Draw probability from 120 T4CC shard crystals

Hey guys, since it felt that I only had drawn cosmic T4CC shards in December (desperately waiting for third mystic T4CC for months), I decided to start a little statistics. Now, after 120 draws (I know, not a sufficient, but a respectable sample), I'd like to let you have look, what, I think, does not look like an equipartition. Each draw was done at different day/night times along the last three weeks, sometime 3 crystals at once, sometimes 20. Also, only the drops from a classic T4CC shard crystal have been included in the data set (i.e., no glory crystals etc).

I really do not like the imbalance of this "equal" drop rate supposed to have with those crystals. Any comment from Kabam what could be the issue here. I hope this is not indented. And I hope there is a better way to find a solution here than to close and delete the thread.

Comments

Laserjunge

BTW: I have dated screenshots for all entries of this statistics. Just in case.

John757

The sample size is way to small. Open about 10k and then you’ll have a closer representation of the whole community. Thousands are opened each day. 120 isn’t even a percent of how many are opened in one day

Laserjunge

John757 wrote: »

The sample size is way to small. Open about 10k and then you’ll have a closer representation of the whole community. Thousands are opened each day. 120 isn’t even a percent of how many are opened in one day

Of course, you are right. I will keep going with this measure. However, 120 is not 10, and this is the amount of an average non-alliance player in the game collectable over roughly a month.

Note that, equal probability of a crystal means also that the statistics for each individual needs to be fulfilled. Otherwise, I, as an individual player, cannot rely on the percentage values given for e.g. featured offers, since this chance does not apply to me.

John757

Each time you open a crystal you have an equal chance of getting any of the classes, that’s equal probability. You are not guaranteed to get an equal amount of each class when you open a ton of crystals. That’s where the RNG enters. Also Each crystal is separate and not influenced by the previous or next crystal. If given a sample of 1 million crystals I’m sure it would even out for the most part but I also know that it’s almost impossible for it to even out completely

John757

Take a 20 sided die and roll it 100 times and see how equal it turns out. That’s what a featured crystal would be like. And roll a 6 sided die for your crystal fragments.

danielmath

Laserjunge wrote: »

John757 wrote: »

The sample size is way to small. Open about 10k and then you’ll have a closer representation of the whole community. Thousands are opened each day. 120 isn’t even a percent of how many are opened in one day

Of course, you are right. I will keep going with this measure. However, 120 is not 10, and this is the amount of an average non-alliance player in the game collectable over roughly a month.

Note that, equal probability of a crystal means also that the statistics for each individual needs to be fulfilled. Otherwise, I, as an individual player, cannot rely on the percentage values given for e.g. featured offers, since this chance does not apply to me.

Actually, 120 is such an insignificant sample that it isn't much different from 10. With a tiny sample size, you'll pretty much always get what you consider to be "off" results

DNA3000

Laserjunge wrote: »

Note that, equal probability of a crystal means also that the statistics for each individual needs to be fulfilled. Otherwise, I, as an individual player, cannot rely on the percentage values given for e.g. featured offers, since this chance does not apply to me.

That's not what equal probability means. The game does not guarantee equal rates. It only guarantees equal odds But by definition, a random sample of crystals is unlikely to generate precisely equal drop rates.

I wrote a quick program to perform this same crystal opening experiment using python, whose random number generator is good enough for this sort of test (it satisfies basic partitioning odds). This is the first ten runs of that program:

[21, 9, 21, 25, 21, 23]
[17, 18, 24, 17, 19, 25]
[24, 19, 16, 22, 21, 18]
[23, 15, 20, 18, 21, 23]
[24, 19, 16, 18, 17, 26]
[23, 19, 14, 19, 22, 23]
[29, 23, 12, 22, 19, 15]
[23, 16, 18, 21, 21, 21]
[20, 16, 32, 14, 17, 21]
[23, 16, 22, 15, 21, 23]

*Usually* the numbers are in the vicinity of the statistical expectation which in this case is twenty. But very often they are about plus or minus five, which is also expected with this many pulls. Occasionally, they are significantly far away, the lowest offender being 9 in the first run on the low side and 29 in the seventh run on the high side. This is what you expect with genuinely random drop odds. For reference, this is what I believe your results were based on your reported percentages above: [11,13,24,25,29,18]. It actually looks remarkably close to run 7.

In fact, one test for *non* randomness is when the numbers end up too even. An experiment often performed in statistics classes in college asks the students to write down a hundred (or some number) of either random numbers or random coin flips (H, T) on a sheet of paper. These are then mixed together with one sheet of handwritten numbers that were themselves generated randomly. The random sheet is almost always very easy to spot, because the human generated numbers, which match people's expectations of what random looks like, is always way too homogeneous compared to genuinely randomly generated numbers.

John757

DNA3000 wrote: »

Laserjunge wrote: »

Note that, equal probability of a crystal means also that the statistics for each individual needs to be fulfilled. Otherwise, I, as an individual player, cannot rely on the percentage values given for e.g. featured offers, since this chance does not apply to me.

That's not what equal probability means. The game does not guarantee equal rates. It only guarantees equal odds But by definition, a random sample of crystals is unlikely to generate precisely equal drop rates.

I wrote a quick program to perform this same crystal opening experiment using python, whose random number generator is good enough for this sort of test (it satisfies basic partitioning odds). This is the first ten runs of that program:

[21, 9, 21, 25, 21, 23]
[17, 18, 24, 17, 19, 25]
[24, 19, 16, 22, 21, 18]
[23, 15, 20, 18, 21, 23]
[24, 19, 16, 18, 17, 26]
[23, 19, 14, 19, 22, 23]
[29, 23, 12, 22, 19, 15]
[23, 16, 18, 21, 21, 21]
[20, 16, 32, 14, 17, 21]
[23, 16, 22, 15, 21, 23]

*Usually* the numbers are in the vicinity of the statistical expectation which in this case is twenty. But very often they are about plus or minus five, which is also expected with this many pulls. Occasionally, they are significantly far away, the lowest offender being 9 in the first run on the low side and 29 in the seventh run on the high side. This is what you expect with genuinely random drop odds. For reference, this is what I believe your results were based on your reported percentages above: [11,13,24,25,29,18]. It actually looks remarkably close to run 7.

In fact, one test for *non* randomness is when the numbers end up too even. An experiment often performed in statistics classes in college asks the students to write down a hundred (or some number) of either random numbers or random coin flips (H, T) on a sheet of paper. These are then mixed together with one sheet of handwritten numbers that were themselves generated randomly. The random sheet is almost always very easy to spot, because the human generated numbers, which match people's expectations of what random looks like, is always way too homogeneous compared to genuinely randomly generated numbers.

Amen

DNA3000

danielmath wrote: »

Laserjunge wrote: »

John757 wrote: »

The sample size is way to small. Open about 10k and then you’ll have a closer representation of the whole community. Thousands are opened each day. 120 isn’t even a percent of how many are opened in one day

Of course, you are right. I will keep going with this measure. However, 120 is not 10, and this is the amount of an average non-alliance player in the game collectable over roughly a month.

Note that, equal probability of a crystal means also that the statistics for each individual needs to be fulfilled. Otherwise, I, as an individual player, cannot rely on the percentage values given for e.g. featured offers, since this chance does not apply to me.

Actually, 120 is such an insignificant sample that it isn't much different from 10. With a tiny sample size, you'll pretty much always get what you consider to be "off" results

Well, 120 is quite different from 10 in terms of margin for error, it is just that the margin is still plenty big at 120. It has been a while since I've done histogram analysis but I think the approximate margin for error for this test is about 50%. In other words, you'd expect to see results 20 plus or minus 10 in most of your runs. With 10 samples the error I think would be something more like 200%: in other words one or two, plus or minus three or four. In other words, wildly different.

Histograms are a little more complex, but for single choice selections (in other words, if we focused on how many pulls were one chosen class, like Cosmic) the margin for error converges much slower than people intuitively think: its about one over square root of the number of trials. In other words, the margin for error for any one class in 120 pulls is about eleven. Put another way, any result from 9 to 31 would be considered a bullseye.

Laserjunge

Thanks for correcting my understanding in statistics. Very insightful.

@DNA3000 thanks for your experiment. So I was just unlucky to end up with one of the extreme cases, with value quite at the error margin. I understand. I will continue with this measure and report back when I have a significantly higher sample.

Cheers.

gohard123

Wow a constructive forum discussion. Never thought I’d see one