I have combed through the various threads and started compiling a list of who has spent what, how many Red Boxes they have opened and how many Jem'Hadar ships they have gotten. Anyone entering a lottery of any sort should have some realistic expectation of what their odds are.
The data are all self-reported via the forums and not completely exact, so I am willing to fudge the drop rate up to 1%. It is striking to see that the people reporting they have gotten the Jem'Hadar ship are mostly those who have opened less than 30 Red Boxes. Many pare reporting they have opened hundreds of Red Boxes and had no luck. Only one player I have seen reported 300 Red Boxes and got one ship. I suspect that there are a great deal of people in the middle who have not bothered to report.
Simply totaling the number of reported box openings (1,604) with the number of reported Jem'Hadar ships (11) I get a drop rate of 0.69%. That's less than 1%.
I am not comfortable with the data I have to run any other sort of data analysis. I would like to run an MTTF to estimate roughly how many Red Boxes you would have to open to get one ship or roughly what your chances of getting a ship are if you open 100 Red Boxes.
If anyone can clearly report their data below, I would greatly appreciate it. Number of Red Boxes opened (total, not just until you found a ship) and how many Jem'Hadar ships you have gotten from those Red Boxes. As a point of interest, I am tracking C-Points and $ as well, but they are not important to the analysis.
5 Red Boxes (recepits)
0 Jem'Hadar ships
At a drop rate of 0.68%, each ship costs effectively 14,600 C-Points or effectively $190.
Granted each player sees a different "cost," but effectively Cryptic sees exactly that per ship obtained via the C-Store boxes. The more observations you have of a random event, the more they work out to exactly what they should be. Flip a coin 10 times, you probably won't see a 50/50 split. Flip the same coin 10,000 times and you will be very close to 50/50.