Hello all,

First off, I want to thank everyone who filled out the survey for taking time out of their days to do so. Here is the link to the google doc that I used to keep track of and analyze the results: Survey Results

Anyway, here is what we found out.

ELT Chocobo Encounter Chance
10.4% (441 survey average)

-Pretty sure we can conclusively state this implies a 10% spawn rate for chocobos (in groups of 3). I'll give additional information at the end of this post that further supports this statement.

PRO Chocobo Spawn Chance
6.3% (61 survey average)

-This one is harder to analyze since we don't know the average number of chocobos that spawn per encounter. As such, this number is the maximum encounter rate. If the average number of chocobos per encounter is 2, then this number needs to be halved to get the actual encounter chance, which would be 3.15%. My guess is the actual encounter chance is somewhere in between.

ADV Chocobo Spawn Chance
0.7% (5 survey average)

-Yeah... this one didn't turn out well.

Corrections Made to the Survey

So, I didn't use all the data that was submitted for several reasons.

1. Some people ran multiple difficulties. This makes it impossible to determine on which difficulty the chocobos spawned, and as such makes the data useless. Sorry to those who submitted such data.
2. Some people had larger numbers of kills for Adrammelech than either Zaleras or Belial. That is impossible, so I couldn't count your data.
3. Some people specified that they were farming a different difficulty than their results indicated. To not introduce errors, I discounted their data.

That being said, we still had a good amount of survey submissions and more than enough to form a decent conclusion, at least about ELT.

Chocobo Percentages

Just for fun, I also calculated the distribution of chocobo colors. They are:

Red - 59.5%
Black - 18.9%
Yellow - 21.6%

My guess is they were going for a 60-20-20 distribution here.

For the Mathematically Inclined

We can interpret the results using a t-table. For a sample standard deviation of 0.02604 and an average of .104, we can be 99.9% confident that a sample of 441 people will have an average somewhere between 0.1 and 0.108. This uses a t value of 3.226 in order to include the 10% we believe the actual value to be.

We can also narrow down the actual chance for ELT by using Chebyeshev's Inequality and the Law of Large Numbers. This will allow us to maximize the probability that our calculated average can be as far (or farther) away from the actual average. I will use several possible actual averages and show the maximum percent of getting the average for ELT that we got in each case.

Getting an experimental probability of 0.104 is not uncommon if the actual probability is 0.1 or 0.11, but becomes increasingly more uncommon the further away from 0.1 you go. This is dependent on the standard deviation of a binomial random variable and a 441 sample size.

Lastly, I know this is very generalized. If I wanted to be SUPER specific, I could've weighted each survey contribution appropriately and calculated a weighted average and weighted standard deviation. In fact, I did do this for the average, but it came out almost the same so I decided not to do so for the standard deviation.

If I made any mistakes, please let me know!

Thanks.