Statics to get a HOTM in the long run does not match the Percentage

Bugs & Issues
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Today we have a 1.3% Percentage of getting a HOTM.

Mathematically speaking we can say that in 77 attempts we could get a HOTM.
At worst mathematically it would take 154 attempts to get a HOTM.

But in the long run this is not true.

My last HOTM was in March 2021 (Telluria), 18 Months ago.
I don’t make so many investments in the Game, I have an average of 15 to 20 attempts per month including all events and the little I spend.
There were months that I added more than 50 attempts, such as in November 2020

This gives us an average of Approximately 350+ attempts in the last 18 MONTHS.

And I didn’t get any HOTM in this period. That’s right none, I’m almost 2 years without getting a new HOTM.

Something is wrong with this 1.3% calculation when we calculate in the long term.

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How does your math compare to the ones in the HOTM threads?

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Hello Ruskin

My topic is about long-term math, not current HOTM.

I’m talking about the 1.3% percentage applied to the last 18 months.

I have more than 350 attempts and I don’t get any of the last 18 Hotm.

Something is wrong with the long-term calculations where statics should stabilize but not occur.
I see a problem with that.

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He was sharing the long term math. Based on that you are one of the roughly 12500 people who have not gotten a hotm in 350 pulls.

It is unfortunately the nature of rng

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That’s not even close to the worst…

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I once needed something between 400-450 pulls to get hotm, so roughly 0.(insert zeros)1% chance of that happening (I’d be interested if someone wanted to do the math, cause I don’t want to lol). I have no idea about the math, I’m just guessing, but I’m probably one of 5000 players who ever had so much unluck. And it was 19 and half months period for me, so something over 1.5 years, so I hope your bad streak ends really soon.

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I understand that there is an Rng behind it.
And that I can just be very unlucky.

However, I believe that as we are talking about percentages, they should stabilize over time.
And it doesn’t happen in HOTM, it seems like the odds are reset at the beginning of the month.
Where should there be considerations behind the Rng.

I published it here because there may be problems with proportional calculations.

We will wait for a return from Sg.

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The problem with “long term” thinking on probabilities is that each pull is completely independent of the ones before them. Every single time, you have a 1.3% chance. If you do a hundred pulls, the chance of NOT getting a HotM is 0.987^100, which is still a 27% chance of not having one. If you do 350 pulls, the chance of NOT getting a HotM is about 1%. Which means you were unlucky, but with millions of players, you’re not alone, but in a small club of people of a few thousand players who missed out.

Many have suggested implementing a “pity counter” to counteract this, but there has been no movement from SG.

My personal experience was going about a year before my 1st HotM (Margaret), then getting one every 5 months (Telluria and Kingston), and then getting a pretty good fraction of them (don’t have the current one, though, or Uraeus). Which just means I have been luckier than you.

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Every summon is an independant event, so unfortunately its mathematically possible to never get a HotM or any 5* Hero, but the probability is very very low. In the case of the author of the thread he is in the range of 1% of all people doing 350 summons and dont getting a HotM, thats very sad but unfortunately possible. On the other side of the gaussian distribution function are those people who summon 10 times and get the hero.
Hopefully your luck will change to the better.

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Don’t hold your breath :stuck_out_tongue_winking_eye:

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Interestingly enough, the odds of going 332 pulls without a hero of the month are also 1.3%. So (and I’m willing to accept this is a fallacy) for every person that pulls a HotM on the first pull after reading this, there will be another who will not pull a HotM in the next 332 pulls (I’m of course assuming that millions of people are going to read this :thinking:).

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If it is left completely random then there is no such thing as a guarantee to ever get one. No matter what number you come up with.

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You cannot say that the statistic prove it wrong as it only consist of 1 sample (your account). If you want to prove it ering eith statistic, you have to randomly pick at least 30 accounts as the sample.

Now about your data, you do not get a single HotM in 350 pulls. That is entirely possible. In fact I also experience it before finally acquiring Devana.

Lets do the math, the probability of not getting HotM in 350 pulls is:
(100%-1.3%)^350 = 0.987^350 = 0.01026 = 1.026%

Do you know the chance to get Mysterzo in Taverns of Legend? Merely 0.1%. That means not getting any HotM in 350 pulls is 10 times more possible than acquiring Myztero in a pull.

Statistic should stabilize but the that is not like what you think. It is not based on time but based on number of data instead. If you want the deviation to be less than 0.5% (fall in between 0.8%-1.8%), you might need thousands of data.

If your merge your data with all players data, it would stabilize into very close to 1.3%. This is because just like there are unlucky people, there are also lucky people, they counter each other and therefore stabilizing it.

As the probability of not getting any HotM in 350 summons is 1.026%, I will give an example with 7 coin throw which have 0.781% of not getting any head. Imagine if there are 128 people asked to throw a coin 7 times (all use the same exact coin), based on probability/combination theory, the expected outcome is:
1 people get 7 head
7 people get 6 head + 1 tail
21 people get 5 head + 2 tail
35 people get 4 head + 3 tail
35 people get 3 head + 4 tail
21 people get 2 head + 5 tail
7 people get 1 head + 6 tail
1 people get 7 tail

The person who get all 7 tail might wonder why it is always head, even claiming that the coin is rigged. However, when all data are combined, the number of head and tail are even, proving that the coin is not rigged, afterall it is the same coin.

It doesn’t matter whether the 7 throws is conducted in the same minute or spaced once a year. Again, stabilization is not about timespan/length, it is about number of data.

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Thanks everyone for the answers.

I came to the sad conclusion that I can be very unlucky, but I’m still into stats, even if in the worst case scenario.

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