# Optimum Morph Level

*If you're trying to maximize your lord stats you should worship a gain-boosting deity and automorph. This article is for those that are trying to morph as quickly as possible.*

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:

- Success probability is linear between 300 (20%) and 500 (50%) and linear again between 500 and 999 (100%).

• Note that, if true, this would theoretically mean levels between 300 & 500 are worth .15% additional chance of success per level, whereas levels after 500 each add only .1% chance of success.

- Expected fail levels is (1000 - level) / 10. I'm aware that this is slightly more than observed, but shouldn'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 success 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 known. Below, I use S(500) to be roughly 550 (since you expect to take 2 attempts to morph, so 50 lost levels).

- S(430) ~ 430 * 0.4 + (1 - 0.4) * [S(480) + 50] ~ 520 [Since success probability at 430 is roughly 0.4)]
- S(370) = 370 * 0.3 * [S(430) + 60] * 0.7 ~ 520
- S(300) = 300 * 0.2 + [S(370) + 70] * 0.8 ~ 530

## Empirical Method

Using Avatar's Twitter feed to collect data, we can take, for example, all the non-999 morphs and see when, on average, a player morphs.

mysql> select sum(level), count(success), sum(level)/count(success) from morph where level!=999 and success=1; +------------+----------------+---------------------------+ | sum(level) | count(success) | sum(level)/count(success) | +------------+----------------+---------------------------+ | 424924 | 814 | 522.019656019656 | +------------+----------------+---------------------------+ (In the table above the success field is a boolean and should probably be called "attempt" instead.)

On average, players morphed at level 522. Chance to morph at this level is 52.2% and is a safe place to start trying.

Is this number the *optimal morph level*? I wouldn't go into it since I'm not a mathematician, but it does correlate with the number presented in the earlier paragraph.

## Bottom Line

Morph early and often.

- Optimum morph level is somewhere around 370-400 (389 should be 33.35% chance of success). If you're risk averse, wait until 520-560 [this minimizes the likelihood of getting perpetually unlucky -- the lower probability morph attempts have a lot more variance].
- TNL/worship etc. don't matter.
- Difference between morphing at 300 and 400 and 500 is not more than 10-20 levels. So it isn't all that important when you morph, as long as you do it early.
- Expected levels you do at hero is roughly 520-550.