RE: Fire Control lock-on musings

Jerry Cantrill wrote:

 >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))

Correct so far.

 >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	

Correct, though the "cumulative odds to hit" is a pretty irrelevant 
comparison (unless you're shooting at targets with a single damage point

remaining) since the amount of damage per "hit" is so different for the
two 
weapon types.

 >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	

Correct.

 >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	

...but here you've done something wrong; I just can't identify what it
is. 
The B3's hit probability at range 0-12 with 1 FCS against a +1 lock-on
DRM 
should be

(5/6)*(1-(1/2)^3) = 0.83*0.88 = 0.73,

not 0.82: of the 83% of the shots that are fired at all (the remaining
17% 
don't get a
lock so can't be fired) 88% hit, so the cumulative P(hit) is 88% of 83%
ie. 
0.83*0.88 = 0.73. At range 12-24 the hit probability is 0.63, and at
range 
24-36 it is 0.42; similarly the P-torp to-hit probabilities with a
single 
FCS against a +1 lock-on DRM are 0.69, 0.56, 0.42, 0.28 and 0.14 
respectively. All of these are (of course) exactly 83% of the hit 
probabilities against a zero lock-on DRM.

 >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	

*These* values OTOH are correct.

 >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,

You mean "...is lowered TO 94%" (0.82/0.88 =~ 0.94), or "...is lowered
BY 6%".

(If you lower a probability of 0.88 BY 94%, you end up with
0.88*(1-0.94) = 
0.053, which
is quite far removed from the B3's hit probability in this case.)

However, the "94%" value is based on the incorrect "0.82" hit rate. The 
real value is
0.73/0.88 = 0.83, ie. exactly identical to the lock-on odds.

***
 >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.

Which is one of the reasons why this is a game balance problem: it
screws 
those ships
which can't *afford* "just 1 more FCS" due to their low Mass - ie. the 
escorts, and to
a lesser extent cruisers.

Regards,

Oerjan
oerjan.ariander@telia.com

"Life is like a sewer.
  What you get out of it, depends on what you put into it."
-Hen3ry