Strategic bombing help

@Douglas333:

Private Panic your input is greatly appreciated.

I’m relatively new to A&A but have an incredible interest in everything WWII.

Although I’m still searching for a clear solution. Perhaps I will be more satisfied playing 1940 global?

Without going too much into maths, I made tables to compare various SBR models according to rules from Global 40, 1942.2, 1942.2 TRIPLE A with Global rules and many more variations, the simplest way to balance SBR for 1942.2 is to increase damage from D6 to D6+2.

Everything else stay the same:
Bombers Attack @1 first strike (if it gets a hit, intercepting defender’s Fighter is immediately removed)
Fighter escort Attack @1 first strike.
Fighter interceptors Defense @2.
To intercept, Fg must be on IC’s TTy. Defender choice to intercept or not.

I found my old OP from my thread:
@Baron:

Hi everyone,
here is a few datas and summary collected after a lot of calculations and messed up tables, here is a real discovery to help any discussion over benefits and disadvantage of various SBR values. Hope you will find interesting numbers to provides some reasons behind intuitive conclusions on SBRs.

I found a useful analysis tool to compare average results of various SBR combat values and cost per unit:
Break even point and ratio:
In Strategic Bombing Raid, it is the number of attacking aircraft unit needed compared to intercepting Fg to get even odds on both sides (+0.00 IPC damage/SBR).
Break even ratio is a fraction number of Strategic bomber over a single intercepting fighter to reach an even odds of winning or loosing IPCs in a single air raid compared to the defender odds of inflicting damage. A ratio above 1 means that you need more than only 1 Bomber against 1 intercepting Fighter to reach a profitable threshold in SBR; while a ratio below 1 means that making a raid with at least 1 bomber against 1 Fighter interceptor is always advantageous for the attacker.

Offensive over defensive cost ratio for same combat values : it is a useful measure to evaluate the comparative higher cost of a given attack value over the same defensive value.
For instance, Tank gives a 1.00 offensive/defensive cost ratio because attack 3 and defense 3 is the same cost at 6 IPCs.
3 air attack over 3 ground defense cost gives Fg A3 C10 vs Tank D3 C6 = 1.67 off/defense IPC ratio.
4 air attack over 4 air defense cost gives StB A4 C12 vs Fg D4 C10 = 1.20 off/def IPC ratio.
2 artillery ground attack over 2 Infantry ground defense gives Art A2 C4 vs Inf D2 C3 = 1.33 off/def cost ratio.
2+2 ground attack over 2+2 ground defense gives Inf+Art A2+A2 C7 vs 2 Inf D2+D2 C6 = 1.17 off/def ratio.
So, this offense/defense cost ratio for the same value goes from 1 to up to 1.67 in regular combat.

Here is a very comprehensive table of various SBR values from stronger to weaker SBR from attacker POV:

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G40.2 SBR OOB
Bomber A1
Damage: 1D6+2
Cost 12

Fighter A1 D1
Cost 10

1 StB A1 doing SBR against 1 Fg D1
D6+2: + 5.486 - 3.667 = +1.819 IPC damage/SBR, 1 vs 1
StB A1 doing SBR against 2 Fgs D1
D6+2: +4.85 - 5.056 = -0.206 IPCs damage/SBR
*9= -1.854, 9 vs 18
Net: -0.035
For 1 StB vs 1 Fg

• 9 StBs vs 18 Fgs
  Break even point: 10 StBs A1 C12 D6+2 vs 19 Fgs D1 C10
  Break even ratio: 10/19= 0.526 StB/Fg
  0.526*12=
  6.32 IPCs/10 IPCs = 0.632 offense/defense cost ratio

---

G40.2 SBR HR
Bomber A0
Damage: 1D6+3
Cost 12

Fighter A1 D1
Cost 10

1 StB A0 damage D6+3 doing SBR against 1 Fg D1
D6+3: +4.514 - 3.667 = +0.847 damage/SBR
*26= +22.022, 26 vs 26
1 StB Att 0 D6+3 doing SBR against 2 Fgs D1
D6+3: +3.762 -5.056 = -1.294 IPCs damage/SBR
*17= -21.998, 17 vs 34
Net: +0.024
For 26 StBs vs 26 Fg

• 17 StBs vs 34 Fgs
  Break even point: 43 StBs A0 D6+3 vs 60 Fgs D1
  43/60= 0.717 StB/Fg break even ratio
  8.6 IPCs/10 IPCs = 0.86 offense/defense ratio

---

G40.2 SBR HR
Bomber A1 First Strike as AAA against up to 2 Fgs which ever the lower,
Damage: 1D6+2
Cost 12

Fighter A2 D2
Cost 10

A1fs as AAA vs up to 2, D6+2 vs D2
1 StB  vs 1 Fg  0.199 IPCs damage/SBR
*10= +1.990, 10 vs 10
1 StB vs 2 Fgs  -0.662 IPCs damage/SBR
*3= -1.986, 3 vs 6
Net: +0.004
For 10 StBs vs 10 Fgs

• 3 StBs vs 6 Fgs
  Break even point: 13 StBs A1fs C12 D6+2 vs 16 Fgs D2 C10
  0.8125 StB/Fg break even ratio
  9.75 IPCs/10 IPCs = 0.975 offense/defense IPC ratio

---

Young Grasshopper HR
G40.2 SBR HR
Bomber A0 but 1 Attack @1 per bomber group
Damage: 1D6+2
Cost 12

Fighter A1 D1
Cost 10

StB 1A1+xA0, D6+2 vs Fg D1

2 StBs A1+A0 against 3 Fgs D1
1 StB A1 vs 1 Fg D1: + 5.486 - 3.667 = + 1.819 IPCs, 1 vs 1
1 StB A0 vs 2 Fgs D1: + 3.183 - 5.056 = - 1.873 IPCs, 1 vs 2
OR
1 StB A1 vs 2 Fgs  D1: + 4.850 - 5.056 = - 0.206 IPCs, 1 vs 2
1 StB A0 vs 1 Fg D1: + 3.819 - 3.667 = + 0.152 IPC, 1 vs 1
Sum: + 8.669 - 8.723 = - 0.054 IPC damage/SBR
Net: -0.054
Break even point: 2 StBs A1/A0 C12 D6+2 vs 3 Fgs D1 C10
0.667 StB/Fg break even ratio with lower number of units
8 IPCs/10 IPCs = 0.8 off/def ratio

1 StB A0 vs 1 Fg D1: + 3.819 - 3.667 = + 0.152 IPC
*25= +3.800, 25 vs 25
1 StB A0 vs 2 Fgs D1: + 3.183 - 5.056 = - 1.873 IPC
*2= -3.746 + -0.054= -3.800, 2 vs 4 + 2 vs 3
Net: +0.00
For 25 StBs vs 25 Fgs

• 2 StBs vs 4 Fgs
• 2 StBs vs 3 Fgs
  Break even point: 29 StBs A1 A0 C12 D6+2 vs 32 Fgs D1 C10
  0.9063 StB/Fg  break even ratio with higher number of units
  10.875 IPCs/10 IPCs = 1.09 offense/defense ratio

---

G40.2 or 1942.2 SBR HR
Bomber A0
Damage: 1D6+2
Cost 12

Fighter A1 D1
Cost 10

StB A0 C12 D6+2 vs Fg D1
1 StB A0 vs 1 Fg D1: + 3.819 - 3.667 = + 0.152 IPC
*25= +3.800, 25 vs 25
1 StB A0 vs 2 Fg D1: + 3.183 - 5.056 = - 1.873 IPC
*2= -3.746, 2 vs 4
Net: +0.054
For 25 StBs vs 25 Fgs

• 2 StBs vs 4 Fgs
  Break even point: 27 StBs A0 C12 D6+2 vs 29 Fgs D1 C10
  0.931 StB/Fg break even ratio
  11.17 IPCs/10 IPCs = 1.12 offense/defense cost ratio
  __

1942.2 OOB with D6+2 G40.2 damage, SBR HR
Bomber A1 First Strike,
Damage: 1D6+2
Cost 12

Fighter A1 First Strike D2
Cost 10

1942.2 A1 first strike D6+2 vs Fg D2
1 StB vs 1 Fg: +4.977 - 4.778 = +0.199 IPC damage/SBR
*50=+9.950, 50 vs 50
1 StB vs 2 Fgs: +3.874 - 7.185 = -3.311 IPCs damage/SBR
*3= -9.933, 3 vs 6
Net: +0.017
For 50 StBs vs 50 Fgs

• 3 StBs vs 6 Fgs
  Break even point: 53 StBs A1fs C12 D6+2 vs 56 Fgs D2 C10
  0.946 StB/Fg break even ratio
  11.36 IPCs/10 IPCs = 1.14 offense/defense cost ratio

---

1942.2 Triple A SBR
or Young Grasshopper G40.2 HR for StB not starting from Air Base
Bomber A1
Damage: 1D6
Cost 12

Fighter A1 D1
Cost 10

1 StB A1 D6 vs 1 Fg D1
1 vs 1: +3.69 - 3.667 = +0.023 IPC damage/SBR
*132= +3.036, 132 vs 132
StB A1 D6 against 2 Fgs D1
1 vs 2 : +2.025 - 5.056 = -3.031 IPCs damage/SBR
Net: -0.005
For 132 StBs vs 132 Fgs

• 1 StBs vs 2 Fgs
  Break even point: 133 StBs A1 C12 D6 vs 134 Fgs D1 C10
  133/134= 0.9925 StB/Fg break even ratio
  11.91 IPCs/10 IPCs = 1.191 offense/defense ratio

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Regular Kid’s Balance Mode
G40.2 SBR HR
Bomber A1
Damage: 1D6+2
Cost 12

Fighter A2 D2
Cost 10

2 StBs A1 against 1 Fgs D2
1D6+2: +10.639 - 7.334 = + 3.304 IPCs damage/SBR
*12=+39.648, 24 vs 12
1 StB A1 vs 1 Fg D2
1D6+2: + 4.723 - 5.333 = - 0.61 IPC dam/SBR
*65= -39.650, 65 vs 65
Net: -0.002
For 24 StBs vs 12 Fgs

• 65 StBs vs 65 Fgs
  Break even point: 89 StBs A1 C12 D6+2 vs 77 Fgs D2 C10
  1.156 StB/Fg break even ratio
  13.87 IPCs/10 IPCs = 1.39 offense/defense IPC ratio

---

G40.2 or 1942.2 SBR HR
Bomber A1 as AAA against up to 2 Fgs which ever the lower,
Damage: 1D6+2
Cost 12

Fighter A2 D2
Cost 10

StB A1 as AAA up to 2 Fg, D6+2 vs 1 Fg D2
2 vs 1  +1.972 *4= +7.888, 8 StBs vs 4 Fgs
1 vs 1  -0.61 *13= -7.930, 13 StBs vs 13 Fgs
Net: -0.042
Break even point: 21 StBs A1 C12 D6+2 vs 17 Fgs D2 C10
21/17= 1.235 StB/Fg break even ratio
14.824 IPCs/10 IPCs = 1.48 offense/defense cost ratio
__

1942.2 OOB SBR with D6 damage
Bomber A1 First Strike
Damage: 1D6
Cost 12

Fighter A1 First Strike D2
Cost 10

2 StBs A1 first strike doing SBR against 1 Fg D2
2 vs 1 : +8.214 - 6.315 = +1.899 IPCs
*10= +18.99, 20 vs 10
1 StB A1fs against 1 Fg D2
OOB 1942.2 D6: +3.8 - 4.8 = -1 IPC damage/SBR
*19= -19.00, 19 vs 19
Net: -0.010
For 20 StBs vs 10 Fgs

• 19 StBs vs 19 Fgs
  Break even point: 39 StBs A1fs C12 D6 vs 29 Fgs D2 C10
  39/29= 1.345 StB/Fg break even ratio
  16.1 IPCs/10 IPCs = 1.61 offense/defense cost ratio

__
Young Grasshopper HR
G40.2 SBR HR mostly implied from D6 Strat Bombers not starting from Air Base
Bomber A0 + 1A1 for StBs group
Damage: 1D6
Cost 12

Fighter A1 D1
Cost 10

3 Strategic Bombers A0 D6 damage doing SBR against 1 Fg D1
3 vs 1: + 8.264 -7.666= +0.598 IPCs
2 Strategic Bombers A0 doing SBR against 1 Fg D1
2 vs 1: + 5.347 -5.666= -0.319 IPCs
*2= -0.638, 4 vs 2
Net: -0.040
7 StBs A0 vs 3 Fgs D1
And
1 StB A1 doing SBR against 1 Fg D1
1 vs 1: +3.69 - 3.667 = +0.023 IPC damage/SBR
Net: -0.017
Break even point: 8 StBs A0 D6 vs 4 Fgs D1
Break even ratio: 8/4= 2.0 StBs/Fg
24 IPCs/10 IPCs = 2.4 offense/defense cost ratio

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G40.2 SBR HR
Bomber A0
Damage: 1D6
Cost 12

Fighter A1 D1
Cost 10

3 StBs A0 Damage D6 doing SBR against 1 Fg D1
3 vs 1: + 8.264 -7.666= +0.598 IPCs
2 StBs A0 doing SBR against 1 Fg D1
2 vs 1: + 5.347 -5.666= -0.319 IPCs
*2= -0.638, 4 vs 2
Net: -0.040
For 3 StBs vs 1 Fg

• 4 StBs vs 2 Fgs
  Break even point: 7 StB A0 D6 vs 3 Fg D1
  7/3= 2.333 StB/Fg break even ratio
  2.333*12=
  28 IPCs/10 IPCs = 2.8 offense/defense IPCs ratio

@Douglas333:

Sorry, I’m sure this has been asked and answered but I haven’t been able to find the answer.

Strategic bombing has basically become non existent in my game with the scrambling fighter rule (which I agree with since its realistic) along with built in AAA multiplied by however attacking bombers… in the factories. IMO it is not cost effective to buy bombers that might not even reach their destination for bombing, or shot down by AAA. Unless I’m just flat out wrong.

Solutions I have come up with but haven’t tried because my opponent and I haven’t had time to play is either make bombers cheaper, and or take away built in AAA and only let purchased AAA units defend.

Suggestions, solutions, any input welcome.

Should be noted we have been playing where any fighter in a territory the bomber(s) fly over can scramble, but only get one attack roll. In which case its a 50/50 the makes it passed that territory

Being the realist I am I realize bomber casualties were high. However, I think they are too costly to simulate the numbers in which they were produced IRL.

Maybe, I’m stupid but need confirmation please.  :?

Not using escorting Fg, here is for SBR 1942.2 OOB rules:
Break even point: 39 StBs A1fs C12 D6 vs 29 Fgs D2 C10
39/29= 1.345 StB/Fg break even ratio

So, every time you have 3 StBs facing 2 Fgs (1.5 StB/Fg), odds are toward attacker.
If you get 4 StBs facing 3 Fgs (1.333 StB/Fg) odds are barely toward defender.
This means it is the bottom threshold, lower than that you are sacrificing Bombers for peanuts.
For instance, 5 StBs facing 4 Fgs, 1.25 StBs/Fg.

With my suggestion to rise damage to D6+2, you get this breakeven point:

Break even point: 53 StBs A1fs C12 D6+2 vs 56 Fgs D2 C10
0.946 StB/Fg break even ratio
11.36 IPCs/10 IPCs = 1.14 offense/defense cost ratio

Basically, with a threshold just below 1 (0.946 StB/Fg) it said every time 1 StB is facing 1 Fg, odds are toward attacker.
OOB, 1 StB vs 1 Fg does not worth the risk to SBR.
Said otherwise, the defender should always intercept in such case.

If the bombers outnumber the fighters by 100%, each bomber has twice the chance of inflicting a 10 ipc fighter loss, than it has of incurring a 12 ipc bomber loss. 1 bomber inflicts 1/6 x 10 ipcs = 1.67 ipc loss to the enemy. If half the fighters then a 1/6 x 12 ipcs x ½ = 1 ipc cost to the SBRing power. A net benefit of 0.67. On the other hand the number of bombers remaining to go on to their target has been reduced. If you redo the calculation without intercepts with this slight reduction in the number of bombers, the SBR net benefit is 0.84 ipcs per bomber + the air raid net benefit of 0.67 per bomber = a total net benefit of 1.51 per bomber.

Of course it is unlikely the fighters would intercept at those odds.

The breakeven point is 1.2 fighters per bomber. That is counter-intuitive for some players. No doubt someone will shout out if I have got the calculations wrong.

1.2 Fg/StB= 0.833 StB/Fg breakeven point
It doesn’t fit for 1942.2 SBR rules.
You probably forgot to consider the first strike capacity from both escorting Fg and Bomber.

Without going too much into maths, I made tables to compare various SBR models according to rules from Global 40, 1942.2, 1942.2 TRIPLE A with Global rules and many more variations, the simplest way to balance SBR for 1942.2 is to increase damage from D6 to D6+2.

Another reason which proved it stays balanced is to compare offense/defense ratio:
Break even point: .931 StB/Fg break even ratio
(.931x12 IPCs= ) 11.17 IPCs/10 IPCs = 1.12 offense/defense ratio

1.12 is similar to what you get for 1 Infantry A2 and 1 Artillery A2 compared to two Infantry D2:
Similar offense (4 points) and defense (4 points) but a bit costlier in offence 7 IPCs/6 IPCs =1.17

In addition, some ICs will be max out more easily. For instance, Russia will be less affected on Karelia’s IC because it only takes 4 hits to be max out, or Caucasus IC’s eight points. Most others requires around 16 IPCs. So +2 is a fine bonus but it remains limited by IC’s caps.

@Douglas333:

Private Panic your input is greatly appreciated.

I’m relatively new to A&A but have an incredible interest in everything WWII.

Although I’m still searching for a clear solution. Perhaps I will be more satisfied playing 1940 global?

Thanks Douglas333. I see that Baron has put up some further analysis and he is far cleverer than I at this stuff.

In 1940 Global each bomber damage roll is increased by 2 so the net benefit to an SBR is increased. I think that is particularly pertinent to that variant because there are a lot more factories around which can reduce the value of damaging any one.

It is a much more complex game and feels like the “complete” A&A experience to lovers of the game.

There are really two different rulesets and one variation.

In 42.2, the bombers come in and their defensive fire is first striking.  The escorting and intercepting fighters fight at “2”, one of the best reasons to have escorting fighters is to have something other than bombers to lose.  Then AAA gets to whack at bombers only.  There is no SBR bonus, and all major factories are different in how they operate.  There is less industrial capacity and building new complexes is less effective than in G40.

In this environment, SBR as an overall tactic is probably less than optimal, but there are many situations where you will have distinct reasons (against Russia, or Italy for example) to destroy the targets even if these raids are costly.  The distances are also shorter, making bringing in escorts more viable.

In G40, the raid comes with interceptors, everyone rolls “1” at the same time, some casualties are taken, and then the bombers run the AAA and if they survive, with a +2 bonus.    Because of the larger number of bombers and the fact that bases are also targets, strategic bombing is a somewhat expensive but fairly effective way of trading $$ for $$.  Especially with Germany paralyzing the Russian economy and America attacking flexibly with either economic or military strikes, these are viable overall strategies to pursue.

Dollar for dollar, it would probably be better to attack ships or breakthrough targets (like killing 1 blocking infantry), because they don’t get to first strike or AAA. but the benefit is that you can choose what the bombers do every round, they are the most flexible unit in the game.  If they can strike units, they do.  When they cant, they can hit bases instead.

There is an alternate G40 where interceptors and escorts fight at “2”.  This wouldn’t seem to make much of a difference in smaller raids, but the reality of the game is that you can pile quite a few fighters onto Japan and WGermany, so many that if they fight at “2”, SBR en masse is less effective.  Enough fighters can dissuade those attacks, and so this rule is pretty game changing.

Also, you could re-insert the rule that AAA units fire at bombers passing over.  This makes them less flexible because their routes have to be taken more carefully.

You could diminish the G40 SBR bonus to +1, or add a SBR bonus of +1 to 42.2.  You could also add the house rule that only bombers departing from a functioning AirBase gain the +2, this is probably the most balancing mod of all of them because it lets players choose the most effective way to base/land their bombers/fighters.

Overall, SBR rules feel somewhat fairly balanced, primarily because the bombers are 12 not 15, the damage they can do in G40 SBR is sort of balanced, tending towards being too damaging….when you add in the flexibility and move 6 they are the best unit…

Dollar for dollar, it may not be a very efficient trade on paper but when Germany makes 70 and Russia 30, it is very much a solid trade.

Pretty good summary of most of the options.
A small correction:

In 42.2, the bombers come in and their defensive fire is first striking.   The escorting and intercepting fighters fight at “2”, one of the best reasons to have escorting fighters is to have something other than bombers to lose.   Then AAA gets to whack at bombers only.

According to OOB 1942.2 optionnal escort and intercept, only intercepting Fg get @2, both bombers and escorts roll together @1 first strike.

One other actual way to balance 1942.2 SBR is to use TRIPLE A optionnal intercept and escort.
All planes @1, like G40 OOB rules, except damage remains D6.
The near 1 break-even point is easy to remember.

1942.2 Triple A SBR
or Young Grasshopper G40.2 HR for StB not starting from Air Base
Break even point: 133 StBs A1 C12 D6 vs 134 Fgs D1 C10
133/134= 0.9925 StB/Fg break even ratio
11.91 IPCs/10 IPCs = 1.191 offense/defense ratio

So attacker knows that 1 StB vs 1 Fg, it is better to add another plane (whether Fg escort or StB) to swing odds toward him.

In this environment, SBR as an overall tactic is probably less than optimal, but there are many situations where you will have distinct reasons (against Russia, or Italy for example) to destroy the targets even if these raids are costly.   The distances are also shorter, making bringing in escorts more viable.

I would add that 1942.2 don’t get as much ressources. Fgs (and StBs) are not cheap and loosing one is hard to replace (especially for Germany which needs a lot of ground investment).
Because of higher risk due to OOB 1942.2 SBR, often attacker will not risk SBR with 1 StB vs 1 Fg @2, and adding 1 escort Fg (first strike @1) will deter defender from intercepting with its one Fg available. Most of the time, SBRs will be done on unattended IC (due to Fgs positionning elsewhere on other TTys or Carriers).

If you want more air interactions, I suggest you use Triple SBR rules for 1942.2 (all planes @1/damage D6).
Risk are lower for both parts. And still let’s everyone hope for “1” rolls.

thanks for pointing that out Baron, I was misapplying that.  Seems ok balance wise but may make the offense too risky esp. against Germany.  As you emphasize, the bombers are even more precious in the small economy versions you have fewer to risk and fewer to lose.

@taamvan:

thanks for pointing that out Baron, I was misapplying that.   Seems ok balance wise but may make the offense too risky esp. against Germany.  As you emphasize, the bombers are even more precious in the small economy versions you have fewer to risk and fewer to lose.

The most difficult part for a fine SBR HR  is that it should not be too much bias toward the attacker, while the intercepting Fighter presence on IC should not be a complete deterrent.

Of the many SBR values suggested in the past years, I believe the Young Grasshopper provides the best incentive for both attacker and defender being part of such raid. Using “1” values only is less a deterrent than @2 (because,  with IC’s AAgun it means around a low 50% odds of survival for 1 StB) or first strike @1 (because a hit forbid interceptor to retaliate).

Here is the mechanics:
Young Grasshopper HR
G40.2 SBR HR
**Bomber A0 but 1 Attack @1 per bomber group
Damage: 1D6+2
Cost 12

Fighter A1 D1
Cost 10**
It is less OP than Global SBR, but these features increase interactions.
How?
This means the first Bomber gets a single @1 while additional StBs bring nothing against interceptors but increase damage on IC.
This is also an incentive to bring Fgs escort to get more @1 against interceptors.
For defender, letting go a few StBs is a costly tactics. Adding a defense @1 per Fg increase odds to shot down at least one bomber, which means less damage on IC.

To compare break even point:
Break even point: 2 StBs A1/A0 C12 D6+2 vs 3 Fgs D1 C10
0.667 StB/Fg break even ratio with lower number of units
8 IPCs/10 IPCs = 0.8 off/def ratio

Young Grasshopper, in 1942.2 order of economy would probably gets around this 2 StBs vs 3Fgs ratio most of the time.
And .667 StBs/Fg is far better for the attacker than the two other methods previously suggested (both near or above 1.00 StB/Fg break even point).

Also, on an StBs only against Fgs scenario, there is no Interception Threshold ceiling: attacker can add an infinite number of bombers (attack remains a single @1 roll), intercepting with only a single Fighter is still  reducing damage for defender. So, this method have the best incentive to make dogfight happen.

Finally, when escorting Fgs are parts of the fight at low numbers, it is easy to judge if it worths the risk to intercept. Each one on one Fg vs Fg nullify each other damage, and 1 escort above interceptor increase damage by 1.667 (10*1/6). Making Interception Threshold ceiling according to the number of escorting Fighter.

So in a case like above with 2 StBs against 3 Fgs, 1 additional escort makes (1.819 + 0.152= +1.971 IPCs damage on average) less damage than 2 full blown StBs on IC (2*2.583= 5.166 IPCs on avg).
With 2 additional escorts, it means 1 full blown StBs on IC (2.583) because if both Fg are taken down, 1 StB is clear, the last StB against the last Fg is at 1.819. Sum 2.583+ 1.819 = 4.402 IPCs on avg.
And this case still better than letting go 2 full blown StBs on IC (4.402 < 5.166).
On 2 StBs with 3 Fgs against 3 intercepting Fgs, it is clear there is no difference between intercept and no interception: escorts and interceptors nullify each other. Both situations are even, so this is the Interception Threshold ceiling. Beyond that, each additional escort over interceptor brings +1.667 IPCs damage on avg. And from a statistical POV, it is better not intercept.

Of course, if defender feels lucky, it is not an unusual situation to have less units than attacker in Axis and Allies in a given combat.

StB 1A1+xA0, D6+2 vs Fg A1 D1

2 StBs A1+A0 against 3 Fgs D1
1 StB A1 vs 1 Fg D1: + 5.486 - 3.667 = + 1.819 IPCs, 1 vs 1
1 StB A0 vs 2 Fgs D1: + 3.183 - 5.056 = - 1.873 IPCs, 1 vs 2
OR
1 StB A1 vs 2 Fgs  D1: + 4.850 - 5.056 = - 0.206 IPCs, 1 vs 2
1 StB A0 vs 1 Fg D1: + 3.819 - 3.667 = + 0.152 IPC, 1 vs 1
Sum: + 8.669 - 8.723 = - 0.054 IPC damage/SBR
Net: -0.054
Break even point: 2 StBs A1/A0 C12 D6+2 vs 3 Fgs D1 C10
0.667 StB/Fg break even ratio with lower number of units
8 IPCs/10 IPCs = 0.8 off/def ratio