Regarding the shotgun status chance calculation...

[Aeuce]

First of all, I'd like to thank the community of the game for being so wonderful and, since I am technically new to the forums, I'd like to apologize beforehand for any mistake in the formatting or discussion aspects.

I've been playing this game for around 6 months now, and as soon as I started following the first Warframe youtubers and browsing the wiki, I came across the following formula to calculate the status chance of any pellet-based weapon, be it a shotgun, the pre-rework quartakk or the zarr:

 

Chance per Pellet = 1 − (1 − Status Chance)^{(1 ÷ Pellet Count)}

 

Now, the equation itself is known by a relatively big amount of people, especially veterans, and surely an even greater percentage of the playerbase knows that to make a pellet-based shotgun status-viable, it must first achieve 100% status chance before multishot.

However, the thing that I've seen nobody mention is that the formula itself isn't just something DE came up with when designing shotguns, but an actual formula used when calculating the probability of an event happening.

This seemingly absurd use of the aforementioned formula has led some to conclude that the status chance calculation for pellet-based weapons should be tweaked to make it so that every weapon of the type can be built for status chance and be effective at the same time:

A thread was fairly recently made about the topic:

While completely avoiding any discussion about the repercussions that the change would have on shotguns that are already powerful without needing to build for status, I'd like to point out something to the people that don't quite understand why or how the formula is used.

When it comes to probability, it is exremely easy to draw parallels using dice as examples, so let's suppose that we are trying to calculate the chance of getting a 5 by throwing 8 six-sided dice at once.

The easiest way to proceed is to write down every single combination of numbers that we could obtain in a throw, and then dividing the amount of combinations that contain a 5 by the total number of combinations.

For reference:

 

http://www.edcollins.com/backgammon/diceprob.htm

 

Now onto the faster way; if we consider that we only know the probability of one die to get a 5, which is undoubtedly 1/6. that is 16.67%, the equation to solve in order to get the overall chance of getting a 5 is:

TC = 1 − (1 − PC)⁽ⁿ⁾

(1 − 0.1667)⁽⁸⁾ = 0.7675 = 76.75%

Where:

TC = total chance after rolling 8 dice at once

PC = per-die chance of getting a 5

n = total number of dice

As you can see, the result of the equation matches real world expectations, and as I'm sure many of you will have noticed, the equation used is just a rearranged version of the formula that DE uses to calculate the per-pellet status chance of shotguns, with the difference that, in my example, we are trying to find the total chance starting from the per-die chance, instead of the opposite.

This also explains why, once reached 100% total status chance, the per-pellet status chance suddenly becomes 100% as well: to be 100% sure that your next shot is going to deal at least 1 proc, you need to make sure that every pellet has at least 100% status chance, because even if all 8 pellets have 99.99% chance of proccing, there is still a chance, however small it may be, that none of them will proc.

I hope this cleared up some confusion about the subject.

Edited August 3, 2018 by Aeuce

[(PSN)Pumba_Beneator]

Yes agreed, this is basic calculation of chance of an event occuring at least once during n trials, when given the probability of the event in one trial.

Same goes when you calculate the chance of getting a rare item with a radiant relic 

- one run is 10%

- two runs is 1 - (90%)^2 = 19 % (and not 20%)

- 4 runs (or radshare) is 1 - 90%^4 = 34% (not 40%)

etc.

Now the status chance per pellet is interesting in case you can proc several effects (corrosif + fire etc) or effects stack.