Looking at Platinum's S2 DPS from attack interval aspect

There might be something similar to this out there, so this is yet again will be another thought experiment.

Pre-calculation thoughts:

Platinum's talent increases her ATK as she attack slower, up to a limit. However, DPS usually scales off very well with lower attack intervals. This creates a seemingly contradictory interaction between talent and the attack interval. Thus, what would be the good compromise on her attack interval so her DPS can be optimal?

My assumptions:

  • I will assume Platinum’s level is at Elite 2 level 35 potential 1 with skill rank 7 and max trust. This will effectively makes her base ATK to be around 528.
  • Time interval will assume arrows fired from Platinum instantaneously hits her opponent the moment she releases it.
  • Unless stated explicitly on the text, stated DPS will assume that the enemy have 0 DEF and 0 RES, essentially giving us only the raw DPS value.

Platinum's DPS Formula Template:

The following image will list all the formula needed to calculate the DPS for Platinum:

platinumDPSFormulae_fixed

Clarification:

Delay uses the min function, which takes the lower between two numbers, separated by a comma in the picture.

Delay’s value will either be one or the attack interval, due to how Platinum’s talent only starts increasing her ATK when at least there’s 1 second delay between her ATK. Otherwise, she receives no bonus.

Talent bonus uses the max function, which takes the higher between two numbers, separated by a comma in the picture.

Talent bonus, on E2 potential 1, increases Platinum’s current ATK to 180% (multiplicative buff). I assume this increase in ATK scales linearly with the delay between attacks, starting to go up from 1 second delay to 2.5 delay. In other words, after a delay of 1 second, talent will grant bonus ATK up to +80% based on time spent between attack interval of 1s to 2.5s.

Analysis:

As you can see, DPS is affected by Base ATK, Attack Interval, and Talent Bonus.

Attack Interval is a function of ASPD modifier, and Talent Bonus is a function of Delay, which is a function of Attack Interval as well.

Therefore, the DPS function actually only depends on 3 variables, which is the base ATK, base attack interval, and the ASPD. Here, we will set the base ATK and base attack interval to a set value based on her stats, which is 528 ATK and attack interval of 1 second.

ASPD, thus, is a free variable that we can project to an axis (which is the X axis in the following section) so we can see its effect from various values on DPS in a graph.

Damage per hit can be calculated by simply multiplying DPS by its attack interval.

image

Platinum's S2 DPS and DPH based on ASPD bonus:

In the graph above, the x axis represents the ASPD modifier. the y axis represents the DPS for yellow line (f), and the DPH for blue line (g). For both function, under them has a table which takes [-60,-20,20] as ASPD as well as its y-value. This will be explained further below.
Other variables represents: a = base attack interval, b = attack interval, c = minimum delay, d = talent bonus.

Brief overview on each ASPD modifier value:

  • The ASPD-60 modifier shows the highest and the limit of Platinum’s S2 DPH (1615.68), and here it is shown that it has the lowest DPS (646.272) out of the three.
  • The ASPD-20 modifier represents the normal case when using S2 since it naturally reduces Platinum’s ASPD by 20. Here it has a DPH of 1017.28 and DPS of 813.824.
  • The ASPD+20 modifier is an arbitrary value for ASPD increase. Any number can work but personally ASPD+20 seems practical and reasonable to achieve after factoring in ASPD reduction from S2. Also, it has the same distance from ASPD-20 quite like the distance from ASPD-60 to ASPD-20 which is 40. It has the highest DPS (1077.12) and vanilla/lowest DPH (897.6).

Readings may be inaccurate from ASPD-100 and lower due to the formula being used, and such won’t be evaluated nor analyzed further. (An error that results from dividing by zero due to (b))

Analysis:

Here, the DPH graph shows that the raw ATK displays a significant increase ranging from ASPD-0 to ASPD-60. However, the actual DPS from yellow line doesn’t go higher and instead keeps being reduced, although its slope is a bit gentler perhaps due to talent bonus, and returns to its previous slope when the talent bonus ATK cap is reached. On the contrary, as ASPD increases on the right side of y axis, the yellow line quickly increases as well while the blue line keeps relatively constant.

At a glance, it seems that the raw ATK per hit increase from talent doesn’t do much justice as we can see that raw DPS decreases instead even when factoring in talent bonuses. However, when enemy DEF is factored in, we will a see a property that emerges from higher DPH.

Platinum's S2 DPS based on Enemy DEF:

Actual DPS is counted by the following formulae:

actualDPScalc

Here we can use the ASPD and DPH we’ve obtained from the previous graph and use it to get the function for actual DPS where the enemy DEF will be interpreted as a free variable to see a continuous interaction between DPS and enemy DEF.
Quick calculation with ASPD modifier of -60, -20, and +20 respectively gives an attack interval of 2.5, 1.25, and 0.833 with 1 as base attack interval.

The first image is the graph for actual DPS when factoring in enemy DEF. The x axis represents the enemy DEF while y axis represents the actual DPS by said function.

The second image is the same graph as the first one, but with markings of (x,y) value that might be important or interesting for you to take a look at. I will be taking some of these numbers for analysis purposes.

Legends:

  • a, represented by the red line, is the actual DPS graph for ASPD modifier of -60, resulting in DPH of 1615.68 and attack interval of 2.5.
  • b, represented by the blue line, is the actual DPS graph for ASPD modifier of -20, resulting in DPH of 1017.28 and attack interval of 1.25.
  • c, represented by the green line, is the actual DPS graph for ASPD modifier of +20, resulting in DPH of 897.6 and attack interval of 0.833.

Analysis:

Here, it is shown that c’s DPS is shown to be the largest when the enemy DEF is 0, followed by b then a. However, c is shown to fall off in damage quicker than the others, as it reaches its minimum damage when faced against enemies with 850ish DEF.
In terms of DPS, it’s higher than a from DEF range of 0 to 538 and higher than b from DEF range of 0 to 658.

b, as it is the default DPS for S2, shows performance that acts as the in-between of a and c, with respectable slope, starting height (when the enemy DEF is 0), and end distance (when the minimum attack threshold is reached).
It is shown here that it is better in terms of DPS compared to a from DEF range of 0 to 418, and better compared to c from DEF range of 658 to 950. Otherwise, it is shown as lower than them.

a, boasting highest DPH out of the three and slowest attack interval, starts out with a comparatively low DPS when faced against b and c. However, a starts to exhibit higher DPS than b at enemy DEF range above 638 and higher than c at enemy DEF range above 539.

Based on the formula, we can tell that the slope is defined by its attack interval while its starting height is defined by it’s actual DPS without any DEF reduction from the enemy. The function with faster attack interval, however, will usually be steeper in slope compared to the slower ones, and the end distance will be defined by its DPH.

Thus, c with the lowest DPH and fastest attack interval is shown to have a very steep and short line progression, and in a we can see that it’s highest DPH and slowest attack interval makes the DPS very stable across various enemy DEFs with gradual slope and far end distance.

In terms of minimum DPS (5% of DPH divided by its interval), a trend is shown in this graph that lower attack intervals exhibits higher minimum DPS, with c having the highest minimum DPS followed by b then a. This is most likely due to the fact that at minimum DPS, hitting in large quantities is more valued compared to hitting in large quality.
To be exact, starting at DEF value of 950, c will have higher DPS than b, and starting at DEF value of 1481, c will have higher DPS than a. b too, starts to have higher DPS than a when it passes enemy DEF of 1514.

Author's conclusion and opinion:

The term optimal DPS here will vary depending on the enemies’ DEF.

It is shown that c (which is Platinum’s S2 with ASPD buff) is actually more optimal when faced against low DEF enemies (up to 500ish DEF), and arguably works better against rushes or swarms.

Debuffing Platinum’s ASPD further, if possible, would make her ideal when facing higher DEF enemies or in situations when large physical burst is needed (1.6k per hit is no joke). However, precise debuffing would be required as debuffing her too much would actually hurt her DPS as the bonus caps on 2.5s attack interval and she wouldn’t get more benefit from lowering it further.

In her default state, that is ASPD-20, Platinum will work fine as the in-between of a and c, with good DPH and ATK interval.

If one is able to tweak her ASPD freely, she may benefit from having access to both high DPH and DPS due to dynamic performance depending on her attack interval, creating a degree of versatility for Platinum. This is, however, just my own opinion on the matter.

Thanks for reading

Any questions, comments, and/or critiques are welcome. My apologies if there are any writings in there that does not suit you.

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Nice analysis
tenor

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this does make me wanna use platinum

if i had one that is

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I always thought Platinum was second ONLY to Exusiai. Guess I was right :fgo_happytomoe:

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Well, I haven’t done any real calculation if we’re talking about DPS, so I’m not too sure about that…

However, I do admire your confidence! :fgo_meltbirb:

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