Tactical Squad Variants and Analysis

[arigatous]

If A > B then A+C > B+C, that's how maths works. If that inequality doesn't hold true, you've made a mistake somewhere

 

May be it would be easier to compare if we take 3 Crusader squads, which is pretty common.

 

3 PS Initiates (one per squad) cost 13*3+4*3=51 points.

 

3 CS Initiates cost 13*3=39 points. For 12 points difference we can buy an additional Neophyte and still have 1 point left.

 

3 PS vs MeQ will do 3*2/3*1/2*5/6=5/6=0.8333W per combat turn + 3 pistol shots.

 

8CS vs MeQ will do 8*2/3*1/2*1/3=8/9=0.8888W per combat turn + 4 pistol shots.

 

So for 51 points vs MeQ we are buying:

PS: 0.833W per turn + 3 pistols + 3 wounds.

 

And for 50 points vs MeQ we are buying:

CS: 0.888W per turn + 4 pistols + 4 wounds => much better deal!

Edited February 6, 2018 by arigatous

[Schlitzaf]

I mean it’s weird

Like 3 attacks to 2 Hits to 1 Wound. 1/6 of 1 of is 16.5, 1-1.65 = 0.835

2 Attacks to 1.32 Hits to 0.66 wounds. 1/6 of 0.66 is 0.11. 0.66-0.11 = 0.55

2 Attacks see above. 2/3 of 0.66 is 0.44. 0.66 - 0.44 = 0.22. 0.55 + 0.22 = 0.77

 

0.835 - 0.77 = 0.065. A regular Marine deals 0.22 Wounds. So for 4 Points or just under 1/3 of a Marine. You get just under 1/3 of Net increased in damage. Also....just so we are clear are you making 3++ Argument about Points Per Damage, based on Chassis and net damage output per point spent and not comparing the actual damage results based on mathhammer of Model vs Model. Because if you do Points per end damage formula, the Plasma Gun is really really inefficient Weapon. Because your actual damage output despite being factually higher, is actually per damage lower per point spent. Its same reasons why Gaurd Lasguns are more mathematically efficient than Marine Bolters simply because they are on a cheaper chassis. But the reality is that the actual effective damage output is more.

 

3++ is bad math. And the method of calculation skews heavy against any upgrade. Once again you cannot ignore the SB. The PowSword is better because how it makes the SB two attacks more reliable.

Edited February 6, 2018 by Schlitzaf

[arigatous]

So for 4 Points or just under 1/3 of a Marine. You get just under 1/3 of Net increased in damage.

 

That's exactly what I'm telling. VS MeQ while buying PS you get 1/3 increase in damage for the cost of 1/3 Marine. My arguments are:

 

1. If AS is worse than 3+, you get less than 1/3 increase in damage for the cost of 1/3 Marine. Actually, if the unit's IS is better than AS (imagine daemons) your damage vs paying for marine is halved.

 

2. When paying for marine in addition to 1/3 CC damage you also get 1/3 wound and 1/3 pistol attack for 4 points. When paying for PS instead you're getting only 1/3 increase in CC damage which is of course worse.

[Schlitzaf]

Because equipment costs points? Its the whole questions of boys vs toys. When you are putting a list together it’s much easier scavenge up 16 Points than 24 Points. 1 PlasmaGunner is equivalent math wise to 3 BolterBros (4 if Over) (1 > 0.66 > 0.44 or 0.55 > 0.37 or 0.45) vs (2 > 1.32 > 0.66 > 0.22). (For curosity sake, 1 powAx = 1 > 0.66 > 0.44 > 0.2966 or 0.30. Or just under half a Regular Initaite). Like the reason PowWeapons are good is because they enable answers and are cheap. A PowSword means for 4 Points, you won’t get stuck wet noodling Marines. By reducing variance, on defending end. With only 2 PowSword attacks you have 50/50 shot of actually killing. Win 3 PowSword attacks its 85/15.

 

(For those curious if we had double Fist, 3 > 1.5 > 1.25 > 1 vs 10 > 6.66 > 3.33 > 1.11. Double Fist is 50 Points and kills a Squad worth of Marines, which is basically same as a DoublePlasmaGun in Rapid. Similar cost too.) If we want to debate boys vs toys, I side with boys, but if we are arguing usability of a 4 Point upgrade over not doing so. I will disagree

[arigatous]

A PowSword means for 4 Points, you won’t get stuck wet noodling Marines. By reducing variance, on defending end. With only 2 PowSword attacks you have 50/50 shot of actually killing. Win 3 PowSword attacks its 85/15.

 

Potentially got your point now and it's actually a cool point. Let's do some count here.

 

Say we have a squad of 5 with combi, special, 2 PS, 2 CS.

 

And an alternative squad with CS instead of PS on Initiate.

 

What will be the chance for both of them to deal at least one wound or at least two wounds to an opposing MeQ squad? That will require a bit of hardcore math :)

 

The chance of CS attack to score at least one wound on MeQ is 1/9.

The chance of PS to score at least one wound on MeQ is 5/18

 

Here's the calculator for binomial probabilities: http://keisan.casio.com/exec/system/1223626305

 

1. At least one wound for 2PS squad: 1 - 0.38*0.55 = 79%

2. At least one wound for 1PS squad: 1 - 0.52*0.44 = 77%

 

So once per roughly 50 combat rounds 2 PS will score a wound where 1PS wouldn't score any. Not exactly what is called reliability :)

 

Now what about at least two wounds? It's a bit more complicated.

 

1. At least two wounds for 2PS squad: 1 - 0.38*0.55 - 0.55*0.43 - 0.35*0.38 = 42%

2. At least two wounds for 1PS squad: 1 - 0.52*0.44 - 0.52*0.38 - 0.44*0.40 = 40%

 

Same story. Once per 50 rounds 2PS squad will score an additional wound.

 

Let's go for at least 3 wounds!

 

1. 2PS squad: 1- 0.38*0.55 - 0.55*0.43 - 0.35*0.38 - 0.43*0.35 - 0.38*0.09 - 0.55*0.18 = 13.8%

2. 1PS squad: 1 - 0.52*0.44 - 0.52*0.38 - 0.44*0.40 - 0.38*0.40 - 0.52*0.14 - 0.44*0.08 = 13.8%

 

The probability of 3+ wounds is indeed too low to be reliable.

 

So do we have more reliability for the four additional points for a given squad? Yes. Is it significant? Seems like not. Could we benefit more if we added another body instead of 3PS in 3 Crusader Squads? Let's see.

 

1. At least one wound for 2PS squad:  79%

2. At least one wound for 1PS squad:  77%

3. At least one wound for 1PS squad + 1 extra body: 1 - 0.52*0.35 = 82%

 

5% over basic setup which means once per 20 rounds. Not really good as well.

 

1. At least two wounds for 2PS squad: 42%

2. At least two wounds for 1PS squad: 40%

3. At least two wounds for 1PS squad + 1 extra body: 1 - 0.52*0.35 - 0.52*0.39 - 0.35*0.40 = 47.5%

 

7.5% over basic setup which means once per 13 rounds which is better but still not enough.

 

What is the reliable add-on which really makes difference? Say, I want to be 90% sure in at least 1 wound.

 

4. At least one wound for 1PS squad + 4 extra bodies with CS: 1 - 0.52*0.17 = 91%

 

Now we're there!

 

What about the probability of 2 wounds?

 

4. At least two wounds for 1PS squad + 4 extra bodies with CS: 1 - 0.52*0.17 - 0.52*0.32 - 0.17*0.40 = 67.7%

 

That's the minimal Crusader squad that offers you at least one wound to MeQ with 90% probability and at least two - with 2/3 probability.

 

Uff. Seems like we all need to switch to Genestealers.

[Schlitzaf]

Why are you using such low squad numbers? At 5 Man, you shouldn’t take a PowSword take a heavy bolter. At 5 Man double Sword/Double Special, 5 Attacks + 3 PowSwords Attacks. That isn’t worth it. The PowSword is needed for Tide Squads to help push more damage in. At that stage your better off going Heavy/Special/Special because you’d rather have raw attack count to ward off bully units and ability to project range. 13-15 Man, when you have 20 odd some attacks, the 1-2 Extra Chainsword attacks are insignificant, but adding an extra PowSword is. The comparison you should be making is now often the third PowSword attack makes a significant increase in killing vs 2 PowSword. The difference between 23 and 25 Chainsword attacks (for those curious its, 23(25)>15.32(16.66)>7.66(8.33)>2.55(2.783). Where 3(2)>2(1.32)>1(0.66)>0.84(0.55)). Or 3.39 vs 3.33.) 4 Points notably increases its damage. All I can having used units and tried only having SB with PowSword and other Sgts, difference between 3 and 2 attacks is noticeable.

 

I just did couple sets 20 rolls using 3 Dice, and one of which is Off Color.

1st Set of 20; The extra attack resulted in dice wounding 6 additional times.

-ExtraDice: 6. NoExtra: 6. NoWounds: 8

2nd Set of 20; The extra attack resulted in dice wounding 7 additional times.

-ExtraDice: 7. NoExtra: 6. NoWounds: 7

3rd Set of 20; The extra attack resulted in dice wounding 2 additional times

-ExtraDice: 2. NoExtra: 8. NoWounds: 10

4th Set of 20; The extra attack resulted in dice wounding 6 additional times

-ExtraDice: 6. NoExtra: 10. NoWounds: 4

5th Set of 20; The extra attack resulted in dice wounding 9 additional times

-ExtraDice: 9. NoExtra; 7. NoWounds: 4

6th Set of 20; The extra attack resulted in dice wounding 4 additional times

-ExtraDice: 4. NoExtra; 10. NoWounds; 6

7th Set of 20; The extra attack resulted in dice wounding 7 additional times

-ExtraDice; 7. NoExtra: 5. NoWounds; 8

8th Set of 20; The extra attack resulted in dice wounding 8 additonal times

-ExtraDice; 8. NoExtra: 9. NoWounds; 3

 

The average of all the results calculated shortly. But just from looking at it the extra dice increase the wound chance by just over 66% (I know hilerious. That rolling 3 dice, that one a third of the times a wound has been caused, is caused by a specific dice). I know this is kinda self proving, a third of your wounds are caused by one third of the dice rolled. But that also means is a one third increase

 

The average additonal wound for 3rd attack is is unless my math fails 6.125. So if you fight 20 times that Is an additional combat Squad worth of Marines dead

Edited February 7, 2018 by Schlitzaf

[Schlitzaf]

So just 2 attacks normally

First Set of 20

TwoWounds: 1. OneWound: 4. ZeroWounds: 15

Second Set of 20

TwoWounds: 2. OneWound: 9. ZeroWounds: 9

Third Set of 20

TwoWounds: 2. OneWound: 9. ZeroWounds: 9

Four Set of 20

TwoWounds: 2. OneWound 7. ZeroWounds: 11

Fifth Set of 20

TwoWound: 1. OneWound: 12. ZeroWounds: 7

Sixth Set of 20

TwoWound: 2. OneWound: 8. ZeroWounds: 10

Seventh Set of 20

TwoWound: 0. OneWound: 8. ZeroWound: 12

Eight Set of 20

TwoWound: 2. OneWound: 7. ZeroWound: 11

 

So this tells us just over 50% of the results were missed and average wound count is somewhere around 12ish attacks. I’ll get actual averages calculated in a second.

 

So I missed Total 84 totals. For every 20 rounds I only wound 9.5 of them with two attacks. Compared to with 3 attacks, I only average hit 13.5. That is 33% increase in reliablity (and over 50%). Which is my point. And by raw wound count on average every 20 wounds you should in total 11 wounds. Or 3.3 net wounds vs Marines. That is 2 Marines just under 40% less than 1 PowWeapon. So if 4 Points, you are easily getting an substantial increased in killing power over not having it

Edited February 7, 2018 by Schlitzaf

[SyNidus]

Ok wow that's more math than i've ever wanted to see in my life.

 

But what does it mean for the non-mathematician like myself? Should i even bother with tactical squads?

 

Is there a role for them when scouts are so much cheaper and more flexible in their deployment and role?

 

Help meeee

[Schlitzaf]

They are mid field durable firefight squads. And Intercessors are better (must be field in mass or 4-6 squads of 5.) unless you really value heavy weapons. Or are Templars and Wolves with Crusaders/GreyHunters.

[Toxichobbit]

They are mid field durable firefight squads. And Intercessors are better (must be field in mass or 4-6 squads of 5.) unless you really value heavy weapons. Or are Templars and Wolves with Crusaders/GreyHunters.

 

Or want a transport that doesn't cost an arm and a leg.

[arigatous]

13-15 Man, when you have 20 odd some attacks, the 1-2 Extra Chainsword attacks are insignificant, but adding an extra PowSword is. 

 

That works exactly in the opposite way :) The more bodies you have at the squad, the less is the significance of an extra PS. If for 5 bodies squad it is 2%, then for 15 bodies squad it would be less than 2%.

 

Let's say you're aiming at doing at least 3 wounds to MeQ with a 15 bodies squad with 2 special, 5 boltguns, 2PS and 7 CS.

 

1. 2PS squad: 1- 0.38*0.07 - 0.07*0.43 - 0.21*0.38 - 0.43*0.21 - 0.38*0.27 - 0.07*0.18 = 65.8%

 

2. trade 1PS for CS: 1 - 0.52*0.06 - 0.52*0.18 - 0.06*0.40 - 0.18*0.40 - 0.52*0.25 - 0.06*0.08 = 64.4%

 

The difference would 1.4% - each 71th battle round that difference would matter.

[Schlitzaf]

I dunno, all I know is that at this point I can I notice a massive constiency difference between two PowSwords and three PowSwords attacks. And my math shows their is a appreciable notable increase with the third PowSword attack.

 

And so some hard dice roll simulations. Like I did above, because your math is wrong. Sense I know from experience and my own math that what you posted cannot be right. Maybe my math is wrong. But the dice rolls (160 iterations twice, with only variance is addition of a third dice) showed that I was correct in my experience. I can do another 160 iterations. When I get home from work.

 

But demonstrably the addition of a PowSword increased kill count by around a third. And the only two attacks gives an average of 9-10 wounds and failing to wound over 50%

Edited February 7, 2018 by Schlitzaf

[arigatous]

Thanks for the inspiration! I've just made an Excel-based reliability calculator which shows the probability of X or more wounds from mixed weapons unit A to unit B, and it's really interesting to play with. Will try to make it a bit more user-friendly later on and upload somewhere :)