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Uptopdownunder wrote:
An average however is a pretty poor reflection on the experiment.

If I have a stone that weighs 1kg and a Meteorite that weighs 1 000 000 kg the average weight of the two objects is 500 000kg.

It's a pretty meaningless number as in small sets the average is not any sort of representation of any particular member of the sample.

Die rolling and 40k is all about probabilities not averages.

However you can convert probability results into a average using standard deviation and ploting it as a bell curve. which can be tested further. both rolling methods can be tested for averages via standard deviation by use of a T test.

Are you suggesting that rather than roll 10D3 we should just roll one and then plot that result on a bell curve to work out how many attacks the Screamers get?

The 10D3 roll is a big difference to the 1D3 x 10. The difference is that it is much less succeptable to bad dice (and good dice.)

Lets just look at it with a smaller sample say 3D3.

If you roll 1D3 x 3 you have 3 equally occuring results. 3, 6 and 9. Each Occur 1/3rd of the time.

If you have 3 D3 you have 7 different results. with the following probabilities

3 = 1/27
4 = 1/9
5 = 2/9
6 = 7/27
7 = 2/9
8 = 1/9
9 = 1/27

So what you end up with is 70% (19/27) of the time you have between 5 and 7 Attacks. So it ends up much more reliable . Essentially your results form a bell curve. So you end up with the top and bottom far less often.

It is a significant improvement to the unit.

Uptopdownunder wrote:
Are you suggesting that rather than roll 10D3 we should just roll one and then plot that result on a bell curve to work out how many attacks the Screamers get?

Absolutly not, your comment eludes to probabilities are not averages. Im saying I can record and test the results as averages.

In my example from a previous post (see below) to this thread. Tally the roll results 10 1's = 10 and so on. If I do this 20 times I can total them and get an average. Once I have an Average, or Mean, I can get a Standard Deviation. Now I can test both methods against each other. I would get something like this (see first and second pic)

http://www.socialresearchmethods.net/kb/stat_t.php

from there I can see which method grants me a better real world model with one roll....which I think most people would agree, even without doing this experiment is the 10D3.

in my example below I use 500-1000 and 100-200. By doing it that many times I ensure that with (92-97% reliability) that both resultant averages will be so close to 20 that we cant' tell which is which, but who whats to sit down and roll that many dice, better to test each resualt on less rolls.

 Rune Stonegrinder wrote:

If I roll 1D3 and apply that result 10 times, and do it enough (typically 500-1000 trials, margin of error = 1/sqroot x, x being the number of trials) I will get an arverage total of aprox. 20 (plus or minus a variable amount) depending on number of trials. The more trials the tighter the variable amount. 1/3 of the results rolled will be a one.

If I roll 10D3 enough times I should come up with 20 (plus or minus a variable amount) faster typically 100-200 trials (cant remember which error test allows for this, it might be a power test) again the more trials the tighter the variable amount. this is where the probablity of 512/59049 or 1/115 apx comes into play you would potentially need to roll 115 times to get 10 ones in one roll.

Outliers: results of 10 and 30 are rare in example number 2, however are common in example 1. This is why example one is never used by most games and why more trials are required to get a average.

LMAO sorry guys never meant my "harmless" comment to turn into a war.



So no, while not the same on a small scale, my statement does in fact hold true that all rolling for each screamer does is get you closer to the median of the total.


Rolling together (which is not the RAW way to do it), gives you a higher chance of getting the minimum or maximum result.

Seriously, the question is answered in the first few posts but the thread goes to a second page arguing about math.

Rules state you roll 1D3 for each screamer that passed over the unit.

Indeed, sorry for starting it all but I find these things quite entertaining and it was nice to see the back and forth.
I'm going to put this in the 'statistics are stupid' category and move on.

Separately. If you do them all as one and multiply you can only get 3 outcomes (10,20 and 30).

Rolling close to 20 is what you'd expect from the average result, but rolling 10 and 30 are rare circumstances since it'd be the equivalent of making 10 feel no pains, or, if you rolled a 1 or a 2 and multiplied, you're taking the equivalent of rolling for 10 3+ armor saves and failing all of them 33% of the time...

I don't get how people started arguing about math over this.