@Spendo02:
@Alsch91:
Spendo, the fact that a 2-interceptor would make you think twice about sending a bomber against a fighter is exactly the point.
If I’ve got interceptors then you should have to send escorts.� The way it is now, interceptors are nearly useless in all but the most extreme cases.
1 IPC Reduction
1 16.67% 0.17
2 16.67% 0.33
3 16.67% 0.50
4 16.67% 0.67
5 16.67% 0.83
6 16.67% 1.00
IPC Cost to Defender per SBR 5.5
Event P LAC IL ID IC NC
Ftr @1 (Miss), AA (Miss Both) 76.39% $0 $0 $11 $8 $8
Ftr @1 (Miss), AA (1 Hit) 4.63% $15 $1 $6 $0 -$0
Ftr @1 (Miss), AA (2 Hit) 2.31% $30 $1 $0 $0 -$1
Ftr @1 (Hit), AA (Miss Both) 15.28% $15 $2 $6 $1 -$1
Ftr @1 (Hit), AA (1 Hit) 0.93% $30 $0 $0 $0 -$0
Ftr @1 (Hit), AA (2 Hit) 0.46% $30 $0 $0 $0 -$0
IPC Cost to Attacker $4 $9 $5
P = Probability of Event occurring
LAC = Value of Aircraft Lost
IL = P * LAC which when summed to $4 is the cost of the SBR to Germany
ID = Damage to the Major IC based off the probability of rolling a 1 through 6 (its rounded from 5.5)
IC = P * ID which when summed to $9 is the cost of the SBR to London
NC = IC - IL which when summed to $5 and cross footed ( $9-$4 ) is the actual damage the SBR causes net of all probabilities.
Event P LAC IL ID IC NC
Ftr @2 (Miss), AA (No Hit) 61.11% $0 $0 $11 $7 $7
Ftr @2 (Miss), AA (1 Hit) 3.70% $15 $1 $6 $0 -$0
Ftr @2 (Miss), AA (2 Hit) 1.85% $30 $1 $0 $0 -$1
Ftr @2 (Hit), AA (No Hit) 30.56% $15 $5 $6 $2 -$3
Ftr @2 (Hit), AA (1 Hit) 1.85% $30 $1 $0 $0 -$1
Ftr @2 (Hit), AA (2 Hit) 0.93% $30 $0 $0 $0 -$0
IPC Cost $7 $9 $2
P = Probability of Event occurring
LAC = Value of Aircraft Lost
IL = P * LAC which when summed to $7 is the cost of the SBR to Germany
ID = Damage to the Major IC based off the probability of rolling a 1 through 6 (its rounded from 5.5)
IC = P * ID which when summed to $9 is the cost of the SBR to London
NC = IC - IL which when summed to $2 and cross footed ( $9 - $7 ) is the actual damage the SBR causes net of all probabilities.
So the change from interceptors rolling @1 versus rolling @2 is approximately 3 IPC to Germany in a 2 Bombers versus 1 Ftr scenario; an entirely possible scenario on G2.
Probabilities were derived from:
(5/6) = Miss from Ftr @1 - meaning you rolled anything but a 1
(1/6) = Hit from Ftr @1 - meaning you rolled a 1
(33/36) = Miss from AA @1 - meaning you rolled anything but a 1 on either die
(2/36) = 1 Hit from AA @1 - meaning the die roll was a 2 and a 1 or a 1 and a 2
(1/36) = 2 Hit from AA @1 - meaning you rolled snake eyes
(4/6) = Miss from Ftr @2 - meaning you rolled anything but a 1 or 2
(2/6) = Hit from Ftr @2 - meaning you rolled a 1 or 2
So in example, a Ftr @1 scoring a hit and AA misses both = 2/6 * 33/36 = 15.28% probability this occurs sequentially.
That probability is multiplied by the value of aircraft lost (either 15 or 30) and also by the most probable value a bomber would score for a successful SBR (5.5 per Bomber).
Then you just subtract the cost from the benefit and get the actual value (or loss) in a German SBR on London of 2 Bombers versus 1 Ftr.
Something else to realize is that this is just a probability evaluation of if you should do something. A positive number indicates a gain, a negative number indicates a loss - obviously you don’t want to do something that is a loss unless there are unmeasurable advantages to gain from it.
The relevant range of IPC damage for both bombers escaping interceptors is as low as 6 IPC or as high as 16 IPC which you have approximately 6% of accomplishing against a single Ftr @1. It drops to just over a 5% chance against a single Ftr @2.
A better expectation, therefore, is to assume +/-1 from 9 IPC if both bombers get through which accounts for just shy of 50% of all probable outcomes.
Edit: Apologies for the terrible column formatting.
On a purely equal playing field, this analysis shows the rules as-are make sense (well done Spendo).
The trouble is, in the game the playing field is not equal; neither Britain nor Russia can compete with the Luftwaffe early on, and as a result a dedicated SB campaign by the Germans makes Sea Lion a certainty (on G3), and Barbarossa a likely certainty (although the evidence is, as of yet, scant).
To cite an extreme example of what I’m talking about, a pure air raid by the Japanese on the fighter stack of the Chinese is often, statistically, a poor decision (as in, the expected losses for the attacker exceed those of the defender). Nonetheless, it is done, for the simple reason that the IPCs themselves have less value to Japan than to China.
The situation is similar with Germany vs. USSR/UK.