Quote:
Originally Posted by borticuscryptic
I found these results interesting enough that I decided to dig into the reward structure of console fabrication. Since these were created under Heretic, I truly didn't know what to expect.
Here are my findings:
1) The quality of the reward outcome of the "Fabricate Prototype" assignment is guaranteed to match the quality of the success' display name. In other words, if your results say "Blue Quality" the console you receive cannot be anything other than Blue (Rare) quality, in all circumstances. No rare chance to upgrade to a better type, or anything like that.
2) Every console available from our random drop tables is represented. Despite the above sample showing zero Phaser Relays (e.g.), they are included in the drop table as a possible result.
3) All console rewards are equally weighted. This is the part I was unsure would be true, but it is  every item on the reward tables has an absolutely equal chance of being rewarded.
The only possible explanation I can offer at this point, is that it's just a matter of sample size. There are 42 different Mk XII consoles you can receive from this assignment (16 Eng, 10 Sci, 16 Tac) of each quality (Green, Blue, Purple) resulting in the total number of potential outcomes being 42*3=126. When you run a sample size of 300, with almost half that many possible outcomes, your odds are invariably going to be too small to create an big enough picture of the entirety.

There is something definitely amiss and while everyone is pointing to sample size issues and "statistically speaking" I can defiantly tell you it is not a sample size issue.
Let us forgo the rarity factor because the op stated those proportion came out the same and were find. Let?s focus on the fact that each console type is not dropping in ?equal? proportion. Is a sample size of 300 sufficient? In statistics, we have two error rates, alpha is the probability of making a type I error (incorrectly rejecting a true null hypothesis) and beta is the probability of making a type II error (failing to reject a false null hypothesis). You only worry about the type II error rate when you do not have a significant alpha (usually >0.05 in most hypothesis testing). When you reject a null hypothesis you have to check is you had enough power (beta and sample size) to ensure you did not make a false rejection.
Now with this primer behind us let us do a simple and quite easy to do statistical test. The type of test that fits this data the best is a chisquare test. For this test, we take our observed values (from the op) and derive expected values. In this case, we know the consoles should drop in equal proportion so the number of expected consoles of a particular type say for science is simply 1/10 = 0.1 * Observed value. The OP had 131science consoles so the expected values following a uniform distribution is 13.1 consoles. He should have received 13.1 of each particular console type (if they drop uniformly). Now for those of you that want to look up the chisquare test there are plenty of hits on Google. Now we have our null hypothesis that says the observed drops = the expected drops and the alternative hypothesis that says the observed drops do not equal the expected drops. I am going to go to the next step.
For the science consoles we get a chisquare value of 31.8, with 9 df, and a probability = 0.000214. Thus, we reject the null hypothesis and the observed drops do not equal the expected drops. Because our alpha is <<0.05 we do not have to worry about a beta error rate or our sample size because the effect is strong.
For the engineering consoles we get a chisquare value of 136.0, with 14 df, and a probability = 4.36x10^22. Thus, we reject the null hypothesis and the observed drops do not equal the expected drops. Because our alpha is <<0.05 we do not have to worry about a beta error rate or our sample size because the effect is strong. By the way I could only find 15 not 16 engineering consoles.
For the tactical consoles we get a chisquare value of 72.36, with 15 df, and a probability = 1.69x10^09. Thus, we reject the null hypothesis and the observed drops do not equal the expected drops. Because our alpha is <<0.05 we do not have to worry about a beta error rate or our sample size because the effect is strong.
Thus, sample size is not the issue here because the effect or magnitude of the difference is so strong. Our conclusions are then within each console group, a particular console type is not dropping uniformly. I have my suspicions it is the way the reward rolls and loot tables are structured. Instead of rolling for rarity, then console group, then console type the system is set to roll first for rarity then console type. All the consoles are pooled and we can now test that hypothesis. So our expected number for a particular console type is 1/41 = 0.02439 * Observed Value which means the op should have received 7.65 of each console type if again they drop uniformly.
Running our chisquare analysis again we get a chisquare value of 263.39, with 40 df, and a probability = 1.14x10^34. Thus, we reject the null hypothesis and the observed drops do not equal the expected drops. Because our alpha is <<0.05 we do not have to worry about a beta error rate or our sample size because the effect is strong. We can say that the consoles do not drop uniformly when they are pooled.
So we can say statistically consoles from the DOFF crafting mission are not dropping uniformly within console type or within the pooled subset. We can also say that with great certainty that the sample size is not an issue because the magnitude of the effects are so great. How is the drop rate then calculated? I cannot answer that, all we can say it is not uniform based on the two scenarios above. More likely the probability of getting a specific console of a specific quality using the OP?s quality rates are:
All Consoles Pooled
Very Rare ? 0.24*0.02439 = 0.005854 = 0.59%
Rare ? 0.51*0.02439 = 0.012439 = 1.24%
Uncommon ? 0.24*0.02439 = 0.005854 = 0.59%
If the OP can provide a breakdown of the qualities we can even go so far as to test that.