Would a CE like Projection or a CE like Chaldea Life Savers fill up Hans' NP gauge faster?
I'm not 100% on this, if someone could confirm it would be nice, but I would think they are the same, since buffs are multiplicative, and therefore commutative. So whether you buff the NP gain rate of arts cards or the NP gain rate of the servant it ends up the same.
All told if it does work this way then it would be recommended to buff arts performance rather than NP gain since arts buffs apply to damage as well.
I think NP gain rate is better why? It applies to all hits meaning if you use arts as your first card then follow it with buster or quick they gain NP too and since a servant gains NP with each hit then it would increase NP gained, but arts performance only works for arts cards and since we're talking about hans here don't think you want damage.
That said I'm not sure so I'd suggest trying it out since I found that equipping my Drake with an NP gain CE is better than Arts effectiveness for NP gain, but dunno about Hans...never used him since I don't know how good he was when I was a noob.
On the other hand, higher arts card effectiveness can also improve your damage.
I think in general Increased NP gain % would perform better than Increased Arts Card Effectiveness % given that the two stats you are comparing are the same percentages for both and the only thing you care about is NP generation. This is because Increased NP Gain % affects NP gained from Arts Cards as well as NP from damage taken and NP gained from quick/buster cards.
For someone like Hans, in general, I think Increased NP Gain % is better since he is not a damage dealer and you are really only concerned with getting off his NP as much as possible.
However for servants like Vlad, Orion, or Squirtoria I would say that Increased Arts Cards Effectiveness % would be better. This is because these servants are NP Arts Damage Dealers meaning the Arts Cards Effectiveness will increase the damage and NP generation of the Arts cards used as well as their NP Damage. The damage gains usually outweigh the minimal increase in NP gain from Damage Taken and Quick/Buster Cards.
Overall most of the time NP is generated through the use of Arts Cards. This makes the two stats very similar overall with the slight edge in NP generation going to the Increase NP Gain stat and a large gain in Damage to the Increase Arts Card Effectiveness stat.
It depends on the individual servant's np gain per hit. This is different for every servant. Some servants like Tamamo lancer have excellent np gain per hit. Others like Shishou have very poor np per hit. It also depends on the number of arts cards in the deck of course and is generally better when used with arts np servants.
Hans has an np gain of 1.66% per hit but also has low hit counts on his attacks with his arts cards having only 1 hit (like most casters). He is the unique case of a support as you'd rarely if ever be using the cards in his deck to do anything other than gain NP and cast NP. Thus, NP gain CEs are better on him if the percentage buff is the same. The 15% gain from chaldea life savers double dips by buffing not only his arts cards but other cards as well. Additionally, it buffs his np gain from taking hits. In contrast the 15% buff from Projection only buffs his arts card np gains.
A contrast to this is Squirtle who thrives with the arts cards in her deck which have multiple hits and with her arts np is suited more to a projection or formal Craft than say a divine banquet or CLS. In her case the arts buff buffs her damage, her np and increases her np gain rather than DB or CLS only increasing np gain.
Hope that was helpful!
Out of curiosity, I really compared Hans and Squirtoria's Arts performance.
In the example you gave, Hans does indeed hit once with a 1.66% NP gain per hit. Squirtoria hits 3x for .59% each, yielding 1.77%. But their Territory Creation ranks are different. Squirtoria gets +.17% to a maximum of 1.94%, while Hans only gets +.0664%, to a maximum of 1.7264%.
So we have an Archer whose NP gain is actually higher than the average Caster's NP per hit, because she hits more than one time per Arts card.
The average Caster's NP per hit (prior to the Summer event) was .98%. The average Archer's NP per hit (prior to the Summer event) was .66%. Turns out the only reason Casters NP more often than Archers is a combination of more Arts cards and Territory Creation, and Squirtoria spits in that statistic's eye.
TL;DR at bottom.
I was eyebrow deep into the math involving this comparison for concrete evidence, and I came to the conclusion that the only difference in NP gain between Arts+ and NP+ CEs lies in the NP gain from OTHER card types.
If you start a chain with an Arts card, the NP+ CE effects all cards involved. Even if you don't, it still affects Quick cards.
Conversely, Arts+ CEs increase damage of Arts cards, but have no effect whatsoever on Quick or Buster cards, regardless of whether or not an Arts card was used to start the chain.
Since Squirtoria has a AAQQB deck, she'll feel the effects of an NP+ card more readily than Vlad, who has an AAQBB deck.
Hans, who has an AAAQB deck but doesn't deal damage on his NP, feels an Arts+ card more, but doesn't particularly care since his damage is so low to begin with.
It's also worth noting that an AQQ chain is going to see way more boost from NP+ than Arts+, because the Arts bonus only affects the card, not the bonus affecting the chain.
Final conclusion: NP+ for characters who care more about NPing MORE, and Arts+ for characters who care about NPing HARDER, because their benefit to NP gain is virtually the same. The real game changer is # of Quick cards in the equipped Servant's deck.
This delving into the math kind of opened my eyes. I won't be putting my Arts+ on pretty much anyone who doesn't have a damaging Arts NP unless they have high base damage without it.
