Match behind gem level and mana cost and the mathmatically proof why blue gem suck so hard.
Guide to Costs and Effect on Gem Level and Color
We all know how much gem cost with out any skill:
60 for G1 240 for combine.
So a G2 gem cost is 60+60+240=360
We can see clearly, the cost of gem is mainly it’s combining cost. Even if you trade you soul with forgotten for a 0 cost gem. After a few grade up, it’s cost will rising and end up preety much same as any other gem.
Classic demon shenanigans
With every grade up, the cost of gem is nearly double.
Or in formula : Mana cost = 2^(G-1)*30+(2^(G-1)-1)*240
The Cost of Power
Because with each grade, the cost is double, we hope the power is also double to keep up. But there is no such thing as hope.
Take a look at purple gem:
The armor it reduce is 2/3.8/7.22. Only a 1.9 time of increase.
With every grade make it 2 times more cost, it only reduce 1.9 times armor.
The growth rate is only 1.9, as for green it’s 1.8, and for orange is 1.38.
Growth rate is define as:
- Gem-power / Gem-power of previous grade.
- If this number is the same in all grade.
- Then this number is it’s growth rate.
Among all color, the blue is the worst, with each grade up it only slows down 2 more %.
An additively increase, not a multiplicative like any other gem.
Even if blue gem can make mob walk backward. Because the cost of blue gem is increase in multiplicative but the power only additively, it will never catch up. Blue gem is doom to be low grade and never worth grading up.
Blue is mathmatically useless. Q.E.D.
The Color Difference
Some wizard attempt to compare the power between different color, may want to draw a plot indicate the power and grade of each gem.
Well this plot can tell us very little thing.
It’s mainly because the magnitude is so different.
To unlock the arcanic secret of gemcrafting, we must seek guidence from math, more specifically Logmatiic function.
Since we are discussing doubling, I am using base 2 for log.
Log (gempower) in base 2
I add in the imaginary hope gem (black), as reference. It double it’s power every time it’s cost double.
This is much better now, then i move all plot vertically a little so they all line up in (0,0).
Now the arcanic secret is well exposed.
In term of power growth rate, the colors order are:
- In early game, under wizard lv 100 Green and purple are in deed powerful and useful.
- They have the best power growth rate,Nearly 2.
- The orange has always been wield card. I will skip it.
- Yellow gem has very low growth rate, you need a good mana income to feed it up.
- FYI, the crit rate is cap at 80%, but the crit multiplier has no cap.
Red gem has second lowest growth rate only 1.16, I never use it other then trail.
Blue is trash. Growth rate is undefinable in blue it just that useless.