The second link shows that the probability of rolling a 5 star massively increased on the 74th roll, as opposed to the 75th, and the third link shows that the probability for rolling a featured weapon on the weapon banner massively increased on the 63rd roll, not the 65th.
Significance: fixing misconceptions that soft pity is 75/65, allowing players to save their primogems more effectively
Estimated 5 star pulls for weapons/characters
Finding: It takes approximately 12.5 5 star pulls to R5 a specific weapon
Average 5 stars pulled for specific rate up 5 star weapon:
r1 weapon (no pity) - 2.5
r1 weapon (with pity) - 2.25
r5 weapon (not starting with pity) - 12.5
r5 weapon (starting with pity) - 12.25
Average 5 stars pulled for rate up 5 star character
c0 character (no pity) - 1.5
c6 character (not starting with pity) - 10.5
c6 character (starting with pity) - 10
Evidence:I made a program to brute force 10,000,000 trials of attempting to R5 a specific rate up 5-star using the pity rules for the weapon banner. On average it will take a player 12.5 5-star pulls to R5 their desired weapon if they only want one of the rate up 5 star weapons. This leads to an average rate of 40% for a specific 5-star weapon on the rate up banner.
Significance: This information can be useful for whales to figure out around how many pulls they will need to get a specific R5 on average.
Resin Efficiency of Acquaint Fates from Character Levelling
Level all characters to 20/40 for the Fate.
From that point, getting them to 50/60 takes around 2 days of F2P resin budget.
This is worth overall, as there are no other ways to convert Resin to rolls. I would treat the 70/80 Fate as a bonus rather than the goal. It costs 5 days worth of resin, which is probably not worth the expected rewards from a single roll.
20/40 is a no brainer for the Fate, do it now to get it out of the way.
20/40 to 50/60 is actually an investment of ~427.2 resin for the fate.
50/60 to 70/80 is 5 days worth of F2P resin budget. Consider if you have no other uses for resin.
Expected 5* weapon rolls to desired 5* using epi path without pity at start: 1.984375
Expected 5* weapon rolls to desired 5* using epi path with pity at start: 1.8125
r5, epi path, no pity to start; expected num of weapons: 9.921875
r5, epi path, pity to start; expected num of weapons: 9.75
r1, no epi path, no pity: 2.5
r1, no epi path, pity: 2.25
r5, no epi path, no pity: 12.5
r5, no epi path, pity: 12.25
Number of Wishes on Weapon Banner to Fully Level a 5 Star Weapon
Better understanding of how the soft-pity system works.
Finding 2: Gacha rate calculator
Evidence: Based on this statistical model, I've made a rate calculator for a specific rate-up 5* char/weapon and 4* char.
Some percentile/pulls needed:
C0 of a rate-up 5* character
C6 of a rate-up 5* character
R1 of a rate-up 5* weapon
R5 of a rate-up 5* weapon
C0 of a rate-up 4* character
C6 of a rate-up 4* character
Small note with these calculations: to keep the amount of calculations/paths to explore down in the 4* char calcs, there's assumed to be no 5*'s to eat up/delay guaranteed 4* char. This will make the required 4* count slightly lower than needed. I've assumed that the difference is negligible.
Better budgeting/planning if users want to be X% sure to get char Y at CZ. Especially more useful for budgeting of higher constellations as averaging of low/high pity pulls. A calculator has the advantage that people can enter their current situation (pity/guaranteed).