"Random" Drop Rate
Ipitydafoo
Member Posts: 10 ★
Hello fellow Summoners,
We have all heard the stories of people getting mysterious amounts of "luck" from opening crystals. Some examples of this include pulling the same Awakening Gem or Rank-up Gem multiple times in a row, or buying multiple 5-Star Hero Crystals, only to pull two or 3 of the same - usually meme tier - Champions. I have recently become one of those statistics. Back when 4-Star Awakening Gems were heavily sought after, I pulled 4 Tech Gems in a row. Now that 5-Star Awakening Gems are in high demand, I have pulled 4 Cosmic Gems in a row. I wish to explore how truly random these drops are.
Kabam has provided their own input on this on the support forums. The example they use is Premium Hero Crystals. They state the following:
"...if you buy a Premium Hero Crystal, and the drop rate for a 4-Star Champion is three percent, this doesn't mean that if you buy 100 Premium Hero Crystals you're guaranteed to receive three 4-Star Champions. This means that you have a three percent chance to get a 4-Star Champion each time you open that crystal."
In other words, they are saying that each pull is independent from the last. This is true, but it also ignores the way probability works in the real world.
Probabilities tends to regress towards the mean as the sample size gets larger. Essentially, this means that the more Premium Hero Crystals you open, the closer you get to that 3 percent threshold of 4-Stars. Are you going to get EXACTLY 3 percent? Of course not. But if you open 1,000 Premium Hero Crystals, you should get 4-Stars out of APPROXIMATELY 3 percent of them. If you were open 10,000 Crystals then the number should get even closer to 3 percent.
To demonstrate this, I used a dice rolling program. Because there are 6 different hero classes, I rolled 6-sided die. Since I opened 4 Awakening Gem Crystals, I rolled 4 dice. This was done 1,000 times, and the results are as follows:
Only two of the 1,000 rolls turned up the same number all 4 times. Only 75 of the rolls turned up the same number three out of 4 times. The remaining 933 rolls turned up a minimum of 3 different numbers
What does this mean in relation to my Crystals, and to the Crystals of Summoners in general? This means that, based on simple probabilities, I should be the outlier. If you asked 1,000 Summoners to open 4 Awakening Gem Crystals, the overwhelming majority of them should be getting at least 3 different classes of gems. There should be very few people getting the same gem 3 or 4 times. The purpose of this thread is to collect that data.
I am interested in the following Crystals:
- 4-Star Awakening Gem Crystals
- 5-Star Awakening Gem Crystals
- Rank-up Gem Crystals - must be the same type of Rank-up Gem. For example, they need to all be Rank 1 to 2, or Rank 3 to 4, for this data to be authentic.
Please let me know the drops of your most recent 4 of these types of Crystals.
Again, the purpose of this thread is strictly for collecting data. This is not the place for debating whether or not drops are truly random. The data will speak for itself, if I can collect enough of it.
Thank you for your time!
We have all heard the stories of people getting mysterious amounts of "luck" from opening crystals. Some examples of this include pulling the same Awakening Gem or Rank-up Gem multiple times in a row, or buying multiple 5-Star Hero Crystals, only to pull two or 3 of the same - usually meme tier - Champions. I have recently become one of those statistics. Back when 4-Star Awakening Gems were heavily sought after, I pulled 4 Tech Gems in a row. Now that 5-Star Awakening Gems are in high demand, I have pulled 4 Cosmic Gems in a row. I wish to explore how truly random these drops are.
Kabam has provided their own input on this on the support forums. The example they use is Premium Hero Crystals. They state the following:
"...if you buy a Premium Hero Crystal, and the drop rate for a 4-Star Champion is three percent, this doesn't mean that if you buy 100 Premium Hero Crystals you're guaranteed to receive three 4-Star Champions. This means that you have a three percent chance to get a 4-Star Champion each time you open that crystal."
In other words, they are saying that each pull is independent from the last. This is true, but it also ignores the way probability works in the real world.
Probabilities tends to regress towards the mean as the sample size gets larger. Essentially, this means that the more Premium Hero Crystals you open, the closer you get to that 3 percent threshold of 4-Stars. Are you going to get EXACTLY 3 percent? Of course not. But if you open 1,000 Premium Hero Crystals, you should get 4-Stars out of APPROXIMATELY 3 percent of them. If you were open 10,000 Crystals then the number should get even closer to 3 percent.
To demonstrate this, I used a dice rolling program. Because there are 6 different hero classes, I rolled 6-sided die. Since I opened 4 Awakening Gem Crystals, I rolled 4 dice. This was done 1,000 times, and the results are as follows:
Only two of the 1,000 rolls turned up the same number all 4 times. Only 75 of the rolls turned up the same number three out of 4 times. The remaining 933 rolls turned up a minimum of 3 different numbers
What does this mean in relation to my Crystals, and to the Crystals of Summoners in general? This means that, based on simple probabilities, I should be the outlier. If you asked 1,000 Summoners to open 4 Awakening Gem Crystals, the overwhelming majority of them should be getting at least 3 different classes of gems. There should be very few people getting the same gem 3 or 4 times. The purpose of this thread is to collect that data.
I am interested in the following Crystals:
- 4-Star Awakening Gem Crystals
- 5-Star Awakening Gem Crystals
- Rank-up Gem Crystals - must be the same type of Rank-up Gem. For example, they need to all be Rank 1 to 2, or Rank 3 to 4, for this data to be authentic.
Please let me know the drops of your most recent 4 of these types of Crystals.
Again, the purpose of this thread is strictly for collecting data. This is not the place for debating whether or not drops are truly random. The data will speak for itself, if I can collect enough of it.
Thank you for your time!
5
Comments
Have you asked 1000 people what gems they pulled?
Your data is flawed.
The problem with RNG is that it's Random to a degree. Anomalies in mathematics occur all the time with weird patterns that aren't seen when you're not necessarily looking for them, and due to the nature of randomness you might see these patterns and consider that it's no longer random, leading to confirmation bias.
If you were to do 1000 runs of 1000 rolls of that dice, you would see deviations on each one of those runs that would either confirm, or disprove the bias.
And every individual successive roll still has an independent chance according to their stated odds, no matter if a larger sample set has tended towards it's “mean” already or not.
And as others have said, you seldom hear in forum from all the majority of cases of people who HAVE gotten a nice distribution. Most likely it tends to be those who have (as according to math there will be) cases where they have unfortunately gotten multiple of the same outcome.
And the thread will never be kept current for long enough to field a large enough sample size, even if it were somehow actually able to solicit a spread of responses to include those that have not had a problem with “bad luck” cases.
You would have to maybe do a reddit form entry system, whereby people would submit EACH ROLL Individually, before even rolling another one (so they will not know in advance whether they might feel slighted in some future roll or not).
No data collection is perfect. The purpose is to be as accurate as possible.
The issue with asking people here is that a large percentage of the people who remember what their AGs were, are the ones that have negative bias towards the idea of rigged RNG. Most people who have no bias, or have had favoured RNG, will not remember what their AGs were. Myself included. I cannot remember what my last AG was let alone the several others that I have opened.
Where have you been, just curious?
Even if you came up with 4 random numbers, for example 1,28,57, and 46, they aren't actually random. These numbers were influenced by your childhood, life experiences, emotions, etc.....
@Arsoz
turns out I'm wrong