So here’s the same visual representation as before: this time, it’s the chances of a 25% event hitting 62 times out of 200 trials.
You’re riiiiiight on the edge of that second sigma - there’s just a 3.2% chance of seeing 62+ hits out of 200 trials - but you’re still there. Going by ±2σ says that you “should probably” see somewhere between 38 and 63 hits, and sure enough, you are.
I’d file that under “annoying improbable but not eyebrow-raising” with the amount of data you currently have.
No, you’re not missing anything, don’t worry about it.
It’s just that I’m probably looking way too much into things.
… And I’m afraid threads like these might bring the same scenario as the loop combo-breaker that brought some uproar just recently 
… Because I believe that even if numbers are somehow (anyhow) different … It’s by such an unnoticeable amount that giving it any priority at all wouldn’t help the state of the game (personal opinion).
One way or another - I’ll probably support you, Sir, with some more data along the way.
Keep up the good work!
Thanks for this. I’ll gather more data in the next days and I hope we’ll see some positive changes.
I believe you’re misunderstanding what people are saying with “reducing pattern”. It’s not about the order that your numbers are in at all, and it should more accurately be called “regression to the mean”.
Basically, it says that your first few samples may have relatively extreme results - but then as you add more samples, you get a little closer to the expected mean. Adding more and more samples gets you even closer to the expected mean. It’s not about the literal “pattern” of your data; it’s about getting more accurate results as the amount of data increases.
Here’s a simple example: if you flip a coin 5 times, you might get 4 heads. Crazy! 80% heads! But then flip 5 more times and get, say, 3 more heads, and now you’re down to 70%. Flip a million times and you’ll almost certainly get exactly 50% heads.
I understand what you mean and I totally agree with the way you named the “phenomenon”, but this was not presented like this at first, and unfortunately, that first affirmation was re-used after, creating confusion. At first, it was this:
And my reflexion against this is that the numbers are going down because the first samples were extreme, not because it’s going to tend to 40%. Maybe that will, but that’s not the reason. You are very true when you say that more samples mean a result that is closer to what it should be, but that is definitely not the meaning of the message I quoted. As I explained just above, if the samples were in a different order, that 40% thing wouldn’t be true anymore, thus I don’t think this argument can be used. I even posted a picture and I think the order of the samples do affect this precise affirmation.
But for the rest, I totally agree with you, that is exactly the way I think and this is exactly why I’m gathering more and more samples.
That definitely is the meaning of the message you quoted. I apologize for not being perfectly clear and assuming you had at least some knowledge of how statistics work…
<pedantic>
You make some valid points, but one thing I think that requires some clarification is that past results do not at all influence future expected outcomes in independent trials (such as a coin flip); to assume otherwise is a gambler’s fallacy. In your case, I assume you meant to say, “Flip a million more times and the outcome with the highest probability is exactly 50% heads,” but even that’s not entirely true; “Flip a million more times and the outcome with the highest probability is 500,004 heads and 500,001 tails” is technically the case, since 5 events have already occurred.
Similarly, in the OP’s case, the expected results assuming the card’s stated probability for the next, say, 1000 Devour attempts are 400 successes, not lessened by the Devours already observed.
</pedantic>
Very interesting.
Correct me if I’m wrong, I’m trying to translate what you explained and what I read from Wikipedia, the formulas are a bit too complicated for me.
So you’re saying that no matter the previous results, the expected outcome should always be the same, is that right?
If you flip a coin and get a large number of heads in a row, the probability of getting head or tails on the next flip is always the same? Getting more heads does not mean that the odds of getting tails increase?
If you flip a coin 150 times and get 100 times head and 50 times tails, you should not expect the next 150 flips to give you 50 times head and 100 times tails, but 75/75?
Lastly, if my devour rate at a given point is below or above the expected value, I should not expect the next devours to “compensate” this. By doing so, I would fall under the gambler’s fallacy?
Thanks in advance for pointing any mistakes in my understanding of this. That was very instructive anyway.
All true but I wasn’t talking about specific future results; I was just explaining how regression to the mean tamps down the aggregate values as the size of the data set increases, and that’s the so-called “reducing pattern” that was brought up previously.
I always appreciate the value of pedantry, though. 
That’s exactly right. People say to themselves, “Well, I’ve failed a hundred times in a row, the next one has to succeed!” But that’s sadly not the case. Statistics are brutal sometimes, and the truth of the matter is that you are never “owed” a win. The chances never improve based on observed history.
Exception: when you are unsure of the chance and trying to determine it based off of observations. 
Yes, that’s true. I place more value in the stated percentages than I probably should. Would be good to see what confidence values this investigation yields.
Just wanted to point out to anyone who cares i have fought 11 battles today against FGE teams, 9 have had 2 kerbys and the other 2 had 1. Kerby cast 7 times total over the 11 battles. Devour procd 0 times. No troops are impervious or indigestible. None were killed by inital damage.
Very small sample size so no conclusions can be drawn from this info