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Hi Guys,

I've been working with standard deviation a lot recently, with the help of a few friends of mine, I've figured out a program which allows one to do wounds standard deviation very easily.

Unfortunately for the time being, it only works for wounds, not hull points and doesn't work at all for rends, or re-roll of one equivalents - I can tell you right now, doing macroprogramming for rends is HELL, also it doesn't really help here because this looks at fianl wound average range.

Don't touch anything that's not blue, if you want to represent a save that doesn't exist, type in one - I know that seems counter intuitive, but it tells the system that 100% of wounds bypass the save roll as opposed to 0%. True/false buttons MUST be true/false, nothing else. Again, you risk ruining your tool if you try to do anything else. Any bugs, let me know and I'll fix them if I have time.

Feel free to edit/alter the code as I present it to you as freeware, but I would appreciate it if you acknowledged it as my work if you intend to use it outside personal use.

Great work, I've been reading and commenting in a few threads regarding standard deviation recently.

HOWEVER, there is an amazing calculator than can tally tons and tons. Shooting vs infantry, shooting vs vehicles, assaulting, assaulting vs vehicles. It even comes with a guide. And it is very user-friendly, the guide isn't needed.

http://www.heresy-online.net/combatcalculator/shooting.php

Hmm... that one doesn't do preferred enemy :(

Pask punisher is not that great at killing Riptides (not counting possible sponson weapons) :(

 Ryan_A wrote:
Great work, I've been reading and commenting in a few threads regarding standard deviation recently.

HOWEVER, there is an amazing calculator than can tally tons and tons. Shooting vs infantry, shooting vs vehicles, assaulting, assaulting vs vehicles. It even comes with a guide. And it is very user-friendly, the guide isn't needed.

http://www.heresy-online.net/combatcalculator/shooting.php

uh,

thanks for hijacking my thread? I don't know how to really respond to this.

This also doesn't really do anything with standard dev so far as I can see.

I don't understand why anyone wants the standard deviation
Forgive me if this is a little ranty but I really enjoy mathhammer.

Standard deviations really aren't helpful in any way with these types of distributions. Its much more informative to me to just calculate the probability distribution. Why bother trying to interpret a descriptor of the distribution when you can just look at the distribution itself? I understand wanting to have some handle on the width of the distribution but the types of binomials we use, the std dev is not going to do that.

So I expect 0.62 +/- 0.77. Okay, what does that mean? Firstly its alarming that you start putting down negative values for number of successes. Despite being less that one sigma away, those regions are inaccessible. Secondly, that 0.77 has no immediate meaning to a player who wants to know what to expect out of his shots.

Really the most useful gauge of the width is a confidence interval. That is to say something like, 90% of the time I will get between 2 and 4 wounds. For a normal distribution one can translate easily between std dev and an interval. For very non-normal binomials, such as we have, this is not trivial to do.

 Scipio Africanus wrote:

 Ryan_A wrote:
Great work, I've been reading and commenting in a few threads regarding standard deviation recently.

HOWEVER, there is an amazing calculator than can tally tons and tons. Shooting vs infantry, shooting vs vehicles, assaulting, assaulting vs vehicles. It even comes with a guide. And it is very user-friendly, the guide isn't needed.

http://www.heresy-online.net/combatcalculator/shooting.php

uh,

thanks for hijacking my thread? I don't know how to really respond to this.

This also doesn't really do anything with standard dev so far as I can see.

How am I hijacking your thread? If somebody is looking for a good standard deviation calculator I'd rather give them more information about alternatives to calculate it.

This website is a forum, you dont post something and you own the right to the subject you post about.

If somebody is reading your thread and wants a "mathhammer made easy" I think the heresy one is a much better alternative. Sorry to burst your bubble, but I'd rather give people more options with different features rather than claiming that your work is the only option.

edited because I can't spell worth crap


Automatically Appended Next Post:
and it does do standard deviation, here is an example of a standard outcome of a rapid for space marine boltgun vs guard:

Wounds:Chance
0 : 2.94%
1 : 14.113%
2 : 28.225%
3 : 30.107%
4 : 18.064%
5 : 5.781%
6 : 0.771%

pretty cool, thanks man.

I made this one a couple years ago. I present it for posterity, so long as the topic is brought up:

Mine works a bit differently, and doesn't consider armor saves, but it's useful for figuring expectable numbers of wounds for large numbers of guardsmen shots.

Also graphs because pictures are shiny.

 Ryan_A wrote:


How am I hijacking your thread? If somebody is looking for a good standard deviation calculator I'd rather give them more information about alternatives to calculate it.

To do so you could've made your own thread. IT would be less obtrusive, I feel.

This website is a forum, you dont post something and you own the right to the subject you post about.

what?

If somebody is reading your thread and wants a "mathhammer made easy" I think the heresy one is a much better alternative. Sorry to burst your bubble, but I'd rather give people more options with different features rather than claiming that your work is the only option.

Yours does something different to mine.

While you're right that it does do SD, It took me a while to find it. In an unbiased critique I didn't find it nearly as easy to use, but that might just be the direct result of me building my own version and having had the tools in front of me the whole time.

This one you present gives you a whole number's chance of turning up. Mine gives you unrounded and unbound standard deviations. This means it is limited to values between 0 and the maximum number you fired, whereas mine doesn't cater to semi-useless information (i.e;, killing 10 guardsmen with 10 boltgun rounds, or a perfect shooting) and presents you information in deviations.

Mine will tell you the pessimistic average of you getting 0sig or better, or -1sig or better, with there being a limitation when you use minute odds in that it can pass under 0 (which is technically not possible)

I can see use in the HO tool, but it also has drawbacks. It can't be used offline during a game, for example. (Or rather it can, but you'd need to know what you were doing to use it there which defeats the purpose of it being simpler.)
You also can't make a graph using that technology, and I find that's a major drawback when I prefer a visual interpretation.

JubbJubbz wrote:
I don't understand why anyone wants the standard deviation

You need to recall exactly what the mean and standard deviation represent. The mean if you can recall is the tendency for results to centralise and the standard deviation is just how spread out around this value your results are. That is why the standard deviation is so important, because with mathhammer we are not using the binomial distribution, we are just taking the average expected outcome, but this does not tell us much if we don't understand just how spreadout our results will be, for argument's sake you have two units that fill the same role in the same FOC slot and both do similar average results to a variety of targets, which do you pick? You pick the one with the lowest standard deviation because its results will sit nearer to the mean, which means its performance will be consistent over multiple games, meaning in a pinch, you have a better idea of what will happen by average it in your head.

 Krellnus wrote:

JubbJubbz wrote:
I don't understand why anyone wants the standard deviation

You need to recall exactly what the mean and standard deviation represent. The mean if you can recall is the tendency for results to centralise and the standard deviation is just how spread out around this value your results are. That is why the standard deviation is so important, because with mathhammer we are not using the binomial distribution, we are just taking the average expected outcome, but this does not tell us much if we don't understand just how spreadout our results will be, for argument's sake you have two units that fill the same role in the same FOC slot and both do similar average results to a variety of targets, which do you pick? You pick the one with the lowest standard deviation because its results will sit nearer to the mean, which means its performance will be consistent over multiple games, meaning in a pinch, you have a better idea of what will happen by average it in your head.

Yes, I understand you want a measure of consistency. My point is that it is no more work to just actually calculate the probability distribution than to try to interpret whatever -1 sigma = -0.10 means. Its not useful at all. If you are going to calculate something just calculate a probability, its much more useful.

JubbJubbz wrote:

 Krellnus wrote:

JubbJubbz wrote:
I don't understand why anyone wants the standard deviation

You need to recall exactly what the mean and standard deviation represent. The mean if you can recall is the tendency for results to centralise and the standard deviation is just how spread out around this value your results are. That is why the standard deviation is so important, because with mathhammer we are not using the binomial distribution, we are just taking the average expected outcome, but this does not tell us much if we don't understand just how spreadout our results will be, for argument's sake you have two units that fill the same role in the same FOC slot and both do similar average results to a variety of targets, which do you pick? You pick the one with the lowest standard deviation because its results will sit nearer to the mean, which means its performance will be consistent over multiple games, meaning in a pinch, you have a better idea of what will happen by average it in your head.

Yes, I understand you want a measure of consistency. My point is that it is no more work to just actually calculate the probability distribution than to try to interpret whatever -1 sigma = -0.10 means. Its not useful at all. If you are going to calculate something just calculate a probability, its much more useful.

-1sig = ~80% chance of this result or better.

It's not overly complicated.

edit: Typo

 Scipio Africanus wrote:


-1sig = ~80% chance of this result or better.

It's not overly complicated.

edit: Typo

This is the point I'm trying to drive home. That figure is totally nonsensical. You're suggesting that 80% or more of the time I get negative one tenth successes? Its non-trivial to convert a std dev into a probability for non-normal distributions. It seems especially silly when its actually no harder to just calculate the accurate probability value instead.

JubbJubbz wrote:

 Scipio Africanus wrote:


-1sig = ~80% chance of this result or better.

It's not overly complicated.

edit: Typo

This is the point I'm trying to drive home. That figure is totally nonsensical. You're suggesting that 80% or more of the time I get negative one tenth successes? Its non-trivial to convert a std dev into a probability for non-normal distributions. It seems especially silly when its actually no harder to just calculate the accurate probability value instead.

What's nonsensicle about it?

Or are you referring to the fact that my math can potentially pull you into negatives? That's hard to interpret correctly, but it only usually happens with extremely low probability or very small numbers, either of which the average is probably more realistic anyway.

JubbJubbz wrote:

Yes, I understand you want a measure of consistency. My point is that it is no more work to just actually calculate the probability distribution than to try to interpret whatever -1 sigma = -0.10 means. Its not useful at all. If you are going to calculate something just calculate a probability, its much more useful.

Allow me to be a bit more succinct, If you want to determine the effectiveness of a unit, there are two ways of determining its effectiveness, working it out binomially or taking an estimate using the average, however taking the an estimate using the average requires the standard deviation to be particularly meaningful. Since it is unlikely that you can remember either method in its entirety you would need some refernce on hand, even if it just for the most common values, thus it makes sense to mqke this reference as short as possible which is where the standard deviation can be useful because it may be easier to have some values and a key with which you can use with the average which is calculated on the fly, as opposed to the binomial distribution results for all outcomes of common scenarios (which would be a lot) not to say of course, that the mean approximation is better, it isnt and for 30 attempts or mord starts to go way off, but unless you have the time to sit down and compile results, the average approximation is far more practical.

@Scipio If you are getting negative %s then there is some flaw in you method, because an outcome, by its definition cannot have a chance <0

Scipio Africanus wrote:
What's nonsensicle about it?

Or are you referring to the fact that my math can potentially pull you into negatives? That's hard to interpret correctly, but it only usually happens with extremely low probability or very small numbers, either of which the average is probably more realistic anyway.

By definition the number of wounds you expect cannot be negative. Neither can any probabilities. You're saying the value at -1 sigma will happen 80% of the time, but that value is negative. You're suggesting that most of the time I get a negative number of successes. That is what is nonsensical. The reason it is happening is because its not so easy to translate sigma's into probabilities for binomials.

Krellnus wrote:Allow me to be a bit more succinct, If you want to determine the effectiveness of a unit, there are two ways of determining its effectiveness, working it out binomially or taking an estimate using the average, however taking the an estimate using the average requires the standard deviation to be particularly meaningful.

what is really making your average more meaningful is a measure of the spread. Standard deviation is a measure of this spread but is a poor one at best for binomials, especially when standard deviation is the same order as the mean. The actual distribution is very asymmetrical about the mean but by just looking at +/- N sigma you are treating it as if it were totally symmetric. Instead of using std. dev. use a different measure of the width, like say, an interval.

Since it is unlikely that you can remember either method in its entirety you would need some refernce on hand, even if it just for the most common values, thus it makes sense to mqke this reference as short as possible which is where the standard deviation can be useful because it may be easier to have some values and a key with which you can use with the average which is calculated on the fly, as opposed to the binomial distribution results for all outcomes of common scenarios (which would be a lot) not to say of course, that the mean approximation is better, it isnt and for 30 attempts or mord starts to go way off, but unless you have the time to sit down and compile results, the average approximation is far more practical.

You are already at the point of making spreadsheets to do the calculations so there its no harder to just actually calculate the probability in an interval about the mean. Additionally its no harder to remember a few key intervals rather than a few key standard deviations. Approximations are great as long as they still faithfully represent the truth albeit at a lesser degree of accuracy. However, when your approximation stops being relatable to reality (such as negative number of wounds), its time to leave it behind.

JubbJubbz wrote:

Krellnus wrote:Allow me to be a bit more succinct, If you want to determine the effectiveness of a unit, there are two ways of determining its effectiveness, working it out binomially or taking an estimate using the average, however taking the an estimate using the average requires the standard deviation to be particularly meaningful.

what is really making your average more meaningful is a measure of the spread. Standard deviation is a measure of this spread but is a poor one at best for binomials, especially when standard deviation is the same order as the mean. The actual distribution is very asymmetrical about the mean but by just looking at +/- N sigma you are treating it as if it were totally symmetric. Instead of using std. dev. use a different measure of the width, like say, an interval.

Nor did I mean to imply as such, as I said its an approximation and one that breaks down easily at that.

JubbJubbz wrote:

Since it is unlikely that you can remember either method in its entirety you would need some refernce on hand, even if it just for the most common values, thus it makes sense to mqke this reference as short as possible which is where the standard deviation can be useful because it may be easier to have some values and a key with which you can use with the average which is calculated on the fly, as opposed to the binomial distribution results for all outcomes of common scenarios (which would be a lot) not to say of course, that the mean approximation is better, it isnt and for 30 attempts or mord starts to go way off, but unless you have the time to sit down and compile results, the average approximation is far more practical.

You are already at the point of making spreadsheets to do the calculations so there its no harder to just actually calculate the probability in an interval about the mean. Additionally its no harder to remember a few key intervals rather than a few key standard deviations. Approximations are great as long as they still faithfully represent the truth albeit at a lesser degree of accuracy. However, when your approximation stops being relatable to reality (such as negative number of wounds), its time to leave it behind.

I guess you are right when you word it like that and I do agree that an interval would be the best bet, but I personally find them boring to calculate myself, even if they do lead to some cool insights.

Jubbz, you simply cut it off at 0. If sigma -1 is lower than 0, then you ignore it and only look at sig 0+ You simply assaume sigma -1/2 and 3 is included in the probability, since they cannot occur.

It's not nonsensicle. You seem to be blocking for the sake of blocking.

You do not seem to understand, when working with probabilities, you cannot have a negative probability, its like saying blue is a number, the two concepts are mutually exclusive a number can either be a probability or it can lie outside the range 0 to 1, but it cannot be both, there is some flaw in you arithmetic to give you such a result.

is the value in the "-3" column (for example) the value -3 σ from the mean? That makes sense, but treating them as probabilities does not make sense, as others have said.

 Dheneb wrote:
is the value in the "-3" column (for example) the value -3 σ from the mean? That makes sense, but treating them as probabilities does not make sense, as others have said.

I haven't treated them as probabilities, have I?

Or do you mean "an 80% chance of this result or better", that kind of thing?