Proving Commission Cycle Theory
This builds off my previous posts!
The Introduction
In case you don't want to read my previous posts, the basic idea is this:
Let's say I had a bag with 3 colored marbles. One red, one green, and one blue.
I ask you to pick a marble.
What's the chance of you getting a specific marble?
It's 1/3 for each one.
1/3 red, 1/3 blue, 1/3 green
Now, let's say you reached in and took a red marble out of the bag.
If I replace that red marble with another marble, then the chances stay the same-- 1/3 for each color.
This is probability with replacement.
However, what if I didn't?
Then the chances change.
There is no longer a red marble in the bag. There's only a blue and green marble.
That means it's 0 chance of red, 1/2 chance of blue, and 1/2 chance of green.
This is probability without replacement.
0 red, 1/2 blue, 1/2 green
The theory of cycle commissions is that commissions follow the second type of probability.
When you do a commission, it gets removed from the bag (the "cycle") until every commission in the bag is completed.
Then, you get a new bag.
The Hypothesis
Now that we have the theory, the question is "How do we prove this?"
The simplest way is for HoYoVerse to confirm it.
So far, however, I do not believe this has been confirmed by them.
Thus it falls on the players to prove this.
Gathering data from multiple players over a long period is one way to do this.
There's still a bit of uncertainty, though.
What if we could create a situation that could only be possible if commission cycles existed though?
The situation is this:
Let's say you grabbed every marble except for the last marble.
In this case, it's green.
What are the chances now?
It's 100% green. There are no other marbles in the bag.
0 red, 0 blue, 1 green
The same will apply to commissions.
By doing every NPC commission except one in the cycle, you are basically guaranteed to get it.
The only exception would be when you don't get an NPC commission.
In that case, it would be like reaching into the bag and grabbing a fistful of air, even if the green marble is in there.
The Proof
I selected 2 accounts.
I chose Inazuma as my commission region, because it has the fewest NPC commissions in its cycle.
You usually only get 0-1 NPC commissions a day, so the number of commissions matches the time needed to clear a cycle.
Throughout December 2022, I spent my time clearing out commissions.
This is basically starting with a full bag of marbles, and taking 1 out every day.
By January 2023, the cycles were pretty much cleared out on both accounts.
Now, the goal is to confirm the near-100% chance of getting the same commission every day.
All throughout January, I logged in to check the commissions, but didn't do them.
The final tally of commissions is below.
AR37 account (30 days):
Is This Novel Amazing? - 27
The Taste of Home - 1
An Art to Be Honed - 1
Non-NPC Commission - 1
AR31 account (28 days):
An Art to Be Honed - 22
The Taste of Home - 1
Non-NPC Commission - 5
The Conclusion
I'm not going to go into hard statistics and analysis like p-values and whatnot, but I think the conclusion is pretty clear.
27 out of 30 days on the AR37 account went to Is This Novel Amazing?
22 out of 28 days on the AR31 account went to An Art to Be Honed.
In both cases, these are pretty rare commissions.
By eliminating (almost) every other possibility, the chances of getting the same commission noticeably increase.
It's pretty safe to say that commission cycles do exist.
Discord: Kramiel#0014
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