, but it doesn't mean it'd be bad for two-handed melee jobs (depends on the actual bonuses), just that Fighter's and Samurai would be better. n-hit builds are overrated.
• What if it's "job ability haste"? Wouldn't it be funny if the bonuses were large enough to obviate the use of Hasso and Haste Samba? Among other things that would follow: why are we using two-handed jobs for TP-burn then?

Samurai Roll and Fighter's Roll... for ninja

Having shown in the past that Fighter's Roll can be better than Samurai Roll for increasing warrior's damage output (despite the lack of consideration of WS delay, which actually would favor Fighter's Roll), I thought it might be nice to have a worked example for ninja (this time accounting for WS delay).

This image (Imageshack host) summarizes the computations, based on 95% hit rate, 15% DA rate, 55% haste, 40% dual wield, and a "cRatio" of 1.5, with a 10% critical hit rate, with Blade: Jin as the weapon skill. The specific katana combination is Hochomasamune/Uzura, which is something I would consider getting as a "high-value" option, meaning that it's a highly effective option that I don't have to waste as much time doing boring shit to get this as I would for other options.

First, let's start with Samurai Roll (augmented by the presence of a samurai). The following is a table summarizing the relative increase in the (theoretical maximum) rate of damage from each of several desirable Samurai Roll outcomes.

Roll total      Bonus     Damage/second     Relative efficiency
---------------------------------------------------------------
 -              -               113.607                       -
 2             42 STP           123.979                   9.13%
 7             26               119.672                   5.34%
 8             30               121.410                   6.87%
 9             32               121.414                   6.87%
10             34               121.458                   6.91%
11             50               126.684                  11.51%

The relative increase for each store TP bonus is decent, but not as high as you would expect for two-handed weapons since the proportion of total damage from Blade: Jin for katana is realistically never going to be as high as the proportion of total damage from the (generally) best weapon skills for two-handed weapons (e.g. Drakesbane, Raging Rush, Tachi: Gekko).

In contrast, Fighter's Roll (here augmented from the presence of a warrior) increases auto-attack damage, weapon skill frequency, and weapon skill damage, so it's not a surprise that Fighter's Roll is generally easily superior to Samurai Roll for increasing rates of damage:

Roll total      Bonus     Damage/second     Relative efficiency
---------------------------------------------------------------
 -               -              113.607                       -
 5             15% DA           129.567                  14.05%
 7             11%              125.291                  10.28%
 8             12%              126.358                  11.22%
10             13%              127.427                  12.16%
11             19%              133.857                  17.82%

Note that these are supposed to be the actual DA percent bonuses after the infamous August 2007 version update (source), you know, the one that resulted in ninja being disregarded as DD. If they were what they were before that update, assuming there was a change (higher than what they are now), Fighter's Roll would be even better.

So, if Fighter's Roll can be shown to be better for the job that gets the least relative benefit from Fighter's Roll (warrior), as well as for ninja (though this could be considered self-evident), are there even any legitimate reasons to use Samurai Roll? No, "TP overflow" is an incorrect and stupid answer that betrays a lack of conceptual understanding.

Now, that's not to say Samurai Roll has no application. Maybe it would be desirable to maximize the ratio of damage efficiency to TP "fed" to a mob rather than consider damage efficiency in isolation. I doubt Monk's Roll would do the job, but a case could be made for Samurai Roll.

Also, if it is desirable to maximize weapon skill frequency, Samurai Roll would generally be better for that purpose than Fighter's Roll. (Also related is maximizing TP per hit, which would be desirable for dancer.)

Also, Fighter's Roll can be said to be "contraindicated" for use with multi-hit weapons (that don't use virtue stones) such as Magian multi-hit weapons. (But this assumes Magian multi-hit weapons are actually good, which is not necessarily true.)

Aspir and Drain modeling: an incomplete picture

Earlier, I made some bold statements (at least by my standards) about the distribution of unresisted values of Drain and Aspir. I proposed a model from which I can make explicit, testable predictions.

Specifically, I wanted to see if the model holds at 114 dark magic skill, which can be attained by subbing /DRK on any job without any native dark magic skill (in my case NIN/DRK). Based on the model I described previously, the maximum Aspir without any potency-increasing equipment used is 114/3 + 20 = 58 MP, and the minimum is half that, or 29 MP.

I went out to cast Aspir on Stone Eaters (North Gustaberg (S)) and after the seventh cast I obtained an Aspir of 63 MP, which exceeds the stipulated maximum, so the model doesn't hold for 114 dark magic skill. The following are the observed data values (in order observed):

51 44 56 49 25 51 63 53 35 62 62 46 41 32 44

I then cast Drain on the same Stone Eaters with 246 dark magic skill (NIN75/SCH35 with Dark Arts) and obtained the following results (stem-and-leaf plot):

   6 | 49
   7 | 
   8 | 4
   9 | 
  10 | 
  11 | 
  12 | 
  13 | 4445
  14 | 68
  15 | 044
  16 | 46
  17 | 37
  18 | 9
  19 | 4
  20 | 23789
  21 | 79
  22 | 026
  23 | 55
  24 | 277
  25 | 36
  26 | 01346

(The reason I used Drain and not Aspir was that my scholar is only level 35, and Aspir is accessible at level 36. I would prefer to gather data for Aspir because Aspir values are obviously less variable than Drain values.)

Given 246 dark magic skill, the predicted maximum for Drain is 266 and the predicted unresisted minimum is 133 (both without any potency gear or day/weather effects), so the distribution of Drain (as represented by the sample) seems consistent with the model.

In conclusion, if one were to be technical in describing the scope of the model I proposed earlier, I would say the model is (likely) valid for Drain between 246 and 300 dark magic skill. It is valid for Aspir between 269 and 300 dark magic skill. And, finally, it is valid for Drain II between 285 and 300 dark magic skill. What happens in the 100s is just not that relevant. (In case you are wondering what data I am referring to, you'd have to check my old posts on Drain and Aspir).