## Shop Data Finale

(As of December 2020) - By AdvancingElk and Wobblins

The lien shop consists of two parts the bottom right slot and the other five slots. They can be treated independently of one another. What is happening in one slot is not affecting the others. And there are a few rules that separate these two parts from on another.

- Legendries can only appear in the bottom right slot

- Commons can never appear in the bottom right slot

- Henceforth, these two parts are treated independently from one another and are referred to as the “legendary slot” and the “other 5 slots” respectively.

- Using 457 data points

- Legendries can only appear in the bottom right slot

- Commons can never appear in the bottom right slot

- Henceforth, these two parts are treated independently from one another and are referred to as the “legendary slot” and the “other 5 slots” respectively.

- Using 457 data points

*”Why do I see epics more often than legendries when they seem to have a lower probability?”*

The other 5 slots each have a 14/110 chance of being an epic.

When you do the math this works out to be: 1-(1-14/100)^5 = 0.494 Almost a 50% chance that one of the five slots is an epic. (Not including the Legendary slot’s much higher chance of being an epic instead of a legendary).

Meanwhile the legendary only appears with a 17/110 chance in a single slot. With the math: 17/110 = 0.155 Much lower

*”What about specifically getting X amount of RARITY?”*

Again the “Legendary slot” and the “other 5 slots” have to be treated independently.

The fact that Legendary can only appear in one copy should surprise no one. The rest is derived from numbers and a little bit of logic that actually comes from the “other 5 slots”.

*”So why the red text?”*

So to separate the different Quantities for each rarity in the "other 5 slots" it was necessary to collaborate the results between rarities. You can obtain the values quoted without this step but doing so requires a total of 436 shop inputs (we have 457 so cutting it close). The same trick however cannot be done with the legendary slot. The E1, E2 separation isn’t so bad. It is possibly to visually confirm that E1 is consistently higher than E2. Determining how much by however would require 1041 shop inputs. Something similar can be said about: R10, R15, R20 in the legendary slot. R20 can be seen to be larger than R15 and R10, but determining exactly how much by would require 540 shop inputs. If R10 and R15 are in fact different, it is by such a small amount that it wouldn’t be possible to tell until for 8775 shop inputs were obtained.

Obviously I haven’t waited this long.

*”So where did the numbers come from?”*

You’ll notice that I haven’t simplified any of my fractions. Also in practice I did the "other 5 slots" first. Obtaining every fraction that was either a denominator of 2750, 1375 or 275 (which can all be displayed as denominators of 2750). So rather wait for thousands of results I cheated. Working out which values both worked with the data obtained and gave fractions of 2750 (this is why for example the R10, R15 and R20 are not an even 1/3rd split despite the fact the data states that they could be).(edited)

Final point:

*”Can’t Dust rerolls be different?”*

This problem was solved before we even started the community project hence the: "Do not feel as if you have to use the dust refresh"

Getting everyone onto the same page computer programs (games) have smaller programs called subroutines. Simple example “Add(3,7)” which will add the numbers given to it. More complex example “Dice(3)” which will pick a random whole number between 1 and the number given to it. You can get different results from this subroutine, but the rules the computer follow are the same every time. We know the game’s subroutines, what variables are used, under what circumstances they are used. We also have a decent idea as to how they work (I.E. background randomisation works on device time) but we don’t know exactly how they work hence the community project. We know the shop refresh subroutine’s name and know the same sub-routine (and variable) is used regardless of what refreshes the shop (time/dust). While the SPD refresh still

*could*have modified rates it’s unlikely. Doing it in another way being harder, more work and more prone to error.