Mathematical analysis/definite guide on "The Nth Degree." (cross-posted from Reddit)

[lawranc]

"Mathematical breakdown of "The Nth Degree". (Gaige Skill Discussion)"

The Nth Degree: Every (10-1)th bullet that hits an enemy will ricochet towards another nearby enemy.


This is an interesting skill. It means that with one point in it, one out of every nine shots will hit two enemies, with two points in it, one out of every eight shots will hit two enemies. I am unaware if there is a class mod that can boost this value, but I am going to work under the assumption that it can go all the way up to 9/5, making every shot ricochet.

Here is the total damage increase for every value of the skill:Value Total Damage Increase
0/5 0%
1/5 11.11%
2/5 12.5%
3/5 14.29%
4/5 16.67%
5/5 20%
6/5 25%
7/5 33.33%
8/5 50%
9/5 100%


Something that must be understood about this skill: It appears to suffer diminishing returns. The first point boosts your damage by 11.11% (1/9), and the second point boosts your damage by 12.5% (2/9). We can see that the second point only grants you 1.39% extra damage.

But due to the nature of this function, it is not strictly diminishing, in fact, that is the only point that the returns decrease. I will refer to the damage added by each point as the marginal damage increase. Here is the marginal damage increase chart:Value Marginal Damage Increase
0/5 0%
1/5 11.11%
2/5 1.39%
3/5 1.79%
4/5 2.38%
5/5 3.33%
6/5 5%
7/5 8.33%
8/5 16.67%
9/5 50%


This means that if you had 8/5 of the skill, the next point would grant you 50% extra damage when there were other nearby enemies. That is pretty huge, but we can't forget about the points it took to get there. This is just to show that it really ramps up. If you can get to the higher values, it could be worth it.

That's where the amortized damage increase comes in. We can divide the total damage increase by the number of skill points needed to get that increase to see the average increase per point. This chart is a little surprising:Value Amortized Damage Increase
0/5 0%
1/5 11.11%
2/5 6.25%
3/5 4.76%
4/5 4.17%
5/5 4.00%
6/5 4.17%
7/5 4.76%
8/5 6.25%
9/5 11.11%


This affirms that the first point is still the best point, but we have a new contender: The 9th point. If you find a class mod with 4+ points into "The Nth Degree", it might be worth it to use it. But there is still one thing we have to look at: What are the options we have that might be BETTER than 11.11% damage per point when multiple enemies are nearby?

I'll propose a scenario. Someone trying to get the top tier skill in Ordered Chaos. Their build might look something like THIS, with three points here and there to unlock the next tier. I took the liberty of filling out Anarchy related skills, as
that is the core of this tree. Your build might look different, but I'll be looking at every skill you could forego to get another point in The Nth Degree.

Here is where I will chime in with my personal opinion, but you can always come to your own conclusion. I am only including this so that others can make an informed decision using their own opinions.

What else could the points go into?Robot Rampage Deathtrap lashes out with a flurry of attacks


I personally don't really like this skill, but I'm not that reliant on DT. It seems to make DT pause, and enemies can move out of the way of this attack. But it is definitely worth more than a few other skills. I'd take it over 6.25% more ricochet damage, but I would rather have 11% ricochet damage than it, for example.Blood Soaked Shields Killing an enemy immediately restores 20% of your shields per level, but you lose 1% of your current health per level.


This skill has diminished marginal utility per point. The first point is great, because it is fairly likely that your shields will be below 80%. The last point, however, is not as good as the first. Due to how shields work, there will ALWAYS be more times when you are at below 80% shields than you are 0% shields. To me, I've seen way too much of the regen wasted at 5/5. I'd rather have some ricochet damage after getting this skill to 3/5, or maybe even some explosions.Annoyed Robot Increases the movement speed of Deathtrap by 7% per level


I don't like this skill, and will always be able to find a better spot for a point. Deathtrap is already pretty fast, and goes through quite a few walls. Death From Above Shooting an enemy while in midair consumes one stack of Anarchy per level to create a rank (one per level) digi-splosion, damaging nearby enemies.


Something to consider with this skill: It works similar to The Nth Degree, you aren't going to have multiples enemies in every fight. You also aren't always going to be jumping. I like this skill because it is fun, but I might not max it because I don't use it that often.

Now what does that mean my build might look like? I got Blood Soaked Shield to 3/5, but I really didn't want anymore than that. I don't see myself losing more than 60% of my shields per enemy. Even that might be pushing it. I also grabbed 3/5 Death From Above, but when it came down to it, I'd rather have Robot Rampage than another point in it. I only put one point in The Nth Degree, but if I didn't like Robot Rampage, I'd probably put another point in it or Death From Above.

I ended up like THIS, but if I had a nifty class mod, it might end up like
THIS.

What should you take from this? It is hard to justify going any more than 2/5 into The Nth Degree unless you have a class mod for it. And like I said, I'm not even sure that class mod exists. I don't want to say that The Nth Degree is a one point wonder, but I definitely won't be putting any more than 2 into it.

[swk3000]

There are no COMs that boost The Nth Degree. It caps at 5/5, so only every 5th bullet will ricochet.

[Atroization]

I was thinking about working this out myself, as every 5th at 5/5 isn't really the best. Sounds like I need to respec.

[keridwen]

is there a list of skills COMs can boost somewhere?

[swk3000]

Here.

[Kolhell]

I approve this math.

[HviteKristsDod]

Excellent calculations. Seems like 2/5 is the best case scenario for Nth degree in its current, non-COM-boostable state.

[Nirf]

The math is solid. I thought the same thing the first time I thought the skill. What I didn't know though was that there is no COM that boosts it. This is a shame. Combined with off and on bugginess of death from above, and the fact that many of the skills aren't necessary if you are trying to maintain a moderate (instead of excessive) anarchy level, this makes almost the whole second half of anarchy close to worthless.

The first 11 points in Anarchy are about the best deal Gaige has anywhere, but everything after is a waste.