**Mastery Loadouts**
Due to issues related to the release of Mastery Loadouts, the "free swap" period will be extended.
The new end date will be May 1st.
Due to issues related to the release of Mastery Loadouts, the "free swap" period will be extended.
The new end date will be May 1st.
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When you do a poll, you are measuring a subset of some whole. If there are a million voters, there is an actual preference for those voters. Some actual number of them would vote one way and the rest would vote the other way (for example). A poll attempts to determine what the whole would do by looking at a representative subset. But how do you know the subset represents the whole? Statistics can calculate the odds that one thousand people picked randomly will match the preferences of the whole. The higher the sample, the more likely the poll matches the whole. In theory, a poll that measured all one million people would be 100% accurate. A poll that measures only one guy is obviously going have a strong chance of being wrong, if the preferences are split in any reasonable way.
When we open crystals to figure out the drop odds, we aren't polling. There is no such thing as all the drops in the world that we are looking at a sample of. Instead, we presume there is a certain chance for each thing to drop, and we are attempting to measure those odds by repeatedly rolling the dice, so to speak. In that case, the margin for error is a quantitative measure of how likely a particular set of odds would actually generate the drops you actually see.
When you do that kind of test, the margin for error is largely based on the number of drops, not the number of pulls. Consider a simple case where we have a crystal that has a 1% chance to drop a 4*, and a 99% chance to drop something else. You open 100 crystals and you get one drop. Your friend opens 100 crystals and gets two. The difference is only one extra drop, but that's the difference between one out of 100 and one out of 50. And what if your friend got his second drop on pull number 98? In that case, had you both tested by opening 97 crystals you both would have only gotten one drop. One drop is just too sensitive to one more or less lucky or unlucky drop.
For more complex math reasons, the margin for error is about 1/SQRT(n) where n is the number of drops. That means in the video above, the margin for error for the measured 4* rate is much higher than the margin for error for the measured 2* rate, because that video sees more 2* champs than 4* champs. The 4* margin for error is actually pretty big, but its still suggestive of being in the general area.
Last thing: margin for error doesn't mean the true value is *definitely* that close. It is just *probably* that close.
Yeah I'm on a couple month hiatus from 4*s in the PHC. Lol
If my calculations are correct, the video shows 12 4* champions, 159 3* champions, and 1829 2* champions. The approximate margin for error is 28.9% for 4*, 7.9% for 3*, and 2.3% for 2* champions. I think if someone believes the margin for error for that video is about 2%, they incorrectly projected the margin for error based on the pulls (2000) rather than the drops (different for each type).
All the percents can get confusing, so it would be better to express the margin for error this way: the 4* result is 12 plus or minus about 3.5, the 3* result is 159 plus or minus 12.6, and the 2* result is 1829 plus or minus 42.8. That means this one test by itself demonstrates that the odds of pulling 4* is most likely to be within 8.5 and 15.5 out of 2000, or 0.43% to 0.78%.
This is a simplified analysis. Because the drops for each rarity are not independent (they have to add up to 100% after all) the true margin for error is not exactly this. But it is close enough for our purposes here.
As I mentioned previously, the crystal opening is not technically a poll. It would best be described as a trial. Colloquially, it doesn't really matter much, but the moment someone tries to apply polling math to the crystal opening, that's when the train will jump the tracks.
The simple difference between a poll and a trial is that your confidence rises the more work you do with both, but polling error can reach zero - if you poll everybody. Trial error can never reach zero, it can only get smaller and smaller, and the smaller it gets, the harder it gets to reduce it even further. Rule of thumb: it takes a hundred times the effort to get one more digit of confidence in your result for a trial. To be confident in the first digit of your 4* result you'd probably have to open about 12,000 PHCs. To be equally confident in your second digit, you'd have to open over a million PHCs. That's crystals, not fragments.
PHC = Class Iso and 3* shards. Remember that. NEVER buy them.
And They say it's going to be easier to get 4 stars
This is good advice. They actually contain pretty good rewards relative to how easy it is to get them when you are well along in the game: far more than most people's dismissal of them would lead you to believe. But they are horrible value if you buy them. I probably open dozens of them a week, and in those quantities even the fragments you get for duping 2* and 3* champions add up quickly. But that 2500 unit 4* crystal offer has more value than the PHC does if you buy it with units, and *that* offer is already horrible.
I don't think you understand how random draws work. Don't feel bad: you are part of the 99% of the human race that has the wrong idea as well.