Tactical Command
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The Bell Formula
http://www.tacticalwargames.net/taccmd/viewtopic.php?f=123&t=9476		 Page 1 of 2
Author:  Raysokuk [ Thu May 17, 2007 6:30 pm ]
Post subject:  The Bell Formula
I've set myself the task of coming up with the best points sytem that I can for BFG! In the end it might not be completely accurate, I doubt that a points formula ever could be, but hopefully it'll be close.

This may take a while so I'm going to add to (edit) this first post as the rules develop.

I'm approaching this as if each ship (or spacestation, or whatever) was a weapon with a set amount of destruction for each game, this value will be the points value.

The average damage caused by one weapon can be quite easily calculated. This will be the starting point: the average damage dealt by all a ships weapons. But Fire Arcs are very important and so must be factored in.

The more game turns it shoots the more destruction it can cause in a game, this will be determined by durability(including manuverability), range and speed(including turning).

So by calculating the average damage a ship can do in a game we will come up with the points value.

Other factors are important to concider like Ld, boarding, special rules etc..

Cheers,

RayB
Author:  blackhorizon [ Thu May 17, 2007 7:09 pm ]
Post subject:  The Bell Formula
All right, this is gonna be interesting!
Author:  CyberShadow [ Fri May 18, 2007 7:52 am ]
Post subject:  The Bell Formula
Extremely interesting. Count me in with this. By points values, do you mean the points value set by GW/SG or are you going to create new values for vessels?

While I am naturely sceptical of any points value, you system does seem interesting. Let me know how I can help out. Can we put the final version in Warp Rift and hosted here?

And.... why are you telling people not to date robots? I know some lovely robots.  ???
Author:  Otterman [ Fri May 25, 2007 9:33 pm ]
Post subject:  The Bell Formula
He's referring to the Futurama episode 'I Dated a Robot'
Author:  Lord Aaron [ Sun May 27, 2007 5:15 am ]
Post subject:  The Bell Formula
I'v seen a few around, but most are easily abused.
Author:  CyberShadow [ Sun May 27, 2007 9:51 am ]
Post subject:  The Bell Formula
Ultimately, any points value system is open to abuse. I firmly believe that the points system is a rough estimate, but that since both sides should be using the same system it is mostly fair.

For example, a space station may be great in defence but really bad in assault scenarios, so the points value wont accurately reflect its effectiveness in the game.
Author:  Raysokuk [ Tue Jun 12, 2007 1:28 pm ]
Post subject:  The Bell Formula
Weapon Comparisons (this post will most likely be edited):

Weapons batteries Strength 6
0-15cm range, cap ship closing (hitting on a 2+): 4+ Armour= 2.5, 5+= 1.66.., 6+= 0.833..
Locked on: 4+ Armour= 3.75, 5+= 2.77.., 6+= 1.5277..
15-30cm range, cap ship closing (hitting on a 3+): 4+ Armour= 2, 5+= 1.33.., 6+= 0.66..
Locked on: 4+ Armour= 3, 5+= 2.22.., 6+= 1.22..
30-60cm range, cap ship closing (hitting on a 4+): 4+ Armour= 1.5, 5+= 1, 6+= 0.5
Locked on: 4+ Armour= 2.25, 5+= 1.66.., 6+= 0.9166..

15-30cm range, cap ship abeam (hitting on a 5+): 4+ Armour= 1, 5+= 0.66.., 6+= 0.33..
Locked on: 4+ Armour= 1.5, 5+= 1.11.., 6+= 0.611 ..
15-30cm range, escort abeam (hitting on a 6+): 4+ Armour= 0.5, 5+= 0.33.., 6+= 0.166..
Locked on: 4+ Armour= 0.75, 5+= 0.55.., 6+= 0.3055..

Bombardment Cannons Strength 4
0-15cm range, cap ship closing (hitting on a 2+): 4+ Armour= 1.66..
Locked on: Any Armour= 2.5
15-30cm range, cap ship closing (hitting on a 3+): 4+ Armour= 1.33..
Locked on: Any Armour= 2
15-30cm range, cap ship moving away (hitting on a 4+): 4+ Armour= 1
Locked on: Any Armour= 1.5
15-30cm range, cap ship abeam (hitting on a 5+): 4+ Armour= 0.66..
Locked on: Any Armour= 1
15-30cm range, escort abeam (hitting on a 6+): 4+ Armour= 0.33..
Locked on: Any Armour= 0.5


Lances Str 2
Any target: Any armour= 1
Locked on: Any armour= 1.5

Pulsar Str 1
Any target: Any armour= 0.875
Locked on: Any armour= 1.734375

Phantom Lance Str 1
Any target: Any armour= 0.833..
Locked on: Any armour= 1.25


Torpedoes Str 4 (ignoring turrets).
Any target: 4+ Armour= 2, 5+= 1.33.., 6+= 0.66..

Eldar Torps Str 4 (ignoring turrets).
Any target: 4+ Armour= 3, 5+= 2.22.., 6+= 1.22..

Bombers 2 Markers (ignoring markers lost to turrets)
0 turrets, 7 attack runs: 4+ Armour= 3.5, 5+= 2.33.., 6+= 1.166..
1 turret, 5 attack runs: 4+ Armour= 2.5, 5+= 1.66.., 6+= 0.833..
2 turrets, 3.33.. attack runs: 4+ Armour= 1.66.., 5+= 1.11.., 6+= 0.55..
3 turrets, 2 attack runs: 4+ Armour= 1, 5+= 0.66.., 6+= 0.33..
4 turrets, 1 attack runs: 4+ Armour= 0.5, 5+= 0.33.., 6+= 0.166..
5 turrets, 0.33.. attack runs: 4+ Armour= 0.166.., 5+= 0.11.., 6+= 0.055..
6 turrets, 0 attack runs: No damage!

Eldar Bombers 2 Markers (ignoring markers lost to turrets, rerolling 3 or less attack runs or if there are no attack runs due to hight turret values)
0 turrets, 8.5 attack runs: 4+ Armour= 4.25, 5+= 2.833.., 6+= 1.4166..
1 turret, 6.5 attack runs: 4+ Armour= 3.25, 5+= 2.166.., 6+= 1.0833..
2 turrets, 4.66.. attack runs: 4+ Armour= 2.33.., 5+= 1.55.., 6+= 0.77..
3 turrets, 3 attack runs: 4+ Armour= 1.5, 5+= 1, 6+= 0.5
4 turrets, 1.66.. attack runs: 4+ Armour= 0.833.., 5+= 0.55.., 6+= 0.277..
5 turrets, 0.611.. attack runs: 4+ Armour= 0.3055.., 5+= 0.2037..., 6+= 0.10185...
6 turrets, 0 attack runs: No damage!


That's all for now,

RayB
Author:  Raysokuk [ Tue Jun 12, 2007 8:10 pm ]
Post subject:  The Bell Formula
Leadership Comparisons (probabilities)

Chance of success with 1D6:

Ld1 = 0.166..
Ld2 = 0.33..
Ld3 = 0.5
Ld4 = 0.66..
Ld5 = 0.833..
Ld6 = Auto
Ld7 = Auto
Ld8 = Auto
Ld9 = Auto
Ld10 = Auto

Chance of success with 1D6 with a reroll:

Ld1 = 0.3055..
Ld2 = 0.55..
Ld3 = 0.75
Ld4 = 0.88..
Ld5 = 0.9722..
Ld6 = Auto
Ld7 = Auto
Ld8 = Auto
Ld9 = Auto
Ld10 = Auto


Chance of success with 2D6:

Ld1 =Fail
Ld2:11 =0.0277..
Ld3:12,21 =0.0833..
Ld4:13,31,22 =0.166..
Ld5:14,41,23,32 =0.277..
Ld6:15,51,24,42,33 =0.4166..
Ld7:16,61,25,52,34,43 = 0.5833..
Ld8:26,62,35,53,44 =0.722..
Ld9:36,63,45,54 =0.833..
Ld10:46,64,55 =0.9166..
Ld11:56,65 =0.9722..
Ld12:66 =Auto

Chance of success with 2D6 with a reroll:

Ld1 =Fail
Ld2 =0.0548
Ld3 =0.1597
Ld4 =0.3055
Ld5 =0.478
Ld6 =0.6597
Ld7 =0.826388..
Ld8 =0.9228
Ld9 =0.9722..
Ld10 =0.993055..

Chance of success with 3D6:

Ld1 =Fail
Ld2 =Fail
Ld3: (1)111=0.0046
Ld4: (3)112, 121, 211=0.0185
Ld5: (6)113, 131, 311; 122, 212, 221=0.0463
Ld6: (10)114, 141, 411; 123, 132, 213, 312, 231, 321; 222=0.0926
Ld7: (15)115, 151, 511; 124, 142, 214, 412, 241, 421; 133, 313, 331; 223, 323, 332= 0.162
Ld8: (21)116, 161, 611; 125, 152, 215, 512, 251, 521; 134, 143, 314, 413, 341, 431; 224, 242, 422; 233, 323, 332= 0.259
Ld9: (25)126, 162, 216, 612, 261, 621; 135, 153, 315, 513, 351, 531; 144, 414, 441; 225, 252, 522; 234, 243, 324, 423, 342, 432; 333= 0.375
Ld10: (27)136, 163, 316, 613, 361, 631; 145, 154, 415, 514, 451, 541; 226, 262, 622; 235, 253, 325, 523, 352, 532; 244, 424, 442; 334, 343, 433=0.5
Ld11: (27)146, 164, 416, 614, 461, 641; 155, 515, 551; 236, 263, 326, 623, 362, 632; 245, 254, 425, 524, 452, 542; 335, 353, 533; 344, 434, 443=0.625
Ld12: (25)156, 165, 516, 615, 561, 651; 246, 264, 426, 624, 462, 642; 255, 525, 552; 336, 363, 633; 345, 354, 435, 534, 453, 543; 444=0.741
Ld13: (21)166, 616, 661; 256, 265, 526, 625, 562, 652; 346, 364, 436, 634, 463, 643; 355, 535, 553; 445, 454, 544=0.838
Ld14: (15)266, 626, 662; 356, 365, 536, 635, 563, 653; 446, 464, 644; 455, 545, 554=0.907
Ld15: (10)366, 636, 663; 456, 465, 546, 645, 564, 654; 555=0.954
Ld16: (6)466, 646, 664; 556, 565, 655=0.981
Ld17: (3)566, 656, 665=0.999
Ld18: (1)666=Auto

Chance of success with 3D6 with a reroll:

Ld2=Fail
Ld3=0.0092
Ld4 =0.03666
Ld5 =0.09
Ld6 =0.1766
Ld7 =0.2977
Ld8 =0.4509
Ld9 =0.609
Ld10 =0.75

That should do it!

Cheers,

RayB
Author:  blackhorizon [ Wed Jun 13, 2007 2:25 pm ]
Post subject:  The Bell Formula
Ya wow.... wait a week and I can make a print and try to comprehend it all! ;)
Author:  CyberShadow [ Thu Jun 14, 2007 10:43 am ]
Post subject:  The Bell Formula
I admit to being a little confused. For example:

Lances Str 2
Any target: Any armour= 1
Locked on: Any armour= 1.5

Can you explain this?

The leadership totals seem fairly straight-forward.

So, how does this work towards some points index?

Thanks.
Author:  Raysokuk [ Thu Jun 14, 2007 1:26 pm ]
Post subject:  The Bell Formula
Sorry I was kinda 'thinking aloud'.

The weapons are average damage versus the specified target (armour, and type of target).
The amount of weapons strength is of roughly an equivelent value (a hard point, or 2) for easy comparison.

The leadership will help determine how likely a ship is to be on special orders, and so increase the cost of whatever part of the ship the special order enhances.

Leadership with 1D6 is only really for ramming with escorts vs capships (or capships versus BB's!).

Leadership with 3D6 usually only involves cellestial phenomenon (going through an asteroid field on AAF, or a Warp Rift), but is possible for ramming or perhaps some other special rule.  

Cheers,

RayB
Author:  Raysokuk [ Thu Jun 14, 2007 5:59 pm ]
Post subject:  The Bell Formula
Now I'm going to factor in Brace, holofield and Necron saves:

BFI 4+ save= 0.5xtotal damage.

Holofield 2+ save= 0.166..xtotal damage +0.166..damage from BM.

(Now the nightmare of Necron saves!)
*Necron BFI is a 2+ save, the armour is reduced from 6+ to 4+, this= 0.166..xdamage from Armour ignoring weaponary.
Necron 4+ save=0.5xtotal damage,
BFI:0.33..xtotal damage(after necron save). So in effect you get 3 times the ammount of hits with the 4+ save! ?

Necron 5+ save=0.66..xtotal damage,
BFI:0.25xtotal damage(after necron save). This would be an effect of 4 times the ammount of hits with a 5+ save!

Necron 6+ save=0.833xtotal damage,
BFI:0.2xtotal damage(after necron save). This would be an effect of 5 times the ammount of hits with a 6+ save!


*Necron BFI is a 2+ save, the armour is reduced from 6+ to 4+, this= 0.5..xArmour dependant weaponary.
Necron 4+ save=0.5xtotal damage,
BFI:1xtotal damage(after necron save). So in effect you gain no benefit! ?

Necron 5+ save=0.66..xtotal damage,
BFI:0.75..xtotal damage(after necron save). Here you would in effect gain an additional 50% hits with a 5+ save.

Necron 6+ save=0.833..xtotal damage,
BFI:0.6..xtotal damage(after necron save). Here you would in effect ?gain 66% extra hits with a 6+ save.


*Re-rollable Armour Dependant (RRAD), like a Locked-on WB.
vs6+ Armour: damage(when not RRAD)x1.833..., /necron save= 4+: 0.9166.., 5+: 1.22.., 6+: 1.5277.. ?
vs4+ Armour RRAD: damage(when not RRAD)x1.5/ 2+ BFI save= 0.75.

Necron 4+ save vs RRAD=0.5xtotal damage,
BFI:0.81..xtotal damage(after necron save). Here you would in effect ?gain 23% extra hits with a 4+ save.

Necron 5+ save vs RRAD=0.66..xtotal damage,
BFI:0.6136..xtotal damage(after necron save). Here you would in effect ?gain 62% extra hits with a 5+ save.

Necron 6+ save vs RRAD=0.833xtotal damage,
BFI:0.490..xtotal damage(after necron save). This would be an effect of roughly 2 times the ammount of hits with a 6+ save!

Cheers,

RayB
Author:  Raysokuk [ Fri Jun 15, 2007 3:18 am ]
Post subject:  The Bell Formula
Now for a really easy one, AAF.

+2d6cm= range of +2-12cm, average of +7cm.
+3d6cm= range of +3-18cm, average of +10.5cm (10 or 11).
+4d6cm= range of +4-24cm, average of +14cm.
+5d6cm= range of +5-30cm, average of +17.5cm (17 or 18?).
+6d6cm= range of +6-36cm, average of +21cm (20, 21 or 23!?).
+7d6cm= range of +7-42cm, average of +24.5cm (24 or 25?).

+D6x10cm= range of +10-60cm, average of +35cm (10, 20, 30, 40, 50 or 60).

Cheers,

RayB
Author:  Raysokuk [ Mon Jun 25, 2007 1:52 am ]
Post subject:  The Bell Formula
Anyway,

For a simple trial of principle I'm going to take a Hades (200pts) versus a Slaughter (165pts).

Turn 1: Hades fires Locked-on at 60cm range causing 1 point of damage, then Slaughter AAF's closing 43cm, fires with 3WB causing no damage.

Turn 2: Hades closes and turns to fire at capital ship closing causing 2 points of damage (1.7) and then performs a teleport attack, the slaughter steams past and turns and shoots (only just within 15cm) causing 2 points of damage (2.1).

Turn 3: The Hades now could turn and shoot and possibly cripple the Slaughter (with 0.1 hits through shields), but AAF(34cm) is a viable option to then turn around and pummle the Slaughter again. If the Slaughter gave chase it wouldn't get within range and the Hades could then turn and broadside the closing slaughter most likely crippling it.  

Now this example is horribly simplistic not giving much leeway for creative tactics or account for other ships, quadratic damage (the more it costs, the more will be shooting at it, so the ship has less overall survivability!), or terrain.


I think a more useable example (target) would be stationary object  (as the tactics for each ship will be obvious).

Assuming the 'space station' has firing capability but isn't using it the Hades slowly moves towards it at an angle on lock-on causing 3hits per turn (against shields). Realistically staying over 30cm away for 2 volleys (6 damage), then moves within 15cm on lock-on with its broadside in arc due to the angle of approach firing off 3 identical volleys before over 15cm away (6.1 damagex3= 18.3!). (5 very effective turns of firing! total damage of 24.3)

The Slaughter AAF's getting 47.5cm across the board at a slight angle, within 30cm and with broadside arc, causing roughly 2 damage. Then locks-on for 2 turns of firing within 15cm causing 8x2 damage =16 (18 damage by turn 3, the hades doing 12.1) , then CTHN just staying in range causing roughly 2 damage (T4:S20/H18.2), then turns and shots causing 4.1 damage (T5:S24.1/H24.3).

That is annoying close at the end of turn 5! (Damn it!) And so isn't a very good example of Quadratics!

Lets assume the space stations range is 30cm and has 2 regenerating shields per turn. So before the ships are in range the Hades has done 2 points of damage. T1 sees the H do 4.1 damage and the Slaughter none(H6.1/S0). T2: H does 4.1, S does 6 (H10.2/S6). T3: H does 4.1, S does 6 (H14.3, S12). Note that shields shouldn't be taken into account when pointing a ship as another ship could take the shields down for it).

So the Hades is (for arguments sake) 16% stronger than the Slaughter, but should NOT cost 16% more because it would then be 16% less durable as it would have 16% more oppostion (meaning it would then cause the same ammount of damage as a Slaughter being on the board for 16% less time!).

I'm ill and my brain has over heated I'll have to get back to this tomorrow when I have more drugs! Floating numbers (16-16%)/2= 6.72, 42% of 16

Cheers,

RayB
Author:  Xavi [ Mon Jun 25, 2007 7:58 am ]
Post subject:  The Bell Formula
By your example, it would seem that the slaughter is undercosted, then :). The Hades costs 21% more points than the slaughter (200/165).

Never thought the numbers would be that close, though. I also never manage to get that much shooting from a slaughter in a single series. I tend to have to CTNH sooner than you have done in your examples, so the shooting performance of my slaughters is slightly sub-par with what you posted. OTOH I tend to board with my slaughters, but hey :)

Appart from that, the average of 2D6 is a straight 7, not 7.5, but that is a minor detail ;) :p Keep it up! Been interesting so far as an in depth analysis of the game mechanics in a controlled environment (not the chaos of a space brawl that most battles happen to be) :)

Xavi
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