Leveling up mods: Probabilities and Math

[kerenskij]

Since we had this discussion on Discord I think it might be nice to post this somewhere permanent and explain in detail.

This post is about the mathematics, more precisely the probabilities, involved in leveling up mods and increasing secondary attributes.

Maybe it makes sense to give a very general overview over how upgrading mods works.

Each mod has a primary stat.
This stat increases every time the mod goes up a level.
In addition to this primary stat, a mod can have secondary stats, up to a maximum of four different secondary stats.
Depending on the color of the mod when you get it, it will already come with some secondary stats.
White mods start with 0 secondaries.
Green mods start with 1 secondary.
Blue mods start with 2 secondaries.
Purple mods start with 3 secondaries.
Yellow/Gold mods start with 4 secondaries.
Secondary stats are increased when the mod reaches level 3/6/9/12.
It is important to understand how they are increased.

For a white mod, at each of those 4 levels, one new secondary stat with a certain value will be added.
The value is, as far as I know, random, but limited to a certain range.

For a green mod, at level 3, the secondary stat that is already on it will increase.
At 6/9/12 a new stat will be added, just like for a white mod.

For a blue mod, at levels 3 and 6, one of the two secondary stats will go up.
It could be one at 3 and the other one at 6 or one can level up twice.
At 9 and 12 new stats are added.

Purple increases existing stats at 3/6/9 and adds a new one at 12.

Finally, Yellow/Gold mods already have all 4 secondaries at level one and thus, at 3/6/9/12 one of the secondary stats will be increased.

This means, that on a Yellow/Gold mod, there is a chance, that ONE secondary stat will be increased FOUR times.
Basically everyone's goal is to get Gold mods with 4 nice secondaries, but most importantly, one of them has to be Speed.
Speed is great!
And then you level it up and pray that Speed goes up as many times as possible.
But you could also (at least theoretically) want a different secondary stat to increase.
You can not control it, but you can always wish .

There are two reasons why level 1 mods improve significantly in value from white to green to blue to purple to yellow/gold.
First of all, the more secondary stats there are on the mod at level 1, the better you know what you spend your money on.
I.e. you can decide to not level up a mod at all if you do not like the secondaries it has.
Secondly, and maybe more importantly, the values on secondaries will be bigger for mods that have more secondaries to begin with,
as the secondaries can then increase at 3/6/9/12 instead of just new ones appearing.

I hope this makes sense so far.

So let's get to the numbers.
In the following I list the chances of leveling up one stat a certain number of times.
0x 25% means, that there is a 25% chance this stat will not level up at all when leveling the mod to 12/15.
2x 50% means, that there is a 50% chance this stat will level up two times when leveling the mod to 12/15.

Green
1x 100%

Blue
0x 25%
1x 50%
2x 25%

Purple
0x 30%
1x 44%
2x 22%
3x 4%

Yellow/Gold
0x 32%
1x 42%
2x 21%
3x ~5%
4x <1%

That's it for now, I might add some more comments to this post later on.
Feel free to ask questions/discuss!

Edit 1:
I promised to give a little probability-calculation-tutorial so here we go.
Probability is about thinking in paths.

Let's try with the simplest case. A green mod.
It has one secondary stat at level 1.
This will increase at level 3, there is no alternative.
So the chance for this secondary stat to increase at level 3 is 1 or 100%.

A little bit more complicated: A blue mod.
Let's say it starts with +Speed and +Health as secondaries.
Here are the things that can happen:
Path 1 Level 3: +Health goes up, Level 6: +Health goes up
Path 2 Level 3: +Health goes up, Level 6: +Speed goes up
Path 3 Level 3: +Speed goes up, Level 6: +Health goes up
Path 4 Level 3: +Speed goes up, Level 6: +Speed goes up
There are four paths, all equally likely and thus each path has a probability of 25% or 0.25.
The sum of the probabilities of all possible paths always has to be 100% (or 1).
Now, to find out the chance that +Speed goes up exactly once when going from level 1 to level 6, you have to add the probabilities of all the paths that have this outcome:
Path 2 (25%) + Path 3 (25%) = 50%

This is all there is to it.
For purple/yellow mods the number of paths simply increases.

Again, please feel free to ask questions if there's anything you don't understand or would like to have explained in more detail.

[Gul Ski]

Great guide...one thing that might be useful is the cost to upgrade each type of mod to the relevant levels (from level 1):

[kerenskij]

Ty Gul, useful numbers!

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