(Discussion) Status Chance Calculations And The Rise Of The Status Chance Build

[Ruriko]

This may seem like a pointless thread, but I've been wracking my brain trying to figure out how Status Chance is actually calculated. This goes beyond the really obvious like that Status Chance increases mods are multiplied into the base status chance of a weapon. Specifically, I'm trying to figure out how Multishot is factored into this calculation. I have yet to figure this out and felt opening this to discussion would allow us to finally figure this out and move onto the REAL question, which I will get to later.

 

For this discussion, I'd like to focus on the Akstellito, one of the most popular sidearms in use currently. There are a number of reasons for this: 1. It has a good status chance at 15% and 2. Sidearms currently have the highest level of multishot in the game at 180%, making it possible to fire 3 shots for every 1 bullet ammo consumed.

 

What we currently know is that Status Chance is multiplicative. Using Pistol Pestilence at max rank provides us with a 60% increase in status chance. .15 x .6 = .9 + .15 = .24. This means that an Akstellito using only Pistol Pestilence as a status increasing mod has a 24% Status chance.

 

Multishot makes this get very weird. I played around with the multishot levels in conjunction with Pistol Pestilence see what the HUD says, but figuring out how the multishot gets into the mix is really confusing and doesn't seem to follow traditional formulas.

 

What is clear is that these numbers represent the chance that 1 status effect will occur per 1 Bullet ammo consumed. The issue is that how these extra bullets are factored into this isn't clear. I've tried several different probability equations and have successfully managed to make the calculation for Pistol Pestilence + Lethal Torrent work, but it is when Barrel Diffusion is added into the mix that all my equations fail.

 

If you don't care about the equations or if math makes your head hurt, please ignore this spoiler section.

 

 

From the HUD

Pistol Pestilence alone: 24% 

Pistol Pestilence + Lethal Torrent: 42.2%

Pistol Pestilence + Lethal Torrent + Barrel Diffusion: 56.1%

 

 

Probability of either Bullet 1 or Bullet 2 triggering a status chance: .24 + .24 - .24^2 = .48 - .0576 = .4224 OR 42.24% (This matches the HUD)

 

Probability of either Bullet 1 or Bullet 2 or Bullet 3 triggering a status chance: .24 + .24 + .24 - .0576 - .0576 - .0576 - (2 x .24^3 = .72 - .1728 - (2 x .013824) = .72 - .1728 - .027648 = .519552 OR 51.9552% (This does not match the HUD which shows 56.1% as the maximum chance of a single status instance)

 

 

The reason I turn to the community regarding this is twofold. First, it will help us to better understand how Shotguns determine their Status Chance Per Pellet, as the likelihood of landing every single pellet on your target is very low unless you're point blank (and sometimes, not even then.) The second reason is more at the heart of this discussion. With the release of the new mods from Tethra's Doom, we can now push the status chance beyond the 100% threshold, making the Status Build actually viable for a number of weapons. On certain weapons (such at the Tysis), it may even be game-breaking. A bonus of +120% Status Chance means a base 50% Status chance becomes 110% before multishot is even considered. 

 

Even weapons with lower overall status chances (such as the Soma with 7.5%) can become somewhat terrifying given their rate of fire. That 7.5% Status Chance becomes 16.5%. Weapons with no spool up time and decent status chance (AKA Boltor Prime with its 10 Fire Rate and 10% Status Chance) become absolute terrors as they unleash status chances at 22% per bullet ammo consumed. Certain status ailments, like Viral and Corrosive, will decimate enemies as Viral is a fixed percentage of max health and Corrosive is a fixed percentage of armor per proc. Even something as overlooked and under appreciated as Blast results in incredibly high amounts of crowd control, while Gas turns single target focused weapons into AoE Death Machines. 

 

To me, it feels like the Status build just became quite significant. Yes, it won't get you those pretty, pretty numbers that are outstandingly high, but you are gaining more viability and flexibility in exchange for that. In many instances, you're trading a meager amount of damage for a massive increase of status procs. 

 

The only way to know is to experiment and to understand the math. That is where I turn to you, my fellow Tenno. What do you think about this?

 

 

[Pythadragon]

For Multishot:

 

The game is rounding the average number of bullets to the nearest whole number. Therefore lethal torrentl (+60%) is rounded to 2 shots, and lethal torrent + barrel difusion (+180%)  is rounded to 3 shots.

 

The status chance shown in the UI screen is the chance for at least 1 status.

 

Here are the proper calculations that the UI screen is using:

 

Base: 24%

Lethal torrent: 42.2%

Lethal torrent + barrel diffusion: 56.1%

 

For lethal torrent - 

1-0.24 = 0.76

0.76^2 = 0.5776

1-0.5776 = 0.4224 (42.24%)

 

For lethal torrent + barrel difusion - 

1-0.24 = 0.76

0.76^3 = 0.439

1-0.439 = 0.561 (56.1%)

 

^ These numbers match up with the UI screen examples you have provided. If anyone needs help understanding the calculations I did, let me know and I will explain step by step.

Edited March 10, 2014 by Pythadragon

[Ruriko]

Pythadragon,

 

The moment I looked at what you did, I literally slammed my head into my desk. I missed the most obvious approach to this and now that I see it, it makes a lot of sense. Thank you for finally putting an end to my frustration! I can live with feeling really stupid. Thank you greatly for your contribution!

[(NSW)Omgwtfl9lbbl]

If you look at one of the shotgun proc threads, I also have all the calculations laid out somewhere if you want to see them. Can't remember where, though.

 

Edit: the basic formula off the top of my head is

 

1-(1-status%)^#bullets = arsenal status %

 

Where status% is your status chance per pellet/bullet and arsenal% is what you see in the arsenal.

 

For instance if you have a shotgun that shoots 5 pellets each with a 7% chance to proc, in the arsenal you would see

 

1-(1-.07)^5 = .304... => ~30.4%

 

To reverse this you would do

 

Status% = 1-(1-arsenal%)^(1/#bullets)

Edited March 10, 2014 by omgwtflolbbl

[TwiceDead]

Pythadragon,

 

The moment I looked at what you did, I literally slammed my head into my desk. I missed the most obvious approach to this and now that I see it, it makes a lot of sense. Thank you for finally putting an end to my frustration! I can live with feeling really stupid. Thank you greatly for your contribution!

No! Rather than live and feel stupid, you should live and rejoice at your ever expanding knowledge! 

Of course if you already knew this then it's a different matter. 

[Pythadragon]

Pythadragon,

 

The moment I looked at what you did, I literally slammed my head into my desk. I missed the most obvious approach to this and now that I see it, it makes a lot of sense. Thank you for finally putting an end to my frustration! I can live with feeling really stupid. Thank you greatly for your contribution!

 

Ruriko - 

 

Glad that helped.

 

I think that it is worth mentioning that in game status chance for multishot is generally always lower than the UI due to rounding the number of projectiles.

 

For example, with lethal torrent (+60%), the average number of projectiles becomes 1.6.

With lethal torrent (+60%) + barrel diffusion (+120%), that average changes to 2.8.

 

Base: 24%

Lethal torrent: 42.2%

Lethal torrent + barrel diffusion: 56.1%

 

Lethal torrent -

1-0.24 = 0.76

0.76^1.6 = 0.6646

1-0.6646 = 0.355 (35.5% vs 42.2%, ~19% difference)

 

Lethal torrent + barrel diffusion -

1-0.24 = 0.76

0.76^2.8 = 0.4637

1-0.4637 = 0.5363 (53.6% vs 52.2% ~5% difference)

Edited March 10, 2014 by Pythadragon

[MechaTails]

I'll throw it out there, all you really need is like 50% chance to inflict status, especially if you're using a fast firing/attacking weapon, to make it proc reliably. At a mere 16%, my Lecta can already stunlock mobs, but I wouldn't rely on it entirely just yet.

[Ruriko]

DarkTails,

 

The reason for pushing beyond that is that the status chance you see is the chance to inflict 1 status. You're fully capable of landing more than that. Weapons like the Tysis go well beyond that, as just using Pistol Pestilence and the new Jolt mod results in 110% Status chance before factoring in Multishot. This means that it will always inflict 1 Status Proc per bullet. It is unclear if it is currently possible to trigger more than one if you exceed the 100%, though most likely not since it would fall under the Critical Hit Chance category.

 

All the formulas that people have presented thus far in this thread cannot account for an over 100% Status Chance. That's what makes this hunt so interesting. There is a master formula for everything, but the fact that we have different equations for Rifles/Pistols/Shotguns leads me to believe that we haven't found it yet. Everyone thus far has contributed a piece of the puzzle, but we're not quite there yet. :D But soon!