In case there is confusion:
The idea is that through many observations it is possible to ascertain/confirm the odds with great confidence based on evidence rather than simply assuming we know.
This is NOT some misguided attempt to change the odds of Danzaburo’s specials__
So…after another 100 simultaneous shots of the two Danza’s specials, 200 simultaneous shots or 400 individual shots in total.
Cumulative (200)
Danza - L
Danza - R
Total
Sword
58
52
110
28%
Bottle
71
86
157
39%
Freeze
71
62
133
33%
Total
200
200
400
#
%
Theory
Sword/Sword
11
6%
11%
Sword/Bottle
42
21%
22%
Sword/Freeze
46
23%
22%
Bottle/Bottle
31
16%
11%
Bottle/Freeze
53
27%
22%
Freeze/Freeze
17
9%
11%
Total
200
100%
Theoretical probabilities of the combinations ASSUMES 1/3 chance for each special. Yes, I too assume the base case is 1/3, this is just a bit of data to be more confident.
200 trials is a good start, but hardly conclusive. Edit - as you showed with the second 200 trials.
No of course not, but that doesn’t mean the underlying math is skewed.
Probability implies that the outcome is inherently uncertain, but this pervasive myth that SG is somehow sabotaging characters toward some nefarious plot is getting a little old.
This really isn’t an accurate position. It is absolutely possible to estimate a distribution by drawing samples. There is plenty of math focused on estimating confidence intervals given those samples.
The distribution in question is known as a multinomial distribution. The maximum likelihood estimator for the probabilities is just:
p_est = (# times x occurs)/(total samples)
The 95% confidence intervals on the estimated probabilities is approximately:
So for 200 samples, the estimated freeze probability is:
39% +/- 6.8%. with 95% confidence
That means that a 33% probability of freeze is still within the confidence interval, and we shouldn’t draw the conclusion that a freeze is more likely than that just yet. If we want to drive the confidence interval down to +/- 1%, then we’d need about 8500 samples. So it’s probably not practical to get a very precise estimate of the probability of freeze. But it absolutely is possible.
I’m not sure I understand the point you are arguing. In TC20, you have a chance to get a 3*, 4*, or 5* hero. I hope you don’t think that the odds of that are 33/33/33, since they are about 75/20/5 from what has been recorded. That’s what some of the other comments in this thread are trying to ascertain; is Danza’s special 33/33/33, or maybe 40/40/20, or maybe 30/30/40?
Just because there are three outcomes does not necessarily mean that the probability of occurrence of each of those outcomes are equal. Yes, with no information, that is the null hypothesis. However, this can be tested by collecting samples.
In the example of a fair ‘3-sided die’, you would expect 33/33/33. However, if the die is weighted, you can get different results. If you collect a large enough sample size of rolls, you can say with a degree of certainty whether or not the die is ‘fair’ and if it favors one or two sides over the other(s).
By the way, it is interesting to see images of 3-sided dice (I’ve not seen one before).
No. The TL;DR is that you don’t appear to understand the math of probability and statistics, so you probably shouldn’t be telling people what is and isn’t possible to do with analysis.
See this is the problem with defending math in general. I have to admit that yes, it IS possible for someone to roll all 3’s for the rest of eternity. What statistics tell us, however, is that the possibility of that happening is vanishingly small.
On balance, OVER TIME AND MANY USES, I can guarantee you that the trend will work out to be 33% 1’s, 33% 2’s, and 33% 3’s.
Human brains are very good at looking for patterns, and if you hit a run of all 3’s, every one of us will be tempted to say that the fix is in.
The correct statistical test is a bit stronger than just testing that the. Freeze probability = 33.333%; it’s that the three probabilities are equal. It is too late on a Friday evening for me to dredge our the test for that, but I think it’s safe to say that the null,hypothesis of equal,odds is well within sampling error.
The 95% confidence bounds I’m quoting is an approximation of a p=0.05 test. If the value is within those bounds, you can’t reject the null hypothesis. If it’s outside, you’d reject the null hypothesis with 95% confidence.
I think we’ve reached a whole other level of pedantic.
Overcomplicating a very simple issue.
The question really comes down to: Who can teach the best math lesson vs. who can just apply real-world common sense.
Before i get off track, There are no published odds for Danza or Rumple. You are told you get “one of these things” and there are “X” number of things.
It is very very clear that the obvious assumption is 1:3.
Why is this even a thing? The title should be “Is this discussion worth it?”
It turns out the human brain sucks at estimating probabilities. Common sense is a bad tool for figuring out things like this. 33% is a good guess, but a guess is the start of getting to an answer, not the final answer itself.
So, for those who actually care how often Danza fires his different abilities, the discussion is relevant.
Fortunately for you, reading threads or individual posts isn’t mandatory. So if the subject or content doesn’t interest you, perhaps just skipping them is your best bet.
There is no math, @Garanwyn. You can type your statistical analyses until you feel very proud of yourself, but the point is that the argument is moot.
Odds are what they will be.
If you are looking to analyze sample sizes, that’s on you. You clearly enjoy talking about math, and unlike @PeachyKeen, I did not pass graduate level statistics to stand toe-to-toe with you. However anyone here can observe how pointless it is to waste time on a larger sample size on a 4* hero to determine how often it freezes when you have one of three options.
Estimating probabilities and confidence intervals from data is the essence of experimental science. It is done tens of thousands of times a day, every day of the year, in every part of the world. Every university in the world with a math department teaches courses on how to do it.
So, it’s hard to express how ignorant it sounds to repeatedly say that estimating probabilities from data is impossible, and that trying to do so is a waste of time, or that there’s “no math.”
People who want to understand what’s really going on with Danzaburo started presenting data and discussing it, then @PeachyKeen decided to come in, repeatedly jump all over that, and tell those people (incorrectly) that they were wasting their time and trying to do something impossible.
If you and @PeachyKeen aren’t interested in this, kindly move along to a different thread and let those of us who do care discuss the data and figure out what we can learn from it. Or stay in this thread and just skip the data and math posts. But whatever you two do, please stop trying to argue that the scientific method doesn’t work, and that we should ignore it in favor of “common sense.”
If what you (and/or Peachy) are saying is that understanding the math will not change how the average player uses Danzaburo, then you’re probably right. The beauty of applied science (i.e. engineering - in this case, software engineering) is that the end consumer doesn’t have to understand how it works to use it.
However, willfully ignoring the fact that, yes, there actually IS math is really disturbing. Making it worse by arguing to stifle people’s curiosity (i.e. “…pointless it is to waste time on…”) is really appalling.
I lvled one but just to have yellow depth for war my other yellow are Rana Vivica 2 Drakes 2 gjackel Wu and a hu Tao that I never use other then Tao they are maxed when I have the mats to max another 5* I think I’ll go Joon over a 3rd Drake, but this little guy was cheap to lvl and makes a good throw in against a purple tank on war
I use him on occasion. I have maxed yellow 5’s I pair him with so his freeze doesn’t really hurt me. He hits pretty decent and I like the boost stats. Not a go to hero for me but on occasion I take him out. I used him through Avalon and he did well. I’m playing around with Mitsuko and Inari now so he’ll be on the bench for a little bit
I’m with Jalia and Garanwyn on this. It’s worth looking into the statistical distribution of danzo’s results as I’ve always wondered if it’s not evenly distributed 33%. Admittedly that could just be confirmation bias on my part. It could still be around there or higher or lower etc. For you math folks, have you come up with a data sample size that’s needed to figure that out with some degree of confidence?
And as for “common sense” in “math,” hahaha, that’s a good one. With that I’m 95% certain some of the above statements are spoken in jest aka trolling.
