# Difference between revisions of "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:

• 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 53% 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. 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.