Arknights: Is Whisperain's Base Skill Worth Using?

After E2, Whisperain gains the base skill Memory Seeker, which boosts Rosmontis's production by up to 20% when the former is in the office and the latter is in a factory.

However, Whisperain only boosts HR contacting speed by 20%, half as much as readily available alternatives like Orchid and Ethan. Is this tradeoff worth it?

Before we continue, if you need a refresher on Rosmontis and Whisperain's base skills, click here:

To calculate the effectiveness of Whisperain's factory boost, we can compare a Whisperain-boosted Rosmontis to alternative options. Let's assume the best-case scenario for Whisperain: that the office is max-level. For simplicity, let's also ignore other Rosmontis synergies like Iris (which don't affect the calculations anyways).

Whisperain can't last 36 hours in the office, so with 12-hour rotations, Rosmontis will work for 24 hours and rest for 12. A factory produces approximately 20 sanity per day before operator boosts. As such, given an alternative base skill with production boost A, we can calculate Rosmontis/Whisperain's daily production increase with this formula: (2/3)(20)(.4 - A).

In other words, if you use Rosmontis and Whisperain together (instead of your next-best alternative), you gain up to 2.67 sanity per day from factory production.

Without Whisperain, Rosmontis boosts production by 20%, so the best alternative will never be lower than 20%.

This is where the fun begins. First of all, how much does an office "produce" in a day, anyways?

Recruitment RNG

Whenever you refresh a set of recruitment tags, there's a chance that a 3-star tag set is turned into a 4-star, 5-star, or 6-star tag set. From this dataset, I estimated the probability that a refreshed tag set could guarantee each rarity from 3 to 6 stars. The dataset also contains data for recruitment results, which I used to estimate the probability that a recruitment would result in an "unexpected" operator of higher rarity. (Have you ever done a tagless recruitment and gotten a 4-star operator?)

Let's give Whisperain the benefit of the doubt: we'll ignore the value of new high-rarity operators for now, and focus only on the green and yellow certs. I created this spreadsheet to calculate the average certs gained from each tag set refresh. Since we're giving Whisperain the benefit of the doubt, I'm assuming we only get 1 yellow cert from 5- and 6-star recruitments.

From the spreadsheet, a tag refresh will give 2.99 green certs and 0.19 yellow certs on average.

Sanity Values

But what are green and yellow certs worth? Here, we have to make a few assumptions. Let's assume that a typical player:

• Has a green cert income high enough to buy everything in the tier 1 shop, tier 2 headhunting permits, and tier 2 recruitment permits, but not enough to buy all manganese ore (the best efficiency elite mat). As such, a green cert's sanity value is based on the manganese ore offer: 0.823 sanity per cert, according to Moe's spreadsheet.

• Spends yellow certs on headhunting permits, and chooses to spend OP on orundum instead of refreshing sanity. As such, a yellow cert is worth at least 66.297 sanity (slightly less if your sanity cap isn't 135).

Office Daily "Production"

To find the sanity value of a single tag refresh, we multiply the sanity value of each cert by the respective average amount gained per refresh. We'll get 2.46 sanity per refresh from green certs, and 12.61 sanity from yellow certs.

Note that 3-star tag sets can be set to 7:40 and still guarantee a 3-star. Higher rarity tag sets should be set to 9 hours to reduce the chance of tags dropping, and will need at least 1 tag selected, both of which increase the LMD cost. In a level 3 office, a 7:40 tagless recruit costs 490 LMD, and a 9:00 recruit with 1 tag selected costs 672 LMD. Multiply the difference by the sanity value of LMD (0.004), and by the probability to get a 4-star-or-above tag set (20.57%), to get 0.15 sanity.

So the total value of a single tag refresh is 2.46 + 12.61 - 0.15 = 14.92. Before operator boosts, the office generates 2 tag refreshes per day, so the office's base production is 29.84 sanity per day

The above calculations are also in this Desmos page.

Comparing

There are many operators with 40% office base skills. Orchid, Ethan, Utage, and Aciddrop have such skills at E0, so nearly all players should have access to multiple of these. Some players may also have access to 45% office skills. Currently, only E2 Eyjafjalla and E2 Provence have such skills.

Any operator boosts HR contacting speed by 5% on top of any base skills. As such:

• Whisperain boosts the office's production to 125%.
• Orchid/Ethan/etc. boost the office's production to 145%.
• Eyjafjalla and Provence boost the office's production to 150%.

There are 3 different office rotations we can examine:

• If the player doesn't have a 45% office skill, they would maintain a constant 40% base skill. If they wanted to use Whisperain, they would rotate Whisperain/Whisperain/40%.
• If the player has a single 45% base skill, they would rotate 45%/45%/40%. If using Whisperain, they would rotate Whisperain/Whisperain/45%.
• If the player has both E2 Eyjafjalla and E2 Provence, they would maintain a constant 45% base skill. If they wanted to use Whisperain, they would rotate Whisperain/Whisperain/45%.

Since we know the office's base production, we can calculate the daily sanity differences between shifts with and without Whisperain, for all 3 cases.

• No 45%'s: 3.98 sanity per day
• One 45%: 4.48 sanity per day
• Two 45%'s: 4.97 sanity per day

In other words, if you use Whisperain instead of an office worker with higher contacting speed, you lose 3.98 to 4.97 sanity per day from office refreshes.

All calculations can be found in this Desmos page.

If you use Whisperain to boost Rosmontis, you gain at most 2.67 sanity per day from factory production, at the cost of at least 3.98 sanity per day from office refreshes. The cost is significantly higher than any potential gain. Thus, it is not worth using Whisperain in the office.

Other Notes

• The value of additional green certs decreases as your green cert income increases (diminishing returns). However, even when setting the value of green certs to zero, it's still much better to avoid Whisperain. You can adjust sanity values to suit yourself in this Desmos page.
• I couldn't find an easy way to account for tags dropping, and the fact that you might need to select multiple tags to guarantee a certain rarity (which increases the LMD cost). These effects should be negligible, though.
• If you care about pulling new 5- and 6-star operators or increasing their potentials, Whisperain is even worse.
• If your 5- and 6-star operators are above potential 1, Whisperain is even worse (since you get more yellow certs when you recruit their dupes).
• If you use your yellow certs to buy 5- and 6-star operators from the shop directly, Whisperain is even worse.
• If your office is not max-level, Whisperain is even worse.

Recently, Saileach was released on the CN server. Her second base skill, "Infectivity", boosts office refresh rate by 20% if the current office worker's boost is below 25%. This means she can boost Whisperain's 20% skill to 40%, but doesn't provide any benefit for conventional office workers like Orchid or Eyjafjalla.

• If you have no 45% base skills, there is no penalty to using Whisperain, as Saileach boosts her to 40%, equal to Orchid, Ethan, and the others.
• If you have a single 45% base skill, using Whisperain loses you 0.50 sanity per day (40%/40%/45% vs 45%/45%/40%).
• If you have two 45% base skills, using Whisperain loses you 0.99 sanity per day (40%/40%/45% vs constant 45%).

These figures are much lower than before, and Rosmontis's increased production, calculated above, is likely greater (depending on your alternative factory workers). So is it worth using Whisperain if you have E2 Saileach? Maybe. These calculations assume the (nearly) worst-case scenario for the value of office refreshes. As you can see in my Other Notes, you may lose much more that what I've calculated here if you want more recruitment operators, or have higher potentials, and so on.