Re: Salvo Missles vs. MT missiles

Laserlight wrote:

 >>Warning: I often express myself quite bluntly and/or cynically.
 >
 >Not "cynically", I don't think, but often "dry" and sometimes
 >"acerbic."

<chuckle> Once again the fact that English is not my first language
makes 
itself felt. While I know what "acerbic" means, it isn't a word I
would've 
thought of on my own <g>

 >>The *total* number of missiles killed will of course go up when you
 >>throw more PDSs at the salvo, but it isn't as simple as saying "2
 >>PDSs will shoot down on average 1.4 missiles" because they're going
to
 >>steal each others' kills
 >
 >(Oerjan, could you post the average expected missile hits against N
 >PDS, for say N= 1 to 10?  That'll save me having to
 >calculate it, and you having to correct my mistakes... ;-) )

I have N = 1 to 9 at hand so can send that immediately; 10 I'll need to 
re-calculate - not difficult to do, but it'll take time I won't be able
to 
spare until some time next week at which time I won't be able to post
the 
results to the list :-( ('Course, with me being effectively off-line for

the next five weeks you have plenty of time to calculate it for yourself

anyway ;-) )

Average values for 1 missile salvo faced by N = 0 to 9 PDSs (the "0"
line 
included for reference):

	 Missile kills	 Avg. #msl
N:	/PDS:	Total:	hits:		Avg dmg:
0	0	0	3.5		12.25
1	0.71	0.71	2.79		9.75
2	0.66	1.32	2.18		7.62
3	0.61	1.83	1.67		5.84
4	0.56	2.25	1.25		4.39
5	0.52	2.58	0.92		3.24
6	0.47	2.83	0.67		2.34
7	0.43	3.03	0.48		1.66
8	0.40	3.17	0.33		1.16
9	0.36	3.27	0.23		0.80

Note the two columns for missile kills; the first shows how many
missiles 
*each individual* PDS kills on average, the second how many missiles all

the PDSs together shoot down. Then there's the column answering LL's
actual 
question, ie. the average number of missiles that hit the target in
spite 
of the PDS fire; and finally the average damage (which is of course
simply 
3.5x the number of hitting missiles.

As Alan pointed out these are *average* values only, and the variance is

pretty big. Just because the *average* damage from a single SM salvo 
opposed by 5 PDSs is 3.24 pts doesn't mean that you'll never see a lucky
SM 
salvo inflict over 30 pts against such opposition; it happens - only not

very often :-/

Also note that the above values are NOT valid for PDS shooting at
*fighter 
groups*. The above table shows the average values for N PDSs shooting at
a 
target with 1D6 sub-targets, which means that if the 1D6 rolls low and
the 
PDSs roll high there'll be a lot of wasted hits.

However, when you're shooting at a full-strength fighter group there are

enough fighters in the target that the risk of wasting kills is low - so

the average number of kills per PDS is much closer to the theoretical
0.8 
than it is for the SM salvo. (Conversely, if the fighter group has taken

previous
losses and is down to 3 fighters or less, the PDSs will on average kill 
*fewer* fighters than the above table suggests.)

In fact, although the target needs an infinite number of "hit points" 
(missiles in a salvo, fighters in a fighter group, hull boxes on a ship 
etc) for the beam dice to really reach their theoretical average of 0.8
dmg 
pts, it turns out that 6 "hit points" is infinite *enough* (<g>) that
the 
rounding error becomes insignificant: a lone beam die shooting at a
target 
with 6 "hit points" will destroy on average 0.7996 of them.

The average total losses from a fighter group with X fighters attacked
by N 
PDS are:
			 X:
N:	1	2	3	4	5	6
1	0,50	0,67	0,75	0,78	0,79	0,80
2	0,75	1,17	1,39	1,50	1,55	1,58
3	0,88	1,50	1,90	2,13	2,26	2,33
4	0,94	1,71	2,27	2,65	2,88	3,03
5	0,97	1,83	2,53	3,05	3,41	3,65
6	0,98	1,91	2,71	3,36	3,84	4,19
7	0,99	1,95	2,82	3,57	4,18	4,64
8	1,00	1,97	2,89	3,72	4,43	5,00
9	1,00	1,98	2,94	3,82	4,61	5,28

If you take the average of each row in this table, you'll get the "total

missile kills" values from the PDS-vs-missiles table above.

Later,

Oerjan
oerjan.ohlson@telia.com

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