I think it’s pretty common knowledge by now that most brands in Splatoon have a higher chance of rolling a certain ability, while having a lower chance of rolling another. For instance, Krak-On gear is five times more likely to get Swim Speed Up, but Defense is half as likely as other abilities to appear on those items. However from just those numbers it’s difficult to get a sense for exactly how much of a chance you have of getting two or three of the same ability on an item, even if you’re using an advantageous brand. That’s why I decided to crunch some numbers and calculate what the probability is of getting different ability combinations, partially so I could have an idea what level of investment it would take to get what I want.
In this analysis, I’ll be using the following terms to refer to the abilities affected by different brands:
“neutral” = an ability that has the normal, base chance to be added to gear
“favored” = 5x more likely to roll than the neutral abilities on that brand
“unfavored” = 0.5x as likely to roll than the neutral abilities on that brand
For tl;dr purposes, I’ll discuss my results first and you can take a look at the link at the end if you want the details about the math.
Chances of getting the favored ability in...
...exactly 1 slot: 42.2%
...exactly 2 slots: 19.3%
...all 3 slots: 2.78%.
...0 slots: 35.1%
Chances of getting a specific neutral ability in...
...exactly 1 slot: 15.2%
...exactly 2 slots: 1.4%
...all 3 slots: 0.06% (1 in 1636)
...0 slots: 83.4%
Chances of getting the unfavored ability in...
...exactly 1 slot: 8.1%
...exactly 2 slots: 0.5% (1 in 205)
...all 3 slots: 0.02% (1 in 6545)
...0 slots: 91.4%
There are also a few brands (KOG, Cuttlegear, and Amiibo) that do not favor any abilities. Here’s what the odds are for getting a specific ability on those:
Exactly 1 slot = 17.1%
Exactly 2 slots = 2.6%
All 3 slots = 0.2% (1 in 455)
0 slots = 80%
There are a couple of interesting takeaways here:
1) If you want an ability that isn’t favored by a brand (e.g. Bomb Range Up) or you don’t like any of the items that are made by a brand that favors it, you’re better off using one of the three brands with no favored abilities over a brand that has it as a neutral or unfavored ability.
2) You have a better chance of getting a single unfavored ability than you do two neutral abilities or three favored abilities.
Also, one metric that I like to think about when trying to wrangle with probabilities is how many times I have to try something in order for the overall chance of success to be more than 50% -- in other words, for the chance of you succeeding at least once to be greater than the chance of failing every time (assuming you don’t succeed before then). Here are those numbers for each case:
1 favored = 2 attempts
2 favored = 4 attempts
3 favored = 21 attempts
1 neutral = 4 attempts
2 neutral = 48 attempts
3 neutral = 1,134 attempts
1 unfavored = 9 attempts
2 unfavored = 142 attempts
3 unfavored = 4537 attempts
What we can take away from this is that if you want three of the same ability, using a brand that favors that ability is really the only feasible option. Of course, it’s not impossible with other brands -- just varying degrees of improbable. Needless to say, trying to get three of an unfavored ability is ludicrous, not to mention the exorbitant costs you would likely incur -- just getting past the 50% barrier would run you 136,110,000 cash.
More info about the calculations here:
https://docs.google.com/document/d/1QnA8xaepy4psSonKUfKPJOQ3FOjUq9B2fPplb1KHqQY/edit