Thursday, July 09, 2009

The Math of Sword and Spell: Phalanx

Every Thursday Araelus is bringing the science to FFXI.

 The Math of Sword and Spell is dedicated not only to the hardcore calculations and statistics of FFXI, but more importantly to helping you use that math without confusing you. You may not know why you are playing better, but rest assured you will be playing better.

This week's edition is part of a series called "Occasionally Replies Two to Eight Times" focusing on reader questions and more in-depth analysis of previous concepts or interesting game features. This week we address Treubond's inquiry regarding Phalanx.

"Just a question, is a fully merited Phalanx II as good as a Phalanx? I thought Phalanx still had a higher damage reduction than a fully merited Phalanx II. You made a comment on it while talking about the Accession Phalanx and was wondering. Or is it just that SCH can't get high enough Enhancing Magic for it to do the full amount a Phalanx would do on a RDM or even a PLD/RDM? Thanks in advance."

Phalanx provides straight numerical damage reduction – and the higher the caster’s Enhancing Magic Skill, the more damage blocked. Thankfully, this skill check occurs during casting, so it is possible to swap gear and maintain the benefits of a high Enhancing skill.

Any job which subs RDM can cast Phalanx, but the capped support skill is 109, resulting in 8 damage reduction. With all available gear, this can be increased to 124, for 10 damage reduction. With merits, ANY/RDM can have 140 skill, for 12 damage reduction.

The most basic comparison of Phalanx results can be made between BLM, PLD, WHM, SCH, and RDM, the only jobs with native Enhancing skill, and thankfully these are the jobs most likely to be subbing RDM.

So different jobs can reach different levels of Phalanx. That’s all well and good, but how do we compare them usefully? What is the key difference between RDM, WHM, and SCH at 271 skill? The WHM and RDM will only be able to apply Phalanx to themselves, while the SCH can cast it once for the whole party. But what about Phalanx II, which only RDM can cast?

Phalanx II can be cast on any party member, and heavily depends on merit level for effect. At first it seems like a terrible spell. It costs 42 MP, twice that of Phalanx, and base duration is one minute less, at 120 seconds. With one merit level, a RDM at 256 skill will get 14 damage reduction from Phalanx II instead of 23 damage reduction from Phalanx.

Every additional merit level in the spell adds 30 seconds of duration and 3 additional damage reduction.

This results in:
Charted against someone casting Phalanx, we find that the only time Phalanx II provides more damage reduction is when fully merited, although it matches Phalanx when at 4 merits and low skill levels.

MP efficiency should be considered in addition to damage reduction. Standard Phalanx lasts 8.57 seconds per 1 MP cost, and Phalanx II at full merits lasts 5.71 seconds per 1 MP. Composure improves Phalanx’s performance for Red Mages to 25.7 seconds per 1 MP, and of course that is only for the caster. Since Scholar can cast on the whole party at once, they get up to 51.43 seconds of effect per 1 MP spent!

Just for the sake of argument, suppose the only person in the party who will really benefit from damage reduction is the tank. In this improbable case, if we only care about Accession landing on one person, which is the same target as a Phalanx II, then it simply returns the MP comparison to Phalanx’s 8.57 sec/MP vs. Phalanx II’s at best 5.71 sec/MP.

What about a Composured Phalanx II, which has at best 17.14 seconds of effect per 1 MP cost? That still pales in comparison to a Composured Phalanx’s 25.7 sec/MP.

Phalanx will always be more MP efficient than Phalanx II.

Overall efficiency is our final goal. The best way to do this is to create an index, which provides a normalized average. Consider that 25 damage reduction over 180 seconds for 21 MP is the result any lazy RDM or SCH can produce wearing their AF gear on an unaltered cast of Phalanx. We’ll score that cast as “100” and treat any other spell result as follows:

Index rating = 100* [(damage reduction * (duration in seconds / MP cost)) / index]

Phalanx at 271 skill needs to be valued at 100, so our “index” constant’s value is 214.28571428571428571428571428571

Since damage reduction, duration, and MP cost are all exact whole numbers, I’m just going to use scads of significant figures in the background and round off for ease of reading.

Composure increases a cast’s value by the expected 3x multiplier. Since multiple targets have the same “increased MP efficiency” effect, Accession will dramatically increase this efficiency score. In the same way, hitting six party members with Noctoshield increases its rating from a measly 11.87 to a more respectable 71.22.

We can gather from this data that Phalanx II should probably be a party-wide spell, at its current MP cost and tiered durations, in line with how Bar-status-ra spells have twice the MP cost of an equivalent Bar-status. Indeed, making Phalanx II AoE would be worth even an MP cost of 60, more in line with the Cure vs. Curaga series. But as a single-target-only spell it will remain sadly lacking against Accession Phalanx.

Red Mages can take heart that they do not need any Stratagems to cast on a party member of their choosing, and that Scholars are not always present.



Players may acquire or add equipment in a different order than shown here. This chart obviously includes some cases where not all available equipment is added, because it would make no difference in damage reduction, such as BLM+gear not including an Augmenting Earring or Genie Huaraches. Other cases show the addition of gear which does not immediately add to damage reduction, such as SCH+AF adding an Enhancing Torque, or “too much” gear added, for example, the WHM shown at 247 skill could remove the Enhancing Torque and remain at 22 damage reduction with 240 skill. This has been done for illustrative purposes.

Phalanx’s damage reduction tiers at increments of 10 Enhancing Magic Skill. Any change to equipment that does not change the skill’s tens-place numeral will not change damage reduction. Please pay attention to your individual skill needs when selecting equipment and merits.

Bar chart in table form:


Anonymous said...

Phalanx 1 either caps at 28 or there is a linear change in the equation at 300 skill. Because of this, a RDM using phalanx at 320 skill produces the same -28 damage as a phalanx @300 skill. This was tested and I think posted in various BG threads.

This means the actual "best" is Phalanx2 with full merits and ample skill (-29), not phalanx1.

Try this thread:

Anonymous said...

Same as above.

Just to add in case it wasn't clear, your graphs and anything talking about 300+ skill is wrong so hopefully you get that corrected or that the people who choose to read this for advice understand this. The rest is accurate to my knowledge.

Araelus said...

(1) I participated in that thread, if you noticed, waiting for some kind of concrete proof the equation changes. Information from "VirtuousSaint" is not reliable, because he alternates between serious commentary and trolling with no warning.

(2) None of the posters put up screenshots to back up the text claims. This is 2009, POIDH. I will change the article when someone has screenshots.

(3) Septimus, whose word I would trust, neither confirmed nor denied the -28 cap.

(4) There is no way to get Enhancing to 325, so Phalanx II never gets to -29.

(5) If you want to post anon, please sign some kind of name so I can respond to a particular commentator? Thanks.

(6) I'm glad the rest of the article (sub-300 skill) was useful. :)