What is the exact Nanophoenix drop rate? (with math)

tl;dr We don't know the Nanophoenix drop chance. Please take survey so mathematics will tell us.

10 second survey

https://docs.google.com/forms/d/e/1FAIpQLSd0azVMleUOxviJRiTZzxwp2jgm_BEyvw9jcvGsSauhPGENWg/viewform


I last applied advanced mathematics to Destiny in figuring out How Overall Light Level is Calculated. Now, I want to figure out the exact droprate of Nanophoenix, but I need your help in collecting data; we need at least 500 – 1000 responses to yield statistically significant results. Your gamertag is required to calculate how many drop chances you have had. Results will be anonymous.

Math warning below:


The droprate of Nanophoenix is a frequent source of controversy. We know it is rare, but no one knows exactly how rare. A previous survey attempted to approximate the droprate, but it failed to take many variables into account:

  • Players do not know how many clears they have

  • Raiding more than three raids a week

  • Continuing to raid after you have gotten the ship

This framework accounts for all of these issues, and more. It takes only a player's gamertag and whether or not they have the Nanophoenix as inputs. Then the following calculations are performed:

  1. I find the number of drop chances a player has had (maximum 1 per character per week). The number of drop chances ranges from 0 to 60 (the hard raid has been out for 20 weeks, number can actually be higher with deleted characters).

  2. Players are split into 61 buckets based on their number of drop chances.

  3. The percentage of players in each bucket who have the Nanophoenix is calculated.

  4. This percentage is plotted against the number of drop chances. In general, the more drop chances you have, the more likely you are to have to ship.

  5. Finally, I calculate the best fit geometric cumulative disribution function by varying the parameter p, the actual drop chance.

  6. From this curve, we can obtain our estimate of the actual drop chance.

This process will be easier to understand once I have data to make a graph.

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