tag:blogger.com,1999:blog-6208362756665014361.post8759481090726523032..comments2023-10-20T07:16:10.544-07:00Comments on Angels of Death: MathHammer Part 2. Flakk Missilescpykehttp://www.blogger.com/profile/15447360797850807908noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6208362756665014361.post-20390329937936026122012-11-13T10:34:10.946-08:002012-11-13T10:34:10.946-08:00I have already played around with binomial distrib...I have already played around with binomial distributions in excel a bit. Thanks for the idea. We actually talked about them in class just two weeks before so it's cool to be able to apply it. I suppose you could approximate a normal distribution with this, but just graphing out the binomial distribution really makes that unnecessary since you can easily see the probability of each number of hits. I'll probably update this post when I have some time. And thanks again for commenting!cpykehttps://www.blogger.com/profile/15447360797850807908noreply@blogger.comtag:blogger.com,1999:blog-6208362756665014361.post-67765776528101763942012-11-13T08:24:01.279-08:002012-11-13T08:24:01.279-08:00Sorry I didn't get back to you sooner. Busy bu...Sorry I didn't get back to you sooner. Busy busy busy!<br />By using a the binomial you get your answer in terms of probability for number of successes a specific condition. This can be made as complex as you want. For discussion purposes I'll make a simple one. Say you have 9 bolter shots on your marines and you define a success as just hitting (to keep it simple). A success then has a 2/3 chance of happening for each shot. You already know the average is 9*2/3= 6 hits. Using the binomial distribution will give you a break down of the probability that each number of hits has. In our example:<br />0 hits: 0.0%<br />1 hit: 0.1%<br />2 hits: 0.7%<br />3 hits: 3.4%<br />4 hits: 10.2%<br />5 hits: 20.5%<br />6 hits: 27.3%<br />7 hits: 23.4%<br />8 hits: 11.7%<br />9 hits: 2.6%<br />The binomial distribution is not a gaussian or "normal" distribution. As such its my understanding that standard deviation isn't strictly applicable. But the idea of such a thing could be approximated for the binomial distribution. In essence its just a measure of the "width" of the bump you see if you were to plot probability vs # of hits. For a normal distribution, one standard deviation (sigma) away from the mean is ~34% above and below that mean. You'll notice our bump is asymmetric showing why this is an approximation at best. knowing the average and the above probabilities you can give a standard deviation like quantity by simply finding the range of hits that +/- 34% lands in. Another option would to be just to quote the average and perhaps the probability of a certain range to give some idea of the width. For example the above would average 6 hits with about 70% chance to get 5 to 7 hits.<br /><br />Happy mathing!Natenoreply@blogger.comtag:blogger.com,1999:blog-6208362756665014361.post-39486173470193424232012-11-09T11:59:23.766-08:002012-11-09T11:59:23.766-08:00You are absolutely right about the whole percent v...You are absolutely right about the whole percent vs. probability. I have actually been changing them over as I remember (that's why the percentages are mixed in with the probabilities). I am actually in a statistics class right now (Biostatistics). I had started making this before the class started so i'm adding new things as we learn them and fixing errors as I see them, so it's a work in progress for sure. And I had no idea excel had a binomial distribution function. I will look into adding that. And a quick question if you don't mind. I was trying to think of a good way to add standard deviation or confidence intervals but I can't think of any way of doing it while still keeping the worksheet simple. Do you have any ideas? And thanks for the input!cpykehttps://www.blogger.com/profile/15447360797850807908noreply@blogger.comtag:blogger.com,1999:blog-6208362756665014361.post-31246979385632504242012-11-09T01:16:13.680-08:002012-11-09T01:16:13.680-08:00Every once and awhile I catch the bug to really ma...Every once and awhile I catch the bug to really math out my warhammer stuff, so it's always pleasing to see others doing it as well. I would, however, like to offer a friendly critique. There is a subtle but important difference between what your calculating and a "probability." What you've actually calculated is an average number of successes (putting percents on this is misleading). You've probably already noticed this in your hades cannon calculation listed as 100% glance. We all know you don't have a 100% chance to glance. What you've calculated is, on average, you will have 1.00 glances; maybe more, maybe less. Although still a useful quantity, better to see it for what it is. If you want to take your mathhammering to the next level, investigate excel's binomial distribution function. Although more complex, it will allow you to calculate actual probabilities of different outcomes which, in my opinion, is a much better comparison.<br />I'll use the heldrake as a quick example. Each shot has 1/4 chance to glance (4+ to hit, 4+ to wound). So the chance for ALL 4 shots to glance is tiny: (1/4)^4 = 0.3%. The chance ALL of them do NOT clance is (3/4)^4 = 32%. It gets much more complex to calculate by hand the other outcomes but thats whats so great about spread sheets; it's automatic!Natenoreply@blogger.com