Math behind Zephyr Melody vs Freyja Melody
Saw a few discussions so I'm here with the math, go down all the way for TLDR.
Any use of seconds are manually timed with melody while hitting king fafnir.
Any use of junlico calculator to match stats have the facilities messed around with to match b1ue's simulator.
From https://b1ueb1ues.github.io/sp/index.html:
2940str RR Bellathorna melody personal dps with C5C5S1 C5C5S1 C5C5S1S3 = 1094+ 385 = 1479
C5C5S1 takes 9 seconds, at 3500 team DPS = 1046
at 5000 team DPS = 1495
total 2940 str Melody DPS at 5000 team DPS = 2975
From https://dragalialost.gamepedia.com/Damage_Formula:
C5C5S1 takes 9 seconds, C5C4S1 takes 8seconds.
C5C5 = C1(97)+C2(97)+C3(63x2)+C4(129)+C5(194) = 643
C5C4 = 643-194 = 449
C5C5S1 DPS = 643x2/9 = 142.888...
C5C4S1 DPS = 643+449/8 = 112.25
C5C4S1 does 0.78557% more dps
With C5C5S1 taking 9 seconds and C5C4S1 taking 8 seconds,
In 180seconds the number of S1 uses goes from 20 to 22.5.
Freyja Bellathorna contribution at 3500 team DPS = 1176.75
at 5000 team DPS = 1681.875
Difference in SP gain rate allows going from
5S3s in 12 C5C5S1 combos (3 cycle S3 repeat) to C5C4S1 C5C4S1 C5S3C4S1 repeat.
When allowed to run indefinitely, you get to perform S3 1.35 times more often.
S3 DPS = 385x1.35 = 514
Using junlico's calculator,
2940str Zephyr Melody switching to Garuda gets you to 1818str
Predicted 1818str Freyja Melody C5C4S1 with 1.35x S3 personal DPS = 1818/2940 * (1094*0.78557+514) = 849.278
With Bellathorna @ 3500 team DPS = 849.278 + 1176.75 = 2026.028
With Bellathorna @ 5000 team DPS = 2531.153 (vs 2975, 15% more DPS)
Required team DPS to match 2940str Melody = (1479-849.278)/(1176.75/1046 -1) x (3500/1046) = 16,856
Ideal team in HMC, from b1ue's sim and junlico calculator for Lowen:
2955str Zephyr GRanzal VC+FRH, 3084str Zephyr Addis RR+CE, 1818str Frejya Melody's personal DPS (without Bellathorna contribution) 3084str Zephyr 50MC Lowen MUB 5.3 BBW CE (for ease of calculation)
Lowen's autoattack damage can be calculated from https://dragalialost.gamepedia.com/Combat_Mechanics ,
placing his autoattack at 90.98% of a blade's autoattack, comparing it to 3084str Addis, a 3084str Lowen contributes 827 DPS. Comparing it to other weapons are less accurate due to having different crit rates (axe) or having different combo (C5FS, C2FS etc.). Blades are closest with the C5 combo. Comparison to other weapons puts Lowen's DPS at 690 to 827, so about 750 or so is more accurate, but using upper limit here.
Ideal Team DPS, with super stacked Lowen = (2821 + 2821 + 849.278 + 827) x 10% blade coab. = 8050.1058
With slightly stacked normal Lowen, MUB Roc 0UB 5.3 BBW JotS, 2519str = 675.49 (upper limit)
Team DPS = 7883.4448
Difference in S1 contribution between Zephyr Melody and Freyja Melody at 8000 team DPS = 298.857, or 12.5% more S1 contribution compared to Zephyr Melody.
Budget HMC team with 2500str 45MC MUB Roc Lin You, 2814str 50MC MUB Roc Addis (RR+CE), 1674str 45MC 0UB 5.3 MUB Freyja Melody (RR+Bellathorna), 300 DPS Lowen
Team DPS = 2448 + 2574 + 782 + 300 with 10% blade coab = 6714.43
Zephyr on either one of Lin You or Addis gives an additional 300str, which is about 330 more, hitting just barely under 7100.
b1ue's simulator severely underestimates average team DPS @ 3500 and @5000. If optimal rotations was assumed for each character's optimal DPS, and given 100% uptime, team buffs actually contributes a whole lot more. Can't calculate how far away optimal DPS is from actual numbers, but all numbers along with team buff contributions will be proportionately lower. Either way, doesn't change the conclusion.
TLDR:
You need 6600 ~16,900 Team DPS for Freyja Melody to contribute more DPS than Zephyr Melody.
So no. Zephyr Melody is better.
PS: With the new weapons for HMC, please don't just flat out use 1.3x whatever str you have.
Use https://www.reddit.com/r/DragaliaLost/comments/c0ifbi/best_weapons_for_hmc_mathematics/ and see how much % more it is compared to 5.3, and use that multiplier instead. E.g. MUB Void sword is 16.91% more than 0UB 5.3 sword, so 1.1691x instead of 1.3.
Edit: fixed math, rip.
Posted Jun 20, 2019, 6:18 AM UTC · edited
You calculated C5C4 as 643-129 but the C5 multiplier you should've subtracted is 194. So it should be C5C4 = 2*643-194 =1092. So the actual C5C4 dps would be 1092/8 = 136.5 which is about 94% of C5C5. This makes sense since it's well known that the blade's optimal dps rotation is to do full combos.
This means your actual predicted melody dps with frejya should've been 1818/2940 * (1094 * .94+514) = 953.745.
You skipped a bunch of steps calculating the team dps needed to match zephyr melody which also caused you to make some small mistakes. You were trying to solve 2975 = 1002.554 + (1045/3500) * x but 1046/3500 ~=0.29 is the multiplier for the dps contribution of a zephyr melody. You should've used (1176.75/3500) ~= 0.33 as that's the contribution of the team buff for a freyja melody. (Using your numbers here, I didn't bother doing it myself). So you actually should've been solving 2975 = 953.745 + 0.33 * x . Solving for x you get that you need a team dps of 6155.318 with frejya melody to match a zephyr melody... running with a team of 5000 dps. If the zephyr melody's team also had 6155.318 dps she'd come out ahead again.
The actual calculation for the break even point should have been (Zephyr melody's personal dps) * (zephyr melody's team buff contribution ratio) * (team dps) = (Frejya melody's personal dps) * (freyja melody's team buff contribution ratio) * (team dps). Plugging in the numbers and letting team dps we have 1479 + 0.29 * x = 953.745 + 0.33 * x. Solving for x we now have that it's only at 13131.4 team dps that Freyja melody matches Zephyr melody's dps. Seems a little more impractical now doesn't it?
It was a good attempt, but long posts like these with lots of numbers in them are what easily mislead people into believing incorrect things because they take things at face value and don't verify the math themselves.
Someone brought up to me that freyja melody using her S3 is a dps loss if we're considering that much overall team dps. Borrowing his numbers, freyja melody has 795 personal dps contribution and a 0.378 team buff contribution ratio while zephyr melody (using S3) has 1516 personal dps and 0.299 team buff contribution ratio. (Numbers from Matt on discord using b1ueb1ue's sim).
So now we have 1516+ 0.299 * x = 795+ 0.378 * x where x is the team dps. Solving, we get that you need the team to have 9126.58 dps for Freyja melody to match Zephyr melody. A little better, but still pretty far past what you'd realistically expect from a team in actual content.
Thanks for spotting that, I actually left the numbers in because I was worried I made a mistake somewhere and missed it. I redid the math and got 16.8k. The loss in ~630 personal DPS requires the 1.125x improved S1 to make up the difference, so a team DPS of 16.8k is required.
Regarding skipping S3, S3 with skill haste contributes about 315 DPS at 1800 str. The 4 seconds (2 S3s) saved every 5cycles (44seconds) lets melody cycle ~10% faster, so about 587.4 C5C4 DPS (vs zephyr melody's 1094), and raises bellathorna team contribution by ~10%, going to ~0.37. unsure about the 9k, because it seems like melody's personal would be way lower than 795 with 1.1k less str and skipping every 2nd C5. Let me know if you spot any more mistakes, and thanks again.
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