Greetings Captains,

This thread is intended to address the spread of Jem'Hadar vessels amongst the fleet. The mechanics for obtaining the vessels are not completely known to us, but we can make some guesses as to how it works.

My last thread got us a good idea for what was happening with the Jem'Hadar ship drop rate. A lot of people posted their experiences to help the community arrive at an educated purchase decision. Unfortunately all the data had to be collected from people's own recollections of their experiences and trusting their honesty. Some posters were confused by what types of boxes they opened and others about how many they opened. It is even possible that some reported false numbers, though I would not accuse anyone specifically. It's just likely that happens on both ends of the data spectrum.

__Known Facts:__- Jem'Hadar ships only come from Red Boxes during the holiday event.
- Each Red Box has a chance of dropping the ship.
- Red Boxes can be bought from the C-Store for 100 CP.
- Red Boxes can be won from the racing event.

__Unknown:__- The drop rate of the Jem'Hadar ship from the Red Boxes.
- The drop rate of the Red Box from the races.
- The quantity of Jem'Hadar ships available (unlimited vs. limited).
- Drop rate distribution type (plain geometric, influenced by other factors?).
- Random number generation system.

**Assumptions:**- The drop rates follow a geometric distribution.
- No other factors influence the chance of the Jem'Hadar ship dropping from a Red Box.
- The drop rate on Tribble is the same as Holodeck.

**Experiment:**
With some help from the community, I was able to assemble 1,000 Red Boxes on the Tribble Test Server. These boxes were opened over the course of about 6 hours (as fast as the data could be recorded and the boxes opened) on December 30th. The contents of each box were individually recorded to collect the most data possible.

__Results:__- 472 (47.2%) Blue Boxes
- 117 (11.7%) 1 Hour Skill Boosts
- 87 (8.7%) Polytronic Acid Hortas
- 68 (6.8%) Exocomps
- 61 (6.1%) Gekli
- 55 (5.5%) Eisilum Crystal Hortas

*
**51 (5.1%) Photonic Tribbles [may have been mixed up with Photonic Science Officer]**
- 32 (3.2%) 8 Hour Skill Boosts

*
**28 (2.8%) Photonic Science Bridge Officers [may have been mixed up with Photonic Tribbles]**
- 24 (2.4%) Federation Junior Officer Cadres

**5 (0.5%) Jem'Hadar Attack Ships**

** It was very late at night and tabbing out of Tribble to record data is not very easy. I know that I accidentally recorded a few Photonic Tribbles instead of Photonic Science Officers. I tried to go back and correct most of them, but may have missed some.*
Jem'Hadar Attack Ships were found in box number 248, 494, 609, 699 and 763. The intervals were 248, 246, 115, 90 and 64. I was nearing the end of the first stack of 250 boxes (after close to 2 hours) and started to lose hope that I would find a ship on Tribble. Thankfully Red Box number 248 yielded a ship, proving they drop on Tribble.

__Box Value:__
I added a C-Point value to each item from the box. The exceptions were the Photonic Tribble, Photonic Science Officer and Federation Junior Officer Cadre. The Photonics were given values of 120 and 160 respectively, since they had similar items in the C-Store. I gave the Junior Officer Cadre a value of 110 C-Points, half the C-Store Duty Officer pack. This is because the Cadres contain fewer officers and are mostly white quality.

Blue Boxes were given no C-Point value. Yes they may technically contain some EC value, but that is far more difficult to assess.

Average C-Points per Box: 109*

Average $ value per Box: $1.37*

*averages may vary slightly based on Photonic Tribble vs. Photonic Science Officer mix-ups. I sorted most of them out, but may have missed a few, throwing the percentages of those two off slightly.

The boxes are technically a winning proposition, which is why many call them "fair". I do have to ask, how many people need 87 Polytronic Acid Hortas? I'm seriously curious, since I have them on Tribble. In reality, the vast majority of the items in the box are things that people had already bought or do not want. Most of them are items you can only use or need one of.

__Statistics:__
It is most likely that there is a flat, even, chance of getting a Jem'Hadar ship from each box. Think of this like a 6 sided die. Your chance of rolling a 1 specifically is described by a geometric distribution. To get the 1 on the first roll is a 1/6 (16.6%). To get a roll of 1 out of three tries would be 1-[1-(1/6)]^3 or 42.1%. This Cumulative Probability describes the chance of rolling a single 1 in three tries.

The Jem'Hadar ship appears to be a 1 on a 200 sided die. Assuming the drop rate is fixed, you only receive a ship when you "roll" a 1.

The Geometric Distribution is not the same as the Normal Distribution. The Mean (average) and Median of the Geometric Distribution are different from each other. The Median will predict what number of boxes must be opened to have a 50% chance of getting the ship. The Mean will predict how many boxes are opened by the average customer before they find a ship. Since each box has the same chance (0.5%) it is certainly possible to open many boxes and not find a ship. That is why the Mean (average) drags out much higher than the Median.

**200 Mean (average) Red Boxes per Jem'Hadar ship.**

138.3 Median (50% chance) Red Boxes
**$250 Mean cost per Jem'Hadar ship via the C-Store.**

$173 Median cost to have a 50% chance at obtaining the ship.
You can see how the average (mean) customer must open up more Red Boxes than is required to have a 50% chance. This is because the boxes have no "memory" and opening an additional box only gives you another individual 0.5% chance, but does not add 0.5% to your previous "total".

__Random Number Generation:__
The customer does not know how their chance of getting a Jem'Hadar ship is generated. Computers can not generate truly random data as we would by simply rolling a die or spinning a roulette wheel. They must rely on algorithms which pull from a set of seed values and (possibly) the system clock. The seed values are generated ahead of time and referenced when a random number is required. The computer then puts that seed value through the algorithm to obtain the "random" number.

We do not know if the random number is generated on the server side or the client side. This may not make any real difference, but it is still an unknown to us.

Most lotteries are performed by an independent accounting firm or some other unbiased party. They typically rely on some sort of real world randomization, whether it is mixing names in a hat or watching ping pong balls swirl around a jar.

Scratch tickets are designed by people or algorithms. There are typically a fixed number of actual tickets and the printing of each type of ticket is designed to control the actual payouts. What appears random has actually been specifically designed.

What Cryptic relies on is most likely a simple flat percentage chance (0.5%) as if rolling a die. We just do not know how that 0.5% chance is assessed.

__Previously Recorded Data:__
In the previous thread, helpful customers had stepped forward to share how many boxes they had opened and how many Jem'Hadar ships they had found. The drop rate appeared to fluctuate between 0.5% and 1%. With such a low actual drop rate, every instance of a ship found drastically affected the measured drop rate. I am sure some people have truly found Jem'Hadar ships out of only a few boxes, but that is most likely the exception, not the rule.

It is difficult to assess how those who chose to report data self-selected. Were they a reasonable cross section of the Red Box opening customers? Were they people with a vendetta after being "unlucky"? Were they people who wanted to flaunt low box numbers or skew things in Cryptic's favor? It is too hard to tell. I simply hoped that over time it proved to be a reasonable cross section. Unfortunately it only takes a few "griefers" to throw the data off.

One poster had suggested that PWE uses a rate of 0.65% for their lottery boxes. Based off of the previously recorded data and the 1,000 Red Box experiment, I believe there is still a strong chance that the drop rate might be 0.65%. It is not possible to fully discount that.

__Holiday Race:__
The Red Boxes are made freely "available" via the holiday racing event. Unfortunately only being able to race once each day makes data collection far more difficult. While some one can simply buy and test 1,000 Red Boxes, to race in 1,000 races takes about 300 characters and one month.

My suspicion is that the drop rate of the Red Boxes from the race is the same as the drop rate from the Jem'Hadar ships from those Red Boxes. I am willing to "spot" Cryptic a full 1% on the Red Boxes from the race. Based on the numbers some people with a lot of characters have been reporting, it is very unlikely that the rate is higher than 1%.

Assessing chances of getting the ship from the race would be governed by the probability of winning a Red Box times the probability of getting a ship from a Red Box. The two events have to happen one after the other. This means you must be very fortunate to win a Red Box, and then you have to be very fortunate again to find a Jem'Hadar ship within that box.

The new probability can be calculated by multiplying the two individual probabilities.

Pr(ship)*Pr(Red Box) = 0.005 * 0.01 = 0.00005 or 0.005%

With a 1% chance of winning the box and a 0.5% chance of finding a Jem'Hadar ship, you would have to run:

**20,000 Mean (average) races per Jem'Hadar ship.**

13,862 Median races (required to have a 50% chance at the ship)
Even with a full 0.65% Jem'Hadar ship drop rate and a full 1% Red Box rate from the race you would need over 10,000 races to have a 50/50 (coin flip) chance at getting the ship.

__Conclusion:__
Every box is a chance to obtain the ship. Unfortunately the chance is so small it is nearly impossible to accurately measure from the consumer's end. The chance has not been clearly communicated to the customer. One could easily believe all items in the box had an equal probability or that there were only a certain number of Jem'Hadar ships that would be given out.