Addressing the Fearmongering

Intro

There has been A LOT of discussion surrounding this new gacha system change, and a lot of people hate the new system despite the new system being objectively better than the old system. If you notice, all the posts that dive into the math, stats, and simulations find that the new system is better than the old system. The other side is fearmongering by bringing up worse case scenarios, what ifs, and anecdotal evidence. I want to address some of the discussion points of the people who oppose the new system.

Anything with a superscript will have a derivation at the bottom of the post.

"If I get the rate-up at 190 pulls, my entire pity gets reset."

Yes, there is a chance this will happen, but it will only happen around 0.9%^(1) of the time, meaning that it will only happen once every 111 students on average. There are around 200 three star students, so assuming you pulled every student since launch (and never spooked anyone), this scenario on average wouldn't have even happened twice... in 5 years... It is worth it in the long run to take on this risk in exchange for the benefits that the new system brings.

"I might end up spending 400 pulls for two characters."

Yeah, that's possible, but it was possible under the old system too. In fact, the chance of that happening under the new system is MUCH LOWER than under the old system, at 1.5%^(2) compared to 6%.^(3)

"The new system might be better than the old system, but only if you're pulling for one student."

Nope, the new system (90.07 pulls on average per student) is better if you're pulling for one (107.8 pulls on average per student), two (96.32 pulls on average per student), or three (91.49 pulls on average per student) students per reset.^(4) It is only worse if you are pulling for 4+ students per reset. At that point, you are probably a whale pulling for dupes.

"The new system disincentivizes pulling for multiple students per reset."

Sure. But why is that bad? The old system allowed for people to pull the first student and spark the second student. And indeed this is a very common scenario, with around a 75%^(5) chance of pulling the first rate-up within 200 pulls allowing you to spark a second student. What if you don't want the second student? Too bad. On the other hand under the new system, the chances of pulling a rate-up within 100 pulls is 75%^(6), much better than the 200 pulls under the old system. In addition, you have the choice of whether to keep going for the second character or save the other 100 pulls for the next character that you want. More options is better than less.

"This new system is more FOMO."

I would argue that the new system is less FOMO than the old system. In the old system, if you don't spend 200 pulls by the reset, all your pity gets wasted. Meanwhile, in the new system, your pity carries forward, so you don't feel pressured to pull until 200. And if you save 24,000 pyroxenes like with the old system before pulling, you are guaranteed the rate-up regardless. Don't be greedy and stupid.

"Nexon will mess with the rates so that they are worse than they say and there's no way to prove it."

This is just shifting the goalpost. First off, there are statistical tests to prove if they are messing with the rates (z test). Second, this has nothing to do with the new gacha system. If they do mess with the rates of the new gacha system, why aren't they doing it now with the old system?

"Statistics doesn't apply to me. I am unluckier than anybody else. 0.9%? It will happen to me every banner. I transcend statistics."

Ok

Conclusion

Don't fall for the doomposting and fearmongering. Do your own research. Will the old system be better than the new system in some cases? Yes. Will the old system be better than the new system on average and over the long run? Definitely not.

Appendix (Derivations)

1. P(getting the rate-up student between 190 and 199 pulls) = \sum_{i=189}^{198} 0.07 * 0.5 * 0.993^{i-1} = 0.009

2. P(spending 400 pulls under the new system) = (0.5*0.993^{198})^2 = 0.015

3. P(spending 400 pulls under the old system) = 0.993^{400} = 0.06

4. a. E[pulls per student under the new system] = \sum_{i=0}^{99} (0.993)^i + 0.5 * \sum_{i=99}^{198} (0.993)^i = 90.07

b. E[pulls per student under the old system] = \sum_{i=0}^{199} (0.993)^i = 107.8

c. E[pulls per 2 students under the old system] = \sum_{i=0}^{199} (0.993^i + i * 0.007 * 0.993^{i-1}) + \sum_{i=200}^{399} 0.993^i = 192.63, (96.32 per student)

d. E[pulls per 3 students under the old system] = \sum_{i=0}^{199} (0.993^i + i * 0.007 * 0.993^{i-1} + \binom{i}{2} (0.007)^2 (0.993)^{i-2}) + \sum_{i=200}^{399} (0.993^i + i * 0.007 * 0.993^{i-1}) + \sum_{i=400}^{599} 0.993^i = 274.46, (91.49 per student)

5. P(pulling >1 character within 200 pulls under the old system) = 1-0.993^{200} = 0.755

6. P(pulling >1 character within 100 pulls under the new system) = 1-0.5*0.993^{99} = 0.751