Nemesis force mathhammer

[ChaoticEric]

So, I was crunching some numbers on the new nemesis force weapons to use as basis for my decision on how to equip my shiny knights from now on. I thought I'd share the results with you in case it helps you in any way.

 

It's based on 10 000 randomizations so it's not 100% accurate but should not be much more difference than 0.1% so I deemed the deviations to be manageable :)

 

As I'm mainly facing other marines, I'm running the numbers vs such opponents. My main assumptions are;

Hitting on 4+, no rerolls

Wounding on 4+ except for halberds which wound on 3+

Armour save of 3+ or worse, i.e. no save against AP3

10 models hitting, all able to strike

 

Base A1 (10 attacks total, 20 with falchions)

 

Swords

2.5 average unsaved wounds

1.4 standard deviation

 

2 wounds or more; 76%

4 wounds or more; 23%

8 wounds or more; <0.1%

12 wounds or more; impossible

 

 

Halberds

3.3 average unsaved wounds

1.5 standard deviation

 

2 wounds or more; 90%

4 wounds or more; 44%

8 wounds or more; 0.3%

12 wounds or more; impossible

 

 

Falchions

5 average unsaved wounds

1.9 standard deviation

 

2 wounds or more; 98%

4 wounds or more; 77%

8 wounds or more; 10.2%

12 wounds or more; 0.1%

 

 

Base A2 (20 attacks in total, 30 with falchions)

 

Swords

5 average unsaved wounds

1.9 standard deviation

 

2 wounds or more; 98%

4 wounds or more; 77%

8 wounds or more; 10.2%

12 wounds or more; 0.1%

 

 

Halberds

6.7 average unsaved wounds

2.1 standard deviation

 

2 wounds or more; 99.7%

4 wounds or more; 94%

8 wounds or more; 34%

12 wounds or more; 1.4%

 

 

Falchions

7.5 average unsaved wounds

2.4 standard deviation

 

2 wounds or more; 99.8%

4 wounds or more; 96%

8 wounds or more; 48%

12 wounds or more; 5%

 

 

Looking at the numbers I'm still not sure exactly what conclusions to draw yet.

[Captain Coolpants]

Sounds pretty clear to me on what wins haha. Just a shame some units (purifiers/interceptors) aren't really worth it. Practically 30 ish ppm for a power armored marine. Just a few poimts more gets you a terminator :-/

[ChaoticEric]

Sounds pretty clear to me on what wins haha. Just a shame some units (purifiers/interceptors) aren't really worth it. Practically 30 ish ppm for a power armored marine. Just a few poimts more gets you a terminator :-/

Exactly that's my problem :)

 

Points not considered, falchions win hands down. With points? Not as easy....

[Captain Coolpants]

Haha I know! It's so annoying. I hate loosing our old helberds. I'd still take them even if they were just +1 initiative.

[ChaoticEric]

Haha I know! It's so annoying. I hate loosing our old helberds. I'd still take them even if they were just +1 initiative.

Yes but with the new halberds it's not so easy. When hammerhand is taken into consideration the swords are just as good as halberds, except for high T opponents, and they're free. Falchions are just monsters when they wound on 2+...

[HiveFleetKelari]

As a former math teacher, I thoroughly approve of making decision on actual statistics (backed up by large sample sizes, even!) over the typical 10 attacks x 3/6 successful hits x 3/6 successful wounds = 2.5 unsaved wounds mathhammer that tends to float around.

 

Being able to see the standard deviation is nice! Swords do less, but are more consistent.  Falchions do way more, but are less consistent, which means that the phases that you roll poorly for them are going to hurt more, since you've paid a premium for them. Maybe we can do some math based on removing approximately 14 points per unsaved wound, but with combat back to us to see how many points we lose in each combat with each option.

 

The other thing to consider is that 7th is still largely a shooty edition. We can mitigate that with Terminators, Paladins, Interceptors, and Strikes by deep striking for the turn 2 assault and with our Purifiers through use of Land Raiders and Stormravens, but it's worth considering. What happens when so many of our expensive models are removed from shooting. Each lost falchion-wielding model is pretty painful.

 

(I too am really mising the +2 Initiative from halberds! Sure, it made them an auto-include, minus the 1/5 hammers per squad, but it was nice to kill marines before they could do anything back to us!)

[ChaoticEric]

As a former math teacher, I thoroughly approve of making decision on actual statistics (backed up by large sample sizes, even!) over the typical 10 attacks x 3/6 successful hits x 3/6 successful wounds = 2.5 unsaved wounds mathhammer that tends to float around.

 

Being able to see the standard deviation is nice! Swords do less, but are more consistent.  Falchions do way more, but are less consistent, which means that the phases that you roll poorly for them are going to hurt more, since you've paid a premium for them. Maybe we can do some math based on removing approximately 14 points per unsaved wound, but with combat back to us to see how many points we lose in each combat with each option.

 

The other thing to consider is that 7th is still largely a shooty edition. We can mitigate that with Terminators, Paladins, Interceptors, and Strikes by deep striking for the turn 2 assault and with our Purifiers through use of Land Raiders and Stormravens, but it's worth considering. What happens when so many of our expensive models are removed from shooting. Each lost falchion-wielding model is pretty painful.

 

(I too am really mising the +2 Initiative from halberds! Sure, it made them an auto-include, minus the 1/5 hammers per squad, but it was nice to kill marines before they could do anything back to us!)

Well, I agree that in terms of absolute numbers, falchions are less consistent than swords but in relative terms the outcome is more reliable. What I mean by relative terms is "standard deviation / average". The second thing is that average - standard deviation for falchions is still higher than average for swords, albeit sometimes not by much, so they are pretty reliable in terms of causing damage :)

 

I'm happy to do scenarios but I'm not sure I completely understamd what you mean by "Maybe we can do some math based on removing approximately 14 points per unsaved wound, but with combat back to us to see how many points we lose in each combat with each option." :)

[BladeGaurd]

So, I was crunching some numbers on the new nemesis force weapons to use as basis for my decision on how to equip my shiny knights from now on. I thought I'd share the results with you in case it helps you in any way.

It's based on 10 000 randomizations so it's not 100% accurate but should not be much more difference than 0.1% so I deemed the deviations to be manageable

As I'm mainly facing other marines, I'm running the numbers vs such opponents. My main assumptions are;

Hitting on 4+, no rerolls

Wounding on 4+ except for halberds which wound on 3+

Armour save of 3+ or worse, i.e. no save against AP3

10 models hitting, all able to strike

Base A1 (10 attacks total, 20 with falchions)

Swords

2.5 average unsaved wounds

1.4 standard deviation

2 wounds or more; 76%

4 wounds or more; 23%

8 wounds or more; <0.1%

12 wounds or more; impossible

Halberds

3.3 average unsaved wounds

1.5 standard deviation

2 wounds or more; 90%

4 wounds or more; 44%

8 wounds or more; 0.3%

12 wounds or more; impossible

Falchions

5 average unsaved wounds

1.9 standard deviation

2 wounds or more; 98%

4 wounds or more; 77%

8 wounds or more; 10.2%

12 wounds or more; 0.1%

Base A2 (20 attacks in total, 30 with falchions)

Swords

5 average unsaved wounds

1.9 standard deviation

2 wounds or more; 98%

4 wounds or more; 77%

8 wounds or more; 10.2%

12 wounds or more; 0.1%

Halberds

6.7 average unsaved wounds

2.1 standard deviation

2 wounds or more; 99.7%

4 wounds or more; 94%

8 wounds or more; 34%

12 wounds or more; 1.4%

Falchions

7.5 average unsaved wounds

2.4 standard deviation

2 wounds or more; 99.8%

4 wounds or more; 96%

8 wounds or more; 48%

12 wounds or more; 5%

Looking at the numbers I'm still not sure exactly what conclusions to draw yet.

Can we get a poison distribution with a accurate lambda? That would tell us more then the probabilities.

[Captain Coolpants]

Are there any possible weapon combos that might fair just as well or better? Like a few helberds and falchions per squad? Or will it always be 'the more falchions the better!'?

[HiveFleetKelari]

As a former math teacher, I thoroughly approve of making decision on actual statistics (backed up by large sample sizes, even!) over the typical 10 attacks x 3/6 successful hits x 3/6 successful wounds = 2.5 unsaved wounds mathhammer that tends to float around.

Being able to see the standard deviation is nice! Swords do less, but are more consistent. Falchions do way more, but are less consistent, which means that the phases that you roll poorly for them are going to hurt more, since you've paid a premium for them. Maybe we can do some math based on removing approximately 14 points per unsaved wound, but with combat back to us to see how many points we lose in each combat with each option.

The other thing to consider is that 7th is still largely a shooty edition. We can mitigate that with Terminators, Paladins, Interceptors, and Strikes by deep striking for the turn 2 assault and with our Purifiers through use of Land Raiders and Stormravens, but it's worth considering. What happens when so many of our expensive models are removed from shooting. Each lost falchion-wielding model is pretty painful.

(I too am really mising the +2 Initiative from halberds! Sure, it made them an auto-include, minus the 1/5 hammers per squad, but it was nice to kill marines before they could do anything back to us!)

Well, I agree that in terms of absolute numbers, falchions are less consistent than swords but in relative terms the outcome is more reliable. What I mean by relative terms is "standard deviation / average". The second thing is that average - standard deviation for falchions is still higher than average for swords, albeit sometimes not by much, so they are pretty reliable in terms of causing damage

I'm happy to do scenarios but I'm not sure I completely understamd what you mean by "Maybe we can do some math based on removing approximately 14 points per unsaved wound, but with combat back to us to see how many points we lose in each combat with each option."

What I meant was assume that we've got ten models fighting a SM tactical squad (140pts). So with falchions on single attack PA models (Strikes) we'll do 5 unsaved wounds or 70 pts worth of "damage". Since we're the same initiative the SM would strike back with 10 attacks. Doing the flat, typical mathhammer, we get 0.8333... unsaved wounds (10 x 3/6 x 3/6 x 2/6) for 20 points of "damage", based on the cost of a Strike plus the cost of a Falchion upgrade, so clearly we come out on top there. But what happens when we fight a SM assault squad (more attacks) or Banshees (more attacks and ignore armor, but lower S) or an Ork mob (more attacks, more models, way cheaper).

By no means am I saying that you should run every possible scenario (what a long rabbit trail that would be), but it is worth thinking about. If I had to hazard a guess, getting hit by a full-strength Ork mob is going to end up being really expensive for us, in terms of points lost in the combat, but fight an assault squad with minimal power weapons should tip in our favor.

It makes me wonder if there are any match-ups that initially look bad (TH/SS Terminators, Ork Meganobz) that might actually be better for us, in terms of points lost.

[ChaoticEric]

 

Can we get a poison distribution with a accurate lambda?  That would tell us more then the probabilities.

Haven't done that since university and I'm not keen on revisiting that for this :)

[Captain Coolpants]

Are there any possible weapon combos that might fair just as well or better? Like a few helberds and falchions per squad? Or will it always be 'the more falchions the better!'?

[ChaoticEric]

What I meant was assume that we've got ten models fighting a SM tactical squad (140pts). So with falchions on single attack PA models (Strikes) we'll do 5 unsaved wounds or 70 pts worth of "damage". Since we're the same initiative the SM would strike back with 10 attacks. Doing the flat, typical mathhammer, we get 0.8333... unsaved wounds (10 x 3/6 x 3/6 x 2/6) for 20 points of "damage", based on the cost of a Strike plus the cost of a Falchion upgrade, so clearly we come out on top there. But what happens when we fight a SM assault squad (more attacks) or Banshees (more attacks and ignore armor, but lower S) or an Ork mob (more attacks, more models, way cheaper).

 

By no means am I saying that you should run every possible scenario (what a long rabbit trail that would be), but it is worth thinking about. If I had to hazard a guess, getting hit by a full-strength Ork mob is going to end up being really expensive for us, in terms of points lost in the combat, but fight an assault squad with minimal power weapons should tip in our favor.

 

It makes me wonder if there are any match-ups that initially look bad (TH/SS Terminators, Ork Meganobz) that might actually be better for us, in terms of points lost.

Now I get what you mean, simulating the whole combat. Should be possible to make a couple of template cases that can be used for comparisons.

 

Simulating the whole fight would be different, my skills in excel aren't sufficient to build a lean file for that. It'd be a monster. However, if we take out things like rerolls, furious charge etc. and keep the fights simple, it might work. I might give it a go over the weekend if I have some spare time :)

[Teetengee]

 

-snip-

 

Can we get a poison distribution with a accurate lambda?  That would tell us more then the probabilities.

 

Um.. it isn't a Poisson distribution. Mean and Variance shouldn't necessarily be equal.

[ChaoticEric]

Are there any possible weapon combos that might fair just as well or better? Like a few helberds and falchions per squad? Or will it always be 'the more falchions the better!'?

To give you a flavour of what happens with fewer models I've done the calculations below.

 

Outcomes per armament are not correlated so sums of the different armaments in the squad should be the same as the total wounds caused by the whole squad, at least in these simplified calculations. I.e., 5 models with swords will cause the same number of wounds regardless of whether they are just five models in the squad or there are 5 models in the squad with falchions as well. I have not included falchions as 5 models with falchions in this are equal to 10 models with swords etc.

 

 

5 models with A1

 

Swords

1.2 average

1 standard deviation

 

0 wounds; 24%

1 wound; 40%

2 wounds; 26%

3 wounds; 9%

4 wounds; 1.6%

5 wounds; 0.1%

 

 

Halberds

1.7 average

1.1 standard dev

 

0 wounds; 13%

1 wound; 33%

2 wounds; 33%

3 wounds; 17%

4 wounds; 4%

5 wounds; 0.5%

 

 

2 models with A1

 

Swords

0.5 average

 

0 wounds; 56%

1 wound; 38%

2 wounds; 6%

 

 

Halberds

0.7 wounds

 

0 wounds; 45%

1 wound; 44%

2 wounds; 11%

 

 

Hammers

0.8 average

 

0 wounds; 34%

1 wound; 50%

2 wounds; 17%

 

 

Sums might not always be exactly 100% as numbers are rounded.

[BladeGaurd]

 

 

-snip-

 

Can we get a poison distribution with a accurate lambda?  That would tell us more then the probabilities.

 

Um.. it isn't a Poisson distribution. Mean and Variance shouldn't necessarily be equal.

 

 

It is count data, with a bottom of zero and only whole integers matter. Sounds to me that it is a poisson with each weapon having a different lambda.

Strait probabilities only real help when it is a normal distribution or can be "approximately normal".

 

[ChaoticEric]

 

It is count data, with a bottom of zero and only whole integers matter. Sounds to me that it is a poisson with each weapon having a different lambda.

Strait probabilities only real help when it is a normal distribution or can be "approximately normal".

 

I'm sure it's not 100% correct but for me it's just easier to think in probabilities and how probable different outcomes are.

[stephane4985]

Can we get a calculation to have the ratio of  something like % agmentation of wounds with flacon / % augmentation of price of the squads if equipped with flacon comapre to others.

 

See what gives the best wounds per points ratio by model.

[ChaoticEric]

Can we get a calculation to have the ratio of something like % agmentation of wounds with flacon / % augmentation of price of the squads if equipped with flacon comapre to others.

 

See what gives the best wounds per points ratio by model.

If you stick with averages I guess you could do it like below. I'm sure there are other ways as well.

 

You pay 210p for a 10 model strike squad.

 

With 10 swords you're causing on average 2.5 wounds, you're paying 84p per wound.

 

With falchions you're paying 250p to cause on average 5 wounds, ie 50p per wound.

 

Or you could say that you have a marginal points cost of 40p for on average 2.5 wounds more, ie 16p per incremental wound.

 

Thing is that this doesn't take into consideration that you die just as easily with falchions as with swords and each dead model the falchions wound output is decreasing twice as much as one dead model with sword.

[BladeGaurd]

R code for the poisson, n= how many times you want to simulate, ss is strike swords, sf is strike falchions, sh are strike halberds. lambda is a quick calculation calibrated to 10 men with out charging vs marines, t is for terminators same assumptions. ?rpois take you to the help site incase you want to look at code syntax or want to make your own.  For the record SAS is better then R but I do not have it on this machine.

n<-100
ss<-rpois(n, 3)
ss

sf<-rpois(n, 5)
sf

sh<-rpois(n, 4)
sh
plot (density(ss), col = "red")
lines (density(sf), col = "blue")
lines (density(sh), col = "green")
?rpois

 

 

ts<-rpois(n, 5)
ts

tf<-rpois(n, 8)
tf

th<-rpois(n, 7)
th
plot (density(ts), col = "red")
lines (density(tf), col = "blue")
lines (density(th), col = "green")

 

ChaoticEric with a SD of 1 around 1 you will not accurately simulate the data because it can/will go into negative numbers.

 

PS: The main issue with the code is that some of it goes pass the top range for them, I recommend either cutting it off mentally or using qpois.

[ChaoticEric]

R code for the poisson, n= how many times you want to simulate, ss is strike swords, sf is strike falchions, sh are strike halberds. lambda is a quick calculation calibrated to 10 men with out charging, t is for terminators same assumptions. ?rpois take you to the help site incase you want to look at code syntax or want to make your own.  For the record SAS is better then R but I do not have it on this machine.

n<-100

ss<-rpois(n, 3)

ss

sf<-rpois(n, 5)

sf

sh<-rpois(n, 4)

sh

plot (density(ss), col = "red")

lines (density(sf), col = "blue")

lines (density(sh), col = "green")

?rpois

 

 

ts<-rpois(n, 5)

ts

 

tf<-rpois(n, 8)

tf

th<-rpois(n, 7)

th

plot (density(ts), col = "red")

lines (density(tf), col = "blue")

lines (density(th), col = "green")

 

ChaoticEric with a SD of 1 around 1 you will not accurately simulate the data because it can/will go into negative numbers.

I know, I noticed that on the smaller number of attacks so I left the SD out :)

[Teetengee]

 

 

 

-snip-

 

Can we get a poison distribution with a accurate lambda?  That would tell us more then the probabilities.

 

Um.. it isn't a Poisson distribution. Mean and Variance shouldn't necessarily be equal.

 

 

It is count data, with a bottom of zero and only whole integers matter. Sounds to me that it is a poisson with each weapon having a different lambda.

Strait probabilities only real help when it is a normal distribution or can be "approximately normal".

 

 

Poissons don't have maximums where these do. Also normal distributions are usually going to be better as these results should be fairly symmetric about the mean. Although if I am going to mathhammer, I usually just math out the whole distribution, with a computer it isn't really that much harder than simulating.

[Ushtarador]

Can you redo the calculations with activated hammerhand? I'm pretty sure they falchions will be a lot stronger in that scenario than the other weapons.

[BladeGaurd]

It is vs MEQ or less, with almost the attacks that hit killing.

[ChaoticEric]

Can you redo the calculations with activated hammerhand? I'm pretty sure they falchions will be a lot stronger in that scenario than the other weapons.

You have some hammerhand scenarios in the thread about how to load out terminators. The short if it, as expected, is that falchions monster it with hammerhand against T4 opponents. You get a bunch more dice and equally good (2+) chances to wound which means that each extra attack is very likely to wound.

 

Edit; this thread; http://www.bolterandchainsword.com/topic/295728-gk-terminators-halberds-or-falchions/