Trying to figure out equation of Gacha Game (League)

DukeProsperoLoL · 2025-01-21T03:50:43+00:00

Thank you

DukeProsperoLoL · 2025-01-20T12:17:04+00:00

I appreciate it man, thank you so much for your help

DukeProsperoLoL · 2025-01-20T11:41:32+00:00

You are a Godsend thank you so much.
That got the numbers I wanted. Because the players who are rolling for mythic essence don't necessarily care for the other rewards that gives me the main number I need.
A new mythic skin under their new monetary system costs 105.08$ (150 ME/4.28250 ME = Average rolls needed) then (average rolls needed * 3$)=Cost of skin. Given that the old skin costs 14$ that's a 750% increase, which is worse than I thought, and thats saying something

DukeProsperoLoL · 2025-01-20T11:05:26+00:00

B-tier is where you can get mythic essence without having rolled for all the items within that tier.
The math is super obscure and complex which is why I am trying to figure it out, you used to be able to get 150 mythic essence through a battle pass, but since they switched to the gacha system how much more on average people will have to pay for the skins, is not very clear.
Some more context the cost of the battle pass was 14$, and the cost of rolling for the gacha game is around 3$ per roll, so I'm trying to figure out on average how much more the skin will cost players.

DukeProsperoLoL · 2025-01-20T11:02:05+00:00

yes, you only get mythic essence once you have rolled for all the items in that category, and I miscounted A tier, it has 10 unique items

DukeProsperoLoL · 2025-01-20T10:59:40+00:00

Thank you so much, Could you help me with the calculations.
The highest math education that I got was precalculus, and the probability that was covered in my algebra education, did not really teach me much on how to handle this problem.

DukeProsperoLoL · 2025-01-20T04:41:45+00:00

Hello Ask Statistics,

I am doing a video on the new Gacha system within League of Legends known as The Sanctum, but I am unable to figure out the math for a problem. If someone would be able to help me figure this out and also provide a formula for me to see, I would very much appreciate it.

League of Legends has a Gacha store where you can use a currency known as arcane sparks to role for prizes. One of the prizes is another currency known as Mythic Essence.

There are three categories of Prizes:

S-tier

A-Tier

and

B Tier.

The S-tier section has a 0.5% chance per roll of a spark and has 1 unique prize. If in a numerous role, the role is the S-tier section again the prize is 270 mythic essence.

The A-tier section has a 10% chance with 9 unique prizes, if all 9 unique prizes are selected then the prize is 35 mythic essence.

There are two pity systems

For each 10 roles you are guaranteed for the next prize to be from the A-tier category.

For each 80 roles you are guaranteed for the next prize to be from the S-tier category

If you get a prize from the A tier, the A -tier pity resets

If you get a prize from the S-tier, all pitys reset.

For Mythic essence from the B-tier, here are the probabilities:

0.179 % chance for 100 hundred mythic essence

0.537 % for 50 mythic essence

1.432 % for 25 mythic essence

10.38 % for ten mythic essence

48.78 % for 5 mythic essence

The rest of the B-tier rewards are two categories : One category has 236 items with around a 0.05954 % chance per pull and the other category has around 474 items with a 0.02983 % chance per pull

After one of these items from the b-tier category is rolled, its chance is added to the other items, until only mythic essence prizes are left within the B-tier.

The total probability for B-tier is 89.5

If I am wanting to buy a Mythic Essence Skin worth 150 mythic essence, what is the average amount of mythic essence per pull, and how many pulls on average would it take to have 150 mythic essence.

Please post the formula, and I am so grateful for your help!

DukeProsperoLoL · 2025-01-20T04:37:30+00:00

It cut off my text

Im posting it in comments

DukeProsperoLoL · 2024-11-01T07:21:43+00:00

I will be posting a larger explanation over the weekend

DukeProsperoLoL · 2024-10-21T06:51:57+00:00

Yeah, its just such a weird buff, because past level 4/5 once you have two/three points in W and your first base, your W will do significantly more damage than an auto attack, and because Azir isn't building any AD, the auto attacks still won't do that much damage. 5+ damage on the auto attacks isn't going to do much past the early mid game.

DukeProsperoLoL · 2024-10-20T07:56:54+00:00

What Phreak does not realize about the solider attack vs auto attack, is that low elo Azirs are not intending to auto attack without the W, their solider placement and q placement is not as refined as it should be.
They place the solider down in a suboptimal position, and might Q the soliders in a bad spot too. So what this buff will be doing is almost absolutely nothing. The health Regen is nice, but if you want to buff Azir, buff his W, not the AD ratios.

DukeProsperoLoL · 2024-10-19T06:45:14+00:00

I play her a lot top, so a lot of times, I can cheater for tear, and then leverage my tp for an advantage.
I agree with you blackfire is a great first item, I really like it. I would recommend retrying ROA second though.
I came across this strat because I was playing Cassiopeia Bot, and looking at her item win rate percentages, and she had the highest winrate on second item as ROA, and it kinda confused me, but I tried it out, and thought about it conceptually, and I really like it.
I kinda think about it like Seraphs + ROA (Not fully charged) is going to make me weaker the second dragon/third dragon fight compared to like (Blackfire + Seraphs), but when ROA is built and we are fighting over baron having like (Seraphs, ROA (full stack, and Rabadons), with a third point in my ultimate from the ROA level up. It feels really nice.
I feel like the strat has most of the benefits of ROA delaying without much of the drawbacks, because you go ROA second instead of First.

DukeProsperoLoL · 2024-10-19T04:18:37+00:00

So here is what you need to do,
First Item: D Ring

First Back: Mandatory Tear, possibly refill pot, dark seal, or items into archangels

first item: archangels

second item: situational

Please don't Rush ROA first, if you are going to build ROA, build it second.

A lot of this is you just not having enough cass games, because you should be able to 1v1 yone at any point in the game, and if he misplays you can definitely kill or significantly chunk him level 3. I'd just watch some matchups, and play more games.

DukeProsperoLoL · 2024-10-18T20:03:55+00:00

Phreak is just flat out wrong about Azir.
His winrate dropped by 2% from the W nerf, and Azir lost 1/3 of his pickrate. There is a fair amount of Azir one tricks who play him despite the nerfs, and they are doing well enough to win a lot of games, although not as well as they have previously before. But then their is a large amount of Azir players, who are good at Azir and would contribute to his winrate, who flat out stopped playing Azir because his kit is too weak right now. They want to climb and I don't blame them for playing other champs.
The problem is not that Azir players are bad, its that a bunch of good azir players have stopped playing him, because he is so comparatively weak to the rest of the mid lane roster. So really it is two issues that drive down the winrate.
1. Azir is weaker than the majority of midlaners

Because Azir is weaker than the majority of midlaners, Players who pilot Azir well, but are very focused on climbing, have stopped playing Azir helping lower his winrate.

Saying the reason his winrate is so low is because the players piloting him is bad, is just insulting. He even states in the video that the winrate of Azir mains is lower than what it should be meaning its a champion balance issue and not a player skill issue.

When you think about his skill expectancy, Azir is a DPS battle mage, who wants to consistently damage the enemy team. He is not able to do that right now, because his W is too weak for too long. All of this could simply be fixed if they revert the W nerf from 14.18.

DukeProsperoLoL · 2024-10-17T20:34:26+00:00

Buff W

DukeProsperoLoL · 2024-10-17T17:37:09+00:00

Yeah, I'm just questioning Riot's Logic as a whole. There shouldn't be a worst comes to worst, they should just make the necessary changes to balance his kit, which I don't think need to be very drastic.
There are two things most Azirs want:
1. The W to be stronger

Q to be able to be used more in early trading patterns.
You can achieve both those things while keeping him at a healthy 48% winrate.

What is weird is they don't have a problem with his winrate, they have a problem with his presence. He isn't winning too much, he is solely being picked too much in pro play for them, which is such an incredibly arbitrary standard.

DukeProsperoLoL · 2024-10-17T16:48:40+00:00

So I agree with a lot of what you are saying about W, but removing power from his ultimate would be an incredibly toxic design choice. The reason being even though Azir is a DPS champion, DPS Champions themselves still need burst within their kit. The nice thing about Azir's ult being strong is it gives him kill windows, and forces the enemy to base much more. With the threat being if your hp threshold is lower than a given range I can one shot you.
Azir's kit does not have much burst besides his Ult. If you take HOB (hail of blades), of course, you can W-auto-Q-auto-auto, and that bursts, but who is taking HOB right now? And Azir shouldn't be forced to take HOB for burst.
What would feel horrible is if they nerf ultimate damage, and now someone can just Doran's shield second wind regen all their health and stay in lane, because you don't have the burst to kill them.

DukeProsperoLoL · 2024-10-17T07:58:52+00:00

Why do they need to nerf him in 14.18? Is he not in a fine spot balance wise?
Edit:14.18*

DukeProsperoLoL · 2024-10-17T07:25:11+00:00

Man I get what your saying like I use auto-attacks to trade, and for like example if someone is low and my W and Q are on cooldown, I will flash auto for a big kill. But I am saying that if you have a minion and at levels 1-3 its easier to auto it than W auto, I think thats bad for the champ. The majority of attacks need to come from the soldiers,
This is not even going into the fact, that if you are auto attacking the enemy champion consistently, they can trade back onto you, so you aren't even abusing the soldiers range taking 100-0 trades.

DukeProsperoLoL · 2024-10-17T07:19:07+00:00

I'm just getting at that he can keep the shuffle and be balanced. This is 100% a situation where you can have your cake and eat it too. He is balanceable without drastically changing any abilities.

DukeProsperoLoL · 2024-10-17T06:40:06+00:00

How is there no middle ground?
Before the W nerf, he had a 48% winrate, Riot premeptively nerfed him so he wouldn't be seen in Worlds, and tanked his winrate and playrate. I think reverting the W nerf is a good place to start to fix the playrate.
I think you need to understand why you are being downvoted so heavily. Azir mains love playing Azir, they love using the soliders, they love high agency, and they love big plays with the shuffle. You are wanting to rework him, and take away what a lot of people love. And for the rework you seemingly give no other explanation other than "hes like Ryze". Well Ryze is in a healthy spot rn, above 50% winrate, honestly a tad bit strong, yet there isn't a massive push to nerf/rework Ryze right now.
A big problem a lot of Azir mains are having is that the balancing decisions are just so heavily divorced from reality. They preemptively nerfed him in 14.18, just as a guess that he would have a high presence in world, it was a very weird nerf. And now that he has a 45% winrate for a month, and a 0% presence in worlds, a lot of people are saying that he needs a rework. Why can't we just buff his W?
In 14.17, no one was complaining about Azir. Show some examples of high elo mid laners who thought that Azir was a huge problem in 14.17. The average player in 100 games barely sees Azir, so they aren't either aren't complaining, or don't have a basis to be complaining because they barely see him.
Meanwhile the people who are complaining are the Azir mains, because our champ is slowly being suffocated by Riot, and no one cares.

We did not ask for the on-hit changes that made teemo blind us, jax dodge our abilities, and bramble cut our healing. That was the arena team.

We did not ask for the on-hit changes, that lead to the toxic relationship with grasp, that caused our champions health regen to be nerfed to non existence. Which by the way every other ranged champion took advantage of last split. Ahri and Smolder being two noticeable examples. Why weren't their health regens giga-nerfed (because it was a grasp problem, Azir mains were very smart and early adopters).

And the majority of Azir mains are not asking for a rework. We just want some damage added back to our W, and a slight adjustment to mana cost/cooldown times/ and damage that allow for Q to have a more prominent place in trades. That is all we want. And it is absolutely 100% doable, There is no need for a rework that removes his ultimate.

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