Optimum Morph Level

This is an attempt to calculate the optimum Morph level. Scroll down for the bottom line if you don't care for the math.

Assumptions:

• Fail probability is linear between 300 (20%) and 500 (50%) and linear again between 500 and 999 (100%).
• Expected fail levels is (1000 - level) / 10. I'm aware that this is slightly more than observed, but shoudn't be more than 10 levels or so.

Let

• S(x) be the expected levels you do if you first try morph at level x
• p(x) is probability of failing at level x
• f(x) is number of fail levels

Then:

S(x) = p(x) * x + (1 - p(x)) [f(x) + S(x + f(x))]

( Note that you do f(x) "half-xp" levels so effectively you only "lose" f(x) levels. )

We can just calculate the above for various x. For simplicity, assume S(some sufficiently high level) is fixed.

Running these numbers for S(500) = 0.5 * 500 + 0.5 * (50 + S(550)) + ... or roughly 550

• S(430) ~ 450 * 0.4 + (1 - f(450)) * [S(500) + 50] ~ 530
• S(370) = 370 * 0.3 * [S(430) + 60] * 0.7 ~ 530
• S(300) = 300 * 0.2 + [S(370) + 70] * 0.8 ~ 540

Bottom Line

Morph early and often.

• Optimum morph level is somewhere around 370. Could be 400. Could be 350.
• TNL/worship etc. don't matter.
• Difference between morphing at 300 and 400 and 500 is not more than 10-15 levels. So it isn't all that important when you morph.
• Expected levels you do at hero is roughly 550.