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 Mad Doc Grotsnik wrote:
The bigger problem with Mathhammer is that it's only useful to a point, as it can't really account in-game oddities, such as terrain density, LoS, and your opponent having sneaky things to mess with the odds.

I mean, it has it's uses, of course it does. Even just looking at the BS difference between a Marine and an Ork, and concluding the Marine is, statistically, a better shot is Mathhammer, just as the statline clearly showing a Carnifex is tougher than a Tyranid Warrior is Mathhammer. When I was weighing up the relative reliability between the Twin Lightning Lock Moirax vs Twin Autocannon War Dog, I was Mathhammering (turns out there, the Lightning Locks exploding 6's and fixed 6 shots each tips the scales in their favour)

But I've always been left scratching my head at those who feel it will enable the writing of an unbeatable list, as such lists are written in a vacuum. They don't, and perhaps can't, allow for what you might face, the mission and objectives being played, amount and type of scenery etc.

This is really it. Mathhammer is A point of a data. A single variable in a equation. It's a good point of a data and one to consider when making decision but not the only point of data and not the final result of the equation.

I find that a basic understanding of it helps people game better too and that many might have that basic understanding built up through trial and error - which can take longer.

It's about being able to look at the basic stats of the unit you've got and several enemy units within range/reach or within two turns reach and being able to work out what to focus on what.

I find it also helps estimate how wel things will achieve a result and helps people get over expectations. Sure that anti-tank shot might be strong, but its got a 1/6 chance of hitting so yeah if it hits its great, but your'e probably going to want to expect it to fail. Going into that roll expecting a failure means the player is more prepared for it and means that they are already formulating alternative plans.

 Overread wrote:
I find that a basic understanding of it helps people game better too and that many might have that basic understanding built up through trial and error - which can take longer.

It's about being able to look at the basic stats of the unit you've got and several enemy units within range/reach or within two turns reach and being able to work out what to focus on what.

I find it also helps estimate how wel things will achieve a result and helps people get over expectations. Sure that anti-tank shot might be strong, but its got a 1/6 chance of hitting so yeah if it hits its great, but your'e probably going to want to expect it to fail. Going into that roll expecting a failure means the player is more prepared for it and means that they are already formulating alternative plans.

It's why something like a Laser Destroyer has misleading Mathhammer, if you only look at the average. It has a really high average because the maximum is so damn high, but you're better off looking at the odds of X Laser Destroyers killing your target in one volley than average damage.

Pyroalchi wrote:
Argg..... my laptop erased my whole long post... okay I try again *sigh*

@ Peregrin: Yes I understand what you are saying, but as I'm also no stranger to statistic I would like to explain my reasoning. If we compare Frag and Krak (or Lascannon, doesn't matter in this situation) on a BS4+ platform against GEQ, mathhamer will tell us the average number of unsaved wounds to be 0.778 (frag and 0.417 (Krak/Lascannon), yet the number of killed models is for some reason listed as being 1 for the Krak which is wrong (it should be 0.417 because damage does not spill). Furthermore we can note that the Krak will never kill more than one model per shot.

If we further look at the probability of hitting exactly 0/1/2/3/4/5/6 times with the Frag we get:
0 hits: 16.41%
1 hit: 31.25%
2 hits: 25.78%
3 hits: 16.67%
4 hits: 7.55%
5 hits: 2.08%
6 hits: 0.26%

which transforms to the following probabilities for killed GEQs:
0: 62.84%
1: 13.89%
2: 11.46%
3: 7.41%
4: 3.36%
5: 0.93%
6: 0.12%

While the Krak has:
0: 58.33%
1: 41.67%

What can we learn from that? While the average damage does not differ much, the Frag has a 23.26% Chance to kill at least two models and a 11.81% chance to kill at least 3. The Krak/Lascannon has 0% chance to kill more than one model. And I think this is an example for weapon differences, that is often overlooked using mathhamer


@Slayer-Fan 123: I have not calculated the Odds, but it can be possible that this is so, as long as all weapons stay on the table and have line of sight.
What I mean is: Lets say I run only tanks and face either 4 ML or 2 HB + 2LC. I have enough firepower to destroy 2 heavy weapons on my turn. In the latter case I would of course kill the lascannons and then only face HB. In the former case, while I can kill of two ML, the other two can still try to pop my tanks.

Or on a similar note due to LOS blocking terrain or models it might happen, that the "wrong" selection of the 2HB/2LC are facing a target or that the heavy bolters shorter range prevents them from reaching a infantry target, the frag missiles could hit, since it is not given, that like in mathhamer all weapons can fire all the time at every target they like.

You forget that no tanks really get MLs, so in terms of this conversation we are discussing a Devastator squad. Soooooooooo how are you choosing the Lascannons to die?

Here's what I don't get about mathhammer.

A 4+ Save passees on a [4, 5, 6].

A 5+ Save passes on a [5, 6].

Why do my 5+ saves pass 50% more than my 4+ saves?

Bharring wrote:
Here's what I don't get about mathhammer.

A 4+ Save passees on a [4, 5, 6].

A 5+ Save passes on a [5, 6].

Why do my 5+ saves pass 50% more than my 4+ saves?

Confirmation bias.

 Peregrine wrote:

 Xenomancers wrote:
Even if this is a troll thread. It's important to look at each step in a process of decision making. It's true that rolling 2 1s on 2 dice is 1/36 but the odds of anything on a d6 are only 1/6 and the rolls have nothing to do with each other. The odds of rolling a 1 don't go down if you already rolled one.

Err, what? You have to look at each step in the process of making a decision but there is no step involved between rolling the first 1 and the second 1. You don't roll a 1, make another decision based on probability, then re-roll the 1. You roll a D6 and if it's a 1 you immediately re-roll it, for total odds of having a 1 as your result after your decision being 1/36. IOW, you're rolling a single strange bell-curve-shaped die with a 1/36 chance of a 1. The fact that the second die has a 1/6 chance of rolling a 1 as part of resolving that combined pseudo-die is only relevant if you interrupt the process to make another decision (for example spending a CP to re-roll it instead of having a general re-roll ability).


Automatically Appended Next Post:

Pyroalchi wrote:
While it is clear that mathematically a missile launcher is worse at anti tank duty than a lascannon and worse at anti infantry than a heavy bolter it keeps some usefulness after the enemy runs out of the prefered target. And it has a chance of messing up target Preference.

This is actually a case where pure math answers the question. Frag missiles are terrible and even under ideal circumstances are not that much better than just using a krak missile, so their value is effectively zero and a missile launcher is just a weaker version of a lascannon. The whole "missile launchers are versatile" argument is entirely from people who haven't bothered to understand the math.

I don't know how you could possible have misunderstood me except for the fact you just try to look smarter than everyone without actually being smarter and enjoy disagreeing with people. The point is the dice rolls are all individual and don't affect each other. A lot of people think because they just rolled a 1 and when they go to command point reroll that it somehow influences the next roll. Just saying it doesn't. Every dice roll is a 1/6 chance that has no effect on each other.

@ Peregrin:

The calculation of the damage against GEQs was aimed at the claim, that Frag-missiles are basically worthless and following that the ML is just a worse LC. My point was that no, the frag has the advantage of having a realistic chance of killing more than one GEQ.

Regarding the part comparing 4 x ML with 2HB +2LC : you are correct that I did not factor in the unit composition. My reason was that playing Guard I assumed that the compared weapon platforms are either infantry/veteran squads or Sentinels with one heavy weapon each.

You realize what your realistic chances listed are compared to killing one dude with a different weapon right?

 Xenomancers wrote:

 Peregrine wrote:

 Xenomancers wrote:
Even if this is a troll thread. It's important to look at each step in a process of decision making. It's true that rolling 2 1s on 2 dice is 1/36 but the odds of anything on a d6 are only 1/6 and the rolls have nothing to do with each other. The odds of rolling a 1 don't go down if you already rolled one.

Err, what? You have to look at each step in the process of making a decision but there is no step involved between rolling the first 1 and the second 1. You don't roll a 1, make another decision based on probability, then re-roll the 1. You roll a D6 and if it's a 1 you immediately re-roll it, for total odds of having a 1 as your result after your decision being 1/36. IOW, you're rolling a single strange bell-curve-shaped die with a 1/36 chance of a 1. The fact that the second die has a 1/6 chance of rolling a 1 as part of resolving that combined pseudo-die is only relevant if you interrupt the process to make another decision (for example spending a CP to re-roll it instead of having a general re-roll ability).


Automatically Appended Next Post:

Pyroalchi wrote:
While it is clear that mathematically a missile launcher is worse at anti tank duty than a lascannon and worse at anti infantry than a heavy bolter it keeps some usefulness after the enemy runs out of the prefered target. And it has a chance of messing up target Preference.

This is actually a case where pure math answers the question. Frag missiles are terrible and even under ideal circumstances are not that much better than just using a krak missile, so their value is effectively zero and a missile launcher is just a weaker version of a lascannon. The whole "missile launchers are versatile" argument is entirely from people who haven't bothered to understand the math.

I don't know how you could possible have misunderstood me except for the fact you just try to look smarter than everyone without actually being smarter and enjoy disagreeing with people. The point is the dice rolls are all individual and don't affect each other. A lot of people think because they just rolled a 1 and when they go to command point reroll that it somehow influences the next roll. Just saying it doesn't. Every dice roll is a 1/6 chance that has no effect on each other.

Technically not true in this case. The first roll impacts the second roll as you only do the second roll if you fail the first one. So, assuming a 2+ (to simplify the case), you have a 1/6 chance to roll a second die. The numbers work out the same, as you have a 0% chance to roll two 1s in a row if your first die isn't a 1. The result of the second roll is not dependent upon the first roll beyond whether it happens, but they aren't entirely independent. Oddly, of all the "snakeeyes" situations that could occur, you brought up one of the few where the second *isn't* truly independent of the first.

The odds of the second die being a 1 in that scenario is a 1/36, whereas in scenarios where they are truly independent, the odds of the "second" die (whichever you label as second - if they're independent, either could be considered second, even if they're simultanious) being a 1 is 1/6 (with 5/6 of those 1s not being snakeeyes).

Not what I am saying. I'm basically trying to say past events that have come to pass - have no actual bearing on future events. Speaking of mental bias that because 10 seconds ago you rolled a 1 - it doesn't magically make your chance to not roll another 1/36. Your chance to roll a 1 is the same as the first time.

You can't actually roll both the dice at the same time and it would be the same odds as rolling them 1 at a time. I am not arguing against that. In the decision making process the the other dice roll does not affect this one. Obviously it's not hard to understand that I just think people attribute that to their calculations when they shouldn't - it's a new roll. It's a 1/6 chance.

 Xenomancers wrote:
Not what I am saying. I'm basically trying to say past events that have come to pass - have no actual bearing on future events. Speaking of mental bias that because 10 seconds ago you rolled a 1 - it doesn't magically make your chance to not roll another 1/36. Your chance to roll a 1 is the same as the first time.

Generally, practically, you are correct. Technically, pedantically, exactly the opposite. If the first roll was a 6, your second roll has a 0/6 chance to be a 1 - because it does not happen. That fact doesn't matter, because in this case, you're only interested if you get two 1s in a row.

More specifically, "because 10 seconds ago you rolled a 1", causes your "chance to not roll another 1/36" to go from 0/36 to 1/6. But represents only 1/6th chance of being the case, so you're still only 1/36 likely to get to 1s in a row. The first die is a 1/6 chance to roll a one. In the particular case you shared, the second die is a 1/6 chance to roll a 1 *if and only if* the first roll failed (rolled a 1). So, while the numbers work out the same, the die rolls are not truly independent.

It is true, though, that once you've rolled a 1 (or whatever), your odds on your next die roll of rolling a 1 are 1/6. And that that's the same as any other "first die" result.

You can't actually roll both the dice at the same time and it would be the same odds as rolling them 1 at a time.

If you can't roll them simultaneously, then they are not truly independent. You might need to keep track of which is first and which is second, but rolling two dice in series and rolling two dice in parallel have the same statistical results - as with any two truly independent actions.

I am not arguing against that.

Not sure I follow. You're claiming it can't be done, then saying you're not making that claim?

In the decision making process the the other dice roll does not affect this one.

Actually, it does in this case. If you CP reroll the first 2+ roll regardless of outcome (meaning, having the first die have no impact on whether you roll the second die), then you go from a 1/36 failure rate to a 1/6 failure rate (if you're rerolling regardless of result, the first roll doesn't matter). As virtually nobody is that boneheaded enough to do that, it's generally assumed the roll is only CP'ed if it failed.

Obviously it's not hard to understand that I just think people attribute that to their calculations when they shouldn't - it's a new roll. It's a 1/6 chance.

It's easy enough to grok, but when you get into the weeds, we find a lot of incorrect beliefs - as evidenced in this thread.

Matchmaker gives me the statiscal back up that something will work x% reality is often different

Pyroalchi wrote:
The calculation of the damage against GEQs was aimed at the claim, that Frag-missiles are basically worthless and following that the ML is just a worse LC. My point was that no, the frag has the advantage of having a realistic chance of killing more than one GEQ.

Your stats don't say what you think they do. The frag missile has a modest chance of killing 1-2 extra models (4ppm each, so that's a pretty small increase in value), and amusingly has a lower chance of killing at least one model. And that's the best possible situation. You're shooting at a T3 target so the wound roll is only a 3+ vs. 2+, and the target doesn't have a good save to negate too many frag wounds. A good weapon doesn't just have a small chance of better performance, it has a decisive advantage. And that simply isn't what you see. The average damage is a marginal improvement and you have to resort to picking the most favorable interpretation of the statistics to get any argument in favor of the frag missile.

In short: a lascannon is almost as good as a frag missile at killing the frag missile's perfect targets, and much better at killing tanks. Always take lascannons over missile launchers.

@ Peregrin:
I still stand to my argument that a chance to kill more than one model CAN be an advantage compared to no chance to kill more than one model. And that this is normally not visible using only mathhammer.
Regarding the example of killing GEQs: There might be situations, were it is necessary to completely wipe a unit for a specific advantage. It could be a Necron warrior squad that should be dead instead of reduced to one model or a unit holding an objective that will give an important victory point or a unit about to bind an important shooty unit like a deathstrike missile in close combat.
Let this unit have 2 models left. Does a Lascannons have any chance of killing the whole unit? No, not even rerolling everything. It is simply impossible. Does a Frag Missile have a chance of achieving that? Yes it does and I, personally count that as advantage. A very situational one, but it is there.

On a similar note, something that is also usually overlooked with mathhammer: the importance of combinatoric with random damage weapons shooting on multi-wound models. The example most familiar for me is the comparison between Battle Cannon and Exterminator Autocannon shooting 2 wound models.
Looking only on Mathhamer the answer seems clear, the Battlecannon is better.
Lets look at the following four model types:
1. Lychguard (5/2/3+/4++)
2. Marines (4/2/3+)
3. Nobz (4/2/4+)
4. Heavy weapons Squads (3/2/5+)

Using Mathhammer we get for the double tapped Battlecannon/Autocannon:
1. 1.167 vs. 1.333 unsaved wounds
2. 1.994 vs 1.333
3. 2.431 vs. 1.778
4. 2.917 vs 2.778
with the average damage beeing just that x 2 and the number of killed models beeing the halved average damage rounded down

Here it seems that the possible combinations of rolling 1s, 2s and 3s are not correctly taken into account. While 8 average unsaved damage on an autocannon always equals 4 killed 2 wound models, 8 average damage on a battlecannon could as well mean 3 (for example rolling 3/1/1/3) or even 2 (1/3/1/3 or 3/1/3/1).

If we take that into account and look at the probabilities for each number of unsaved wounds for Battlecannons and Autocannons (I wrote a skript for that) and then factor in all the combinations of x unsaved battlecannon hits and how many models are really killed we get the picture in the pictures below:


What we can see here is, that the battlecannon kills significantly less models than would be expected. In numbers the average killed models are:
1. 0.83 vs. 1.33
2. 1.4 vs. 1.33
3. 1.76 vs. 1.78
4. 2.13 vs. 2.78

So again, what can we learn from that? The Exterminator Autocannon is still kind of crappy, but it is statistically not as bad compared to the battlecannon as Mathhamer would have us think it is. Against the Lychguard is is about 60% more effective as the Battlecannon instead of the expected 10% advantage, against the Marines and nobz it is about as effective as the BC and not worse as mathhammer would suggest and against the HWS it is better, even if mathhamer suggest it would be worse.

If the chance is super low as the chance to kill no models, it isn't an advantage. Over a 1000 games you'll see that. That's how averages work as much as you want to deny the concept.

Pyroalchi wrote:
@ Peregrin:
I still stand to my argument that a chance to kill more than one model CAN be an advantage compared to no chance to kill more than one model. And that this is normally not visible using only mathhammer.
Regarding the example of killing GEQs: There might be situations, were it is necessary to completely wipe a unit for a specific advantage. It could be a Necron warrior squad that should be dead instead of reduced to one model or a unit holding an objective that will give an important victory point or a unit about to bind an important shooty unit like a deathstrike missile in close combat.
Let this unit have 2 models left. Does a Lascannons have any chance of killing the whole unit? No, not even rerolling everything. It is simply impossible. Does a Frag Missile have a chance of achieving that? Yes it does and I, personally count that as advantage. A very situational one, but it is there.

On a similar note, something that is also usually overlooked with mathhammer: the importance of combinatoric with random damage weapons shooting on multi-wound models. The example most familiar for me is the comparison between Battle Cannon and Exterminator Autocannon shooting 2 wound models.
Looking only on Mathhamer the answer seems clear, the Battlecannon is better.
Lets look at the following four model types:
1. Lychguard (5/2/3+/4++)
2. Marines (4/2/3+)
3. Nobz (4/2/4+)
4. Heavy weapons Squads (3/2/5+)

Using Mathhammer we get for the double tapped Battlecannon/Autocannon:
1. 1.167 vs. 1.333 unsaved wounds
2. 1.994 vs 1.333
3. 2.431 vs. 1.778
4. 2.917 vs 2.778
with the average damage beeing just that x 2 and the number of killed models beeing the halved average damage rounded down

Here it seems that the possible combinations of rolling 1s, 2s and 3s are not correctly taken into account. While 8 average unsaved damage on an autocannon always equals 4 killed 2 wound models, 8 average damage on a battlecannon could as well mean 3 (for example rolling 3/1/1/3) or even 2 (1/3/1/3 or 3/1/3/1).

If we take that into account and look at the probabilities for each number of unsaved wounds for Battlecannons and Autocannons (I wrote a skript for that) and then factor in all the combinations of x unsaved battlecannon hits and how many models are really killed we get the picture in the pictures below:

Spoiler:

Lychguard:

Marines:

Nobz:

HWS:

What we can see here is, that the battlecannon kills significantly less models than would be expected. In numbers the average killed models are:
1. 0.83 vs. 1.33
2. 1.4 vs. 1.33
3. 1.76 vs. 1.78
4. 2.13 vs. 2.78

So again, what can we learn from that? The Exterminator Autocannon is still kind of crappy, but it is statistically not as bad compared to the battlecannon as Mathhamer would have us think it is. Against the Lychguard is is about 60% more effective as the Battlecannon instead of the expected 10% advantage, against the Marines and nobz it is about as effective as the BC and not worse as mathhammer would suggest and against the HWS it is better, even if mathhamer suggest it would be worse.

You realise mathhammer isn't just the averages right? It takes the other considerations into account. You have demonstrated that the average wounds and expected kills differ in this situation. Using mathhammer for both,

I did not use mathhamer for both but wrote my own skript to include the permutations of roling D3 for damage. To illustrate my point go to mathhammer and let it target an enemy with Toughness 4, 2 Wounds and a save of 5+ (its an extreme example just to get round numbers which will be easier to show what I mean)
representing a weapon with D3 damage like the battle cannon
Shots: 6, BS A, Weapons Strength/AP/Damage 8/-2/D3 => you get exactly 5 unsaved wounds and mathhammer claims that would equal 5 killed models. But this it not correct!

There are a number of permutations of these 5 damage rolls that do not kill 5 models as are (X representing any roll between 1 and 3 and Y a roll of 2 or 3)
1/X/1/X/1: kills only 2 models, 9 possible combinations
Y/1/X/1/X: kills only 3 models, 18 possible combinations
1/X/1/X/Y: kills only 3 models, 18 possible combinations
1/1/Y/Y/1: kills only 3 models, 4 possible combinations
Y/Y/1/1/1: kills only 3 models, 4 possible combinations
...
and the list goes on. It is easy to see that as long as ANY of those 5 dice rolls is a one, these 5 unsaved wounds can not kill 5 models. And since there is NO combination that kills more than 5 models (since damage does not spill) the average kill count of 5 unsaved battle canon hits can not reach the 5 claimed by mathhammer. That was my point and I think it is rather easy to see.



@ Slayer-Fan123: coming back to my calculation on Frag Missiles firing on GEQs: 23% to kill more than one model is not "super low". Especially when the chance to hit nothing at all is over 50% for both weapons. Yes you are right when we talk about firing Frag missiles on lets say Terminators were the Frag Missiles chance to kill more than one model would be so low, that it doesn't matter, but there are a lot of targets out there that are really squishy and even squisher than a GEQ (Poxwalkers, Conscripts, Kroot...)
3

Pyroalchi wrote:
I did not use mathhamer for both but wrote my own skript to include the permutations of roling D3 for damage. To illustrate my point go to mathhammer and let it target an enemy with Toughness 4, 2 Wounds and a save of 5+ (its an extreme example just to get round numbers which will be easier to show what I mean)
representing a weapon with D3 damage like the battle cannon
Shots: 6, BS A, Weapons Strength/AP/Damage 8/-2/D3 => you get exactly 5 unsaved wounds and mathhammer claims that would equal 5 killed models. But this it not correct!

There are a number of permutations of these 5 damage rolls that do not kill 5 models as are (X representing any roll between 1 and 3 and Y a roll of 2 or 3)
1/X/1/X/1: kills only 2 models, 9 possible combinations
Y/1/X/1/X: kills only 3 models, 18 possible combinations
1/X/1/X/Y: kills only 3 models, 18 possible combinations
1/1/Y/Y/1: kills only 3 models, 4 possible combinations
Y/Y/1/1/1: kills only 3 models, 4 possible combinations
...
and the list goes on. It is easy to see that as long as ANY of those 5 dice rolls is a one, these 5 unsaved wounds can not kill 5 models. And since there is NO combination that kills more than 5 models (since damage does not spill) the average kill count of 5 unsaved battle canon hits can not reach the 5 claimed by mathhammer. That was my point and I think it is rather easy to see.

You realise that mathhammer isn't only about averages? Those other scenarios can be and are taken into account by probability calculations.

For example you can calculate the probability of killing X or more models. Or the probability of the entire spread. Against a 2 wound model, even using averages, for a D3 weapon you should be weighting your damage to be 5/3 instead of 2 on average. Its still math hammer.

Battlecannon: 2d6 shots. Average 7. D3 damage. Average 5/3.
Let's assume Tank Commander with reroll 1s. 7/9 to hit.

Average dead Primaris: 7*5/6*5/3*2/3*1/2 = 350/108 = 3 Dead


I understand you wrote your own script, but it's either using maths (and is thus a form of mathhammer) or its wrong. I get the impression it isn't wrong. As you can see above even using a simple average you get better results when you do the maths correctly.

Pyroalchi wrote:
I did not use mathhamer for both but wrote my own skript to include the permutations of roling D3 for damage. To illustrate my point go to mathhammer and let it target an enemy with Toughness 4, 2 Wounds and a save of 5+ (its an extreme example just to get round numbers which will be easier to show what I mean)
representing a weapon with D3 damage like the battle cannon
Shots: 6, BS A, Weapons Strength/AP/Damage 8/-2/D3 => you get exactly 5 unsaved wounds and mathhammer claims that would equal 5 killed models. But this it not correct!

There are a number of permutations of these 5 damage rolls that do not kill 5 models as are (X representing any roll between 1 and 3 and Y a roll of 2 or 3)
1/X/1/X/1: kills only 2 models, 9 possible combinations
Y/1/X/1/X: kills only 3 models, 18 possible combinations
1/X/1/X/Y: kills only 3 models, 18 possible combinations
1/1/Y/Y/1: kills only 3 models, 4 possible combinations
Y/Y/1/1/1: kills only 3 models, 4 possible combinations
...
and the list goes on. It is easy to see that as long as ANY of those 5 dice rolls is a one, these 5 unsaved wounds can not kill 5 models. And since there is NO combination that kills more than 5 models (since damage does not spill) the average kill count of 5 unsaved battle canon hits can not reach the 5 claimed by mathhammer. That was my point and I think it is rather easy to see.



@ Slayer-Fan123: coming back to my calculation on Frag Missiles firing on GEQs: 23% to kill more than one model is not "super low". Especially when the chance to hit nothing at all is over 50% for both weapons. Yes you are right when we talk about firing Frag missiles on lets say Terminators were the Frag Missiles chance to kill more than one model would be so low, that it doesn't matter, but there are a lot of targets out there that are really squishy and even squisher than a GEQ (Poxwalkers, Conscripts, Kroot...)
3

It IS low because a game lasts maybe 5 turns or so. Looking at it like that, you're gonna accomplish that once on average per game.

@ Drager: Yes, I think I understand you better now (and of corse the skript uses math). I think I misunderstood the topics question. I got the impression that the question revolves around using the website mathhammer (https://www.mathhammer8thed.com/) compared to reality.
Based on this assumption I wanted to illustrate, that the website seems to not be programmed in a way that takes into account the different permutations of roling more than one D3 or D6 for damage on multiple wound models (and in some cases seems to forget that damage does not spill). Since a lot of discussions here on Dakka seem (to my eyes) be based on data calculated with the site mathhammer, I found it important to mention this, especially since I think there are a variety of weapon options who are widely regarded as inferior to useless, while they are at least less so, if you do the math correctly.


@ Slayer-Fan 123: I'm a bit confused why you deem 23% low. Yes I know, this means in a 5 rounds game this will on average only happen once per gamer PER MISSILE LAUNCHER. And if the whole question I wanted to give some input to is "does the frag missile have any advantage at all compared to Krak/Lascannon", this should be taken into account. As mentioned above the chance to kill any GEQ with a lascannon/krak is 41.67%, the chance to kill any GEQ with a FRAG missile is 37.16% but since the chance to kill more than one is 23.26% it means that about 2/3 of the time the Frag kills, it kills more than one model. Yes that is only interesting if you shoot this heavy weapon at GEQs at all, but still the missile launcher has some abbility the Lascannon has not regarding flexibility in target selection.

 JNAProductions wrote:

It's why something like a Laser Destroyer has misleading Mathhammer, if you only look at the average. It has a really high average because the maximum is so damn high, but you're better off looking at the odds of X Laser Destroyers killing your target in one volley than average damage.

No the Laser Destroyer has high average because it has such a high Low-End/Floor. 1's, 2's and 3's =3 isn't bad. By the same token, I was pointing out before it was released the difference between the Macro Plasma and the Laser Destoryer was going to be pretty minimal, and only really at the extreme ends of Toughness/Wounds spectrums.


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Bharring wrote:
Here's what I don't get about mathhammer.

A 4+ Save passees on a [4, 5, 6].

A 5+ Save passes on a [5, 6].

Why do my 5+ saves pass 50% more than my 4+ saves?

They probably don't. My guess is you're seeing a version of what's called The Fallacy of Misleading Vividness with a little cluster illusion and confirmation bias feeding a Gambler's fallacy. Making a 5+ save leaves a bigger more lasting impression in your mind, so you remember more of those successes than you do the ho-hum 50-50 saves of a 4+. It works in reverse for people with Terminators remembering the 1's they roll for armor saves They don't remember the 5 times they saved, they remember the one time they didn't.. So those events stick in your head more, making you think that's the normal, and will stay normal.

Pyroalchi wrote:
@ Drager: Yes, I think I understand you better now (and of corse the skript uses math). I think I misunderstood the topics question. I got the impression that the question revolves around using the website mathhammer (https://www.mathhammer8thed.com/) compared to reality.
Based on this assumption I wanted to illustrate, that the website seems to not be programmed in a way that takes into account the different permutations of roling more than one D3 or D6 for damage on multiple wound models (and in some cases seems to forget that damage does not spill). Since a lot of discussions here on Dakka seem (to my eyes) be based on data calculated with the site mathhammer, I found it important to mention this, especially since I think there are a variety of weapon options who are widely regarded as inferior to useless, while they are at least less so, if you do the math correctly.

I didn't even know that website existed! I always run the calculations myself when working out probabilities and even occasionally post the working as here. Glad we were just talking at cross purposes. Mathhammer to me has always just meant doing mathematical calculations to work out probabilities simulating a specific 40k/Warhammer scenario.

@ Drager: nice, than we are on the same page again

And yes, mathhammer is a good word for this General theoretical approach, yet it is my impression that a majority of people prefers using established skripts like for example this website instead of calculating themselves and therefore use the term mathhammer more in this sense. That's not a bad thing at all, but leaving out things like dice roll permutations, beeing somewhat inconsequent with damage spilling and not demonstrating things like probabilities to kill no model at all or more than one model, lead to some errors in weapon comparisons.

And following that some options are ruled out in the majority of discussions I read as "strictly inferior due to mathhammer" while they don't really are in my opinion (read OPINION, I'm aware that the situations I described are special). And this leads in some cases to people complaining that their model XY that they build an edition ago is now useless which is a pitty.

Regarding the general topic of this tread: How well does a theoretical approach match reality: Slayer-Fan123 wrote to posts ago directed at me:

Over a 1000 games you'll see that. That's how averages work as much as you want to deny the concept.

And I think that describes it very good, even if a bit confrontative. Calculating all the probabilities before hand will give you a good impression on the average damage/number of wounds, number of killed models etc. And over a large number of games your results will most likely approach that average. Yet in each single game there might be units performing surprisingly well or bad, since a single game is not a situation were a weapon fires 1000 times and you get an average. And this is important to keep in mind if one chooses between models with random number of shots and damage vs. fixes number of shots and damage. Even if the former might have a higher average damage and will sometimes perform much better than expected, it has also a higher chance to perform much worse than expected. Fixes number of shots/damage might be less effective playing 1000 games, but in each single game, they inherit a lower chance to significantly underperform their expectations.


Therefore what "mathhammering" lead me to believe (that is again totally a personal opinion, do with it what you want), that it is a good idea not only to include units with the better average damage/killrate but also at least some with a low probability to seriously underperform. Also I personally think, that weapons with mixed anti-tank, anti-infantry ammunition (like grenade launchers and missile launcher) do have their place and are less useless as one might think only looking on the average damage/kill rate.

You also have to consider the possibilities, not the exact average result.

For Example, you have 8 guns which hit on 4+, wound on 4+ and cause D6 damage. Average 4 hits, 2 wounds, and 7 damage.

You could also have an average of 7 damage from guns which hit on 6's and wound on 6's with one damage - 7x6x6 = 252 shots.

The difference is that the second version is more likely to achieve it's average, as a single dud dice roll here or there will have a minimal effect on the system - if 1 more shot misses than average, that's 1/252th of the system, so minimal effect. If 1 more misses on the first, that's 1/8th of the system - a much larger effect.

You also have the damage potential to consider - the second version could, with extremely slim odds, cause 252 wounds. The first system can only cause 48. However, it would take a commonly bad roll to cause 0 wounds with the 8 shots. it would take a ludicrously bad roll to cause 0 wounds with the 252 shots.

if you're relying on averages, better to do so with massed firepower rather individual powerful shots.

And of course you would have to consider the amount of damage your baffled opponent will do to you if you start rolling 252 lasgun shots against his Land Raider

But you are totally right in stressing that with massed firepower those averages are a really good hint on performance.

I do feel that Mathhammering does often overlook potential in favour of average.

Yes, averages exist for a reason and are important to bear in mind. But, when up to your elbows in a game, being able to spot where, with a bit of luck, you can take something out is also useful.

To stick to the Lascannon vs Missile Launcher example. Yes, a Lascannon is a very reliable weapon. It does what it does, and it does it well. But as others have said, it can still on tonk at most a single model each turn (unless we include making enemy vehicles explode, which I suppose we could overall). But, that Frag Missile? It could drop two or more models. And that might be enough to battleshock the remainder off the board.

Sure, the average may not look good. But the potential remains.If you focus solely on average and Mathhammer during the game, you're blinding yourself to other possibilities. They may not be outright game winning - but they can shift the pattern of the game in your favour.

Consider. A tank is down to a single wound. In it's turn, it poses a threat to something you need alive for your next turn. But, all your heavy weapons have shot this turn, hence it's on that single wound. If you purely Mathhammer, because your remaining options are low-chance, you may just leave it, and hope it's degraded stats stop it killing stuff. But, if you look a bit further? Maybe, just maybe, you've got a bunch of pistols in range. If they've nothing better to do that turn, why not have a crack? Low chance is better than no chance. And you only need a bit of luck to pull it off.

Obviously if you have nothing better to do with a gun, you're gonna use it suboptimally rather than not use it at all. I think most folks use the averages to see where they can *best* use the weapon. In your tank example, let's say you had those pistols in range of the tank AND in range of a group of infantry. Sure, you could try to plink the tank and likely fail, but the better option would be to fire on the infantry because you're far more likely to take them out than the tank.

Depends on what killing the infantry might achieve. Which again, is where purely mathhammering starts to fall down, as you can't factor in the oddities of a game.

If those infantry are looking to push me off an objective? Yes, absolutely use your pistols on them. If nothing else, it's making them easier to handle in the next turn. But, if the pistol squad are about to charge them anyway? Might as well go for the tank, depending on how my chances in the forthcoming scrap are looking.

But again, this isn't encouraging wasteful firepower. If you've a better target, shoot that. Instead, it's demonstrating that pure mathhammering as an approach to gaming is full of flaws and downsides

Plus, shooting a Knight in the pills with an Autopistol, and taking that last wound is the sort of story you'll remember

Pyroalchi wrote:
*stats*

Thanks for that! I concur on mathhammer websites failing to give the full spread of results taking into account multiwould targets!