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Misconception in FEH summon rate

Long post ahead but I just wanna clear out a (apparently) common misconception in FEH summon rate, which I thought was true before.

This info about appearance rate comes from gamepedia and a few japanese feh website.

3% appearance rate does not mean 3% for each colour, it means 3% for all those focus units, hence if there are 3 focus units, divided by 3 so 1% each, in overall. But if you only pull for a single colour, say red, there is of course no chance of getting non-red focus, that 1 red focus unit (1%) will be factored into the other possible red units that can come out (about 30% for all units all stars), making it about 3.2% of getting it if you pull only that particlar colour. In comparison green has less units so if you summon only green it is more likely to get the unit you wanted. But do note that it takes account of the rate of that colour appearing over other colours so in actual the chance of getting that focus unit is still 1% but you can at least avoid some pity breakers.

The problem is sharing colours. For example the death blow banner has 2 red focus unit, omitting the rate of them appearing in non-focus 5* pool (negligible rate), it is 2% chance of getting a focused red 5*. Factor in the red orbs appearance rate (about 30%), 2%/32%=6.25%. That is 6.25% of getting a red focused unit if you pull only reds. Divide by 2 that is 3.175%, though slightly lower but remember it makes red orbs appear more likely. Sharing colours only makes it more difficult to avoid pity breakers when you have high pity rate as you can't avoid the same colour focus unit percentage, but the actual rate of getting a particular 5* in overall and in a particular colour is the same, NOT CUT INTO HALF LIKE 1.5%. Problem only lies in avoiding pity breakers, not lower appearance rate.

Legendary banner has 8% rate but since there are equal number of focus units for each colour it becomes 2% for each colour, but instead of divide by 2 it is divided by 3 hence legendary red 5* will be about 2.08% for a particular unit in particular colour. But the overall rate is still 8/12=0.67% for a particular unit instead of 1% in 3 unit focus banner.

I do apologise for the giving wrong advise before, and it haunts me thinking that someone might have given up his/her favourite Bridelia because of this. I hope that others will not make the same mistake as I do.

Asked by Moral Rights6 months 1 week ago

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If I understand correctly, the argument is:
On a banner with three focus units and no colour sharing, the appearance rate of any focus unit is 1%.
On a banner with three focus units and colour sharing, the appearance rate of any focus unit is still 1%.

The only thing that changes, then, is that you have additionally a 1% rate of obtaining a focus unit that you might not have wanted.

I'm still working on my own calculations to try to confirm or refute the logic and calculations you offered for the chances of getting a desired focus unit when colour sniping.

UPDATE: Confirmed that when sniping a colour on a banner in which two of three focus units are that colour, chances of obtaining that hero are worse only by about 0.1% compared to non-shared colour banner.

Yeah my argument is basically that there is no such thing as 1.5% in shared colour banner, only that you have higher chance of getting pity broken even when you are only pulling for that particular colour.

Just realised that it is so long therefore it appears more confusing that it should be.

Here's an explanation by Phoenixmaster on how to use this.

https://www.youtube.com/watch?v=sSjUbsyMtII

They explain how it works, and it's not truly 1 percent. It's alot more math than you said, and it really depends on the units around. Enjoy!

Ermm actually both the video and I are speaking the same thing. 1% was in overall theory and the example they gave was the rate of getting a 5* for a particular colour, which is the important bit as we always snipe for colours. And as I gave example for death blow banner, similar logic applied to the spring banner in the same method as I did in the video, and due to the shared colour in green back then and low number of green orbs appearing (about 18%) it jumps up to 10% instead of my example of 6%. Numbers will be different depending on each banner but the importance is to rebut the idea that shared colour banner has less appearance rate, which is not true. Don't take the numbers I gave too seriously because I omitted a lot of details and explanation. It would be too long and too technical if I do so but you still get the rough range anyway.

I think it's important to add that on legendary banners, your chance of getting any particular 5* is significantly worse than on any 3% banner, not because three characters share the colour, but because the 8% is shared between 12 units.

You know banners that have themes revolving around a particular skill like this Death Blow banner isn't really bad when it comes to color sharing. I don't recommend pulling on such banners if you just want a particular unit. But if you need a skill like Death Blow and having higher chances of getting a unit with it because said banner have Siegbert and WT Reinhardt on reds, it's quite a deal. Even better is if you don't have either unit yet. I reckon this is much better than trying for Klein in colorless hell. If he's a focus unit though without color sharing, that's golden.

The point is, though, to pick up a Klein or a Sothe or etc. while trying for someone like L.Robin.

I would also add that the colourless pool improves slightly. More recent additions include Nanna, who gives drive def at 4*, and Legault with his atk tactic which doesn't even cost us 20k feathers, unlike L'Arachel's res tactic. I still like my chances less than in red or blue, but at least for where I am now, I don't find colourless to be so bad.

Yup. If you just want one of the focus unit, sharing colours meaning that you can aim only for that colour and having almost double (or triple if 3 units sharing the colour) chance of getting one of them (divide by 2 or 3 for each if them in particular). That's the kind of deal that most people did not realised and misconceived about the summoning mechanism.