Optimal skills distribution

Overview

Optimal skills tables, Skills allocator notebook for a custom setup, a full explanation of the theory of skills optimization, some discussion on the Amplifiers skill and more.

Introduction

This guide will talk about the optimal skills distribution of uncapped skills for high level players.
The capped skills are either useless or should be maximized around the time the uncapped ones get to 30-50.

The guide will deal in SP, which is the number of skill points you leave free to be allocated in the uncapped skills, after you’ve filled your capped skills and left enough for initial mana.

Some prerequisites for it to be useful are:

• Having explored most of the game fields, to get all the useful skills (there is a section below for the non MP players on flash sites, who cannot obtain certain skills), this wiki page[gemcraft.wikia.com] will help collecting them all
• Being level high enough to have capped the basic skills, have enough SP spare for mana and enough to put on uncapped skills, I’d say at the very least WL 2k
• Using the optimal endgame gems: you don’t need to follow the Extreme End Game Guide 1.1 to the letter, but you must use OBR and YBR gems
• Having read the Extreme End Game Guide 1.1 glossary, as I use that terminology here.

If you prefer having a general hint rather than a list of precise numbers, there is a skill hierarchy and we can rank the skills from higher to lower optimal level:
TColors≳BBound>>Leech>>Traps>>CritHit>Reson
The Amps skill is difficult to place, but should generally be around the same level as Resonance.

Next section will talk about the theory behind the optimal skill distribution, if you just want optimal numbers head to the “Skills table” section.

Skills distribution theory

Warning: math ahead

First of all we need to figure out how many skill points every skill level costs, it’s pretty straightforward, to buy up to the Nth level of a skill you need:

Then we need to understand which skills are important to raise, given a defined playstyle:
True Colors, BloodBound, Leech, Traps, Critical Hit, Amplifiers and Resonance are the obvious choices, as we use OBR, YBR, SlowBR gems and O, Y amps.

Chain Hit and Slowing are not needed, you may want to dump some points in them at mid level,
but at high level the BBound modifier gets you all the CH/Slow you could ever want.

To make things easier we won’t consider amplifiers for now, so we just have to deal with triple gems and know which part of TC to apply.

At this point we need to see what effect those skills have on the game stats, so let

be the level of every skill (name got from their initial) and ‘ta’ be the bonus granted by your talismans.

The raw bonuses look like:

where TCs is the skill part of TC and TCd is the damage part of TC, both for triples.

I assume your gems are at the speedcap (all the decent gems get to the speed cap before g40) and rangecap, so we don’t bother with those parts.

Now let’s consider what we want to maximize, we’ll divide the problem in 3 parts:

Understanding managems

The power of a managem is its displayed leech, which is given by:

So the merit figure for a managem is bb*leech, as there is no way to influence the hitLevel via skills.

We now figure out how the skills influence this product, we get:

Putting it together, we get that the power of a managem is:

So finally we know what is the quantity we need to optimize for mana gaining:

if we were to maximize this with respect to tc,b,l,t over the constraint of a maximum expendable SP, we’d get the best setup for mana farming.

But then we need to kill monsters, too, so let’s

Understanding killgems

The power of a killgem is its displayed max damage times its displayed crit (times 0.8 times 0.5, which are constants so we never care about those), which is given by:

So the merit figure for a killgem is bbound^2 *damage*crit, as there is no way to influence the hitLevel via skills.

We now figure out how the skills influence this product, we get:

Putting it together, we get that the power of a killgem is:

So finally we know what is the quantity we need to optimize for killing:

if we were to maximize this with respect to tc,b,c,r over the constraint of a maximum expendable SP, we’d get the best setup for killing monsters.

Sadly, we can’t maximize just M or K, we need to keep a balance between the two and the next section will find the best balance with some reasonable assumptions.

Joining M and K together

The basic idea is that the final goal is building the best killgem possible and mana is just needed to build bigger managems to get more mana to finally build a killgem.

So, let’s assume a base managem power is P, with skills it becomes M*P, which allows us to gather M times more mana as before, allowing us to make a killgem M times more costly.
But we know how much damage a killgem gains when we put more mana in it, it’s given by the growth equation:

where gk is the growth of the combine method we use on the killgem.

Luckily finding combine growths is exactly what gemforce does, so we have all the possible combines and their growths and we can estimate this, the skill allocator uses the growth of the 16c for killgems:

but the exact growth doesn’t matter much in the final result, so you are good even if you use ‘U’ or 719k combine, or you can give the growth of your favorite method to the allocator notebook for finetuning.

Now, adding in the benefit provided from K, we have:

which seems the right function to aim to maximize…

But wait, there’s more!

If we can get more mana from skills, we can use that mana to make better managems, to gather even more mana, to build even better killgems.

As before, if we now gather M times more mana, we can build managems M times more costly and we get:

where the value of the growth is again 16c managems.

At this point, if P was the skillless mana and M*P the skill mana, we can get more upgrading the managem, to reach:

But now, we have a better managem, we get more mana, we can upgrade again.

And again, and again, and again.
In the high level gems approximation we can take the limit, which yields:

Now, with this new mana increment we build a killgem, putting it together with the previous killgem formula we have:

this is the formula we need to maximize to have the best skill setup, and that’s exactly what the notebook does.

The number gk/(1-gm) tells you how much you need to prioritize mana skills over kill skills (luckily TC and BB overlap) and it’s around 4, which means that mana skills are much more important than kill skills.

From maximizing this function it can be seen that the skills always have a certain order from best to worst (which corresponds to the power they have in GP), which gives the skill hierarchy I wrote in the introduction.

Skill allocator notebook

To actually do the computations needed I wrote a Mathematica notebook, which gets your SP number (and some minor parameters, if you like, but the defaults are mostly fine) and computes the best skills setup with that SP number.

It’s the program that built the table in the next section.

You can retrieve it from the skill-allocator repository[github.com]: Notebook URL[github.com]

Skill table

Here follows a table of optimal distribution for multiples of 5k skill points.
If you have a number somewhere in between two points just interpolate in some way.
For a perfectly tailored distribution use the Notebook in the previous section.

For the latest version, up to 400k SP (and a better table rendering) look at the version in the repo[github.com]

Amplifier skill

Including the Amplifiers skill in the standard computation is very difficult, because the improvements it brings depend on the ratio of manacost of a gem on its amps.

Conversely, the optimal gem/amps cost ratio depends massively on the amps skill, which makes this problem impossible to solve exactly (unless someone with a huge amount of free time wants to integrate gemforce and the skill allocator together).

Gemforce, though, accepts the value of the amp skill to get the best ratio and can give us some constraints:
even at very high amps skill (>500) the amps still stay below half of the value of the mana/killgem, which helps us estimating the maximum power we can get from the amps skill.

At present day values and levels I value the Amplifiers skill power more or less as Resonance, but I cannot show the math, as it’s a mess (will do, if asked).

For players without Magician Pouch (flash sites only)

Players without Magician Pouch suffer the fact they have no Bbound skill and that they don’t have black gems in every stage.

When black gems are available, the best strategy is the same as the normal one (OBR and YBR), with the skill distribution obtained by forcing BB skill to be 0.

Follows the table for fields with the black gem (better version at the repo[github.com]):

If the field you are playing has no black gems you’ll need to use white (or no bound at all).
In this case the optimal distribution changes markedly, as you don’t have the TC bonus for bloodbound (poolbound benefits from TC, but the scaling is too small to make a difference)

In this case the formulas described in the theoretical section change to:

where ‘go’ and ‘gy’ are the growth of the bound-less gems.
Be careful that this is valid for gems at the speed cap, if you cannot reach the speed cap yet you should keep the mana skills higher than this.

Here follows a table for fields with no black gem (better version at the repo[github.com]):

Credits

12345ieee – Author of the guide
Suuper – Help with math

If this project helped you and you wish to help by contributing, please contact me, leaving a
new Github issue[github.com] or opening a new pull request.
You can also help by donating some money for my time:
Donate to this project using Paypal[www.paypal.com]