Some mathematical models considering Cinderhulk and SF Cape

First model: sum[(16+18)(1+t/20),t=0,10]-43*11= -5.5

t goes from 0 to 10 ticks at 1 ticks/sec and the duration of SF cape burn is 11 ticks, which is 10 seconds because you have a tick at the beginning of the first second and at the end of the first second. The negative value means that Cinderhulk deals less damage than SF cape for the same duration. The 16 is the base value and 18 is the bonus from level. So this is the most damage you will do over the rampup duration.

Second model: sum[(8+9)(1+t/20),t=0,10]-43*6= -24.25

t goes from 0 to 10 **ticks at 2 ticks/sec to make the duration 5 seconds (because of a similar situation as above). SF cape also has 6 ticks since it remains ticking at 1 tick per second. The base value is 8 instead of 16 because there are now 2 ticks per second. Because the absolute value of the negative result is larger, the shorter ramp up time actually causes Cinderhulk to deal LESS damage over the ramp up

Third model: sum[(16+18)(1+t/20),t=0,5]-43*6= -28.5

t goes from 0 to 6 ticks at 1 tick per second. Comparing the third and second models compares how much of a difference is lost. Thus, while the second model is (and should) be a strictly better situation, it is not that much of an improvement.

Fourth model: sum[(16+x)(1+t/20),t=0,5]-(25+x)*6= 3x/4-42 f(x)=0; x=56 Using the First model but allowing champion level to vary, the fourth model is the total difference of damage after ramp up between Cinderhulk and SF Cape. F is negative for the entire domain of [1,18]

Conclusion: the building of Cinderhulk is independent of the passive; one should only consider the health bonuses vs Warrior in order to snowball lanes with AD early and building SF cape later if immolation is needed on a champion. Whether that's an easy decision to make or not (health gives infinite returns when reaching a burst threshold and ~0 if it doesn't) depends on how skewed jungle picks are. Burst champions, like Kha'zix will have a harder time counterganking, but steady dps champions like Shyvana will come out on top.

Prediction: Cinderhulk will diminish the presence of assassins and ambushers in the jungle.

Still won't kick Lee Sin out though.