SBR comparative analysis, a real breakthrough

  • '17 '16

    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 cost ratio.
    6 attack points from Tanks against 6 Infantry defense gives A6 C12 vs D6 C9 = 1.33 off/defense IPC ratio.
    6 attack points from Tanks against 6 Artillery defense gives A6 C12 vs D6 C12 = 1.00 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.

    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.

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


    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

      Approximative Interception Threshold: from 1.55 StB/Fg and less
      31 StBs vs 20 Fgs =+80.094
      31 StBs vs no interception 31*2.583 = + 80.073
      So odds of damage are slightly lower with no interception (80.073-80.094= -0.021) but near zero differential.

    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

    Interception Threshold, StBs attack only: none, always beneficial to intercept.
    Interception Threshold, StBs and Fgs escorts: same number as escort Fgs


    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

    Interception Threshold, StBs attack only: none, always beneficial to intercept.
    Interception Threshold, StBs and Fgs escorts: same number as escort Fgs
    __

    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

    Approximative Interception Threshold: 2.25 StBs/Fg
    9 StBs vs 4 Fgs:
    50.297 - 26.949 = +23.348
    1 StB vs 1 Fg,  +4.977 - 4.778 = +0.199 IPC damage/SBR
    2 StBs vs 1 Fg, +11.162 - 6.315 = +4.847 IPCs damage/SBR
    3 StBs vs 1 Fg + 17.079 - 7.928 = + 9.151 IPCs damage/SBR run*2= +18.302

    1StB vs no, D6+2: +4.583 - 2 = +2.583 IPCs damage/SBR
    9 StBs vs no interception 9*2.583
    +41.247 - 18.000 = + 23.247
    So odds of damage are slightly higher with interception ( 23.247 - 23.348 = -0.101 ) but still a small differential.


    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

    Approximative Interception Threshold: from 1.5 StBs/Fg and less
    3 StBs vs 2 Fgs: +2.760
    2 StBs vs 1 Fg : +8.403 - 5.666 = +2.737 IPCs
    1 StB vs 1 Fg : +3.69 - 3.667 = +0.023 IPC damage/SBR
    +2.917 - 2 = +0.917 IPC damage/SBR*3=
    +8.751 - 6 = +2.751 IPC damage/SBR for 3 StBs and no interception
    So odds of damage are slightly higher with interception (2.751 -2.760= -0.009) but very near zero differential.


    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

      Approximative Interception Threshold: from 2 StBs/Fg and less

    2 StBs vs 1 Fg : +8.214 - 6.315 = +1.899 IPCs
    +2.917 - 2 = +0.917 IPC damage/SBR*2=
    +5.834 - 4 = +1.834 IPC damage/SBR for 2 StBs and no interception
    So odds of damage are slightly higher with interception (1.834 -1.899= -0.065) but very near zero.
    __
    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


    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

  • Hi Baron

    I am sure this is really valuable stuff and thanks for sharing. It merited an attempt to understand it properly and here I have failed. :-(

    If you are happy to take the time to explain further, then read on!

    I did my own calculation for a 1 bomber vs 1 fighter SBR and came up with the following:

    Possibility of Bomber being shot down by fighter = 1/6
    Loss if bomber lost = 12 ipcs
    Impact = 1/6 x 12 = -2 ipcs

    Possibility of Fighter being shot down = 1/6
    Gain if fighter killed = 10 ipcs
    Impact = 1/6 x 10 = + +1.67 ipcs

    Possibility of Bomber being shot down by factory
    Bomber surviving = 5/6
    Possibility of Bomber being shot down by factory = 1/6
    Loss if bomber lost = 12 ipcs
    Impact = 5/6 x 1/6 x 12 = -1.67 ipcs

    Damage to factory
    Bomber surviving = 5/6 x 5/6 = 25/36
    Average D6 + 2 dice roll = 5.5
    Impact = 25/36 x 5.5 = +3.82 ipcs

    OVERALL IMPACT = -2 + 1.67 - 1.67 +3.82 = +1.82 ipcs

    That agrees with your +1.819 ipc damage/SBR. So far, so good.

    Recalculating for 1 bomber vs 2 fighters:

    Possibility of Bomber being shot down by fighters = 1/6 + (5/6 x 1/6) = 0.306
    Loss if bomber lost = 12 ipcs
    Impact = 0.306 x 12 = -3.67 ipcs

    Possibility of Fighter being shot down = 1/6
    Gain if fighter killed = 10 ipcs
    Impact = 1/6 x 10 = + +1.67 ipcs

    Possibility of Bomber being shot down by factory
    Bomber surviving = 1 - 0.306 = 0.694
    Possibility of Bomber being shot down by factory = 1/6
    Loss if bomber lost = 12 ipcs
    Impact = 0.694 x 1/6 x 12 = -1.39 ipcs

    Damage to factory
    Bomber surviving = 0.694 x 5/6 = 0.579
    Average D6 + 2 dice roll = 5.5
    Impact = 0.579 x 5.5 = +3.18 ipcs

    OVERALL IMPACT = -3.67 + 1.67 - 1.39 + 3.18 = -0.21 ipcs

    Why does that not agree with your -1.854 ipcs?

    Not sure that I then understand why you netted the two figures, nor the relevance of the offence/defence cost ratio, so this really is one step at a time for me! :roll:

    Cheers
    PP

  • '17 '16

    Hi Private Panic,
    what is bolded is the results for each type of SBR.
    The rest is the last calculation which allowed me to get the final result.
    I do not want to provides all other undigestible pre-existent tables (but needed to reach the results) because it brings too small benefits for analysis to go to such details when talking on a wider scope.

    About offense/defense cost ratio, it provides a number to compare with what happen in OOB regular combat. All A&A game is based on giving an advantage to defender by making the same attack number a bit costlier. For instance, all OOB regular ratio goes from 1 to 1.667 costlier for the same attack value than defender.

    So, when comparing OOB G40 SBR, you get an incredible 0.632 off/def cost ratio.
    A completly reverse situation than any other aspect of regular combat between units!
    The attacker needs a very little investment to reach an even odds to score damage against defender.
    It shows why StBs are clearly OP compared to other SBR values.


  • You both seem to arrive at the same outcome for StB A1 doing SBR against 2 Fgs D1:
    G40 D6+2: +4.85 - 5.056 = -0.206 IPCs damage/SBR*9= -1.854

    But Baron Munchausen multiplies this 0.206 with a factor of 9. Could you explain this BM, I’m not sure what this factor is doing there.

    EDIT: I strongly discourage using math like it’s used in that line. Equations like +4 - 5 = -1 *9 are false, and hurt my feelings. [/math-nazi]


  • Ozymandiac is right - it is Baron’s multiplication by 9 which throws me off. Thanks for spotting that Ozy.

    Thanks for your reply Baron. Still not got it but will look again tomorrow. My brain hurts!

  • '17 '16

    @Ozymandiac:

    You both seem to arrive at the same outcome for StB A1 doing SBR against 2 Fgs D1:
    G40 D6+2: +4.85 - 5.056 = -0.206 IPCs damage/SBR*9= -1.854

    But Baron Munchausen multiplies this 0.206 with a factor of 9. Could you explain this BM, I’m not sure what this factor is doing there.

    EDIT: I strongly discourage using math like it’s used in that line. Equations like +4 - 5 = -1 *9 are false, and hurt my feelings. [/math-nazi]

    To find the break even point, you need to reach a near zero either positive or negative (+ or - 0.0).
    To get it you must confront a positive occurance such as 2 StBs vs 1 Fg against a negative occurance, sometimes a 1 StB vs 1 Fg or 1 StB vs 2 Fgs.
    Then you must find the multplication factor for each which gives a sum near zero odds of comparative damage offender vs defender.
    For example, G40 OOB needs 9 times 1 StB against 2 Fgs to get a total negative value of -1.854 IPCs for a single run of 9 StBs against 18 Fgs.
    Adding 1 StB vs 1 Fg gives positive value of +1.819.
    So when 10 StBs raids against 19 Fgs, you reach a break even point.
    Small variation is negligeable but due to difference between both odds: -0.035 and not a perfect zero.

  • '17 '16

    @ShadowHAwk:

    You cannot scale this type of attack effectively without taking into account the maximum damage you can do.

    Max damage is 20 so 4 bombers will damage maximum the rest will add 0 damage.

    It is still true my calculation doesn’t consider this ceiling factor.
    It is not perfect but it still provides a good basis for comparing between SBRs values.
    Once you know what is the break even point in a given set of values, you know when you plan an SBR, if the odds still on your side even it is a borderline riskier attack.

    In 1942.2, it can be less than 20, 16 even 6 or 4.
    It will be the next challenge to consider this 20 maximum damage factor per IC at most.

    However, the scale of break even poit is still true.
    If you have 5 StBs attacking 9 Fgs, for a 0.556 StB/Fg value, it is above .526 StB/Fg.
    So it stay in favor of the attacker.
    Now, the attacker must approximate is odds of maxing out the IC.
    A rough calculation gives 5 StBs * 5.5 = 27.5 IPCs.
    But, it will probably loose one StB. 4 StBs *5.5 = 22 IPCs. A max out result.
    It can be possible to use my OOB tables to get a more precise result, to find a more on the line limit.
    1 vs 1: + 5.486 - 3.667 = +1.819 IPC damage/SBR
    StB A1 doing SBR against 2 Fgs D
    1 vs 2 : + 4.85 - 5.056 = - 0.206 IPCs damage/SBR
    *4 = +19.4 - 20.224 = - 0.824 IPC

    5 vs 9 Fgs: +24.886 - 23.891= +0.995
    So, 2 bombers will be lost (near -24 IPCs).
    3 StBs will roll dmg, for 5.5 = 17.5 IPCs. No maxout.
    Or 1 Fg will be destroyed +10 IPCs, it gives around 15 IPCs damage on IC.

    So, my point is that no matter the high number of units implied in the calculation, break even point it still correct. The adjustment on 20 IPCs CAP must be made in game to evaluate if a given situation  gives good odds for attacker and if it still worth even if it gets max out on IC.

    Also, defender should ask if it worth the case to intercept.
    For instance,
    1 StB doing SBR without interceptor
    Sum: +4.583 - 2 = +2.583 IPCs damage/SBR
    *5 = +22.915 -10 = +12.915 IPCs damage/raid
    The difference is near 12 IPCs (12.915-0.995), so intercept reduces the benefits of the attacker.

    But no intercept brings a 20 Max out on avg, +22.915. So, instead of 13  IPC, it will be a +10 IPCs on the defender due to cap at 20. A calc maniac can then compare pros and cons of intercept.

  • '19 '17 '16

    So you are saying for G40 OOB, there is a positive expected value for a bombing raid with 2SBs vs 3 ftr intercepting? Interesting that’s not what I expected.

    I get for the IC:

    • 40% chance of doing 11 damage average
    • 15% chance of doing no damage
    • 45% chance of doing 5.5 damage average
      For the fighters:
    • 1/36 chance of doing 20 damage
    • 10/36 chance of doing 10 damage
      Average damage = 10.22 total.

    For the bombers:

    • 15% chance of 24 damage
    • 45% chance of 12 damage
      Average damage for attacker: 8.95

    Interesting. Seems you’re correct.

  • '17 '16

    @simon33:

    So you are saying for G40 OOB, there is a positive expected value for a bombing raid with 2SBs vs 3 ftr intercepting? Interesting that’s not what I expected.

    I get for the IC:

    • 40% chance of doing 11 damage average
    • 13% chance of doing no damage
    • 47% chance of doing 5.5 damage average
      For the fighters:
    • 1/36 chance of doing 20 damage
    • 10/36 chance of doing 10 damage
      Average damage = 10.31 total.

    For the bombers:

    • 13% chance of 24 damage
    • 47% chance of 12 damage
      Average damage for attacker: 8.76

    Interesting. Seems you’re correct.

    You will find on this link the whole post on OOB G40 SBR calculations.
    http://www.axisandallies.org/forums/index.php?topic=35614.msg1391984#msg1391984

    The mistake in your calculation is that Fgs interceptors can roll 3 dices to kill up to 2 StBs.
    16/216 to kill 2 bombers. 7.4%
    75/216 to kill 1 bomber. 34.7%
    125/216 no kill. 57.9%

    StBs roll /Fgs roll / AAA roll
    1/3616/21636/36  = 96/46656  2 StBs killed by Fg vs 2 Fgs
    1/3675/2166/36 =  75/46656  1 StB killed by Fg and 1 StB killed by AAA vs 2 Fgs
    1/3675/21630/36 =   375/46656  1 StB by Fg vs 2 Fgs
    1/36125/2161/36 = 125/46656  2 StBs killed by AAA vs 2 Fgs
    1/36125/21610/36 = 1250/46656  1 StB killed by AAA vs 2 Fgs
    1/36125/21625/36 = /46656  no casualty vs 2 Fgs

    10/3616/2166/6 = 960/46656    2 StBs killed by Fg vs 1 Fg
    10/3675/2161/6= 750/46656  1 StB  by Fg and 1 StB killed by AAA vs 1 Fg
    10/3675/2165/6 = 3750/46656 1 StB by Fg vs 1 Fg
    10/36125/2161/6 = 1250/46656  1 StB killed by AAA vs 1 Fg
    10/36125/2165/6 = 6250/46656  no casualty vs 1 Fg

    25/3616/2166/6 = 2400/46656   2 StBs killed by Fg vs no casualty
    25/3675/2161/6 = 1875/46656    1 StB by Fg and 1 StB killed by AAA vs no casualty
    25/3675/2165/6 = 9375/46656  1 StB by Fg vs no casualty
    25/36125/2161/6 = 3125/46656   1 StB killed by AAA vs no casualty
    25/36125/2165/6 = 15625/46656  no casualty at all

    Results:
    Bombard on IC: 22500/46656 * ((1+2) +(6+2) IPCs)/2= +11 IPCs) = + 5.305 IPCs
    Bombard on IC: 18000/46656 * ((1+2) +(6+2) IPCs)/2= +5.5 IPCs) = + 2.122 IPCs
    Killing 2 Fgs: 1296/46656 +20 IPCs =  + 0.556 IPC  2.778%
    Killing 1 Fg: 12960/46656 +10 IPCs = + 2.778 IPCs  27.78%
    1 StB killed: 18000/46656
    -12 IPCs = - 4.630 IPCs  38.58%
    2 StBs killed: 6156/46656
    -24 IPCs = - 3.167 IPCs  13.19%

    Sum: +10.761 - 7.797 = + 2.964 IPC damage/StB

    THIS TABLE NEED EDITION SORRY…

  • '19 '17 '16

    No mistake. I’m including the AAA.

    If one is shot down by the interceptors, it has a 1/6 chance of not living to tell the tale.
    If none are shot down by the interceptors, they have a 1/36 chance of neither living to tell the tale.

    So that makes the chance of two not proceeding to bomb the IC:

    7.4% + 37.7% / 6 + 57.9% / 36 = 15.3%

    Without rounding I get 14.8%.

    (5/6)**5 = 40% though. That is the chance of them both getting through.

    I’ll correct my odds above.

  • '17 '16

    @simon33:

    No mistake. I’m including the AAA.

    If one is shot down by the interceptors, it has a 1/6 chance of not living to tell the tale.
    If none are shot down by the interceptors, they have a 1/36 chance of neither living to tell the tale.
    So that makes the chance of two not proceeding to bomb the IC:

    7.4% + 37.7% / 6 + 57.9% / 36 = 15.3%

    Without rounding I get 14.8%.

    (5/6)**5 = 40% though. That is the chance of them both getting through.

    I’ll correct my odds above.

    I forgot to include this little AAA vs 2 StBs in my last post, I will correct this soon.

    The result must be +1.613 IPC/raid
    +1.819 - 0.206 = +1.613

    1 StB A1 doing SBR against 1 Fg D1
    D6+2: + 5.486 - 3.667 = +1.819 IPC damage/SBR
    StB A1 doing SBR against 2 Fgs D1
    D6+2: +4.85 - 5.056 = -0.206 IPCs damage/SBR

  • '19 '17 '16

    I see where you’ve gone wrong. If two planes get through the interceptors, there are two AAA shots, not one.

  • '15 '14

    Hi guys,

    my opinion on that. If you guys just enjoy doing such analysis - which I would really understand - then this stuff is nice.

    However the practical use of that analysis in the game close to zero.

    The following things are not btw calculated:
    1. 1 SBR damage =/= 1 IPC cost. In many cases UK or Russia does not need to repair each damage immediately and can perfectly build even with 1-5 damage
    2. Next to the cost of a bomber the threat projection must be considered in case a bomber gets lost. A bomber not being on the map after the German turn can significantly influence the Allied options. Thus, the attacker risks more than 2 IPC from each shot at1 against the bomber.

    In a nutshell: A&A is a complex game and such analysis will not provide significant support to master the game.

    However, if this is just fun for you guys, of course something I appreciate. I didn’t want to sound rude, just express that I find this aspect isnt’t crucial to master the game.

    Cheers,
    Tobias

  • '19 '17 '16

    I don’t completely agree, JDOW. It does have some effect on the game to know that you can be outnumbered and still have a positive expected value from an SBR. I would not have expected that.

    One person I play with reckons that SBR would be more reasonable if the air raid part all rolled at a 2 rather than a 1. That way you could do a more effective counter to it.

  • '17 '16

    @JDOW:

    Hi guys,

    my opinion on that. If you guys just enjoy doing such analysis - which I would really understand - then this stuff is nice.

    However the practical use of that analysis in the game close to zero.

    The following things are not btw calculated:
    1. 1 SBR damage =/= 1 IPC cost. In many cases UK or Russia does not need to repair each damage immediately and can perfectly build even with 1-5 damage
    2. Next to the cost of a bomber the threat projection must be considered in case a bomber gets lost. A bomber not being on the map after the German turn can significantly influence the Allied options. Thus, the attacker risks more than 2 IPC from each shot at1 against the bomber.

    In a nutshell: A&A is a complex game and such analysis will not provide significant support to master the game.

    However, if this is just fun for you guys, of course something I appreciate. I didn’t want to sound rude, just express that I find this aspect isnt’t crucial to master the game.

    Cheers,
    Tobias

    @simon33:

    I don’t completely agree, JDOW. It does have some effect on the game to know that you can be outnumbered and still have a positive expected value from an SBR. I would not have expected that.

    One person I play with reckons that SBR would be more reasonable if the air raid part all rolled at a 2 rather than a 1. That way you could do a more effective counter to it.

    I would add that some people play also 1942.2 on both TripleA and boardgame.
    If played according to OOB, it is not the same as Global SBR, neither TripleA SBR nor SBR board version.

    And all the factors you mentionned still apply in this three different SBR rules.

    The breakthrough is about summarizing in a single ratio to remember.
    No one clearly explained it to me that way.
    All my tables made for each SBR rules were giving many numbers for a lot of different situations.
    Absolutely not easy to manage.

  • '19 '17 '16

    Follow on question. What is the ratio of interceptors to unescorted bombers needed to justify interception?

    SB continuing to target does:
    average damage = 5/6 * 5.5 - 12*1/6 = 2.5833

    So where ‘a’ strat bombers are intercepted by ‘b’ fighters
    damage saved = 2.5833 * b - 1/6 * 10 * a

    Netting to zero damage saved:
    10/6 * a = 2.5833 * b

    a/b = 2.5833 * 6 / 10 = 1.55

    So two interceptors are very slightly ahead against 3 unescorted strat bombers, assuming that all damage will be repaired and will not max out the IC’s damage.

  • '17 '16

    @simon33:

    Follow on question. What is the ratio of interceptors to unescorted bombers needed to justify interception?

    It depends on which SBR system used.
    G40 OOB SBR is quite hard on interceptors because it usually increase the average odds of damage if a Fighter try to intercept when there is the same number of escorting Fg.

    The chart is below.
    From a direct SBR on IC to 1 intercepting Fg, it reduce the odds from 2.583 to 1.819.
    But 1 StB and 1 escort is more destructive if you intercept with 1 Fg:
    3.972 IPCs/raid.
    As defender, you should not intercept because you help your opponent:
    giving 3.972 (intercept) - 2.583 (no intercept) = +1.389 additional damage on average!

    If you have 1 Fg and 1 StB against 2 interceptors, the odds will be quite similar than no intercept:
    2.445 compared to 2.583.
    So, only when you have 3 interceptors against 1 Fg and 1 StB that it really worth to risk Fgs on intercept mission.

    G1940 OOB SBR:
    1 StB doing SBR without interceptor
    Sum: +4.583 - 2 = +2.583 IPCs damage/SBR run

    1 StB A1 against 1 Fg D1 damage: 1D6+2
    Sum: + 5.486 - 3.667 = + 1.819 IPC damage/SBR run

    1 StB A1 doing SBR against 2 intercepting Fgs D1
    Sum: + 4.85 - 5.056 = - 0.206 IPCs damage/SBR run

    1 StB & 1 Fg A1 doing SBR against 2 intercepting Fgs D1 damage: 1D6+2
    Sum: +7.775 - 5.33 = + 2.445 IPCs damage/SBR run

    2 StBs A1 doing SBR against 2 intercepting Fgs D1 damage: 1D6+2
    Sum: +10.973 - 7.334 = + 3.639 IPCs damage/SBR run

    1 StB & 1 Fg A1 doing SBR against 1 intercepting Fg D1
    Sum: + 7.639 - 3.667 = + 3.972 IPCs damage/SBR run

    2 StBs A1 doing SBR against 1 intercepting Fg D1
    Sum: +11.459 - 5.666 = + 5.793 IPCs damage/SBR run


  • '17 '16

    @simon33:

    Follow on question. What is the ratio of interceptors to unescorted bombers needed to justify interception?

    SB continuing to target does:
    average damage = 5/6 * 5.5 - 12*1/6 = 2.5833

    So where ‘a’ strat bombers are intercepted by ‘b’ fighters
    damage saved = 2.5833 * b - 1/6 * 10 * a

    Netting to zero damage saved:
    10/6 * a = 2.5833 * b

    a/b = 2.5833 * 6 / 10 = 1.55

    So two interceptors are very slightly ahead against 3 unescorted strat bombers, assuming that all damage will be repaired and will not max out the IC’s damage.

    On your numbers, I’m not sure about your methodology.
    Here is what the previous chart gives:
    1 StB vs 2 Fgs = -0.206
    1 StB vs 1 Fg = +1.819
    Sum 2 StBs vs 3 Fgs = +1.613 IPCs average damage per raid.

  • '19 '17 '16

    1 SB + 1ftr vs 2ftr, it is about line ball, I agree. Going to be based on whether the defending fighters are worth more or less than the attacking ones.

    I’m looking at the scenario of 3SB vs 2 ftr. Is it worth intercepting? It seems that it is line ball.

    Actually, I got it slightly wrong. It is very slightly not worth intercepting 3SB vs 2ftr. But 4 vs 3 will be worthwhile so long as IPCs are worth the same to each side and the major IC is undamaged.

  • '17 '16

    @simon33:

    1 SB + 1ftr vs 2ftr, it is about line ball, I agree. Going to be based on whether the defending fighters are worth more or less than the attacking ones.

    I’m looking at the scenario of 3SB vs 2 ftr. Is it worth intercepting? It seems that it is line ball.

    Actually, I got it slightly wrong. It is very slightly not worth intercepting 3SB vs 2ftr. But 4 vs 3 will be worthwhile so long as IPCs are worth the same to each side and the major IC is undamaged.

    StB A1 against 1 Fg D1 damage: 1D6+2
    Sum: + 5.486 - 3.667 = + 1.819 IPC damage/SBR run
    AND
    2 StBs A1 doing SBR against 1 intercepting Fg D1
    Sum: +11.459 - 5.666 = + 5.793 IPCs damage/SBR run
    Total: 3 StBs vs 2 Fgs
    +16.945 - 9.333 =+7.612
    3 StBs vs no interception 3*2.583=
    +13.749 - 6.000 = + 7.749
    So it is a very small difference. (-0.137 against no interception)
    You can decide to destroy some more StBs with your interceptors at that point indeed.
    If the ratio is 1.5 StB/Fg or below you have a go for interception indeed.

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