# Yet Another Scintillant Drop Chance Post - This Time with Statistics

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I know I've done at least 15 T2 bounties but I'm not sure how many more so I'm just going to assume 15 for this. With 15 T2 bounties we have two chances for scintillant to drop for a total of 30 drop chances which is the recommended minimum sample size for statistics. Assuming Deimos bounties work the same as those on Earth and Venus then the first two stages are what matters since only they can give the common drop we want, scintillant. With 5 options each at 20% reward chance we should expect at 40% chance per bounty and after 15 bounties we should expect 6 scintillant drops. However, after these 15 runs I have received 1 scintillant drop. The following steps will be via the t-test.

Sample size of 30 and degrees of freedom 29.

For each drop we have a probability of 20% for 1 scintillant, giving us an expected drop of 0.20 scintillants per drop chance.
Summing this over 30 chances we have a Dsum of -5.

Filling in the formula we come to:

t = (-5/30)/sqrt{[25-(25/30)]/[(29)(30)]}
t = (-6)/sqrt(24.167/870)
t = (-6)/sqrt(0.0278)
t = -6/0.167
t = -36

Since t-values + only indicates direction we can treat it as an absolute value when grabbing a p-value. I then used the following table to find my p-value. Table was obtained from https://www.statisticshowto.com/tables/t-distribution-table/

The first is for one-tailed and the second for two-tailed:

DF A = 0.1 0.05 0.025 0.01 0.005 0.001 0.0005
ta = 1.282 1.645 1.960 2.326 2.576 3.091 3.291
1 3.078 6.314 12.706 31.821 63.656 318.289 636.578
2 1.886 2.920 4.303 6.965 9.925 22.328 31.600
3 1.638 2.353 3.182 4.541 5.841 10.214 12.924
4 1.533 2.132 2.776 3.747 4.604 7.173 8.610
5 1.476 2.015 2.571 3.365 4.032 5.894 6.869
6 1.440 1.943 2.447 3.143 3.707 5.208 5.959
7 1.415 1.895 2.365 2.998 3.499 4.785 5.408
8 1.397 1.860 2.306 2.896 3.355 4.501 5.041
9 1.383 1.833 2.262 2.821 3.250 4.297 4.781
10 1.372 1.812 2.228 2.764 3.169 4.144 4.587
11 1.363 1.796 2.201 2.718 3.106 4.025 4.437
12 1.356 1.782 2.179 2.681 3.055 3.930 4.318
13 1.350 1.771 2.160 2.650 3.012 3.852 4.221
14 1.345 1.761 2.145 2.624 2.977 3.787 4.140
15 1.341 1.753 2.131 2.602 2.947 3.733 4.073
16 1.337 1.746 2.120 2.583 2.921 3.686 4.015
17 1.333 1.740 2.110 2.567 2.898 3.646 3.965
18 1.330 1.734 2.101 2.552 2.878 3.610 3.922
19 1.328 1.729 2.093 2.539 2.861 3.579 3.883
20 1.325 1.725 2.086 2.528 2.845 3.552 3.850
21 1.323 1.721 2.080 2.518 2.831 3.527 3.819
22 1.321 1.717 2.074 2.508 2.819 3.505 3.792
23 1.319 1.714 2.069 2.500 2.807 3.485 3.768
24 1.318 1.711 2.064 2.492 2.797 3.467 3.745
25 1.316 1.708 2.060 2.485 2.787 3.450 3.725
26 1.315 1.706 2.056 2.479 2.779 3.435 3.707
27 1.314 1.703 2.052 2.473 2.771 3.421 3.689
28 1.313 1.701 2.048 2.467 2.763 3.408 3.674
29 1.311 1.699 2.045 2.462 2.756 3.396 3.660
30 1.310 1.697 2.042 2.457 2.750 3.385 3.646
60 1.296 1.671 2.000 2.390 2.660 3.232 3.460
120 1.289 1.658 1.980 2.358 2.617 3.160 3.373
1000 1.282 1.646 1.962 2.330 2.581 3.098 3.300

Two-tailed

DF A = 0.2 0.10 0.05 0.02 0.01 0.002 0.001
ta = 1.282 1.645 1.960 2.326 2.576 3.091 3.291
1 3.078 6.314 12.706 31.821 63.656 318.289 636.578
2 1.886 2.920 4.303 6.965 9.925 22.328 31.600
3 1.638 2.353 3.182 4.541 5.841 10.214 12.924
4 1.533 2.132 2.776 3.747 4.604 7.173 8.610
5 1.476 2.015 2.571 3.365 4.032 5.894 6.869
6 1.440 1.943 2.447 3.143 3.707 5.208 5.959
7 1.415 1.895 2.365 2.998 3.499 4.785 5.408
8 1.397 1.860 2.306 2.896 3.355 4.501 5.041
9 1.383 1.833 2.262 2.821 3.250 4.297 4.781
10 1.372 1.812 2.228 2.764 3.169 4.144 4.587
11 1.363 1.796 2.201 2.718 3.106 4.025 4.437
12 1.356 1.782 2.179 2.681 3.055 3.930 4.318
13 1.350 1.771 2.160 2.650 3.012 3.852 4.221
14 1.345 1.761 2.145 2.624 2.977 3.787 4.140
15 1.341 1.753 2.131 2.602 2.947 3.733 4.073
16 1.337 1.746 2.120 2.583 2.921 3.686 4.015
17 1.333 1.740 2.110 2.567 2.898 3.646 3.965
18 1.330 1.734 2.101 2.552 2.878 3.610 3.922
19 1.328 1.729 2.093 2.539 2.861 3.579 3.883
20 1.325 1.725 2.086 2.528 2.845 3.552 3.850
21 1.323 1.721 2.080 2.518 2.831 3.527 3.819
22 1.321 1.717 2.074 2.508 2.819 3.505 3.792
23 1.319 1.714 2.069 2.500 2.807 3.485 3.768
24 1.318 1.711 2.064 2.492 2.797 3.467 3.745
25 1.316 1.708 2.060 2.485 2.787 3.450 3.725
26 1.315 1.706 2.056 2.479 2.779 3.435 3.707
27 1.314 1.703 2.052 2.473 2.771 3.421 3.689
28 1.313 1.701 2.048 2.467 2.763 3.408 3.674
29 1.311 1.699 2.045 2.462 2.756 3.396 3.660
30 1.310 1.697 2.042 2.457 2.750 3.385 3.646
60 1.296 1.671 2.000 2.390 2.660 3.232 3.460
120 1.289 1.658 1.980 2.358 2.617 3.160 3.373
8 1.282 1.645 1.960 2.326 2.576 3.091 3.291

Given that our t-value doesn't appear on even a p=0.001 for our degrees of freedom, we have strong evidence to conclude that drop rates are not actually 20% and must be bugged.

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46 minutes ago, Roland_Snow said:

30 drop chances which is the recommended minimum sample size for statistics.

Where did you get this? I just did a quick google and this is what I found https://www.dummies.com/education/math/statistics/how-to-determine-the-minimum-size-needed-for-a-statistical-sample/

49 minutes ago, Roland_Snow said:

With 5 options each at 20% reward chance we should expect at 40% chance per bounty

Isn't it should be 36%? 1-(1-20%)^2?

I can't say anything for the rest, my school days were long behind me lol

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When taking statistics courses in university I was always told from my prof that 30 was the minimal size for most tests involving random sampling or other sampling methods.

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Also, the two drops are independent so they add instead of multiply like you suggested.
I had to refer to my old textbook a few times to double check the formulas and how to use them. The textbook didn't have any stat tables so I had to find those online.

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Acquired more data for 29.0.4 update.
Using t-test again with 30 sample size and two-tail p-value tables.

For the T1 bounty, assuming the same drop rates as on Earth and Venus bounties, the rare drop is at 8.333% for an expected total scintillate of 2.5 after 30 drop chances.
For the T2 bounty, again assume similarity but now at 20% and expecting 6 drops.

After 30 drops chances on both the T1 and T2 bounties I ended up with 2 scintillate drops on both the T1 and T2 bounties. Both tests will use 29 degrees of freedom.
For T1 bounties that gives a t-score of 1.
For T2 bounties that gives a t-score of 10.

Using the above tables we can see that my T1 bounty results are well within the realm of chance and the drop rate is very likely to be accurate.
As for my T2 bounty data, it is still very anomalous from the expected results since it still falls far off to the right of the p-score table. This would suggest that either the drop rate is still below 20% or my assumption of 20% drop rate for common T2 bounty rewards is incorrect.