3rd Edition Weapons Systems

Flamebeast · August 2, 2017

Most of the points in the OP are either changes in name only, or fixes the FFG were working on before we got disbanded. Good to see our work is being used, even if we aren't being credited.

S..Mike · August 3, 2017

In your example, the 2 markers are applied however the owning player decides.

Paladin21 · August 4, 2017

Need some clarification on the Linking/AD rules. In the original post, everything is dealt with in terms of models. Lead model plus linking models. Remove AD based on total damage to models that contributed, etc. Can you self-link in the new system? The summary, as provided, doesn't allow for it. When you link, do all weapons that link in have to be of the same type? If not, how do you figure out how to remove AD from the success pool? Do you add in all possible degradations based on which damages are applied to which systems? If you self-link weapons, do you count your damage accumulations per system, or is it just one reduction since it's a single model? If it's one reduction and there are multiple weapon system types, how do you account for that?

Just a few messy questions I came up with while pondering another issue.

murphy'slawofcombat · August 6, 2017

On 7/30/2017 at 2:17 PM, Meatshield said:

Again this doesn't address the key point of specific faction vs specific faction boosts.

The whole premise of torps being stronger applies to everyone, it is not a specific faction vs specific faction boost, unlike v3 Kinetics which are.

Yes, I agree and I will also say if it ain't broke don't fix it. the shields and kinetics cancel each other out or balance as is in V2. Denzi's get an up when you took FF out of the equation and that is what I believe

Xerkics · August 6, 2017

Im more concerned with how cloaks are way weaker now against ALL kinds of weapons.

CoreHunter · August 6, 2017

More planet fall shenanigans working its way into armada. Why is that? A half baked Simi stillborn v2 of a game system is being forced into the more successful system. When the v2 rules of planet fall was put out for players to test primary complaints remains focuse fire and command point balance issues.

And now the better version of cloak is being replaced for no reason. And the retractable plating defence that was awesome is gone. If sectored shielding remains that makes the removal of retractable plating even more ridiculous as they both need a token to represent.

CoreHunter · August 6, 2017

Also not seeing any point to renaming range bands just calling them range 1-4 is fairly simple and quick. Even in planet fall this was a silly decision.

murphy'slawofcombat · August 6, 2017

On 8/2/2017 at 9:03 PM, Spartan_FA_Mike said:

In your example, the 2 markers are applied however the owning player decides.

sorry i feel it should be 2 per ship assuming they are all w/n 4"

Mathhammer · August 6, 2017

@Spartan_FA_Mike

I was discussing the 3.0 rules and a question cam up this weekend

Given 3 ships (ship A, B C)

All 3 ships have 2 points of damage on the

All 3 ships have 3 primary weapons W1,W2,W3

Question:

If I combine all weapons into a single attack

(A-W1 + A-W2 + A-W3) + (B-W1 + B-W2 + B-W3) + (C-W1 + C-W2 + C-W3) - (A-D + B-D + C-D) =

>> Do I only remove 6 dice from the success ? (2 damage per ship)

Question

If I combine across the ships to form three attacks

(A-W1) + (B-W1) + (C-W1) - (A-D + B-D + C-D) =

(A-W2) + (B-W2) + (C-W2) - (A-D + B-D + C-D) =

(A-W3) + (B-W3) + (C-W3) - (A-D + B-D + C-D) =

>> Does each attack remove 6 dice from their success pool? ( 2 damage from each ship)

Question

If I combine all the weapons per ship into a single attack:

(A-W1 + A-W2 + A-W3) - (A-D) =

(B-W1 + B-W2 + B-W3) - (B-D) =

(C-W1 + C-W2 + C-W3) - (A-D) =

>> Do I only loose 2 dice from each succcess pool? (from the ship attacking)

In Summary:

In the new system it would always be better to

Best > combine all weapons on a single ship

Meh > combine all weapons across multiple ships

bad > combine single weapons across ships.

So the damage pool reasserts itself every time I add in a new ship, where the old damage pool asserted it self every time I added in a weapon.

azrael · August 8, 2017

I am liking that there can be a lot more differences between weapons now. This could really make ships firepower feel different. If it does the same as the change from v1 (2 types of weapon) to v2 (about 7) AND easier/different linking values

Looking forward to using them to blow the enemy away

WestAustralian · August 8, 2017

Wow @Mathhammer.

Started reading above--^

Living up to your Forum Name. I feel like my brain has been Math Hammered!

S..Mike · August 8, 2017

I'm an engineer, and I had to read it a couple times to make sure I understood.

It generated a couple of clarifying questions on my side, so I'll respond back when I have those definitive answers.

Xerkics · August 8, 2017

Removing successes rather than dice seems counter intuitive for the system thats all about exploding dice.

Sniddy · August 8, 2017

It's not all about it, and a dice is about 0.8 of a success so it's not huge

-5 success or -5 dice, is only 1 difference and if you roll hot.....so I can live with either way one can lead to some hilarious shots into nothing rolling 8 sixes from nowhere...so

Mathhammer · August 8, 2017

@Spartan_FA_Mike

UPDATE: added the .81 probability @Spartan_FA_Mike quoted in a follow up post.

UPDATE: Clearly marked confidence verses probability

Okay lets talk about the number of success and how the new math effects it.

Summary:

In undamaged ships the numbers are - 1 hit (because the weapon is an odd number)
In damaged ships the numbers belly out the more ships brought in.

The biggest changes I see is:

Once there is damage It is better to link a single ship together.
If the damage on a ship plus 2 is equal to the total number of dice the ship can provide, then don't add that ship.
Long range shots with damage ships is weaker than before.

Math work:

Given: Average Hits is the exact number of hits with at least an 80% chance (See appendix)

Given the following ship

Terran Cruiser Teuton
- No weapon Shielding
3 ships
    Tc1,Tc2,Tc3
Weapons
    P1   = [5,7,3]
    Psf1 = [3,4,2] (version 3 supporting fire)
2 Damage Profiles
    D1 = 0
    D2 = 2

(*) Example Terran Cruise Teuton
(-) Version 2.0 Math

Link the Fixed weapons ( no damage)
Dice Pool = Tc1(P1[1])-Tc1(D1)+(Tc2(P1[1])- Tc2(D1) + Tc3(P1[1])- Tc3(D1) ) / 2
Dice Pool = 7-0+(7-0+7-0)/2
Dice Pool = 14
80% confidence
Average hits = 8
.81 probability
Average hits = 11

Link the Fixed weapons (equal damage)
Dice Pool = Tc1(P1[1])-Tc1(D2)+(Tc2(P1[1])- Tc2(D2) + Tc3(P1[1])- Tc3(D2) ) / 2
Dice Pool = 7-2+(7-2+7-2)/2
Dice Pool = 10
80% confidence
Average hits = 5
.81 probability
Average hits = 8

Link the Fixed weapons (mixed numbers)
Dice Pool = Tc1(P1[1])-Tc1(D2)+(Tc2(P1[0])- Tc2(D1) + Tc3(P1[3])- Tc3(D2) ) / 2
Dice Pool = 7-2+(5-0+3-2)/2
Dice Pool = 8
80% confidence
Average hits = 4
.81 probability
Average hits = 6

Link the Fixed weapons (max range damaged)
Dice Pool = Tc1(P1[3])-Tc1(D2)+(Tc2(P1[3])- Tc2(D2) + Tc3(P1[3])- Tc3(D2) ) / 2
Dice Pool = 3-2+(3-2+3-2)/2
Dice Pool = 2
(minimum of 1 Attack Dice per additional contributing Weapon System. pg. 62)
Dice Pool = 3
80% confidence
Average hits = 1
.81 probability
Average hits = 2

(-) Version 3.0 Math

Link the Fixed weapons ( no damage)
Dice Pool = Tc1(P1[1]) + Tc2(Psf1[1]) + Tc3(Psf1[1])
Dice Pool = 7+4+4
Dice Pool = 15
Average hits = AvgHits(Dp)-Tc1(D1)-Tc2(D1)-Tc3(D1)
80% confidence
    Average hits = 8-0-0-0
    Average hits = 8
.81 probability
    Average hits = 12-0-0-0
    Average hits = 12

Link the Fixed weapons (equal damage)
Dice Pool = Tc1(P1[1]) + Tc2(Psf1[1]) + Tc3(Psf1[1])
Dice Pool = 7+4+4
Dice Pool = 15
Average hits = AvgHits(Dp)-Tc1(D2)-Tc2(D2)-Tc3(D2)
80% confidence
    Average hits = 8-2-2-2
    Average hits = 2
.81 probability
    Average hits = 12-2-2-2
    Average hits = 6

Link the Fixed weapons (mixed numbers)
Dice Pool = Tc1(P1[1])-Tc1(D2)+(Tc2(P1[0])- Tc2(D1) + Tc3(P1[3])- Tc3(D2) ) / 2
Dice Pool = 7+3+2
Dice Pool = 12
Average hits = AvgHits(Dp)-Tc1(D2)-Tc2(D1)-Tc3(D2)
80% confidence
    Average hits = 6-2-0-2
    Average hits = 2
.81 probability
    Average hits = 9-2-2-2
    Average hits = 3

Link the Fixed weapons (max range damaged)
Dice Pool = Tc1(P1[3]) + Tc2(Psf1[3]) + Tc3(Psf1[3])
Dice Pool = 3+2+2
Dice Pool = 7
Average hits = AvgHits(Dp)-Tc1(D2)-Tc2(D2)-Tc3(D2)
80% confidence
    Average hits = 3-2-2-2
    Average hits = 0
.81 probability
    Average hits = 5-2-2-2
    Average hits = 0

Appendix:
Dice rolling Chart (C code 1000000 dice group rolls per line)

Cliped at above 79%

                                      Percentage to get at least this many hits. (4+)
  Hits       0     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18 Rest
Dice( 1) 100.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 2) 100.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 3) 100.0  87.5   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 4) 100.0  93.7   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 5) 100.0  96.9  86.4   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 6) 100.0  98.5  92.2  80.2   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 7) 100.0  99.2  95.6  87.4   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 8) 100.0  99.6  97.6  92.2  82.9   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 9) 100.0  99.8  98.6  95.2  88.6   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(10) 100.0  99.9  99.2  97.1  92.6  85.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(11) 100.0 100.0  99.6  98.3  95.3  89.8  81.8   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(12) 100.0 100.0  99.8  99.0  97.0  93.2  87.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(13) 100.0 100.0  99.9  99.4  98.2  95.5  90.9  84.3   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(14) 100.0 100.0  99.9  99.7  98.9  97.1  93.8  88.6  81.6   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(15) 100.0 100.0 100.0  99.8  99.3  98.1  95.8  91.9  86.3   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(16) 100.0 100.0 100.0  99.9  99.6  98.8  97.2  94.4  90.0  84.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(17) 100.0 100.0 100.0  99.9  99.8  99.3  98.1  96.1  92.8  88.0  81.7   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(18) 100.0 100.0 100.0 100.0  99.9  99.5  98.8  97.4  94.9  91.2  86.0  79.4   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(19) 100.0 100.0 100.0 100.0  99.9  99.7  99.3  98.3  96.5  93.6  89.5  84.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(20) 100.0 100.0 100.0 100.0  99.9  99.8  99.5  98.8  97.5  95.4  92.2  87.7  82.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(21) 100.0 100.0 100.0 100.0 100.0  99.9  99.7  99.2  98.3  96.8  94.3  90.7  86.0  80.0   0.0   0.0   0.0   0.0   0.0    0.0

Mathhammer · August 8, 2017

@Spartan_FA_Mike

@WestAustralian

Summary:

In undamaged ships the numbers are the same.
Always link on a single ship first an foremost
If the total dice from the additional ship is less than equal to the damage +2 it's not worth it.
Damage ships are quickly useless accept for low percentage hopes and dreams.
If your linking just one weapon off a ship with 2 or more damage it's not worth it.

UPDATE: Add the .81 probability numbers

Given:

3 ships with each having 2 - 6 dice weapons total of 6 hull points
each weapon is 3 dice for supporting fire.

1 Ship 1 Weapon Version 2.0

Lead  Support  Total Damage     Final  Hits
Dice   Dice     Dice  per     80%   40%   .81
   6     0       6     0       3     5     5
   5     0       5     1       2     4     4
   4     0       4     2       1     3     3
   3     0       3     3       1     3     2
   2     0       2     4       0     2     2
   1     0       1     5       0     1     1

1 Ship 1 Weapon Version 3.0

Lead  Support  Total Damage     Final  Hits
Dice   Dice     Dice  per     80%   40%   .81
   6     0       6     0       3     5     5
   6     0       6     1       2     4     4
   6     0       6     2       1     3     3
   6     0       6     3       0     2     2
   6     0       6     4       0     1     1
   6     0       6     5       0     0     0

Link 1 Ship 2 Weapon Version 2.0

Lead  Support  Total Damage  Final  Hits
Dice   Dice     Dice  per     80%   40%
   6     3       9     0       4     8
   5     2       7     1       3     6
   4     2       6     2       3     5
   3     1       4     3       1     3
   2     1       3     4       1     3
   1     1       2     5       0     2

Link 1 Ship 2 Weapon Version 3.0

Lead  Support  Total Damage  Final  Hits
Dice   Dice     Dice  per     80%   40%
   6     3       9     0       4     8
   6     3       9     1       3     7
   6     3       9     2       2     6
   6     3       9     3       1     5
   6     3       9     4       0     4
   6     3       9     5       0     3

Link 3 Ship 1 Weapon Version 2.0

Lead  Support  Total Damage     Final  Hits
Dice   Dice     Dice  per     80%   40%   .81
   6     6      12     0       6    10    10
   5     5      10     1       5     9     8
   4     4       8     2       4     7     6
   3     3       6     3       3     5     5
   2     2       4     4       1     3     3
   1     2       3     5       1     3     2

Link 3 Ship 1 Weapon Version 3.0

Lead  Support  Total Damage  Final  Hits
Dice   Dice     Dice  per     80%   40%
   6     6      12     0       6    10
   6     6      12     1       3     7
   6     6      12     2       0     1
   6     6      12     3       0     0
   6     6      12     4       0     0
   6     6      12     5       0     0

Link 3 Ship 2 Weapon Version 2.0

Lead  Support  Total Damage     Final  Hits
Dice   Dice     Dice  per     80%   40%   .81
   6    15      21     0      13    18    17
   5    12      17     1      10    14    14
   4    10      14     2       8    12    11
   3     7      10     3       5     9     8
   2     5       7     4       3     6     6
   1     5       6     5       3     5     5

Link 3 Ship 2 Weapon Version 3.0

Lead  Support  Total Damage     Final  Hits
Dice   Dice     Dice  per     80%   40%   .81
   6    15      21     0      13    18    17
   6    15      21     1      10    15    14
   6    15      21     2       7    12    11
   6    15      21     3       4     9     8
   6    15      21     4       1     6     5
   6    15      21     5       0     3     2

Appendix A:

Cliped at above 79%

                                      Percentage to get at least this many hits. (4+)
  Hits       0     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18 Rest
Dice( 1) 100.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 2) 100.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 3) 100.0  87.5   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 4) 100.0  93.7   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 5) 100.0  96.9  86.4   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 6) 100.0  98.5  92.2  80.2   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 7) 100.0  99.2  95.6  87.4   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 8) 100.0  99.6  97.6  92.2  82.9   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 9) 100.0  99.8  98.6  95.2  88.6   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(10) 100.0  99.9  99.2  97.1  92.6  85.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(11) 100.0 100.0  99.6  98.3  95.3  89.8  81.8   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(12) 100.0 100.0  99.8  99.0  97.0  93.2  87.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(13) 100.0 100.0  99.9  99.4  98.2  95.5  90.9  84.3   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(14) 100.0 100.0  99.9  99.7  98.9  97.1  93.8  88.6  81.6   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(15) 100.0 100.0 100.0  99.8  99.3  98.1  95.8  91.9  86.3   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(16) 100.0 100.0 100.0  99.9  99.6  98.8  97.2  94.4  90.0  84.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(17) 100.0 100.0 100.0  99.9  99.8  99.3  98.1  96.1  92.8  88.0  81.7   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(18) 100.0 100.0 100.0 100.0  99.9  99.5  98.8  97.4  94.9  91.2  86.0  79.4   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(19) 100.0 100.0 100.0 100.0  99.9  99.7  99.3  98.3  96.5  93.6  89.5  84.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(20) 100.0 100.0 100.0 100.0  99.9  99.8  99.5  98.8  97.5  95.4  92.2  87.7  82.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(21) 100.0 100.0 100.0 100.0 100.0  99.9  99.7  99.2  98.3  96.8  94.3  90.7  86.0  80.0   0.0   0.0   0.0   0.0   0.0    0.0

Appendix B:

Cliped at above 39%
                                      Percentage to get at least this many hits. (4+)
  Hits       0     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18 Rest
Dice( 1) 100.0  50.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 2) 100.0  75.0  41.7   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 3) 100.0  87.6  62.5  39.6   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 4) 100.0  93.8  77.1  56.3   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 5) 100.0  96.9  86.5  70.0  52.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 6) 100.0  98.4  92.2  80.2  64.7  48.7   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 7) 100.0  99.2  95.6  87.4  75.0  60.6  46.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 8) 100.0  99.6  97.5  92.2  82.9  70.6  57.1  43.8   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice( 9) 100.0  99.8  98.6  95.2  88.6  78.9  66.9  54.1  41.8   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(10) 100.0  99.9  99.2  97.1  92.6  85.1  75.1  63.5  51.4  40.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(11) 100.0 100.0  99.6  98.3  95.3  89.8  81.8  71.7  60.5  49.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(12) 100.0 100.0  99.8  99.0  97.0  93.2  87.0  78.6  68.6  57.8  47.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(13) 100.0 100.0  99.9  99.4  98.2  95.5  90.9  84.2  75.7  65.8  55.3  45.1   0.0   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(14) 100.0 100.0  99.9  99.7  98.9  97.1  93.8  88.6  81.6  73.0  63.3  53.3  43.5   0.0   0.0   0.0   0.0   0.0   0.0    0.0
Dice(15) 100.0 100.0 100.0  99.8  99.3  98.1  95.8  91.9  86.3  79.0  70.3  60.8  51.2  41.8   0.0   0.0   0.0   0.0   0.0    0.0
Dice(16) 100.0 100.0 100.0  99.9  99.6  98.8  97.2  94.4  90.0  84.0  76.5  67.8  58.6  49.2  40.3   0.0   0.0   0.0   0.0    0.0
Dice(17) 100.0 100.0 100.0  99.9  99.8  99.3  98.2  96.1  92.8  88.0  81.6  74.1  65.4  56.4  47.4   0.0   0.0   0.0   0.0    0.0
Dice(18) 100.0 100.0 100.0 100.0  99.9  99.6  98.8  97.4  94.9  91.2  86.0  79.4  71.8  63.3  54.5  45.8   0.0   0.0   0.0    0.0
Dice(19) 100.0 100.0 100.0 100.0  99.9  99.7  99.2  98.2  96.4  93.6  89.4  83.9  77.2  69.5  61.2  52.6  44.3   0.0   0.0    0.0
Dice(20) 100.0 100.0 100.0 100.0  99.9  99.8  99.5  98.8  97.6  95.4  92.2  87.7  82.0  75.2  67.5  59.3  51.0  42.8   0.0    0.0
Dice(21) 100.0 100.0 100.0 100.0 100.0  99.9  99.7  99.3  98.4  96.8  94.3  90.8  86.0  80.1  73.2  65.5  57.4  49.3  41.5    0.0

Edited August 9, 2017 by Mathhammer
Added some .81 numbers

WestAustralian · August 9, 2017

Wow @Mathhammer. Thanks for diving into the maths on these dice. I wonder if these results will surprise the Developers and Playtesters. Hopefully your conclusions have already been apparent in play testing.

BTW, thanks for your conclusions, I can't concentrate on the numbers for that long.

Once the rules are final I will expect a nice list of conclusions

Hive · August 9, 2017

Okay, @Mathhammer,so to put it in layman's terms- any given ship in a squad has to be contributing at least 2 more dice than the amount of damage it has taken, or it will be better off firing on its own rather than linking. Is this correct? If that's the case, given 2.0's stat blocks, the majority of medium ships when damaged at all will only want to link in their ideal range bands, right?

Bessemer · August 9, 2017

(Head Explodes)

S..Mike · August 9, 2017

So, that's a lot of numbers.

One correction to the supporting dice assumption, the half values from AD are rounded up, not down, so the supporting fire on these ships would be at 4, not 3.

Not sure why you capped the percentage on your tables the way you did. There is a disconnect somewhere though, in that an exploding dice generates ~0.8 hits on average. I wrote up a small python script to actually roll the dice a bunch of times, repeating the roll when a '6' came up, just to verify this.

So, to utilize your scenarios:

(*) Example Terran Cruise Teuton
(-) Version 2.0 Math

(Version 3 Math comparison in red to avoid scrolling up and down the screen)
Link the Fixed weapons ( no damage)
Dice Pool = Tc1(P1[1])-Tc1(D1)+(Tc2(P1[1])- Tc2(D1) + Tc3(P1[1])- Tc3(D1) ) / 2
Dice Pool = 7-0+(7-0+7-0)/2 (7+4+4)
Dice Pool = 14 (15)
Average hits = 11 (12)

Link the Fixed weapons (equal damage)
Dice Pool = Tc1(P1[1])-Tc1(D2)+(Tc2(P1[1])- Tc2(D2) + Tc3(P1[1])- Tc3(D2) ) / 2
Dice Pool = 7-2+(7-2+7-2)/2 (7+4+4)
Dice Pool = 10 (15)
Average hits = 8 (12-6 = 6)

Link the Fixed weapons (mixed numbers)
Dice Pool = Tc1(P1[1])-Tc1(D2)+(Tc2(P1[0])- Tc2(D1) + Tc3(P1[3])- Tc3(D2) ) / 2
Dice Pool = 7-2+(5-0+3-2)/2 (7+3+2)
Dice Pool = 8 (12)
Average hits = 6 (9)

Link the Fixed weapons (max range damaged)
Dice Pool = Tc1(P1[3])-Tc1(D2)+(Tc2(P1[3])- Tc2(D2) + Tc3(P1[3])- Tc3(D2) ) / 2
Dice Pool = 3-2+(3-2+3-2)/2 (3+2+2)
Dice Pool = 2 (7)
(minimum of 1 Attack Dice per additional contributing Weapon System. pg. 62)
Dice Pool = 3 (7)
Average hits = 2 (5-6 = 0) (yeah, not good here, but we're not hitting ships in either case with so few hits)

So, yes, there does come a point when your ships are damaged to the point where an attack isn't doing much. It probably wasn't doing much at that long range anyway. Consider, though, if you were to place a Focused Fire order on this squadron. That +1 to-hit pushes your average hits/die to ~0.99...making even a damaged squadron dangerous.

Torpedoes (and any other encased weapon) become much more important during the latter stages of the game. As are boarding and targeted strikes, where you can take the PD Network offline.

Mathhammer · August 9, 2017

6 hours ago, Spartan_FA_Mike said:

So, that's a lot of numbers.

One correction to the supporting dice assumption, the half values from AD are rounded up, not down, so the supporting fire on these ships would be at 4, not 3.

Not sure why you capped the percentage on your tables the way you did. There is a disconnect somewhere though, in that an exploding dice generates ~0.8 hits on average. I wrote up a small python script to actually roll the dice a bunch of times, repeating the roll when a '6' came up, just to verify this.

So, to utilize your scenarios:

(*) Example Terran Cruise Teuton
(-) Version 2.0 Math

(Version 3 Math comparison in red to avoid scrolling up and down the screen)
Link the Fixed weapons ( no damage)
Dice Pool = Tc1(P1[1])-Tc1(D1)+(Tc2(P1[1])- Tc2(D1) + Tc3(P1[1])- Tc3(D1) ) / 2
Dice Pool = 7-0+(7-0+7-0)/2 (7+4+4)
Dice Pool = 14 (15)
Average hits = 11 (12)

Link the Fixed weapons (equal damage)
Dice Pool = Tc1(P1[1])-Tc1(D2)+(Tc2(P1[1])- Tc2(D2) + Tc3(P1[1])- Tc3(D2) ) / 2
Dice Pool = 7-2+(7-2+7-2)/2 (7+4+4)
Dice Pool = 10 (15)
Average hits = 8 (12-6 = 6)

Link the Fixed weapons (mixed numbers)
Dice Pool = Tc1(P1[1])-Tc1(D2)+(Tc2(P1[0])- Tc2(D1) + Tc3(P1[3])- Tc3(D2) ) / 2
Dice Pool = 7-2+(5-0+3-2)/2 (7+3+2)
Dice Pool = 8 (12)
Average hits = 6 (9)

Link the Fixed weapons (max range damaged)
Dice Pool = Tc1(P1[3])-Tc1(D2)+(Tc2(P1[3])- Tc2(D2) + Tc3(P1[3])- Tc3(D2) ) / 2
Dice Pool = 3-2+(3-2+3-2)/2 (3+2+2)
Dice Pool = 2 (7)
(minimum of 1 Attack Dice per additional contributing Weapon System. pg. 62)
Dice Pool = 3 (7)
Average hits = 2 (5-6 = 0) (yeah, not good here, but we're not hitting ships in either case with so few hits)

So, yes, there does come a point when your ships are damaged to the point where an attack isn't doing much. It probably wasn't doing much at that long range anyway. Consider, though, if you were to place a Focused Fire order on this squadron. That +1 to-hit pushes your average hits/die to ~0.99...making even a damaged squadron dangerous.

Torpedoes (and any other encased weapon) become much more important during the latter stages of the game. As are boarding and targeted strikes, where you can take the PD Network offline.

The math differences is probably down to the act you rolled one die and I was rolling groups of dice. In a real world scenario multiple dice rolling is better modeled by a Binomial probability model. The issue with using the formula directory is the math for computing the odds of a single success isn't simple. So I rolled groups of dice (1 million groups rolled) and then capped my odds at getting at least X number of success 80% of the time. This gives a good feeling for what you can see, and what you can play to in numbers. The second breakdown I added a 40% level to allow for people to see more of what they "hope" to see.

I will update the post above with your notes and see how it rolls out.

@Spartan_FA_Mike

I will say after doing this, and considering it after the fact I think this new dice mechanism should be thrown out. It has fundamental flaw that has nothing to do with numbers. Using the system started to give me a bad taste because of how the mechanics work.

Compute Dice Pool
Roll dice pool
Subtract hits
Opponent resist the damage
Apply the effects

Step 3 should never be after step 2. Rolling the dice is where a player generates their hope and dreams, that magic number of seeing successes. And with version 3.0 right after your like, nope, give me 9 of those dice rolls back. The "feeling" or "emotions" that set of steps generates will leave a negative feeling in the player; which, I think in the long run will damage their view of the game. I was considering some ways to swap steps 3 and 2 in the back of my head, the simplest is to add up the damage from the primary ship and all ships linking. The primary can be counted twice if it is a primary weapon and a link weapon) the subtract from the dice pool. (At least I was rolling numbers around this seemed about right).

I will stress I think forcing a player to remove successes from their dice pool leads to bad feelings about the game even if mathematically it's sound.

Xerkics · August 9, 2017

2 minutes ago, Mathhammer said:

The math differences is probably down to the act you rolled one die and I was rolling groups of dice. In a real world scenario multiple dice rolling is better modeled by a Binomial probability model. The issue with using the formula directory is the math for computing the odds of a single success isn't simple. So I rolled groups of dice (1 million groups rolled) and then capped my odds at getting at least X number of success 80% of the time. This gives a good feeling for what you can see, and what you can play to in numbers. The second breakdown I added a 40% level to allow for people to see more of what they "hope" to see.

I will update the post above with your notes and see how it rolls out.

@Spartan_FA_Mike

I will say after doing this, and considering it after the fact I think this new dice mechanism should be thrown out. It has fundamental flaw that has nothing to do with numbers. Using the system started to give me a bad taste because of how the mechanics work.

Compute Dice Pool

Roll dice pool

Subtract hits

Opponent resist the damage

Apply the effects

Step 3 should never be after step 2. Rolling the dice is where a player generates their hope and dreams, that magic number of seeing successes. And with version 3.0 right after your like, nope, give me 9 of those dice rolls back. The "feeling" or "emotions" that set of steps generates will leave a negative feeling in the player; which, I think in the long run will damage their view of the game. I was considering some ways to swap steps 3 and 2 in the back of my head, the simplest is to add up the damage from the primary ship and all ships linking. The primary can be counted twice if it is a primary weapon and a link weapon) the subtract from the dice pool. (At least I was rolling numbers around this seemed about right).

I will stress I think forcing a player to remove successes from their dice pool leads to bad feelings about the game even if mathematically it's sound.

Right on there about bad feelings taking away things post roll always feels sucky . Glad someone mathed this out properly for a change so its not just a feeling.

Xystophoroi · August 9, 2017

Hmmm. From the PoV of the shooting player:

"The die is cast!"

vs

"The die is cast and then I remove some of what it says."

S..Mike · August 9, 2017

2 hours ago, Mathhammer said:

The math differences is probably down to the act you rolled one die and I was rolling groups of dice. In a real world scenario multiple dice rolling is better modeled by a Binomial probability model.

Actually, I had the python script roll the dice 1,000,000 times, in a series of combinations, say 15d6, one million times. Or 5d6, or 2d6, or whatever, that million times. The script is actually rolling dice and exploding the 6's, counting the hits and finding the average number of hits for whichever combination you choose. Regardless of the number of Xd6 you throw, the average result you can expect is ~0.799 hits per die in your initial throw.

Numerical modeling vs. simulation aside,

2 hours ago, Mathhammer said:

I will say after doing this, and considering it after the fact I think this new dice mechanism should be thrown out. It has fundamental flaw that has nothing to do with numbers. Using the system started to give me a bad taste because of how the mechanics work.

Compute Dice Pool

Roll dice pool

Subtract hits

Opponent resist the damage

Apply the effects

I can accept that it 'feels wrong' to you, and to others. I agree with you that it has nothing to do with the numbers, so we can leave that part out. We're dealing with emotion which is not something we can model in the computer, at least not within our scope here.

First off, the linking dice pool mechanic of 2nd Edition is a barrier for entry to new players. Every time I have had to teach the game, this step in firing the weapons has been a headache to get people to remember how to work with. Just look at the comparison between the math: Dice Pool = 7-2+(5-0+3-2)/2 vs. (7+3+2). The formula on the left is enough to turn away potential players.

As for the argument "You take away the success that I rolled, and that is bad" the equal argument can be made that "I didn't even get to roll as many dice as I thought, you took it away before I even had a chance to get something." At some point your going to be removing results due to damage, shields, PD, or whatever. The revised system makes for an easier and faster method for shooting. For all of us that did it the 2nd edition way, it's an adjustment. But for new players (and we need those people to come in), they probably won't notice the difference.

It's not fundamentally flawed, but it is different from what you are used to.

Xystophoroi · August 9, 2017

3 minutes ago, Spartan_FA_Mike said:

First off, the linking dice pool mechanic of 2nd Edition is a barrier for entry to new players. Every time I have had to teach the game, this step in firing the weapons has been a headache to get people to remember how to work with. Just look at the comparison between the math: Dice Pool = 7-2+(5-0+3-2)/2 vs. (7+3+2). The formula on the left is enough to turn away potential players.

I don't think people are arguing for retaining the 2nd edition rules exactly. People seemed generally very positive about the split Lead/Linked change AND treating damage across squadrons rather than individual ships.

So. 3 ships, lead 6, linked 3, one ship has 1 damage, one has 2.

6+3+3 (lead+linked) - 3 (damage) means roll 6 dice rather than roll 9 dice, subtract 3 successes.

3rd Edition Weapons Systems

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