Once upon a time, raid free units were game changing. Nowadays, people barely even notice them outside of their trust masters and former fusion-hell. This is understandable, given that most reviews are in terms of resource management, which includes pulls, enhancement spendings, and the occasional rare "others". That, and raid free units typically kind of suck in comparison to their current equivalent-star bases. These units, however, do benefit newer players with a limited unit pool, and as such, will be written with that in mind.

As this is a new unit with a 7★ with alot of moves, I'll go a little more in depth than I would normally do (which is happening alot more now). Without further ado...

Immortal Flame Katy - Raiders of the Free Review

Limit Burst

Enchanting Melody (7★, 20 LB)

• 8-Hit Magic damage (8.3x-11.8x) to all enemies
• Increase ATK/MAG/DEF/SPR (100%) for 3 turns to all allies
• Kingsglaive Frames82-8-8-8-8-8-8-8

Things to note: IF.Katy's LB has a 20% damage boost at level 120. As a result, the effective modifier becomes 9.96x-14.16x.

Trust Reward

Everlasting Fantasy (Materia)

• MP 20%
• Increase MAG (30%) when equipped with an instrument
• Decrease chance of being targeted

Super Trust Reward

Empowering Earrings (Accessory)

• HP 20%, SPR 20%
• Enable use of "Encouraging Aura" (30 MP; random effect, see below)
  • (25%) Cure all status effects for one ally
  • (25%) Remove all debuffs from one ally
  • (25%) Restore 25% HP and MP to one ally
  • (25%) Increase ATK/MAG/DEF/SPR by 100% for 3 turns to one ally

Note: For the most part, ignore the active ability, as it's too random and diverse to reliably have it help you.
Edit: This is basically a lesser Genbu Ring without the Def component. Genbu Ring is a free craft, but painful depending on how much you like farming the Realm of the Dragon King. IMO: there's no reason to make the STMR if you have access to plenty of GRing's or comparable accessories, or willing to run through RotDK multiple times.

Notable Skills

Wheel of Fortune

• Use Fortune skills twice in one turn

Fortune - Luck of the Draw

• 1-Hit Magic damage (6x) to all enemies
• Randomly use one of the following:
  • (40%) Decrease ATK/MAG (55%) for 3 turns to all enemies
  • (40%) Decrease Def/SPR (55%) for 3 turns to all enemies
  • (20%) Decrease ATK/MAG/DEF/SPR (60%) for 3 turns to all enemies
• Multi-castable

On paper, you should be able to refresh a minimum of 55% break on the statistically average case scenario. In reality, I would not rely on this as your breaking move, especially not for the first turn breaks. The numbers are also lower than the meta-break numbers. I only mention this as a "Hail Mary" move in the event you really need to break, but have no other options on the table.

Fortune - Anyone's Call

• 12-Hit Magic damage (6x) to all enemies
• Randomly use one of the following:
  • (40%) Increase ATK/MAG (100%) for 3 turns to all allies
  • (40%) Increase DEF/SPR (100%) for 3 turns to all allies
  • (20%) Increase ATK/MAG/DEF/SPR (100%) for 3 turns to all allies
• Multi-castable
• Tornado Frames80-12-12-12-12-12-12-12-12-12-12-12

See above regarding random affects, though I'm more forgiving due to buff being a lower priority than breaks. Interesting thing to note, if I'm reading the skill internals correctly, the buff happens first, followed by the damage.

Fortuna's Gift

• Use own LB gauge to fill ally's gauge

This mention is more for newer players, but entrust-like abilities fill based on percentage. Example, if IF.Katy has her gauge 50% filled when she uses this, the ally will gain 50% of his/her/its gauge, regardless of how much either LB costs.

Fortune - Lucky Streak

• Heal (1200 HP, 3.4x) to all allies
• Recover MP (30) to all allies
• W-castable

Better-than-Curaga-strength heal with lowish-moderate MP heal. The skill costs less MP than it restores, so IF.Katy should be net-gaining MP when using this skill.

Fortune - Out of Luck (lvl 110)

• Randomly use
  • (40%) 5-Hit Magic damage (8x) to all enemies
  • (30%) 5-Hit Magic damage (12x) to all enemies
  • (30%) 5-Hit Magic damage (16x) to all enemies
• Multi-castable
• Chaos Wave Frames52-20-20-20-20

On average, damage modifier will be 11.6x. Good that she has a chaining family with many of the current and future meta magic damage dealers, but being non-elemental and limited to 2 casts/turn does hurt her viability to chain with them.

Dualcast

• Use magic twice in one turn

Jackpot (lvl 105)

• 7-Hit Magic damage (10x) to all enemies
• Restore HP/MP (100%) to caster
• Enable skill for 4 turns to caster: Triple Black Magic
• Divine Ruination Frames70-7-5-7-7-7-7
• 5 turns CD, available on turn 1

Triple-BM is the main prize here. The restore are very nice though as triple-cast tends to eat through MP quickly, with the damage great for making this setup round not a complete dead turn as far as damage is concerned. Note that this is only usable with black magic, compared to Dualcast above which can be used in conjunction with any magic.

Firaja (Magic)

• Fire magic damage (2x) with consecutive increase (4 times, 1x each, 6x max) to all enemies

Thundaja (Magic)

• Lightning magic damage (2x) with consecutive increase (4 times, 1x each, 6x max) to all enemies

Raging Ice (Magic)

• Ice magic damage (1.2x) with consecutive increase (9 times, 1.2x each, 12x max) to one enemy

Raging Water (Magic)

• Water magic damage (1.2x) with consecutive increase (9 times, 1.2x each, 12x max) to one enemy

Tornado (lvl 105, Magic)

• Wind magic damage (2.5x) to all enemies
• Decrease wind resistance (50%) for 3 turns to all enemies
• Tornado Frames80-12-12-12-12-12-12-12-12-12-12-12

Quake (lvl 105, Magic)

• Earth magic damage (2.75x) to all enemies
• Decrease earth resistance (50%) for 3 turns to all enemies
• Quake Frames160-22-21-22-23-23-22-23

Flood (lvl 105, Magic)

• Water magic damage (2.5x) to all enemies
• Decrease lightning resistance (50%) for 3 turns to all enemies
• Flood Frames133-12-12-12-12-12-12-12-12-12-12-12

Freeze (lvl 105, Magic)

• Ice magic damage (2.75x) to all enemies
• Decrease ice resistance (50%) for 3 turns to all enemies
• Freeze Frames140-14-14-14-14-14-15-15

See these magic moves. Large amount of elemental coverage with chaining family. However, all of these combo's have issues to them, from missing corresponding chaining/finishing move, or wrong imperil for the flood chains, or not being able to fully cap certain combos. Also worth noting, for her Raging Ice/Freeze (II/III-cast) and Raging Water/Flood (III-cast only) combos, they must be spark chained or else they will break (edit: apparently, there are some reports that RIce/RIce/Freeze breaks even when sparked when tested with Mediena). This is a detriment if you're not perfect with your chains as both of these are her best movesets. Edit: Technically, RIcex2/Tornado is stronger due to being able to fully capping all hits, but is dependent on external imperils.

Notable Others

• Immune to sleep silence, and paralyze
• Entrust, 50% LB gauge fill rate (from TM ability), and low LB cost
• Increased rare item drop rate (50%)
• Increased gil obtained in battle ( 100%)
• 10% innate MP-resfresh (from TM abilitiy)
• 60% chance of countering physical/magical attacks with slight AoE HP/MP restore (1/turn, 30% without TM ability)
• Increased potency of healing items ( 200%)
  • For comparison purposes, Ilias has a 100% item potency
• Can equip light shields, which has application for elemental restance

Notable Issues

• Bad stats for a 7★ unit (comparable to a really good 6★ unit)
• Damage is very reliant on maintaining her stacks, which she loses if she dies due to low survivability stats
• Lacks resistance to several status ailments, notable confusion and petrify
• Certain chaining moves have issue (like flood having lightning imperil instead of water)
• Certain chaining combos have issues (notably, missing many matching elemental skill pairing)
• Many utility moves are locked behind RNG
• Sources of magical instruments are fairly limited, and those that exist are fairly weak. Expect to forgo the harp mastery at higher levels.

Interesting Tidbit

• Better Katy
• Nugget is Katy's micro teacup poodle IRL. Go figure.

Nude Expeditions

^{Subject to rounding errors
Success capped at 16%, anything above is solely for comparison purposes
No gear equipped or using a 0-statted variant for mastery
Parentasis denote with Harp mastery
7★★ denotes with TMR and STMR equipped, with S/TMR stats calculated}
Expedition Charts

Nude Comparisons

• NEW All units will only have access to one of their own TMR, unless noted otherwise (mostly to equalize TM ability access). If the unit has easy access to their STMR, it can also be used for themselves.
• If any passive are conditional on equip, assume that the unit have a 0-statted variant of it equipped. For example, Marquis de Leon is wielding an I-can't-believe-it's-not-Not-a-knuckle ^{or a 0-calories Diet Knuckle, but with all the great taste}.
• Also assume spark chaining, whenever chaining math is done
  • Assume exactly 2 chainers, with the result calculation being damage dealt by a single chainer
  • Assume single-element for physical/hybrid, unless otherwise stated
• Base stat's only, no pots of any sort.
• If Limit Burst is used, calculation is done using a Lvl 1 version (unless noted otherwise).
• All units will get a minimum of 40% stat boost while in battle (via Leadership - Rain)
• All units will get a minimum of 35% imperil (Crazy Day)
• Using the below formula for calculations and comparisons, unless noted otherwise:
  • Reg Damage = (Stat²⁾ * Skill.Mod * Chain.Mod * Imperil * (Lvl.Correction)
  • Evo Damage = (Mag² SPR²⁾ / 2 * (1 EVO.MAG) * Skill.Mod * Chain.Mod * Imperil * (Lvl.Correction)

Popstar Katy Immortal Flame Katy^7★★

^{note to self: change picture to Blue Katy if it's up. Otherwise, pretend this note doesn't exist.}

Note: This includes both IF.Katy's TMR and STMR (1 each; STMR is survivability padding only)

HP: 5544
Mag pre-buff: 354
Mag post-buff: 433.4 / 551.6 (via Leadership/LB, respectively)
Def pre-buff: 144
Def post-buff: 196.5 / 275.1 (via Leadership/LB, respectively)
Spr pre-buff: 177
Spr post-buff: 222 / 288.6 (via Leadership/LB, respectively)
Imperil: 35%/50% (via Crazy Day or Tornado/Flood/Freeze, respecitively)
  * Assume imperil applied already for T1 (ie: stack rest)

Limit Burst
  (433)^2 * (8.3*1.2) * 3.295 * 2.2 = 13,536,713
  (551)^2 * (8.3*1.2) * 3.295 * 2.2 = 21,920,004
Jackpot
  (433)^2 * 10 * 2.968 * 2.2 = 12.242,281
  (551)^2 * 10 * 2.968 * 2.2 = 19,823,930
Fortune - Out of Luck (W-Cast)
  (433)^2 * 11.6 * 3.07 * 2.2 * 2 (W-cast) = 27,858,615
  (551)^2 * 11.6 * 3.07 * 2.2 * 2 (W-cast) = 45,111,465
Tornado x2
  (433)^2 * 2.5 * 3.778 * 1.5 * 2.2 * 2 (Dualcast) = 11,687,501
  (551)^2 * 2.5 * 3.778 * 1.5 * 2.2 * 2 (Dualcast) = 18,925,575
Tornado x3
  (433)^2 * 2.5 * 3.851 * 1.5 * 2.2 * 3 (III-cast) = 17,869,998
  (551)^2 * 2.5 * 3.851 * 1.5 * 2.2 * 3 (III-cast) = 28,936,894
Firaja   Tornado
  T1: (433)^2 * (2*4*1.35   2.5*3.552*1.5) * 2.2 = 9,948,916
      (551)^2 * (2*4*1.35   2.5*3.552*1.5) * 2.2 = 16,110,283
  T5: (433)^2 * (6*4*1.35   2.5*3.552*1.5) * 2.2 = 18,858,393
      (551)^2 * (6*4*1.35   2.5*3.552*1.5) * 2.2 = 30,537,402
Firaja x2   Tornado
  T1: (433)^2 * (2*2.9*1.35   3*4*1.35   2.5*3.62*1.5) * 2.2 = 15,511,152
      (551)^2 * (2*2.9*1.35   3*4*1.35   2.5*3.62*1.5) * 2.2 = 25,117,214
  T3: (433)^2 * (6*2.9*1.35   6*4*1.35   2.5*3.62*1.5) * 2.2 = 28,652,631
      (551)^2 * (6*2.9*1.35   6*4*1.35   2.5*3.62*1.5) * 2.2 = 46,397,215
Flood   Thundaja    
  T1: (433)^2 * (2.5*3.552*1.35   2*4*1.5) * 2.2 = 9,894,469
      (551)^2 * (2.5*3.552*1.35   2*4*1.5) * 2.2 = 16,022,117
  T5: (433)^2 * (2.5*3.552*1.35   6*4*1.5) * 2.2 = 19,793,888
      (551)^2 * (2.5*3.552*1.35   6*4*1.5) * 2.2 = 32,052,250
Flood   Thundaja x2
  T1: (433)^2 * (2.5*3.552*1.35   (2 3)*4*1.5) * 2.2 = 17,319,033
      (551)^2 * (2.5*3.552*1.35   (2 3)*4*1.5) * 2.2 = 28,044,717
  T3: (433)^2 * (2.5*3.552*1.35   (6 6)*4*1.5) * 2.2 = 34,643,017
      (551)^2 * (2.5*3.552*1.35   (6 6)*4*1.5) * 2.2 = 56,097,449
Flood   Raging Water
  T1: (433)^2 * (2.5*3.568*1.35   1.2*4*1.35) * 2.2 = 7,639,876
      (551)^2 * (2.5*3.568*1.35   1.2*4*1.35) * 2.2 = 12,371,254
  T8: (433)^2 * (2.5*3.568*1.35   12*4*1.35) * 2.2 = 31,695,465
      (551)^2 * (2.5*3.568*1.35   12*4*1.35) * 2.2 = 51,324,477
Flood   Raging Water x2
  T1: (433)^2 * (2.5*3.568*1.35   (1.2 2.4)*4*1.35) * 2.2 = 12,985,563
      (551)^2 * (2.5*3.568*1.35   (1.2 2.4)*4*1.35) * 2.2 = 21,027,526
  T6: (433)^2 * (2.5*3.568*1.35   (12 12)*4*1.35) * 2.2 = 58,423,897
      (551)^2 * (2.5*3.568*1.35   (12 12)*4*1.35) * 2.2 = 94,605,836
Raging Ice   Freeze
  T1: (433)^2 * (1.2*4*1.5   2.75*3.568*1.5) * 2.2 = 9,040,644
      (551)^2 * (1.2*4*1.5   2.75*3.568*1.5) * 2.2 = 14,639,518
  T8: (433)^2 * (12*4*1.5   2.75*3.568*1.5) * 2.2 = 35,769,076
      (551)^2 * (12*4*1.5   2.75*3.568*1.5) * 2.2 = 57,920,877
Raging Ice x2   Freeze
  T1: (433)^2 * ((1.2*2.2 2.4*4)*1.5   2.75*3.8125*1.5) * 2.2 = 14,059,882
      (551)^2 * ((1.2*2.2 2.4*4)*1.5   2.75*3.8125*1.5) * 2.2 = 22,767,171
  T6: (433)^2 * ((12*2.2 12*4)*1.5   2.75*3.8125*1.5) * 2.2 = 52,519,125
      (551)^2 * ((12*2.2 12*4)*1.5   2.75*3.8125*1.5) * 2.2 = 85,044,237
Raging Ice x2   Tornado
  T1: (433)^2 * ((1.2*4 2.4*4)*1.35   2.5*3.552*1.5) * 2.2 = 13,512,707
      (551)^2 * ((1.2*4 2.4*4)*1.35   2.5*3.552*1.5) * 2.2 = 21,881,131
  T6: (433)^2 * ((12*4 12*4)*1.35   2.5*3.552*1.5) * 2.2 = 58,951,041
      (551)^2 * ((12*4 12*4)*1.35   2.5*3.552*1.5) * 2.2 = 95,459,440
Quake x2 (off-chained)
  (433)^2 * 2.75 * 3.4915 * 1.5 * 2.2 * 2 (Dualcast) = 11,881,313
  (551)^2 * 2.75 * 3.4915 * 1.5 * 2.2 * 2 (Dualcast) = 19,239,415
Quake x3 (off-chained)
  (433)^2 * 2.75 * 3.544 * 1.5 * 2.2 * 3 (III-cast) = 18,089,951
  (551)^2 * 2.75 * 3.544 * 1.5 * 2.2 * 3 (III-cast) = 29,293,063

Recommended Rotation (3-turns)
   Fortune - Out of Luck x2 (lesser buff)
   Fortune - Out of Luck x2 (lesser buff)
   Fortune - Out of Luck x2 (lesser buff)
  Avg: 27.858 Mil (First 3 turns)
Recommended Rotation (Long, ignoring RIce/Tornado due to small increase and different elements)
   LB (Unless if well geared and/or using comparable/better buff)
   Jackpot
   Flood   Raging Water x2
   Flood   Raging Water x2 (lesser buff)
   Flood   Raging Water x2 (lesser buff)
  Avg: 48.962 Mil (5-Turn Rotation, Asymptote)

For the comparison, I'll be mostly looking at each units innate damage with some consideration to other things like survivability and utility. I've included a seperate build below for maximizing her damage. This ignore STMR, limited, premiums, and IW stats, but does include her event gear and her own STMR (or would if it helped her in any substantial way).

Mag Damage Build

HP : 5,700
MP : 592
MAG: 1,827
DEF: 297
SPR: 374
LB :  20%

Enchanting Melody (LB)
  (1827)^2 * (8.3*1.2) * 3.295 * 2.2 = 240,998,607
Jackpot
  (1827)^2 * 10 * 2.968 * 2.2 = 217,953,411
Fortune - Out of Luck (W-Cast)
  (1827)^2 * 11.6 * 3.07 * 2.2 * 2 (W-cast) = 523,029,441
Tornado x3
  (1827)^2 * 2.5 * 3.851 * 1.5 * 2.2 * 3 (III-cast) = 318,145,523
Firaja x2   Tornado
  T1: (1827)^2 * (2*2.9*1.35   3*4*1.35   2.5*3.62*1.5) * 2.2 = 276,150,204
  T3: (1827)^2 * (6*2.9*1.35   6*4*1.35   2.5*3.62*1.5) * 2.2 = 510,112,323
Flood   Thundaja x2
  T1: (1827)^2 * (2.5*3.552*1.35   (2 3)*4*1.5) * 2.2 = 308,336,518
  T3: (1827)^2 * (2.5*3.552*1.35   (6 6)*4*1.5) * 2.2 = 616,761,157
Flood   Raging Water x2
  T1: (1827)^2 * (2.5*3.568*1.35   (1.2 2.4)*4*1.35) * 2.2 = 231,186,297
  T6: (1827)^2 * (2.5*3.568*1.35   (12 12)*4*1.35) * 2.2 = 1,040,140,066
Flood   Raging Water
  T1: (1827)^2 * (2.5*3.568*1.35   1.2*4*1.35) * 2.2 = 136,015,266
  T6: (1827)^2 * (2.5*3.568*1.35   12*4*1.35) * 2.2 = 564,284,908
Raging Ice x2   Freeze
  T1: (1827)^2 * ((1.2*2.2 2.4*4)*1.5   2.75*3.8125*1.5) * 2.2 = 250,312,756
  T6: (1827)^2 * ((12*2.2 12*4)*1.5   2.75*3.8125*1.5) * 2.2 = 935,015,455
Raging Ice   Freeze
  T1: (1827)^2 * (1.2*4*1.5   2.75*3.568*1.5) * 2.2 = 160,953,601
  T8: (1827)^2 * (12*4*1.5   2.75*3.568*1.5) * 2.2 = 636,808,759
Quake x3
  (1827)^2 * 2.75 * 3.544 * 1.5 * 2.2 * 3 (III-cast) = 322,061,414
Raging Ice x2   Tornado
  T1: (1827)^2 * ((1.2*4 2.4*4)*1.35   2.5*3.552*1.5) * 2.2 = 240,571,218
  T6: (1827)^2 * ((12*4 12*4)*1.35   2.5*3.552*1.5) * 2.2 = 1,049,524,987

Rotation (Short)
    Fortune - Out of Luck x2
  Average Damage: 523.02 Mil
Recommended Rotation (Long, ignoring RIce/Tornado due to small increase and different elements)
    Jackpot
    Flood   Raging Water x2
    Flood   Raging Water x2
    Flood   Raging Water x2
    Flood   Raging Water
  Average Damage: 780.531 Mil (5-Turn rotation)

*Ignoring buffs in damage math

Ashe Ashe

Unenhanced Ashe (no TMR)

HP: 3986.4
Mag pre-buff: 261
Mag post-buff: 326.25 (via Mediate)
Def pre-buff: 124
Def post-buff: 173.6 (via Leadership)
Spr pre-buff: 130
Spr post-buff: 188.5 (via Mediate)
Imperil: 0% (non-elemental)

Heaven's Fury
  (326)^2 * 3.067 * 3.07 * 2 = 2,001,106

Rotation
    Mediate
    Heaven's Fury
    Heaven's Fury 
    Heaven's Fury
    Heaven's Fury
  Average Damage: 1.600 Mil (5-Turn rotation)
    4.7% of IF.Katy's short rotation

Enhanced Ashe

HP: 4711.2
Mag pre-buff: 348
Mag post-buff: 442.25 (via Leadership)
Def pre-buff: 127
Def post-buff: 176.6 (via Leadership)
Spr pre-buff: 130
Spr post-buff: 214.5 (via Leadership)
Imperil: 0% (non-elemental)

Heaven's Fury 2
  (422)^2 * 4 * 3.07 * 2 = 4,373,743

Rotation
    Heaven's Fury
  Average Damage: 4.373 Mil (1-Turn rotation)
    15.7% of IF.Katy's short rotation

• Ashe can AoE heal while chaining
• Both can AoE heal status ailments
• IF.Katy deals significantly more damage
• IF.Katy has better elemental coverage
• IF.Katy has better/more diverse chaining families
• IF.Katy can AoE buff team (reliably via LB)
• IF.Katy can self-sustain (via Jackpot)
• IF.Katy has dualcast (and unlockable black triple cast)
• IF.Katy is tankier (even if you ignore the STMR)

Short answer, Katy wins. With her BiS for Mag damage, she still does less damage ^{61 mil} than IF.Katy. Looks like Ashe needs to work harder to break the game.

Popstar Katy Popstar Katy^7★★

HP: 4851
Mag pre-buff: 315
Mag post-buff: 375 (via Leadership)
Def pre-buff: 144.1
Def post-buff: 196.5 (via Leadership)
Spr pre-buff: 282.2
Spr post-buff: 348.6 (via Leadership)
Evo Mag:  50%
Imperil: 0% (non-elemental)

Eye See You (LB, ignore chaining)
  (375^2   348^2)/2 * 1.5 * (15.4*1.2) * 2.2 = 7,980,640
Command - Backup Dancer Rush (W-cast)
  (375^2   348^2)/2 * 1.5 * 7 * 2.2 * 2 (W-cast) = 6,045,939
Command - Bass Blast (Off-chained, W-cast)
  (375)^2 * 2.75 * 2.665 * 2.2 * 2 (W-cast) = 4,534,664
Command - Showtime
  (375^2   348^2)/2 * 1.5 * 8 * 3.07 * 2.2 * 2 (W-cast) = 21,212,611

Rotation
    Dress Rehearsal
    Command - Showtime x2
    Eye See You (LB)
    Command - Backup Dancer Rush x2
  Average Damage: 15.623 Mil (4-Turn rotation)
    56.1% of IF.Katy's short rotation
    31.9% of IF.Katy's long rotation

• PS.Katy can summon any party Esper
• PS.Katy can fill esper gauge
• PS.Katy can ignore physical/magical mitigation
• IF.Katy deals significantly more damage
• IF.Katy can take advantage of killers
• IF.Katy has better elemental coverage
• IF.Katy has more diverse chaining families
• IF.Katy has better party support utility
• IF.Katy has better self-sustain

First, PS.Katy's damage is artifically augmented with Evo Mag. If we add in killers, then the comparison here will drop unfavorably against PS.K. That aside, with perhaps the exception of esper-based missions and enemy mitigation, IF.Katy is better in almost every way compared to PS.Katy. When including proper gearing, PS.Katy ^{359 Mil} still loses to IF.Katy.

Lekisa enh. Lexa

HP: 3031
Mag pre-buff: 432.1
Mag post-buff: 491.7 (via Leadership)
Def pre-buff: 116
Def post-buff: 162.4 (via Leadership)
Spr pre-buff: 207
Spr post-buff: 262.2 (via Leadership)
Imperil: 65% (via Tornado 2)
  Note: Assume imperil already applied

Tornado 2   Aeroja
  T1: (491.7)^2 * (2.5*3.552*1.5   2*4*1.5) * 2 = 12,243,176
  T2: (491.7)^2 * (2.5*3.552*1.5   3*4*1.5) * 2 = 15,144,403
  T3: (491.7)^2 * (2.5*3.552*1.5   4*4*1.5) * 2 = 18,045,629
  T5: (491.7)^2 * (2.5*3.552*1.5   6*4*1.5) * 2 = 23,848,083

Rotation (3-turns, assume imperil already applied)
    Tornado 2   Aeroja
    Tornado 2   Aeroja
    Tornado 2   Aeroja
  Average Damage: 15.144 Mil (3 turns)
    54.4% of IF.Katy's short rotation
Rotation (Asymptote)
    Tornado 2   Aeroja
  Average Damage: 23.848 Mil
    85.6% of IF.Katy's short rotation
    48.7% of IF.Katy's long rotation

• Lexa can increase party's Earth/Wind resistance
• IF.Katy deals more damage
• IF.Katy has better elemental coverage
• IF.Katy has more chaining families
• IF.Katy has better non-niche party support
• IF.Katy is tankier

Unless you need the elemental resistance or the boss is extremely weak to wind-element (in which case its a slight bonus towards Lexa), IF.Katy is better. Once again, same thing even with gearing ^{315 Mil}.

Majin Fina enh. Dark Fina^7★★

HP: 5866.9
Mag pre-buff: 560 (not included:  50% TDH/W)
Mag post-buff: 640/860 (via Leadership/Lost Paradise, respectively; not included:  50% TDH/W)
Def pre-buff: 211.25
Def post-buff: 278.85 (via Leadership)
Spr pre-buff: 277.45
Spr post-buff: 384.85 (via Leadship)
Imperil: 35%/50%/60%/120% (via Crazy Day/Quake/Boreas Gale/Lost Paradise, respectively)

Hell's Judgement (LB)
  (640)^2 * 7.6 * 2.476 * 1.35 * 2.2 = 22,891,836
  (860)^2 * 7.6 * 2.476 * 2.20 * 2.2 = 67,360,685
Boreas Gale
  (640)^2 * 7.6 * 3.552 * 1.5 * 2.2 = 36,488,871
  (860)^2 * 7.6 * 3.552 * 1.5 * 2.2 = 65,886,644
  (640)^2 * 7.6 * 3.552 * 1.6 * 2.2 = 38,921,463
  (860)^2 * 7.6 * 3.552 * 1.6 * 2.2 = 70,279,087
Dystopia 2
  T1: (640)^2 * 7.1 * 1.35 * 2.2 = 8,637,235
      (860)^2 * 7.1 * 2.20 * 2.2 = 25,415,614
  T3: (640)^2 * 12.1 * 1.35 * 2.2 = 14,719,795
      (860)^2 * 12.1 * 2.20 * 2.2 = 43,313,934
Tornado x2
  (640)^2 * 2.5 * 3.778 * 1.6 * 2.2 * 2 (W-cast) = 27,235,450
  (860)^2 * 2.5 * 3.778 * 1.6 * 2.2 * 2 (W-cast) = 49,178,074
Quake x2 (off-chained)
  (640)^2 * 2.75 * 3.4915 * 1.5 * 2.2 * 2 (W-cast) = 25,956,648
  (860)^2 * 2.75 * 3.4915 * 1.5 * 2.2 * 2 (W-cast) = 46,868,988

Rotation
    Lost Paradise
    Boreas Gale
    Hell's Judgment (LB)
    Boreas Gale
    Tornado x2
    Boreas Gale
    Hell's Judgment (LB)
    Boreas Gale
    Tornado x2 (lesser buffed)
    Boreas Gale (lesser buffed)
  Average Damage: 52.091 Mil
    187.0% of IF.Katy's short rotation
    106.4% of IF.Katy's long rotation

• eDFina generally deals more damage (more if she counter)
• eDFina has dark element resistance
• eDFina is tankier
• eDFina can give AoE 70% elemental resistance to fire/wind/earth/dark
• IF.Katy has better elemental coverage
• IF.Katy has more chaining families
• IF.Katy offers better non-niche party support
• IF.Katy has better self-sustain

Finally, some real competition. From a damage/survivability aspect alone, Dark Fina wins unless the fight gets very long. However, in a long run situation, the damage difference is marginal. In addition, IF.Katy's long rotation is very reliant on keeping her stacks, which get fairly hard if she dies alot given her stats. That said, IF.Katy has more elements in the event of needing to switch elements on the fly. Between the eDFina's survivability and IF.Katy's elements, I'll call it a close victory for DFina for the niche elemental coverage which even veteran's will be eyeing.

For actual gearing, eDFina ^{390 Mil} will actually lose the damage race to IF.Katy by a significant margin. Better mods, dual/triple-cast, and chain capping will do that once the stat difference significantly decreases. That said, DFina is signifcantly tankier.

Trance Terra enh Trance Terra^7★★

HP: 6670.5
Mag pre-buff: 453.1 (not included:  30% TDH/W)
Mag post-buff: 531.9/689.5 (via Leadership/Full Magical Activation, respectively; not included:  30% TDH/W)
Def pre-buff: 175
Def post-buff: 240.2 (via Leadership)
Spr pre-buff: 277.5
Spr post-buff: 348.32 (via Leadership)
Imperil: 35% (via Crazy Day)

Chaos Wave
  (531)^2 * 4.2 * 2.2 * 2.2 = 5,731,703
  (689)^2 * 4.2 * 2.2 * 2.2 = 9,650,128
Chaos Wave (IV-cast)
  (531)^2 * 4.2 * 3.535 * 2.2 = 9,209,804
  (689)^2 * 4.2 * 3.535 * 2.2 = 15,506,001
Chaos Dark/Flare
  T1: (531)^2 * 4 * 2.89 * 1.35 * 2.2 = 9,680,623
  T6: (531)^2 * 14 * 2.89 * 1.35 * 2.2 = 33,882,181
      (689)^2 * 14 * 2.89 * 1.35 *  2.2 = 57,045,418
Chaos Dark/Flare (IV-cast)
  T1: (531)^2 * (4 6 8 10) * 3.7225 * 1.35 * 2.2 = 87,284,721
  T2: (689)^2 * (12 14*3) * 3.7225 * 1.35 * 2.2 = 283,415,344
  T3: (689)^2 * (14*4) * 3.7225 * 1.35 * 2.2 = 293,912,208

Rotation (Short)
    Chaos Dark/Flare x4 (lesser buff)
    Full Magical Activation
    Chaos Dark/Flare x4
  Average Damage: 123.566 Mil (3-Turn)
    357% of IF.Katy's short rotation
Rotations (Long)
    Full Magical Activation
    Chaos Dark/Flare x4
    Chaos Dark/Flare
    Chaos Dark/Flare (lesser buff)
    Chaos Dark/Flare (lesser buff)
    Chaos Dark/Flare (lesser buff)
  Average Damage: 75.433 (6-Turn rotation)
    270.8% of IF.Katy's short rotation
    154.1% of IF.Katy's long rotation

• eTTerra deals more damage
• eTTerra has 40% AoE elemental resistance buff for fire/ice/lightning
• eTTerra has 30% physical evasion
• eTTerra has 30% innate elemental resistance fire/ice/lightning
• eTTerra is mildly tankier (more w/ evasion and elemental attacks)
• IF.Katy has more status ailment immunities (sleep/paralyze)
• IF.Katy has better elemental coverage
• IF.Katy has more chaining families
• IF.Katy offers better non-niche party support
• IF.Katy has better self-sustain

Damage-wise, TTerra wins by significant margins. However, similar to DFina above, while TTerra has some weaker elemental defensive coverage, IF.Katy has general party support in addition to more diverse elemental damage coverage and chaining family. I'm giving this to TTerra, though IF.Katy might be worth considering for longer fights depending on your teams support capabilities.

If you compare with good gearing, eTTerra ^{short-1,521 mil; long-900 mil} outdamage IF.Katy still, though for long fights, it's fairly close. TTerra is significantly tankier though.

Ultima High Seraph Ultima^7★★

HP: 5299.2
Mag pre-buff: 744.6 (not included:  60 TDW)
Mag post-buff: 832.2 (via Leadership; not included:  60% TDW)
Def pre-buff: 128
Def post-buff: 179.2 (via Leadership)
Spr pre-buff: 315.2
Spr post-buff: 394 (via Leadership)
Imperil: 75% (via Twister)

Divine Ultima (LB)
  (832)^2 * 21 * 2.2 = 31,980,748
Twister x4
  (832)^2 * 4.5 * 3.889 * 1.75 * 2.2 * 4 (IV-cast) = 186,559,698
AM-Ultima x3
  T1: (832)^2 * (7.5 10 12.5 15) * 3.38 * 2.2 = 231,631,994
  T3: (832)^2 * (20*3) * 3.38 * 2.2 = 308,842,659
AM-Ultima x4
  T1: (832)^2 * (7.5 10 12.5 15 17.5) * 3.535 * 2.2 = 336,464,128
  T1.5: (832)^2 * (17.5 20*3) * 3.535 * 2.2 = 417,215,518
  T2: (832)^2 * (20*4) * 3.535 * 2.2 = 430,674,083
Unholy Darkness
  (832)^2 * 6.25 * 1.35 * 2.2 * 4 (IV-cast) = 513,976,32

Rotation (First 3-turns)
    Return   AM-Ultima x3
    AM-Ultima x4
    AM-Ultima x4
  Average Damage: 359.840 Mil (3 turns)
    1291.7% of IF.Katy's short rotation
Rotation (Long)
    Return   AM-Ultima x3
    AM-Ultima x4
    AM-Ultima x4
    Divine Ultima (LB)
    AM-Ultima x4
    AM-Ultima x4
  Average Damage: 343.920 Mil (6-turn rotation)
    1234.5% of IF.Katy's short rotation
     704.4% of IF.Katy's long rotation

• HS Ultima deals signficantly more damage
• HS Ultima slightly tankier (more for mag attacks)
• IF.Katy has better elemental coverage
• IF.Katy has more chaining families
• IF.Katy offers better party support
• IF.Katy has better self-sustain, particularly for long fights

HS Ultima deals so much more damage. It's so much that I no longer care about IF.Katy's support abilities for this comparison.

With gearing, HS Ultima still deals significantly more damage ^{short-3,155;long-2,785 mil}, though the gap has shrunken considerably due to the MAG stats becoming significantly more comparable.

Summer Folka & Citra Summer Folka & Citra^7★★

HP: 6195
Def pre-buff: 130
Def post-buff: 286 (via Devil Deluge)
Spr pre-buff: 569.4
Spr post-buff: 655/826.2 (via Leadership/Devil Deluge)
Evo Mag:  130%
Imperil: 70% (via LB)


Fun in the Sun (LB, ignoring chain)
  (826)^2 * 2.3 * 27 * 1 (no imperil) = 42,369,339
  (826)^2 * 2.3 * 27 * 1.7 = 72,027,877
Summon - Wave/Sunshine (W-Cast)
  (655)^2 * 2.3 * (3*3.223   18*4   21*4) * 1.7 * 2.2 = 611,396,979
  (826)^2 * 2.3 * (3*3.223   18*4   21*4) * 1 (no imperil) * 2.2 = 571,941,832
  (826)^2 * 2.3 * (3*3.223   18*4   21*4) * 1.7 * 2.2 = 972,301,114
Wave/Sunshine   Sparkling Wave
  (826)^2 * 2.3 * (3*3.223   18*4   43*4) * 1.7 * 2.2 = 1,488,767,672

Rotation (first 3 turns)
    Devil Deluge
    Summon - Sunshine
    Summon - Sunshine
  Average Damage: 381.294 mil
    1368.7% of IF.Katy's short rotation
Rotation (long)
    Devil Deluge
    Fun in the Sun (LB)
    Summon - Wave/Sunshine   Sparkling Waves
    Summon - Wave/Sunshine x2
    Summon - Wave/Sunshine x2
    Summon - Wave/Sunshine x2 (weaker buff)
  Average Damage: 681.189 (6-turn rotation)
    2445.2% of IF.Katy's short rotation
    1391.3% of IF.Katy's long rotation

Note: Cilka Evo Damage
       = (SPR^2) * (1   EVO.MAG) * Skill.Mod * Chain.Mod * Imperil * (Lvl.Correction)

• Cilka deals significantly more damage
• Cilka can ignore damage mitigation
• Cilka can grant undead/demon killer buffs to the party
• Cilka can grant break/status ailment immunity to the party
• Cilka can imbue light element to party's physical attacks
• Cilka can grant physical chaining move to the party
• Cilka has better party recover support
• Cilka has better defensive stat buffs
• Cilka has AoE water/light element resistance buffs
• Cilka can increase party's LB fill rate
• IF.Katy can buff offensive stats
• IF.Katy can benefit from killers
• IF.Katy can entrust

Like PS.Katy's comparison, Cilka's comparisons are larger by comparison due to Evo Mag. If we include killers, notably from Espers, then the increase from Evo Mag more or less vanishes. Even if we completely ignore said boost, Cilka still outdamages IF.Katy by significant amounts. The only notable thing that IF.Katy has over Cilka is a cheap entrust, for really expensive LB's.

If you consider gearing, like everyone else, Cilka's damage ^{short-2,599 mil;long-5,630 mil} stop being as wildly above IF.Katy's, though still remains significant. That said, this gap shrinks even further if you consider running the appropriate killers. Significantly magically tankier than IF.Katy.

Conclusion - New Player Variant

For starters, the damage kit on IF.Katy is not bad. While her best long-rotation moveset primarily uses her ice-/water-element damage, her element flexibility gives her leeway if the you need multiple elemental coverage in a given turn. In addition, she has multiple chaining families, which helps greatly when chaining with a stronger unit (like a friend). Also, because of "Jackpot", she can easily maintain her MP with minimal external support, something that many units, particularly meta-mages, have issues with. Damage-wise, depending on gearing, being somewhere between Dark Fina and Trance Terra is not a bad place to be for a minimal-effort free unit.

On the support side, she less impressive, but still usable. Notably, with a low LB-cost, 50% innate LB-fillrate, and an Entrust-like ability, she can reasonably provide LB-support to more LB-expensive unit. On an average case scenario, she can fill any unit's LB about every 4 turns with no other gearing besides her S/TMR. Alternatively, IF.Katy can instead use her own limit burst to provide a 100% full-stats buff, which can be kept up fairly reliably because of said LB-support. Not meta numbers, but they're usable still. She can also assist the party in other ways by healing the party and restoring MP. The HP heal is more for side-healing due to the modifiers, but the MP heal is fairly notable for on-demand recovery of upwards of 60 MP. Even outside of battle, IF.Katy can increase rare drop rates and gils drops. The latter in particular is particular notable for newer players, as there are plenty of initial gil-sinks, notably, 7★ awakenings.

All-in-all, a pretty good unit for new players.

Conclusion - Veteran Variant

For starters, the damage kit on IF.Katy is not great. First, only her ice-combo doesn't suffer major issues all her combos suffer from some kind of issue. For all the other ones, They're imperiling the wrong element (Flood), does not have the corresponding chaining/capping move, cannot fully cap the move (RIce/RIce/Freeze), or ^{Edit: due to reports} breaks the chain (RIce/RIce/Freeze again). In addition, almost all of the moveset rely on maintaining her stacks, with the strongest ones being amongst the slowest ones to build. If you plan on using her, spoiler alert, she may be losing them fairly often due to her lack of tankiness. And being between Dark Fina and Trance Terra is not a great place to be with their damage being eclipsed by newer units.

If we move outside of the black magic abilities, her Chaos Wave move also suffers. No element, so it cannot take advantage of imperils or elemental weaknesses, and also build slower. In addition, it limited to a maximum of 2-casts, compared with the many CW chainers that casts signicantly more. Ontop, of it, the damage is fairly RNG, with the maximum dealing double the lowest amount. For people trying to cross thresholds at the correct time, this variablity can cause issues. Not to the extent of Fixed Dice, but still not amazing.

In addition, her innate mastery and S/TMR are not very good. Harps are not particularly well built for mag, and that won't change for the near future. As a result, she's going to be losing her 50% harp mastery. Both her TMR and STMR are not very good, so expect to replace them with something better, and her TM ability bearly affects her damage output. This means that she is likely to lose her TM ability, which includes not only the auto-refresh, but also the lesser hightide, which will affect her ability to Entrust.

The less I talk about the support, the better. Most of her abilities are either locked behind RNG and/or are not close to meta-strength usage. That said, I won't say no to an AoE 60 MP heal, though our sources of on-demand MP is getting better and more diverse with time. As for loot boosters, eXon is still better. All that said, the entrust and support for it is fairly decent.

Not a good place for veterans, but the fact that she's better than the other Katy is a plus.

^{Math Fix Status: Satisfied}

Thanks for the gild.

^{Edit 1: Adding RIce/RIce/Tornado to calculation, wording stuff}