Re: Shields, was Re: Armor (long)
From: Brian Bell <103311.1205@C...>
Date: Fri, 8 Nov 1996 12:21:21 -0500
Subject: Re: Shields, was Re: Armor (long)
Below are some stats that take into account losses to threshold rolls. I
have
selected a Privateer (18 tons), Escort Cruiser (26 tons), and
Battledreadnought
(60 tons). This shows the increasing damage protection and lower cost
(per point
of protection) as ships increase in size. (Best displayed in a
mono-spaced font)
Average damage per Die
no screens: 0.666666
level 1: 0.5
level 2: 0.333333
level 3: 0.166666
Average dice per damage:
no screens: 1.49
level 1: 2.00
level 2: 3.00
level 3: 6.00
Chance to reduce screens at 1st threshold roll:
no reduction: 83% (5/6,10/12,15/18) (.833333)
loose at least 1 level: 17% (1/6, 2/12, 3/18) (.166666)
loose at least 2 levels: 8-11% (1/12,2/18) (.083333-.111111)
loose all screens: 6% (1/18) (.055555)
*NOT cumulative! 17% contains the 8-11% which contains the 6%
Chance to reduce screens at 2nd threshold roll:
no reduction: 81% (.805555)
loose at least 1 level: 19% (.194444)
loose at least 2 levels: 9-12% (.090277-.123457)
loose all screens: 6% (.058641)
Chance to reduce screens at 3rd threshold roll:
no reduction: 77% (.767747)
loose at least 1 level: 23% (.232253)
loose at least 2 levels: 10-14% (.101376-.138698)
loose all screens: 6% (.062080)
Formulas to simulate loss due to threshold rolls:
No screens remain constant
Before First Threshold: Figure maximum avg. gain
After 1st Threshold: 2nd Threshold: 3rd Threshold:
L1 L2 L3 L1 L2 L3 L1 L2 L3
No Change: 83% 83% 83% 81% 81% 81% 77% 77% 77%
-1: 17% 9% 6% 19% 10% 7% 23% 13% 9%
-2: 8% 5% 9% 6% 10% 8%
-3 6% 6% 6%
Subtract the no screen level # dice from the Before First Threshold
total for
a level of protection. Multiply the Difference by the No Change %.
Level One: Multiply Difference by the -1 %, divide by 2, multiply by
1.49. Add
results of -1, and No Change.
Level Two: Multiply Difference by the -1 %, divide by 3, multiply by
2.
Multiply Difference by the -2 %, divide by 3, multiply by 1.49. Add
results of
-1,-2, and No Change.
Level Three: Multiply Difference by the -1 %, divide by 6, multiply by
3.
Multiply Difference by the -2 %, divide by 6, multiply by 2. Multiply
Difference
by -3 %, divide by 6, multiply by 1.49. Add results of -1,-2,-3, and No
Change.
Examples:
--------------------------------
Privateer (18 tons)
9 damage: 4,5
To reach the 1st threshold level:
Screen Level - # dice - dice saved - damage saved
none - 5.96 - -
level 1 - 8.00 - 2.04 - 1.36
level 2 - 12.00 - 6.04 - 4.03
level 3 - 24.00 - 18.04 - 12.03
To reach the 2nd threshold level (destruction):
Screen Level - # dice - dice saved - damage saved
none - 7.45 - -
level 1 - 9.57 - 2.12 - 1.41
level 2 - 14.47 - 7.02 - 4.68
level 3 - 27.56 - 20.11 - 13.41
Totals
Screen Level - Dice - Damage - Dice/ - Damage/ - Cost/ - Cost/
Saved - Saved - Tons - Tons - Die - Damage
level 1 - 4.16 - 2.77 - 1.39 - 0.92 - 6.01 - 9.03
level 2 - 13.06 - 8.71 - 2.18 - 1.45 - 3.82 - 5.74
level 3 - 38.15 - 25.44 - 4.24 - 2.83 - 1.97 - 2.95
------------------------------
Escort Cruiser (26 tons)
13 damage: 4,4,5
To reach the 1st threshold level:
Screen Level - # dice - dice saved - damage saved
none - 5.96 - -
level 1 - 8.00 - 2.04 - 1.36
level 2 - 12.00 - 6.04 - 4.03
level 3 - 24.00 - 18.04 - 12.03
To reach the 2nd threshold level:
Screen Level - # dice - dice saved - damage saved
none - 5.96 - -
level 1 - 7.91 - 1.95 - 1.30
level 2 - 11.57 - 5.61 - 3.74
level 3 - 22.04 - 16.08 - 10.72
To reach the 3rd threshold level (destruction):
Screen Level - # dice - dice saved - damage saved
none - 7.45 - -
level 1 - 9.94 - 2.49 - 1.66
level 2 - 14.41 - 6.96 - 4.64
level 3 - 27.30 - 19.85 - 13.23
Totals
Screen Level - Dice - Damage - Dice/ - Damage/ - Cost/ - Cost/
Saved - Saved - Tons - Tons - Die - Damage
level 1 - 6.48 - 4.32 - 2.16 - 1.44 - 3.86 - 5.79
level 2 - 18.61 - 12.41 - 3.10 - 2.07 - 2.67 - 4.03
level 3 - 53.97 - 35.98 - 6.00 - 4.00 - 1.39 - 2.08
-------------------------------
Battledreadnought (60 tons)
30 damage: 7,7,8,8
To reach the 1st threshold level:
Screen Level - # dice - dice saved - damage saved
none - 10.43 - -
level 1 - 14.00 - 3.57 - 2.38
level 2 - 21.00 - 10.57 - 7.05
level 3 - 42.00 - 31.57 - 21.05
To reach the 2nd threshold level:
Screen Level - # dice - dice saved - damage saved
none - 10.43 - -
level 1 - 13.85 - 3.42 - 2.28
level 2 - 20.26 - 9.83 - 6.55
level 3 - 38.58 - 28.15 - 18.77
To reach the 3rd threshold level:
Screen Level - # dice - dice saved - damage saved
none - 11.92 - -
level 1 - 15.80 - 3.88 - 2.59
level 2 - 23.05 - 11.13 - 7.42
level 3 - 43.66 - 31.74 - 21.16
To reach the 4th threshold level (destruction):
Screen Level - # dice - dice saved - damage saved
none - 11.92 - -
level 1 - 15.58 - 3.66 - 2.44
level 2 - 22.87 - 10.95 - 7.30
level 3 - 42.82 - 30.90 - 20.60
Totals
Screen Level - Dice - Damage - Dice/ - Damage/ - Cost/ - Cost/
Saved - Saved - Tons - Tons - Die - Damage
level 1 - 14.53 - 9.69 - 4.84 - 3.23 - 1.72 - 2.58
level 2 - 42.48 - 28.32 - 7.08 - 4.72 - 1.17 - 1.77
level 3 - 122.36 - 81.58 - 13.60 - 9.07 - 0.61 - 0.92
===============================
Summary:
Level 1
Ship Class - Dice - Damage - Dice/ - Damage/ - Cost/ - Cost/
Saved - Saved - Tons - Tons - Die - Damage
Privter - 4.16 - 2.77 - 1.39 - 0.92 - 6.01 - 9.03
E Cruis - 6.48 - 4.32 - 2.16 - 1.44 - 3.86 - 5.79
BDrdnt - 14.53 - 9.69 - 4.84 - 3.23 - 1.72 - 2.58
Level 2
Ship Class - Dice - Damage - Dice/ - Damage/ - Cost/ - Cost/
Saved - Saved - Tons - Tons - Die - Damage
Privter - 13.06 - 8.71 - 2.18 - 1.45 - 3.82 - 5.74
E Cruis - 18.61 - 12.41 - 3.10 - 2.07 - 2.67 - 4.03
BDrdnt - 42.48 - 28.32 - 7.08 - 4.72 - 1.17 - 1.77
Level 3
Ship Class - Dice - Damage - Dice/ - Damage/ - Cost/ - Cost/
Saved - Saved - Tons - Tons - Die - Damage
Privter - 38.15 - 25.44 - 4.24 - 2.83 - 1.97 - 2.95
E Cruis - 18.61 - 12.41 - 3.10 - 2.07 - 2.67 - 4.03
BDrdnt - 122.36 - 81.58 - 13.60 - 9.07 - 0.61 - 0.92
Brian Bell
103311.1205@compuserve.com
http://ourworld.compuserve.com/homepage/fthome.html