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Kinda had this idea hit me.

Could mathhammer be used to pick an army? to actually figure out what unit(s) are the best in the game/army?

Just a thought.

Sure! how do you define best?

The number of variables means it is infeasible to do.

given you have to take into account at least 10 dimensions of variation (game size, terrain load out, mission type, mission setup, game length etc....) you're loking at something fairly insane!

I'm talking about the best over all unit quality.

I have plenty of time to kill.


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I would have to say the units that take the least damage and put out the most pain.

Im not looking for pretty tactics or fancy armys, this is more or less something I am doing outta curiousity *looks at all of his ancient space marines from God-knows-when*

subarugeek wrote:Kinda had this idea hit me.

Could mathhammer be used to pick an army? to actually figure out what unit(s) are the best in the game/army?

Just a thought.

Hey, I'm a computer science major with heavy background in probabilistics, so I should weigh in on this.

Theoretically possible, but too infeasible to bother trying. At least until we get quantum computers.

You can mathhammer things in a vacuum, like who wins between 200 points worth of tacmarines and 200 points worth of IG infantry on a field with no terrain, etc.

Hell, you could even be able to generate a reasonable model of that particular scenario for every reasonable terrain configuration possible, if you roughly reduced it to a grid of some kind.

Now we just have to do this for every possible army list at every possible point value at and account for every possible movement, target decision, etc. This is certainly possible, but in a stricly theoretical sense. We don't have powerful enough computers to compute this data quickly enough to have the answer within the next thousand years or so.

We have to keep in mind that while most of the game scenarios can be reduced to averages (let's say, count all movement angels with n=30 degree divisions instead of 1 degree divisions, and use averages instead of calculating every possible dice roll scenario), but there are still a ridiculous (albeit finite) number of scenarios to run through.

The fact is, there is probably an objectively quantifiable all-comers list that, if played with perfect tactics in every decision, will have a higher chance of winning than any other list overall. But we will probably never discover this list except by accident, and we will never be good enough players to figure out how to play this list perfectly without the aid of a computer. So it's all moot anyway.

Mathhammer is great for comparing units via different metrics, analyzing common scenarios, and simple unit evaluation (how good is a multi-melta compared to a lascannon for busting AV14?). Mathhammer is not so great for determining the best army list due to the insane number of variables involved.

How do you define quality?

Resistance to Str 4 Shooting?
Ability to Wound T6?
Ability to wound Armour 14?
...

you can define the list of qualities that are desireable
then you can take a unit and empirically define it's abilities in each category.
you can then decide which categories you require
and then you can build your army list.

Look at just one aspect.
Getting a Destroyed result or better against AV 14 (Shooting).

You need at least Str 8 shooting.
You need to account for Probability of Hitting.
You need to account for the Damage Chart.
You can account for Range and mobility (call it threat radius).
And then you can deal with wargear options (Tac Marines + Melta+ Droppod) CAN accomplish the above for X points.

Dont flame me for this but what is mathhammer?

skipmcne wrote:How do you define quality?

Resistance to Str 4 Shooting?
Ability to Wound T6?
Ability to wound Armour 14?
...

you can define the list of qualities that are desireable
then you can take a unit and empirically define it's abilities in each category.
you can then decide which categories you require
and then you can build your army list.

Look at just one aspect.
Getting a Destroyed result or better against AV 14 (Shooting).

You need at least Str 8 shooting.
You need to account for Probability of Hitting.
You need to account for the Damage Chart.
You can account for Range and mobility (call it threat radius).
And then you can deal with wargear options (Tac Marines + Melta+ Droppod) CAN accomplish the above for X points.

Along these lines, OP, you really need to define what "best" is. As I said above, if "best" is "most likely to beat any given list" then you just can't answer it feasibly.

If "best" is "most likely to defeat any of these 10 lists I commonly see at tournaments", then you're still screwed, although less equally so.

But sometimes narrowing the context of your search is the only way you can get a reasonable answer. For example, you can analyze the effectiveness of all wargear at your disposal at killing all sorts of vehicles (AV10-14). Then you assign probabilities to the likelihood of seeing each of those armor values. (I would probably use AV10: .15 AV11: .25 AV 12: .4 AV 13: .1 AV 14: .1 against my usual metagame). Cross reference these values to maximize your overall "destroyed" results and build accordingly.

Now, the problem here is that you're not establishing a "best overall" or even an objective "best at killing vehicles", but it's incredibly helpful in building an good force.


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VikingScott wrote:Dont flame me for this but what is mathhammer?

Mathhammer is the use of probability and statistics to analyze the effectiveness of units and armies in-game.

It is wrongfully characterized as "useless" by those who do not understand the importance of these two subjects, and also wrongly characterized as all-important by those who misunderstand the scope of these two subjects. Mathhammer not only includes the ability to apply probabilistic models to the the game, but also the ability to recognize the bounds of these models.

Basically, more often than not, a person who is adept at Mathhammer is a better player than someone who is not.

Cheers for that.
I didnt know what it was but still managed to do some sort of debased form of it!

Hmmm...

Maybe a better way of saying this would to try to figure out if there is an army that is unbalanced at all.
I'm guessing that the Daemonhunters are, the Grey Knights in power are freaking beastly.

The answer to Mathhammering Everything is 42

Right now I am working on a chart that might be interesting.
It deals with WS/BS/Saves
Anything that requires a 1D6 roll and its probability

subarugeek wrote:Hmmm...

Maybe a better way of saying this would to try to figure out if there is an army that is unbalanced at all.
I'm guessing that the Daemonhunters are, the Grey Knights in power are freaking beastly.

You would be guessing wrong. Severely wrong, as it were. Point for point, PAGKs are some of the worst models in the game.

Right now I am working on a chart that might be interesting.
It deals with WS/BS/Saves
Anything that requires a 1D6 roll and its probability

I would appreciate us if you told us exactly what this chart entailed. We might be able to save you a lot of time.

Ahh crap.

Basically the chart deals with probablities for the number of units you have to hit/save. For instance, 5 SM's would hit 3.3 times statistically on the roll. But the chart that I am making will show the statistics in case they miss, which if lets say you have those 5 marines, one miss, then statistically you will have 2.6 hits assuming that the dice behave in a manner that statistics would favor. I am a bit of a newb, I am no math major or computer major, I am a high school drop out studying to be a nurse that joined the army and loves Subarus and 40k.

subarugeek wrote:Ahh crap.

Basically the chart deals with probablities for the number of units you have to hit/save. For instance, 5 SM's would hit 3.3 times statistically on the roll. But the chart that I am making will show the statistics in case they miss, which if lets say you have those 5 marines, one miss, then statistically you will have 2.6 hits assuming that the dice behave in a manner that statistics would favor. I am a bit of a newb, I am no math major or computer major, I am a high school drop out studying to be a nurse that joined the army and loves Subarus and 40k.

That'll take a long time, and is honestly kind of unnecessary. You're much better off using a quick formula to analyze a given situation. Since you're rolling a lot of d6s, you tend to end up somewhere around the average anyway. I mean, if you roll 100 d6s, you tend to see about as many 1s as you do 6s, etc. But if you add them all up, the vast majority of the time it's going to be a number between 300 and 400. Luckily, discrete probability (which encompasses most of basic wargame analysis) is piss easy to understand once you get the basics. It's all basic multiplication.

The basic format of a formula in this way is:

[number of shots or attacks] * [chances of hitting] * [chances of wounding] * [chances of opponent saving] = number of dead models

or

[number of shots/attacks] * [chances of hitting] * [chances of penetrating] * [chances of getting the vehicle damage result I want] = the percentage that I'm going to take out a tank or whatever.

It's much simpler to just open a google tab and do things out this way for a quick analysis of a squad against other targets. I'm actually working on a couple scripts to help people do that, simply because it's a pain to whip out the calculator every time.

And once you have that, you can divide that number by the number of points you spent on it to get an idea of unit effectiveness in that particular situation versus another unit.

Your idea isn't bad, it's just that there are so many variables in who the target will be for a given unit (shooting at IG conscripts versus Necron Immortals are going to be wildly different results for a lot of armies) that you'd need to make a veritable buttload of tables to get any meaningful information.

Is it possible to automate battles in.....what's the name of that program that let's people simulate battles over the internet?....anywho, if it's possible to set up a program that simulates 2000 pt armies facing off against each other 100 times each and then produces a report of the results, you might be able to extrapolate a rough idea.

While I suppose it is not impossible to statistically find the best army, it is very near impossible to. Much like others have said, you would have to run down just about every possibility of every unit against every other unit it could face. Just to start...

Take a tac marine

Probability to hit with shooting
Probability to hurt T3, T4...etc.
probability to get past 2+ armor, 3+ armor, etc at each T level
Probability that your target is in cover and what cover save it would get.
Feel no pain? Invulnerable saves?
Same thing with close combat...hit, wound, saves against everything conceivable.
Could it hurt armor? What armor? Probability to hurt each armor level...
Weapon ranges, how often are they in range? What is the probability they will be in range on turn one, turn two?
How many points do they cost? Do they score? What armies are most present where you play?

I could go on..just too many questions to take into account. Rinse and repeat for every other unit ever in every codex.

agnosto wrote:Is it possible to automate battles in.....what's the name of that program that let's people simulate battles over the internet?....anywho, if it's possible to set up a program that simulates 2000 pt armies facing off against each other 100 times each and then produces a report of the results, you might be able to extrapolate a rough idea.

Like I said, that's not nearly as feasible as it sounds, due to time constraints. [And as far as I know, that program doesn't have an AI function to automate battles, and even then that would only determine which army would be better at winning with an AI pilot]

While I suppose it is not impossible to statistically find the best army, it is very near impossible to. Much like others have said, you would have to run down just about every possibility of every unit against every other unit it could face. Just to start...

Take a tac marine

Probability to hit with shooting
Probability to hurt T3, T4...etc.
probability to get past 2+ armor, 3+ armor, etc at each T level
Probability that your target is in cover and what cover save it would get.
Feel no pain? Invulnerable saves?
Same thing with close combat...hit, wound, saves against everything conceivable.
Could it hurt armor? What armor? Probability to hurt each armor level...
Weapon ranges, how often are they in range? What is the probability they will be in range on turn one, turn two?
How many points do they cost? Do they score? What armies are most present where you play?

I could go on..just too many questions to take into account. Rinse and repeat for every other possible configuration of all other units ever in every codex.

Fixed that for ya...

Ostrakon wrote:

subarugeek wrote:Ahh crap.

Basically the chart deals with probablities for the number of units you have to hit/save. For instance, 5 SM's would hit 3.3 times statistically on the roll. But the chart that I am making will show the statistics in case they miss, which if lets say you have those 5 marines, one miss, then statistically you will have 2.6 hits assuming that the dice behave in a manner that statistics would favor. I am a bit of a newb, I am no math major or computer major, I am a high school drop out studying to be a nurse that joined the army and loves Subarus and 40k.

That'll take a long time, and is honestly kind of unnecessary. You're much better off using a quick formula to analyze a given situation. Since you're rolling a lot of d6s, you tend to end up somewhere around the average anyway. I mean, if you roll 100 d6s, you tend to see about as many 1s as you do 6s, etc. But if you add them all up, the vast majority of the time it's going to be a number between 300 and 400. Luckily, discrete probability (which encompasses most of basic wargame analysis) is piss easy to understand once you get the basics. It's all basic multiplication.

The basic format of a formula in this way is:

[number of shots or attacks] * [chances of hitting] * [chances of wounding] * [chances of opponent saving] = number of dead models

or

[number of shots/attacks] * [chances of hitting] * [chances of penetrating] * [chances of getting the vehicle damage result I want] = the percentage that I'm going to take out a tank or whatever.

It's much simpler to just open a google tab and do things out this way for a quick analysis of a squad against other targets. I'm actually working on a couple scripts to help people do that, simply because it's a pain to whip out the calculator every time.

And once you have that, you can divide that number by the number of points you spent on it to get an idea of unit effectiveness in that particular situation versus another unit.

Your idea isn't bad, it's just that there are so many variables in who the target will be for a given unit (shooting at IG conscripts versus Necron Immortals are going to be wildly different results for a lot of armies) that you'd need to make a veritable buttload of tables to get any meaningful information.

Thanks to the wonders of excel Ive finished the chart.
Wasnt hard.
I figure I am going to start with just WS/BS.
Hey I got an idea- point to skill statistic ratios.
That might be worth something-right?


Tell me what you guys think would be worthwhile.

Ostrakon wrote:
Fixed that for ya...

ya ya...

From personal experience, you can go over math hammer until you bleed out your ears and still it won't mean diddly. It's better to just play the game and find out what works best for you than to try and calculate it out on paper first. If you are unsure on some units before you buy them then proxy them.

Axyl wrote:

Ostrakon wrote:
Fixed that for ya...

ya ya...

From personal experience, you can go over math hammer until you bleed out your ears and still it won't mean diddly. It's better to just play the game and find out what works best for you than to try and calculate it out on paper first. If you are unsure on some units before you buy them then proxy them.

Problem I have...
1. Havent been into WH40K since High School
2. My WRX is more or less a 2.5RS right now that I cannot drive. WH40K money normally is going into fixing the thing for AutoX. Needs a turbo. Crapping a rotated mount GT3076R and intercooler is NOT easy on my salary.
3. I get bored. Very bored.

Axyl wrote:

Ostrakon wrote:
Fixed that for ya...

ya ya...

From personal experience, you can go over math hammer until you bleed out your ears and still it won't mean diddly. It's better to just play the game and find out what works best for you than to try and calculate it out on paper first. If you are unsure on some units before you buy them then proxy them.

In a way it does, but games take a while to finish, whereas you can get a quick feel for unit effectiveness with mathhammer with 10 minutes and a calculator. Plus, dicking around with mathhammer lets you figure out some things you might not have known about your army.

For example, a lot of people take Heavy Destroyers as anti-vehicle, but if you do the math regular destroyers are point-for-point better at taking out vehicles AV11 or lower and are more likely to produce meaningful results against AV12 and higher. And against AV12, the monolith ends up being far more useful than H. Destroyers. And that's not counting either units' ability to clean up against infantry.

Well, I'm not trying to say never math-hammer anything either. Heck I've calculated out the effectiveness of most of all the str8+ nid weapons in the new dex vs armor (click here for that). Plus with math-hammer you can also find out that an assault cannon is better vs armor than a single las cannon (discounting range).

I guess my point is that you shouldn't pick an army or your units based solely on calculations, they can certainly help, but your army shouldn't be all about the numbers.

Oh, and in your situation subarugeek, I would probably begin obsessing over numbers and calculations myself if I wasn't able to get a game in. Some sort of effectiveness to points ratio table would probably be worth a read.

I guess my point is that you shouldn't pick an army or your units based solely on calculations, they can certainly help, but your army shouldn't be all about the numbers.

Oh, god no. That's just leading to disappointment. Armies should be picked on aesthetic and fluff considerations. Someone wise when I was starting to play told me that "Rules and whatnot can change, and your overpowered army can get nerfed. But the models you painted will be always be there."

Ostrakon wrote:

I guess my point is that you shouldn't pick an army or your units based solely on calculations, they can certainly help, but your army shouldn't be all about the numbers.

Oh, god no. That's just leading to disappointment. Armies should be picked on aesthetic and fluff considerations. Someone wise when I was starting to play told me that "Rules and whatnot can change, and your overpowered army can get nerfed. But the models you painted will be always be there."

Very true.
I am more then likely going to do a silly themed army that I can make uber-nasty to play against.

The ratio thing is basically going to work out like this (I'm going to start with SM) you would lets say list out the squad, then tally up the points, and depending on your style (melee ranged) you would then determine what you are getting. For instance Marines are 17 points each and attack twice, so its a 6.6:85 ratio. Now lets say that you were debating adding a Marine, instead of doing________ else where, one Marine would increase your ratio to 7.9:102, which is about a 20% increase in both. The impact that Marine made is nominal for the points spent.

That is where I am so far, and its looking flawed because it would theoretically favor many small squads in terms of absolute gain- in percentage.

EDIT: Ill fix later, the numbers are wrong. All wrong.


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Ill have the numbers later, but I have a feeling I am onto something with this though.

As a huge fan of mathhammer, I don’t see this as being feasible. There are a lot of factors that simply can’t be represented by a numerical value or the numerical value would be impossible to obtain.

One extremely important variable is the environment. What’s the likelihood this supposed Optimized Army (henceforth known as OA) will be matched against a standard, Nidzilla, Jetlock council, nob biker, or even simple vanilla marines, mechanized guard, or anything else. If you were somehow able to optimize an army in a vacuum but, turns out your pool of opponents run armies that, either by accident or intent, run armies that just happen to have some serious advantage over the OA, than what you’ve done is meaningless. A simple scenario would be a OA that happens to contain some sort of “perfect” balance between anti-infantry and anti-AV would actually be at a serious disadvantage in the current highly mechanized meta-game because their anti-AV has been optimized for average AV opposition when they’ll actually have a great likelihood of encountering a lot of AV.

Another factor I consider impossible to calculate is movement. We all understand the strategic value of units that can move 12”, 24” or fleet, but how does that translate into a mathematical variable? A Wave Serpent is a pricy transport but it’s a fast skimmer which gives it a lot of value. It can capture/contest objectives and react to battlefield conditions extremely quickly – but that’s not something that can be objectively evaluated… I’d take my sub-optimal all-mechanized Eldar army over an OA any day because of the enormous versatility I have, but that’s not something that can be represented in any objective way.

Ostrakon wrote:Now we just have to do this for every possible army list at every possible point value at and account for every possible movement, target decision, etc. This is certainly possible, but in a stricly theoretical sense. We don't have powerful enough computers to compute this data quickly enough to have the answer within the next thousand years or so.

Surely our computers are more than capable of performing the requisite calculations. I would think the coding of all those variables, and determining what constitutes a variable in the first place (and then how to best illustrate it numerically), would be the most time-consuming portion of the task.

The other issue though is synergy in regards to units and how they support one another. On paper a brood of venomthropes are pretty ineffective for their points value. However they do have a place in some armies, etc.

Terminus wrote:

Ostrakon wrote:Now we just have to do this for every possible army list at every possible point value at and account for every possible movement, target decision, etc. This is certainly possible, but in a stricly theoretical sense. We don't have powerful enough computers to compute this data quickly enough to have the answer within the next thousand years or so.

Surely our computers are more than capable of performing the requisite calculations. I would think the coding of all those variables, and determining what constitutes a variable in the first place (and then how to best illustrate it numerically), would be the most time-consuming portion of the task.

You would be incorrect.

You know how we needed supercomputers like Deep Blue to beat humans at chess?

40k is several times more complex than chess. Chess has a finite number of possible board positions. Even if you reduced 40k to a grid system (let's say a 48 x 72 grid for 1 square inch "spots"), you'd have 54 times the number of board configurations as chess - assuming both players had 16 models! More likely each player is going to have 50 or more models, and this doesn't linearly increase the time it takes to compute it, it does so EXPONENTIALLY! And can you imagine how screwed we game theorists would be regarding chess if players could choose to forgo their rooks to take a second queen? To account for all these differences (and linearizing the game board, which makes it not terribly realistic ANYWAY) it would probably take 100 Deep Blues working in unison to compute these calculations by the year 3000.

Hey guys, great discussion on the merits and challenges of Mathhammer. I just wanted to offer up a spreadsheet that I developed when I was bored and wanted to learn to code VBA macros. It allows you to pick a shooter and target and up to 6 different weapons and then computes the expected number of unsaved wounds for each weapon based on the characteristics of the units/weapons you chose. I haven't gotten around to doing vehicle shooting or close combat (this is harder because of the effects of initiative), but you might find it useful.

Cheers.