Said hypothetical elvaan mnk/war will have base 80 str 73 vit 67 dex, 292 h2h skill. For this I will assume berserk is up and eatting pizza to cap acc. Greater colibri have 67 vit and 278 def with assumed Dia III on them and are lvl 82. Gunna ignore haste, double attack, and kick attacks as they will effect the speed at which you gain tp and more or less the dmg you get in that time the same. I say more or less cause obviously dmg from kicks wont be boosted more from spharias higher base dmg but will still get the crit hit boost so putting them about the same on kicks. But meh that's really icky to do. Also assume 6 hit asurans on average.
For tp gear I will assume astrolabe, Full usukane, sea torque, brutal, triumph, rajas/flame ring, BB, and Cuch. That would give a total of + 7 skill, 22 dex, 39str, 19 Stp.
That will give you a total of 299 skill, 89 dex 119 str, and 13 stp to tp in. Which would put your att with 522 or 547 att. Based on not having that much more dex then mob agi assume a 5% crit hit rate from dex. That would to an fstr of 14
For ws gear I will assume mostly the same except swap out usu head for MKE with 4 str 15 wsacc and 4 agi 2% ws dmg, hands for bandomusha kote, legs for hachiryu and wait for WW. This will raise str to 123, vit to 78, att to 552 and 577. That would calculate out to an fstr of 15
Base dmg for hand2hand is the weapon dmg +fstr + natural dmg.
Natural dmg is skill *.11= 32.
Fstr caps are done by weapon rank+8 and for h2h weapon rank is (weapon dmg +3)/9.
Spharai: DMG: +23 Delay: +86 Attack +20. Assumed 5% chance to do double dmg on melee hits.
Weapon rank: (23+3)/9 = 2. So puts fstr cap at 10. Yay we so over cap on ws and tp (in retrospect probably should've chosen gear slightly differently oh well)
Don't feel like doing that math so putting it into ffxicalculator that puts it at 6.4 sec base delay at 75, and 16 hits for 100% tp so really 14 with the ws or 7 attack rounds. Which would end up being 44.8 sec.
Tp round:
So base dmg is = Weapon dmg + fstr + natural dmg: 23+10+32= 65.
Ratio = att/def: 547/278= 1.96
Cratio = Ratio - .05*lvl dif: 1.96-.05*7= 1.61
Min pdif = -0.8 + 1.2 * cRatio: -.8 + 1.2*1.61= 1.13
Max Pdif = 1.2 * cRatio: 1.2 * 1.61 = 1.93
For simplisity I'll just use the average of 1.53. Or 2.53 on crit hits.
Average pdif with crit hits will will be: .95 * 1.53 + .05 *2.53= 1.58
Dmg per hit is base dmg* pdif: 65*1.58 = 102.7
So dmg till 100%: 14 * 102.7 = 1437.8.
Average 5% chance do to 3X dmg: 1437.8 *3 *.05 + .95 * 1437.8 = 1581.58
Asuran fist:Modifiers: STR:10% ; VIT:10%
Damage Multipliers by TP:
100%TP 200%TP 300%TP
1.00 1.00 1.00
And assuming 6 hits would be total of 6.0 for ftp
Wsc = .83*(.1 *str +.1 * vit): .83*(.1 *123 +.1 * 78)= 16
For ws base dmg is = Weapon dmg + fstr + natural dmg +wsc: 23+10+32+16= 81.
Ratio = att/def: 577/278= 2.07 capped to 2.00
Cratio = Ratio - .05*lvl dif: 2.00-.05*7= 1.65
Min pdif = -0.8 + 1.2 * cRatio: -.8 + 1.2*1.65= 1.18
Max Pdif = 1.2 * cRatio: 1.2 * 1.65 = 1.98
For simplisity I'll just use the average of 1.58.
ws dmg = base dmg* pdif * ftp: 81* 1.58 * 6.0 = 767
Total dmg per ws cycle = dmg from ws + tping: 767 + 1581.58 = 2348.58
Average dmg/sec: 2204/44.8 = 52.423
Destroyers: DMG: +18 Delay: +48 Critical hit rate +6%.
Weapon rank: (18+3)/9 = 2. So puts fstr cap at 10. Yay we so over cap on ws and tp (in retrospect probably should've chosen gear slightly differently oh well)
Don't feel like doing that math so putting it into ffxicalculator that puts it at 5.8 sec base delay at 75, and 18 hits for 100% tp so really 16 with the ws or 8 attack rounds. Which would end up being 46.4 sec.
Tp round:
So base dmg is = Weapon dmg + fstr + natural dmg: 18+10+32= 60.
Ratio = att/def: 522/278= 1.87
Cratio = Ratio - .05*lvl dif: 1.87-.05*7= 1.52
Min pdif = -0.8 + 1.2 * cRatio: -.8 + 1.2*1.52= 1.02
Max Pdif = 1.2 * cRatio: 1.2 * 1.52 = 1.82
For simplisity I'll just use the average of 1.42. Or 2.42 on crit hits.
Average pdif with crit hits will will be: .89 * 1.42 + .11 *2.42= 1.53
Dmg per hit is base dmg* pdif: 60*1.53 = 91.8
So dmg till 100%: 16 * 91.8 = 1468.8
Asuran fist:Modifiers: STR:10% ; VIT:10%
Damage Multipliers by TP:
100%TP 200%TP 300%TP
1.00 1.00 1.00
And assuming 6 hits would be total of 6.0 for ftp
Wsc = .83*(.1 *str +.1 * vit): .83*(.1 *123 +.1 * 78)= 16
For ws base dmg is = Weapon dmg + fstr + natural dmg +wsc: 23+10+32+16= 76.
Ratio = att/def: 552/278= 1.98
Cratio = Ratio - .05*lvl dif: 1.98-.05*7= 1.63
Min pdif = -0.8 + 1.2 * cRatio: -.8 + 1.2*1.63= 1.15
Max Pdif = 1.2 * cRatio: 1.2 * 1.63 = 1.95
For simplisity I'll just use the average of 1.55.
ws dmg = base dmg* pdif * ftp: 76* 1.55 * 6.0 = 706
Total dmg per ws cycle = dmg from ws + tping: 706 + 1468.8
= 2174.8
Average dmg/sec: 2174.8/46.4 = 46.870
tl;dr Relic wins by 11.8% under those conditions. Though it will be closer when berserk is down though would pretty much require doing most that calculations again to see how much