Still working on SBR mechanics and searching better ways to analyze and compare various ones, especially OOOBs (G40.2, Triple A 1942.2, 1942.2) and Balanced Mode, I got this idea.
Questions: can this be relevant and is the name appropriate?
I believe it can be useful for players to know the ratio of StBs over Fighter which gives a beneficial odds if defender choose to intercept instead of just letting StBs flying on IC and bombard.
So, between the floor ratio (break even point) which going below gives better odds on the defender and make an SBR statistically unoptimized to launch against too many defending interceptors and the ceiling ratio in which it becomes statistically unoptimized to intercept too many assaillant’s StBs, there is a gap in which it is statistically better to launch interceptors than doing nothing.
For now, the only name I think is “Interception Threshold Gap”.
For example, on OOB G40 SBR, 1 StB can be launched against 2 Fgs and odds of making more damage than loosing IPCs are near zero almost. So this is the break even floor.
On the other side, when there is 4 StBs against 2 Fgs, odds of making damage are increased if defender elect to intercept. The even point odds of damage between intercept and no intercept is near 3 StBs against 2 Fgs. This is the interception threshold ceiling.
So an Interception Threshold Gap for G40 SBR is approximately between .5 StB/ Fg and 1.5 StB/Fg.
This means for G40 SBR defender side that any case his Fgs are overwhelmed above 3 vs 2, he should lets his IC’s AAAs do the job and risk no Fg.
For example 5 StBs against 3 Fgs gives a too high 1.667 StBs/Fg ratio.
So, based on numbers only, defender is advised to not intercept.
Here is a first draw definition:
Interception Threshold:
It is a number which provides an effective ratio of StBs over Fg to launch intercepting Fgs, above this ratio it means StBs outnumbered too much defender’s Fgs so odds for damage are better if defender let them face IC’s AAA only. Anything below this ratio means it is a good fight and odds of receiving damage are lower if Fgs are launched.
Can you help me being clearer to provide an easy player helping guidelines?
Is there a better name to this concept?
Thanks.
If I’m following along right it seems to me that you are looking for a “Point” and not a “Gap”. Yes there is a gap there but you’re searching for the point to which you would recommend not using the fighters. Is that correct?
I would consider shortening that term or at least give it a name that you could use an acronym. For instance Fighter Interception Gap would be “FIG” or Fighter Interception Point would be “FIP”. Another one that comes to mind is Fighter Interception Threshold “FIT”.
I don’t know if this helps but I wish you luck.
Also, I might point out that the dice can still screw you.
I once had a game where 5 German bombers were running an SBR on Moscow’s IC. Russia had 5 fighters so we figured that was pretty good odds. The Junkers weren’t even scratched while 4 Yaks went down in flames.
I know this isn’t typical, but just pointing out that you can’t always rely on some type of system.
Also, I might point out that the dice can still screw you.
I once had a game where 5 German bombers were running an SBR on Moscow’s IC. Russia had 5 fighters so we figured that was pretty good odds. The Junkers weren’t even scratched while 4 Yaks went down in flames.
I know this isn’t typical, but just pointing out that you can’t always rely on some type of system.
It is a dice game unless playing lowluck.
You can accuse the god of dice but your partners cannot accuse you from taking a long shot on that one.
5 StBs vs 5 Fgs, at 1:1 ratio provides odds with a clear go for intercepting instead of letting StBs fly over IC.
Near 4 IPCs less damage on average if intercept (9.095 < 12.915).
OOB G40 SBR: damage: 1D6+2
1 StB doing SBR, no interceptor*5
Sum: +4.583 - 2 = +2.583 IPCs damage/SBR run *5 = 12.915 IPCs on avg.
1 StB A1 against 1 Fg D1 *5
Sum: + 5.486 - 3.667 = + 1.819 IPC damage/SBR run *5
27.43 - 18.335 = 9.095 IPCs on avg.
Losing 4 Fgs, 40 IPCs, plus 5*5.5= 27.5 sum: 67.5 IPCs damage.
40 IPCs more loss than avg (27.43) and attacker should have lost 1.5 StBs (18.335).
So, if damage on IC is avg, this exceptionnal battle is 58.5 IPCs above the avg loss for defender!
Fortunately, IC was probably maxed out, for 20 IPCs, for a real 60 IPCs loss.
If I’m following along right it seems to me that you are looking for a “Point” and not a “Gap”. Yes there is a gap there but you’re searching for the point to which you would recommend not using the fighters. Is that correct?
I would consider shortening that term or at least give it a name that you could use an acronym. For instance Fighter Interception Gap would be “FIG” or Fighter Interception Point would be “FIP”. Another one that comes to mind is Fighter Interception Threshold “FIT”.
I don’t know if this helps but I wish you luck.
Thanks.
Yes, there is two aspects. The top Fighter Interception Point or Threshold, FIP or FIT sound cool, which beyond it is not odds effective to intercept.
And, for the attacker perspective, the margin between even odds of making damage (xxx damage on IC and Interceptors - yyy damage on StBs = 0 IPCs) and the FIT point is the Fighter Interception Gap (FIG sounds great since it is similar too an older acronym for Fighter) in which the odds effective ratio provides an incentive for air-to-air combat in SBR.
This Gap can be use as a way to lure interceptors while risking StBs losses (when attacker can more easily lose some).
Something like escorted US bombers daylight raids on Europe to lure Luftwaffe into an attrition war.
Also, I might point out that the dice can still screw you.
I once had a game where 5 German bombers were running an SBR on Moscow’s IC. Russia had 5 fighters so we figured that was pretty good odds. The Junkers weren’t even scratched while 4 Yaks went down in flames.
I know this isn’t typical, but just pointing out that you can’t always rely on some type of system.5 bombers will on average do 25 damage. You can only take 20 damage so you should not intercept at all in this case. It is a losing proposition for the germans to attack because of your AA so let him waste bombers that way.
This is not accurate.
5 bombers against IC’s AAA are going to make on average 23 IPCs with a 10 IPCs loss,
for 13 IPCs (12.915) net damage.
OOB G40 SBR: damage: 1D6+2
1 StB doing SBR, no interceptor*5
Sum: +4.583 - 2 = +2.583 IPCs damage/SBR run *5 = 12.915 IPCs on avg.
+22.915 - 10 = 12.915
On the opposite, intercepting 5 bombers on 1 on 1 basis makes 9 IPCs (9.095) on average.
So, it is a 4 IPCs gain for defending russian player in this case (9 minus 13 = -4).
1 StB A1 against 1 Fg D1 *5
Sum: + 5.486 - 3.667 = + 1.819 IPC damage/SBR run *5
+27.43 - 18.335 = 9.095 IPCs on avg.
Talking damage done by StBs, it increase only by 4.515 (27.43- 22.915) in intercept case.
But defender increase damage on StBs by 8.335 IPCs (10 - 18.335) if he intercepts.
5 StBs vs 5 Fgs, at 1:1 ratio provides odds with a clear go for intercepting instead of letting StBs fly over IC.
Even considering IC’s Max out at 20 IPCs (instead of 22.915), it remains near 1 IPC less damage on average if intercepting (9.095 < 9.915).
So it is not stupid at all to intercept these 5 bombers, while it is not dumb either to throw 5 bombers on a single IC (even without AirBase on TTy) knowing that 5 Fgs can intercept and on average you maxed it out with 5 bombers (23 IPCs) but not with 4 StBs (18.332 IPCs).
This scenario is right into the G40 SBR Interception Gap or FIG from .5 to 1.5 StB/Fg.
Against 5 possible interceptors, the attacker could have launched between 3 to 7 StBs to get positive results and lure russian Fighters in air combat.
At 8 StBs, 8/5= 1.6 StB per Fg it is a no go for interception, IC’s AAA will do more damage.
Below 3 StBs (3/5= .6 StB/Fg), there would be more damage on attacker part if interceptors are launched, this is not a sound option.
This FIG provides opportunities to increase dogfights and creates situations which give more tactically sensitive decisions.
This is what I would try to clearly explain to provide a general guideline for players.
The 20 IPCs max damage on IC add another parameters.
It can be specifically address here, knowing that anything above 5 StBs is going to maxed out ICs, thus limiting damage on defender’s part.
1 StB doing SBR, no interceptor*6
Sum: +4.583 - 2 = +2.583 IPCs damage/SBR run *6 = 15.498 IPCs on avg.
+27.498 - 12 = 15.498 but maxing out results gives 20 - 12 = 8 IPCs net damage for this run.
1 StB A1 against 1 Fg D1 *6
Sum: + 5.486 - 3.667 = + 1.819 IPC damage/SBR run *6= 10.916
+32.916 - 22.00 = 10.916 IPCs on avg.
1 StB doing SBR, no interceptor*7
Sum: +4.583 - 2 = +2.583 IPCs damage/SBR run *7 = 18.081 IPCs on avg.
+32.081 - 14 = 18.081 but maxing out results gives 20 - 14 = 6 IPCs net damage for this run.
1 StB A1 against 1 Fg D1 *7
Sum: + 5.486 - 3.667 = + 1.819 IPC damage/SBR run *7 = 12.733
+38.402 - 25.669 = 12.733 IPCs on avg.
To be continued…
Numbers will follow after New Year Eve,
The 20 IPCs Max on IC probably demands at most 6 StBs against 5 Fgs, simply because Fgs damaged in dogfight are exchange for IPCs damage not effective beyond 20 on IC.
Thus still making an even call for russian player whether or not launch Fgs against germans StBs, in the case above.
Happy New Year every A&A fans !!!
:-D :-D :evil: :-o :-D :-D
In G40, attacking bombers and defending fighters roll for 1’s.
Say you have x bombers and y defending fighters. The attacker will lose y/6 bombers on average, for an IPC loss of 2y. The defender will lose x/6 fighters, an IPC loss of (5/3)x.
The remaining x-y/6 bombers will be fired on by the AAA’s. These will kill (x-y/6)/6 of them, a further 2x-y/3 of IPC loss for the attacker.
(In both of the above cases, I’m assuming neither side outnumbers the other by a factor of 6 or more, else all planes on the weaker side will die).
The remaining (5/6)(x-y/6) bombers will do damage to facilities. Each will do 3.5 IPC’s of damage on average.
Therefore, the attacker lost 2y+2x-y/3=(5/3)y+2x IPC’s. Meanwhile, the defender lost (5/3)x+(7/2)*(5/6)(x-y/6)=(55/12)x-(35/72)y IPC’s.
For these to be equal, we need (55/12-2)x=(5/3+35/72)y, which becomes (31/12)x=(155/72)y. This simplifies to y=(6*31/155)x, which becomes y=(6/5)*x. Therefore, 5 bombers against 6 fighters, or 50 bombers against 60 fighters will cause the same IPC loss on both sides (assuming facility damage isn’t maxed out).
