Question about the Critical Star Drop Cap

Hello all, I’ve come to you with a question regarding the critical star formula. This is going to be very long winded, but if anyone is actually willing to read through it, I would very much appreciate it. If not, I understand, as its a lot of potentially boring stuff lol.

First things first, if you look at this oft cited page you’ll see that the formula is as follows:
(baseStarRate + firstCardBonus + (cardStarValue * (1 + cardMod)) + serverRate + starDropMod - enemyStarDropMod + criticalModifier) * overkillModifier + overkillAdd

Now, if you look to the bottom of the page, you’ll notice that the author notes that critical star rate is capped at 300%


Tohousniper98 made a video about critical star gen not long ago, where he mentions at 7:36 to 7:48:

The game hardcaps total stargen chance at 300%, meaning that the max number of stars servants can generate per hit is 3, and any buffs over 300% stargen are pointless.

Now, perhaps I was misinterpreting what Touhou was trying to say here, but when he says the max number of stars servants can generate per hit is 3 and thus the max stargen is 300% (3 guaranteed stars), I took that at face value.

However, this would imply that, say, Jack the ripper could never produce more than 67 stars in a single turn:
5 hits for her first quick @ 3 per hit = 15
5 hits for her second quick @ 3 per hit = 15
5 hits for her third quick @ 3 per hit = 15
4 hits for her extra @ 3 per hit = 12
+10 for using a quick chain
= 67 total

If you go to Gamepress’s command chain calculator, however you can easily surpass this limit.
Here’s a hypothetical scenario of Jack the Ripper, with a 200% quick card buff (you could achieve that ingame through swap buff stacking with Skadi), and at best it says she can generate 73 stars. So what gives?

I went and made a hypothetical scenario on the spreadsheet calculator as well, but once again, I was able to go over 67 stars.


In fact, as you see here, it is not abiding by a 300% cap for either of the middle two cards.

I was thoroughly confused by this point, and looked to the FGO Subreddit’s Discord server for help. I was informed that, rather than a servant’s maximum star generation as a whole being capped at 300%, only the stargen up portion is capped at that:
image
This would make sense, as if you go back to the screenshot from Kyte’s post:


You’ll see that he says star rate is capped at 300%, and star rate is only ever mentioned in the context of starDropMod, so again, it would make senses if starDropMod is the only thing that’s capped, and starDropMod refers to stargen buffs.

So then, the implication here now is that if we look at Jack again, and we were to hypothetically give her a 10,000% stargen buff, and we don’t buff her in ANY other way, and we don’t even use a quick chain or anything, that hypothetically she could not generate more than 15 stars (5 hits * 300%) on one quick card, and that, as Touhou said, anything after 300% would be pointless. Back to the calculator we go.


Here we see that I’ve given Jack only our hypothetical 10,000% stargen buff, which is supposed to be hard capped by the game at 300%, and yet that does not seem to be reflected here.
image
Indeed, the calculator is more than happy to ignore the supposed 300% cap.
Gamepress’s calculator caps the amount of buffs you can enter at 1,000%, so I can’t perfectly replicate my 10,000% example, but even at 1,000%, you can see some chains where even without any other buffs, jack can generate over 15 stars from her quick card.

So in the end, I have no idea whats going on.
Is it that the game physically stops adding on stargen buffs if you try to pass 300% which would mean that the user (me) is at error for even trying to enter a stargen value over 300% into the calculator? If so, why does gamepress’s calculator let you enter up to 1000% and not up to 300%, and why doesn’t the spreadsheet ignore after 300%?

If that isn’t the case, then what is it I am missing that is being reflected in these calculators? Why are they letting Jack generate stars that would go over this supposed 300% cap on the stargen buff?

If anyone actually read through all of this, thank you very much, and hopefully you can help answer this burning question of mine haha.

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I’m not sure how accurate the calculator would be since it doesn’t have the restrictions that the game has, though Jack going slightly over 67 could be the enemy drop rate perhaps?
Have you attempted it in the game? I could try it myself, but I’d have to borrow someone with a 100% star gen buff to apply to Jack to try to go past the limit.

In Jack’s case it doesn’t matter too much since going past 50 stars is useless aside from skills that require stars to activate, but if it isn’t as hard capped as we think it is, then it could help other servants perhaps. I think the star cap is pretty well researched though from what I’ve seen.

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When they talk about the 3 star per hit, they are talking about the number of star gen. Instead of using calculators, why don’t you try it in game? All formulas used here can give wrong result if the programmer just didn’t input it in.
There are caps to buffs, be it def down, buster (or other colour) up, Np damage up and crit damage up. As far as I know, attack up is the only limitless buff damage wise. The star gen buff they talk about probably is along the same line. The 3 star per hit cap is different from this.

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I haven’t really tried it in game, as I don’t know if I have the proper servants skills leveled to be able to expiriment with very high stargen buffs and see if they are producing more stars than it would seem should be possible based on my understanding of kytes comments and touhous vid.

I guess that would be the natural next step though if there isn’t a clear definitive answer.

And yeah, I’m inclined to believe if anything the calculators are just not factoring in the limit, but I can’t discount the possibility I was missing something obvious, hence why this was something I wanted to ask about.

Thank you for the replies yall :)

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I read that post and watched touhous video before this. I was not aware of the technical thing about where exactly in the formula the 300% limit applied.

Like some of the others mentioned, my first thought would be doubt the accuracy of the spreadsheet. I’m not heavy into computer science, but wouldn’t really trust anything fully* if isn’t the code itself. The spreadsheet might not have the limiters built in. (Not really sure if there are better emulators if the code out there.)

Also, it seems like empirical testing would definitely be the next step. If you try to go that route then I think Caster Gilgamesh would be ideal (with the 100% star-rate up) Additionally, if for whatever reason you are having trouble reaching high star-gen up percentages on Jack you could instead, try to find a MHX and pit her against sabers while using her third skill. This way you get +100% star-rate up to begin with and two Caster Gils (or one Shakespeare and Casgil ) can bring you to the theoretical limit of 300%. That might help.

Finding maxed skills on these servants might be a little hard, but I hope these ideas help a bit. Best of luck on the trials.

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Well, the other option if the skill levels aren’t maxed is to use the plugsuit to have a third character support in the test, such as Caesar or someone else with a high star gen buff.

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That would work too.

Circe also has a 50% party-wide Star-rate up skill now that I reviewed some of the ones that have these. With her recent rank-up Medusa’s NP also has a 50% star-rate up too so no leveling needed for that, except maybe a K-scope if fast access is needed.

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Alright, from some simple testing, here are my results:

Jack w/ 306% stargen & quick card used as the third card (no overkill or crit etc):
Spreadsheet prediction: 25 ~ 27 stars
Actual result: 15 stars (And note that again, as I mentioned in my original post, this would be the maximum stars Jack could generate with one quick if 300% or 3 stars was a hard cap on the stars that could be generated per hit)
Note: the 16th is from Shakespeare’s 2nd arts, hard to see in the gif, look to saber’s left by her foot

Same scenario as above but 46% quick card damage buff:
Spreadsheet prediction: 29 ~ 30 stars
Actual result: 15 stars

Same scenario as above except quick card used first:
Spreadsheet prediction: 22 ~ 25 stars
Actual result: 15 stars
Note: Once again, Shakespeare makes that 16th, this time with his first arts card, hard to see again but look toward the right of the middle of Saber’s sprite to see it.

Jack w/ 348% stargen and quick card used as third card:
Spreadsheet Prediction: 26 ~ 29 stars
Actual Result: 15 stars

(Looks like gamepress stopped liking my GIFS after this point :frowning:)

Jack quick chain w/ 206% stargen & 100% quick card bonus
Spreadhseet Prediction: 87 ~ 95 + 10
Actual Result: 57 + 10 (And note that again, as I mentioned in my original post, this would be the maximum stars Jack could generate if 300% was a hard cap on star generation as a whole)
Screen_Recording_20200715-035051_FateGO_1

Jack NPQQE chain w/ 206% stargen & 100% quick card bonus
Spreadsheet Prediction: 81 ~ 90 + 10
Actual Result: 54 + 10 (and note that Jack’s NP is 4 hits, not 5, so if 300% were a hard cap, 54+10 would in fact be the cap of a NPQQE chain from jack)
ezgif.com-optimize

Jack quick chain w/ 206% stargen & 100% quick card bonus and one crit at the end:
Spreadsheet Prediction: 87 ~ 97 + 10
For good measure, I tested this one on the Gamepress calc as well, and it estimated 94 stars.
Actual Result: 57 + 10
Screen_Recording_20200715-035051_FateGO_2

Jack quick chain w/ 206% stargen & 100% quick card bonus and one crit at the beginning:
Spreadsheet Prediction: 87 ~ 97 + 10
Actual Result: 57 + 10
Screen_Recording_20200715-035051_FateGO_4

Note: For all stargen amounts, I added 11% in my writeup here over the value I inserted in the spreadsheet, as the spreadsheet automatically adds Jack’s 11% passive, So when I say 206, I actually entered 195 in the spreadsheet.

So In the end, it looks like neither the spreadsheet nor the gamepress calculator is factoring in the 300% stargen limit. And for that matter, from my testing at least, 300% does seem to be a hard limit on the entire thing, as I could not go over 15 stars for an individual card (5x300%) nor could I go over 67 for a quick chan (15x3)+(4x3)+10 even when adding 100% quick card damage from double Skadi. When I had asked the subreddit’s discord, as seen in my original post, they seemed to suggest that cardmods (and other factors) could surpass the hard limit of 3 stars per hit, but again, I couldn’t get that to happen. In other words, this all seems to reaffirm the statement Touhousniper98 made in his video, that “the max number of stars servants can generate per hit is 3.” At least based on my testing here, that is the case.

Anyway, while these results are certainly not absolutely 100% conclusive by any means, as I didnt test every type of factor to see if they could go over 3 stars per hit, nor did I test with a full 400%+ stargen buff, I’m pretty satisfied by what was discovered in these tests.

Thanks all for the input, I find this stuff really interesting :)

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Good research! I made the gamepress calc, just forgot to cap stars to 3 per hit.

Edit: Command Chain Calculator updated!

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