RE: Fire Control lock-on musings

I want to throw some numbers out to see the empirical effects of a D6 to
lock-on roll.

In essence, a die roll modifier is applied to a "Break Lock-on" number.
If the defender has to roll a 7 or better on a D6, then a Lock-on is
automatic if the DRM is +0. If the DRM is +2 then the defender will
break the Lock-on when he rolls a 5 or 6. (However the DRM is determined
the result will be what the defender adds to his die roll to compare to
7+.)

This makes the odds of a Lock-on equal to  1-((1-(6-DRM)/6)^(#FireCons))

If DRM=+1 the odds of successful Lock-on is 83% w/1 FCS and 97% w/2 FCS.

If DRM=+2 the odds of successful Lock-on is 67% w/1 FCS and 89% w/2 FCS.

If DRM=+3 the odds of successful Lock-on is 50% w/1 FCS and 75% w/2 FCS.
But to get an 88% chance of a lock-on the BDN would have to dedicate 3
FCS to its target. Maybe DRM+3 should be the max.

Comparing a Class-3 Beam and a Pulse Torp, the current odds of a hit and
average damage inflicted are...

1 FireCon w/Lock-on DRM: +0	Lock-on odds = 100%

Shielding Level of Target: Unshielded
Cumulative Odds to Hit at Each Range Band
    Weapon	 6mu	12mu	18mu	24mu	30mu	36mu
Class-3 Beam	0.88	0.88	0.75	0.75	0.50	0.50
Pulse Torpedo	0.83	0.67	0.50	0.33	0.17	

Shielding Level of Target: Unshielded
Average Damage Points Inflicted at Each Range Band
    Weapon	 6mu	12mu	18mu	24mu	30mu	36mu
Class-3 Beam	2.40	2.40	1.60	1.60	0.80	0.80
Pulse Torpedo	2.92	2.33	1.75	1.17	0.58	

Now looking at the odds of a hit and average damage inflicted with a
Lock-on DRM=+1...

1 FireCons w/Lock-on DRM: +1	Lock-on odds = 83%

Shielding Level of Target: Unshielded
Cumulative Odds to Hit at Each Range Band
     Weapon	 6mu	12mu	18mu	24mu	30mu	36mu
Class-3 Beam	0.82	0.82	0.69	0.69	0.44	0.44
Pulse Torpedo	0.78	0.60	0.44	0.29	0.14	

Shielding Level of Target: Unshielded
Average Damage Points Inflicted at Each Range Band			
     Weapon	 6mu	12mu	18mu	24mu	30mu	36mu
Class-3 Beam	2.00	2.00	1.33	1.33	0.67	0.67
Pulse Torpedo	2.43	1.94	1.46	0.97	0.49	

Due to the "only" 5/6 chance of the Lock-on roll. The Odds of a Hit for
the B3 is lowered by 94% up to 12mu, 91% up to 24mu, and 88% up to 36mu.
The Odds of a Hit for the PT is lowered by 93% to 6mu, 90% to 12mu, 88%
to 18mu, 86% to 24mu, and 85% to 30mu.

Though the relative difference in the to hit averages decreases with
range, the Average Damage is reduced by the Lock-on odds of 83% for both
weapons at all ranges. I suspect the former is due to the different
to-hit mechanics, I was not (too) surprised with the relative difference
of the average damage numbers.

If the defenders are ready to roll their "Break Lock-on" dice as soon as
the firing ship has announced all its targets, I think that each turn
would not feel noticeably longer. And I would expect this “lesser
average damage per shot” to add just a couple of turns to most games.
And the firing ship just has to allocate 1 more FCS then the target gets
DRM to have 95% or more change to lock-on. So though the mechanics and
execution of this extra roll may not be much, the determination of the
DRM+# could get very involved very quickly.

-jerry cantrill