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Math hammer is a tool for deciding what's possible. I think people expect to much, or use it wrong. I don't expect grots to kill terminators, but they are an important tool, and do what they are supposed to, same as math hammer.

Dracos wrote:Some people even make the horrific error of saying that if you have a 1/3 chance of doing something, you need to do it 3 times for it to happen. That is not true at all. It might happen in one attempt, or it might not happen after 3 attempts.

This is true, but talking in this way pairs nicely with standard deviation.

If you have something that happens a third of the time, and you roll one die for it, the most expected result is that it will not happen. If you roll three times, the most expected result is that it will happen once. It's this expectation that allows you to judge if something is good at doing something in a vacuum.

For example, a single BS3 autocannon destroys a piece of AV12 on a .05. What does that number actually mean? Well, one way of judging it is to think that you need 20 rounds of shooting for the destruction of the vehicle to be the most expected result. Yes, it doesn't mean 20 shots = destroyed vehicle, because it could happen on the first shot or might not happen after 40, but neither of those are very expected results.

Phototoxin wrote:Mathammer works assuming : you play on a featureless board, with perfect movement (6" not 5.9 or 6.1) against an idiot who cannot think or react.

Sort of.

One of the strengths of mathhammer is that it is able to control for variables. Of course, just because you control for them doesn't mean that they go away when you're in the actual game. When you describe stuff using math, often those control variables need to re-enter the statement.

For example, "Assuming that you've moved the weapon into range and that the particular shot doesn't have cover, a BS3 meltagun against AV12 should do X". If those variables aren't true, then you can recalculate.

On a final note, while I haven't had math be ALL that useful while on the table top, it is definitely the thing to do while list building, when you have the time and calculator to hash things out.

I often use mathhammer to determine if a potential combat is a fair fight.

If the odds aren't significantly in my favor, I usually stay away from it, since I prefer to stack the odds in my favor as much as possible. That being said, If I'm in a fight where the reward for getting lucky is high enough, even with really bad odds, I will go for it more often than I probably should.

Mathhammer is just a tool to assist in selecting and -in the case of the internet - a way to express why A is valued over B in your opinion.

For instance if I am focused on survivablity and ranged potiential for my troop choices. I am playing eldar and have 3 basic choices -
Guardians, Dire Avengers or EJB. My key is I want speed and I want maximum chance to avoid close combat while I want to be firing them as much as possible.

1. Speed: EJB are the obvious choice here but I can always go for wave serpent guardians or Dire Avengers.
2. Avoid CC: EJB assault move makes that the best but obviously 18" range DAs will put out more fire than equivalent 10 guardians. I could mathhammer the options but this seems pretty obvious to me.

3. I want them to fire so 5-man DAs in serpents cowering is not the style i want to play. What is the best of the three and why
DA + wave serpent put out more but bikes are probably almost as good - the issue is cost vs effectiveness. I can put a probable number on the bikes vs the DA+wave serpent option. Perhaps one is superior vs one opponent vs the other but mathhammer allows me to put a number on that efficiency.
4. If they do get in CC, which layout is more survivable and/or resilient. Finally for the cost which one is best. Mathhammer can help me put a number on my gut feeling. I may even be surprised and find something I didn't expect. (e.g. An enhance warlock with bikes is better than an embolden warlock. Or perhaps no warlock is best no matter what.)

Mathhammer is not a be-all end-all empirical number but it is a tool to get a straight comparison on what tactically is of value to you and what can most effectively meet your criteria. It might even be a cause for a certain build for me and a test for a game. (e.g. 20-man guardian squads with a guide will perform better than a DA squad for the points. So in my next game I want to try the 20-man guardians to see if tactically I can get that mathematical model to prove itself in a game. I may find that the 12" range element is the most important thing and I couldn't get them to prove my math or understanding its limitations better I may add in some other factor.

Mathhammer helps me make decisions where my gut feeling and experience may feel hazy on the conclusion but it never is an absolute.

I use probability within 1 standard deviation to determine what is most likely to happen in a direct conflict between two known units.

I also use math to create points-efficiency indices between two similar units, like a Hydra and a Vendetta. Clearly the Vendetta is better, but how much better is it at 130 points versus 75 points? Is 1 Vendetta worth 1.75 hydras? Indices have been very helpful in allowing me to tweak competitive lists against an expected array of opponents.

In the end, mathhammer is just a tool. In a game with only about 6 possible outcomes in any one situation, you'd be foolish to ignore what simple probability can tell you about likely outcomes. But math will never win you a game. Understanding the math, and understanding how to play the game ultimately will give you more tools in your box than someone who refuses to do one or the other. Inevitably having a good grasp on as many facets of play, or tools, as possible will give you an edge over someone with fewer tools at their disposal.

Mathhammer is a tool in wargaming. It isn't the entirety of wargamming. That's why you don't see statisticians who have never played before winning 'ard Boyz.

It's a great way of showing how good one weapon is vs another, and it's a good tool for determining exactly how damaged a CC-oriented unit needs to be before your shooty unit should consider charging.

And, it's a great way of actually resolving those debate on the forum of "Who would win in CC, a Daemon Prince or Shrike?" without having to have a million people chime in with anecdotes.

I think the people disparaging mathhammer either don't acknowledge that they use it when they play, or are simply terrible players.

Do you fire bolters at a land raider? No because the math says that they will never damage it no matter how many times you try. If you were capable of making that decision before doing it in game, congratulations, you just mathhammered.

40k is a game of math represented by models on a board, however else you want to dress it up. The painting and modelling aspect is a different thing entirely.

And for those shouting "play the game" and use your own experience, you're simply using a different set of data to make your decisions than someone who goes with general probability.

What it comes down to for me is that 40k is too damn expensive to just try everything and see what works. So I ask questions on Dakka (which wouldn't exist without people that believe in the effectiveness of mathhammer) and run the numbers myself. I want to know what to expect out of my units in any given situation before I put them on the board. I don't have the money or time to waste on buying and trying every random combination my army could run.

Buying a model based on its looks or fluff is one thing (or psychological effect in the case of Marbo, for me), but winning can be a fun part of the hobby too. I spend less time modelling than I do playing the game, so I want to know that the things I invested so much time, effort and money into are worth it.

Ailaros wrote:For example, a single BS3 autocannon destroys a piece of AV12 on a .05. What does that number actually mean? Well, one way of judging it is to think that you need 20 rounds of shooting for the destruction of the vehicle to be the most expected result. Yes, it doesn't mean 20 shots = destroyed vehicle, because it could happen on the first shot or might not happen after 40, but neither of those are very expected results.

This is the exact type of bad use of the math that I was referring to.

Saying "one way of judging it is to think that you need 20 rounds of shooting for the destruction of the vehicle to be the most expected result. " is not what the math is telling you. When you say the most expected result, what do you mean?

The math you used only tells you is that you will average a single destruction result over 20 attempts at those odds - that's it. The way you are saying it is not false per say, its just not reflective of what this math is telling you. This might occur attempt 1, attempt 7, attempt 19, attempt 31... etc. There is no way of determining when it will occur, so saying you need 20 rounds of shooting is not at all what this math told you.

That's why this is a bad use of the math. Off the top of my head, I would think term you used, "the most expected result", would be any result that occurs more frequently than the other results. In this case it has to be nothing, as you miss 50% of the time.

edit: Just for reference, the above scenario has a 52% chance of having reached a destroyed result by the 14th attempt. Maybe that's what you mean by "the most expected result". Either way your method was wrong for trying to see what your chances are destroying it over multiple shots. it should be

1- (chance to not destroy) to the Nth power. N is the number of attempts you want to try for. So my method was simply to take a calculator, and multiple .95 by itself until I got under .5, which was 14 if I was correct in counting the number of times I hit the enter button. FYI after 20 shots its ~64%

Dracos wrote:The math you used only tells you is that you will average a single destruction result over 20 attempts at those odds

Which is roughly the same as saying...

Ailaros wrote:one way of judging it is to think that you need 20 rounds of shooting for the destruction of the vehicle to be the most expected result.

... when you use standard deviation.

The difference between a straight-up percentage and standard deviation is that standard deviation gives you expectation ranges, while a percentage does not.

No its not (RE comparison of the two statements). That is not the same thing at all. I said early on that a probability distribution was the correct tool, so you don't need to preach to the choir. But your statement is FALSE and not what the math is telling you.

edit: See my addition to the above post. Over 14 attempts you have a 52% chance of having destroyed the vehicle, after 20 you have 64%. You statement about needing 20 shots is false, and not equivalent to saying you will average 1 per 20 shots.

Dracos wrote:No its not (RE comparison of the two statements). That is not the same thing at all. I said early on that a probability distribution was the correct tool, so you don't need to preach to the choir. But your statement is FALSE and not what the math is telling you.

edit: See my addition to the above post. Over 14 attempts you have a 52% chance of having destroyed the vehicle, after 20 you have 64%. You statement about needing 20 shots is false, and not equivalent to saying you will average 1 per 20 shots.

If you have a 5% chance of destroying it, the average number of shots you have to take to destroy it is 20. This is useful if you expect to have a set number of shots and multiple targets and are wondering how many you will destroy on average. Example: You're expecting to take a total of 100 shots over the course of a game. You should average 5 tanks destroyed, so if you're expecting to face 8, you'll need some additional firepower to take them all out.

But, if you absolutely need to destroy a single target right now and want to know how many shots to dedicate to it, it's not nearly that simple and you have to do a more intensive calculation. As you're showing.

Ailaros's linked calculation isn't all that useful for this probability assessment. If you assume 20 shots, you get an average of 1 kill. And, by the RMS calculation he's showing, you get a standard deviation of 11.11. So, he's saying you get anywhere between -10 and 12 kills as "normal".

A library patron just made a comment that I thought applied to this situation. "It's not just about facts and figures. It's about relationships." To me that sums up the gaming/hobby experience.

Lotta bad mathhammer flying around.

There is no "Average you need to roll/do/etc to get X" unless you're referring to a point at which the probability reaches infinity (or whatever point you decide is a certainty, which is alot higher than 66%). 20 shots at a 5% success rate is around 66% chance of success.

Standard deviation is also not a magic wand that turns a pile of data into a super combat prediction tool. Ailaros' batreps will often showcase some exclamation along the lines of "they didn't perform average/per statistics/as predicted!" etc, which is a pretty good example of the misapplied math Dracos is talking about.

Dracos wrote:No its not (RE comparison of the two statements). That is not the same thing at all. I said early on that a probability distribution was the correct tool, so you don't need to preach to the choir. But your statement is FALSE and not what the math is telling you.

I'm sorry I said that the statement "after 20 shots, you should expect one thing to be destroyed" is the same as "you should expect it to take 20 shots to destroy one thing"?

MikeMcSomething wrote: 20 shots at a 5% success rate is around 66% chance of success.

Dracos wrote:edit: See my addition to the above post. Over 14 attempts you have a 52% chance of having destroyed the vehicle, after 20 you have 64%. You statement about needing 20 shots is false, and not equivalent to saying you will average 1 per 20 shots.

But what does that MEAN?

That's the problem with straight-up percentage statistics. How do you know if you're unlucky if you shot at something 20 times and it didn't do anything?

MikeMcSomething wrote:Standard deviation is also not a magic wand that turns a pile of data into a super combat prediction tool. Ailaros' batreps will often showcase some exclamation along the lines of "they didn't perform average/per statistics/as predicted!" etc, which is a pretty good example of the misapplied math Dracos is talking about.

So, how do you determine if a person was lucky or not?

If only there was some way to do this... like using statistics or something...

loranafaeriequeen wrote:A library patron just made a comment that I thought applied to this situation. "It's not just about facts and figures. It's about relationships." To me that sums up the gaming/hobby experience.

Sure, but how do you compare things? How do you determine relationships?

Ailaros wrote:one way of judging it is to think that you need 20 rounds of shooting for the destruction of the vehicle to be the most expected result.

Perhaps what I'm finding disagreeable is this sentence. I don't think I'm reading it the same way you are reading it. Can you please elaborate on what you mean here?

What does "the most expected result" mean?

Monster Rain wrote:I suppose so. I would honestly rather play a lot of games, win or lose, and hone my list through trial and error than do it with spreadsheets./quote]

Thats how I do it. I spread their sheet around with as many different lists as I can.

As I'm reading it, that sentence means that after 20 shots, the laws of statistics say you would have rolled at least one 'destroyed' result. It doesn't say that you WILL have rolled that, or that it WILL take 20 shots to destroy, just that after 20 shots, stats says you should roll destroyed at least once.

Ailaros wrote:So, how do you determine if a person was lucky or not?

You don't.

You're saying "I shot 50 lasguns so I should have killed 3 space marines and I didn't so the universe was bad/I was unlucky/whatever" when you should be saying "I killed 3 space marines which is a result within x standard deviations of the mean"

The universe doesn't(can't) care how much math you did beforehand when you roll your attacks, the math just shows you where your particular data point lies when you calculate the final result. It might be one of the less common results in a given sample space, which you could construe as ''lucky'' or ''unlucky'' if you wanted, but that's just being superstitious. Standard deviations are just bookmarks that show you how far apart results like 3 dead space marines and 8 dead space marines are.

And even that rudimentary understanding [of the limitations of probabilistic forecasting] can be useful to the technician tweaking an army list against an array of expected scenarios.

sourclams wrote:And even that rudimentary understanding [of the limitations of probabilistic forecasting] can be useful to the technician tweaking an army list against an array of expected scenarios.

Of course, the point is you say "My vendettas are X% likely to outperform my Hydras in Y scenario" and Ailaros is saying "My vendettas didn't outperform my Hydras so something is wrong"

It is at times a subtle distinction, but one that makes the difference between people thinking mathematics as a concept is useless for a wargame because it's all people waving a pocket calculator shouting "Arrg I didn't roll the statistics or something" instead of understanding how probability can actually be applied to a game.

Dracos wrote:What does "the most expected result" mean?

I'd consider a result "expected" if it were within one deviation of the mean.

MikeMcSomething wrote:

Ailaros wrote:So, how do you determine if a person was lucky or not?

You don't.

If you choose to disbelieve that a person's luck can be determined or is in any way knowable, that's fine.

Of course, it makes it awfully difficult to engage in effective list building. That and it's definitely a philosophical position that isn't held in the majority, mostly because it's not useful.

MikeMcSomething wrote:Of course, the point is you say "My vendettas are X% likely to outperform my Hydras in Y scenario" and Ailaros is saying "My vendettas didn't outperform my Hydras so something is wrong"

Actually, in that case it wouldn't be "something is wrong" it would be "I'm being really unlucky".

Of course, that requires one to believe that if one is lucky or not can be determined.

Dracos wrote:

Some people even make the horrific error of saying that if you have a 1/3 chance of doing something, you need to do it 3 times for it to happen. That is not true at all. It might happen in one attempt, or it might not happen after 3 attempts.

This may be me trolling... if so, I blame the fact that I am on pain medication and don't know any better. However, I say the above quite often. Now, when I say that, I don't really mean that it WILL ALWAYS AND ABSOLUTELY TILL THE END OF TIME IN CAPSLOCK take 3 shots to kill something that I have a 1/3 chance of killing. I, as I believe is the case with most people, am simply stating that, assuming that I have a 1/3 chance of getting lucky, a 1/3 chance of getting unlucky, and a 1/3 chance of rolling average, I should still set myself up so that I am, on average, killing whatever target it is that I think I will be firing at.

As far as experience goes: While mathammer is the way that I figure out what units might work well together, I generally let experience be the judge of that.


Mathhammer works. But it's a lot more difficult to use than it appears. If you had a perfect equation, one that took in to account terrain, range, movement, and luck (luck being gravity, air pressure, and jesus), then you could map out your entire game.

The fact is, obviously and thankfully, we don't have such a method, but ignoring a tool as useful as mathhammer is... unwise I believe.

Ok Ailaros, so right now, in your chair at your computer, tell me in completely objective terms how ''lucky'' you are. Feel free to provide references to well-known psychics, or perhaps any leprechaun consultants that might be able to help your explanation.

MikeMcSomething wrote:Ok Ailaros, so right now, in your chair at your computer, tell me in completely objective terms how ''lucky'' you are.

well I can help with this: I never kill tanks with auto cannons. Therefore, as awesome as they are, I prefer the auto-las pred over the rifle dread

Comparing the output of 2 different guns versus a type of opponent works okay, like deciding "what is better kill ratio against Tau Firewarriors, HB or AC?" but beyond that, comparing squads from different armies is far more situational to be reduced to an equation.

And 3 shots that have a 1/3 chance of succeeding wind up with a about a 72% chance of success, which is quite a ways from 100%.

This is a useful example, because "Ill probably kill that guy, I have 3 rolls of 5+" is the same thing as "Ill probably kill that guy, I have better chances than a 3+, but worse than a 2+"

That's how I think about it as well. Or rather, if I'm looking at a single Marine sitting on an objective that I absolutely need to kill, I figure I'll need to cause 5 wounds to give myself better than a 95% chance of success, which is my 'comfort zone'.

MikeMcSomething wrote:And 3 shots that have a 1/3 chance of succeeding wind up with a about a 72% chance of success, which is quite a ways from 100%.

I'm sorry... but... how does this work out?

Okay, the problem with your 0.05 chance and your percentages: most people are forgetting that you can succeed multiple times.

First off, the number is actually 1/18, or 0.055555. When you roll 18 times, the number off successes is most likely to be exactly 1. At 17 rolls, the probability of rolling zero successes is about 36%, and the probability of rolling exactly one success is the same.

The problem with looking at is as "I need to roll 18 times for it to happen" is that you basically ignore that when working with probability, it includes the chance of multiple successes. As pointed out, at 13 (I think it was 14 for the 0.05 value) rolls you become more likely to succeed (> 1 result) than to fail (0 results).

Usually, if you have a 1/x chance, you need far fewer than x rolls to be likely to succeed.

Here's the equation:
p = probability of success
are = target number of successes
n = number of attempts

probability = [n! / r!(n-r)!] * p^r * (1-p)^(n-r)

If you're shooting at vehicle, you're not really looking for more than one success, so you're looking for when the probability of not failure is better than 50%. So, when 1 - {probability when "r" = 0} > 0.5

If you make an excel sheet and plug in some numbers, you'll see that if your probability is 1/x, then at x tries, a single success is the most likely outcome. At 2x tries, two successes is the most likely outcome. Notice I'm not saying at least one or at least two.

So, at the end of the day, you should only have to fire 13 BS 3 Autocannons at an AV 12 target to have a better than 50/50 chance at rolling a destroyed result somewhere in there.

Mathhammer is not everything. Mathhammer tells you things like "take autocannon teams instead of missile launcher teams for fighting vehicles" and other such combat statistics.