SBR comparative analysis, a real breakthrough

  • '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.

  • '17 '16

    Sorry,
    I bumped this thread to get more easily some datas.
    Baron

  • '17 '16

    Now it has been put arbitrarily in HR forum (for no apparent reason), I bump it again.

    I need to reintroduce another important concept in first post: offence/defense cost ratio.

    It will explain a possible issue about A0 C5 StBomber D6 damage.

  • '17 '16

    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.

    However, for G40 OOB SBR it is quite better than anything above:

    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 IPCs=
    6.32 IPCs/10 IPCs = 0.632 offense/defense cost ratio
    Approximative Interception Threshold: from 1.55 StB/Fg and less

    To provide another extreme comparison point in the spectrum of SBR, I will use
    Balanced Mode StB A1 C12 vs Fg A2 D2 C10:
    Break even point: 89 StBs A1 C12 D6+2 vs 77 Fgs D2 C10
    1.156 StB/Fg break even ratio
    *12 IPCs=13.87 IPCs/10 IPCs = 1.39 offense/defense IPC ratio
    This is very similar to tank against infantry (1.33) off/def cost ratio.

    Now, this is what happen with C5 A0 D6 bomber vs Fg A1 D1 C10:

    Break even point C5, 1D6 damage: near 1 StB A0 vs 2 Fgs D1 C10: 0.5 StB/Fg
    1 StB A0 vs 2 Fgs D1 : + 2.025 - 2.106 = -0.081 IPCs
    12 StB vs 23 Fgs: exactly 0.522 StB/Fg
    No FIT (Fighter Interception Threshold), always beneficial to Intercept.

    0.522 StB/Fg*C5 StB / C10 Fg = 0.266 offense/defense cost ratio

    It is litterally over 50% less than G40 OOB SBR (0.632 vs 0.266) and this is already far below regular combat off/def values (see above).

    The good thing is StB having no attack value, it cost nothing trying to intercept them.
    But, for the cost, StBs are now twice as effective than G40 OOB bombers when trying to intercept or counter them with C10 Fg.

    And StB A1 C5 vs Fg A2 D2 C10 would be more broken with their attack capacity on costly Fg:
    Break even point: 16 StBs vs 31 Fgs, 16/31= 0.516 StB/Fg
    0.516 StB/Fg*C5 StB / C10 Fg = 0.258 offense/defense cost ratio
    This will be slightly more cost effective than A0 StB (0.266) and, in addition, a bunch of StBs will be a pretty good deterrent against interception.

    However, to my surprise, keeping StB A0 C5 D6 damage but rising Fg to A2 D2 (or A1 D2) bring a better but similar off/def cost ratio value to OOB G40 (0.632) : 0.567 offense/defense cost ratio
    And has a slightly lower break even ratio than Balance Mode (1.39 StB/Fg) but without any Fighter Interception Threshold due to A0 Bomber.

    Here is the calculation:
    Break even point StB A0 C5, 1D6 damage vs Fg A1 D2: 17 StBs vs 15 Fgs: 1.133 StBs/Fg
    1.133 StBs/Fg*C5 StB / C10 Fg = 0.567 offense/defense cost ratio

    @Baron:

    Black Elk Strategic Bomber 5 IPC A1 D0

    Strategic Bomber in air-to-air combat SBR:
    Attack 1
    Bombard IC or AB or NB damage: 1D6

    Fighter in air-to-air combat SBR:
    Attack 2
    Defend 2

    Tactical Bomber in air-to-air combat SBR:
    Attack 1
    Bombard AB or NB damage: 1D6

    IC’s AAA: @1 against each Strategic Bomber
    Naval Base or Air Base: @1 against each Strategic Bomber or Tactical bomber

    Break even ratio for x StB A1 vs y Fg D2 C10:
    OOB G40 SBR: 10/19= 0.526 StB/Fg
    Cost 5 D6 damage: 16 StBs vs 31 Fgs, 16/31= 0.516 StB/Fg

    Cost 6 D6 damage: 19 Stbs vs 29 Fgs, 19/29= 0.655 StB/Fg

    Fighter Interception Threshold (FIT) and Fighter Interception Gap (FIG)
    G40 OOB: from 1.55 StB/Fg and less   (.526 to 1.55)
    Cost 5: near 6 StBs vs 4 Fgs= from 1.5 StB/Fg and less (.516 to 1.5)

    Cost 6: near 5 StBs vs 3 Fgs= from 1.67 StB/Fg and less (0.655 to 1.67)

    Break even point C5, 1D6 damage: near 1 StB A0 vs 2 Fgs D1 C10: 0.5 StB/Fg
    1 StB A0 vs 2 Fgs D1 : + 2.025 - 2.106 = -0.081 IPCs
    12 StB vs 23 Fgs: exactly 0.522 StB/Fg
    No FIT (Fighter Interception Threshold), always beneficial to Intercept.

    Break even ratio: 16 StBs D6 dmg A1 C5 vs 25 Fgs D2 C7 = near 0.64 StB/Fg
    1 StB A1 C5 vs 1 Fg D2 C7
    1D6: +3.111 - 2.222 = +0.889 IPCs damage/SBR7= +6.223
    1 StB A1 C5 doing SBR against 2 intercepting Fgs D2 C7
    1D6: +2.463 - 3.148 = -0.685 IPCs damage/SBR
    9= -6.165 [Diff.: +0.058]

    Fighter Interception Threshold (FIT): 5 StBs A1 C5 vs 2 Fg D2 C7 = 2.5 StBs/Fg.
    So the FIGap is between .64 StB/ Fg to up to 2.5 StBs/Fg

    @Baron:

    1942.2 SBR Black Elk hypothesis

    Strategic Bomber
    Attack 0
    Damage 1D6, 1D6+2
    Cost 5

    Fighter
    Attack 1
    Defense 2
    Cost 10

    Break even point StB A0 C5, 1D6+2 damage vs Fg A1 D2:  21 StBs vs 30 Fgs: 0.700 StB/Fg
    1StB D6+2 vs 1Fg D2: + 3.056 - 2.222= + 0.834 IPC damage/SBR12= +10.008
    1StB D6+2 vs 2Fgs D2: +2.037 - 3.148 = -1.111 IPC damage/SBR
    9= -9.999 (Diff.: +0.009)
    21 StB vs 30 Fgs:   0.700 StB/Fg
    No FIT (Fighter Interception Threshold), always beneficial to Intercept.

    Break even point StB A0 C5, 1D6 damage vs Fg A1 D2: 17 StBs vs 15 Fgs: 1.133 StBs/Fg
    1 StB D6  vs 1Fg D2: + 1.944 - 2.222 = -0.278 IPC damage/SBR13 = -3.614
    2 StBs D6 vs 1Fg D2: +4.861 - 3.056= +1.805 IPCs damage/SBR
    2= +3.610 (Diff.: -0.004)
    17 StBs vs 15 Fgs: 1.133 StBs/Fg
    No FIT (Fighter Interception Threshold), always beneficial to Intercept.

    And for my own home-brewed HR with StB C5 vs Fg A2 D2 C7 off/def cost ratio is:

    Break even ratio: 16 StBs D6 dmg A1 C5 vs 25 Fgs D2 C7 = near 0.64 StB/Fg
    0.64 StB/Fg *C5 StB / C7 Fg = 0.457 offense/defense cost ratio not that bad compared to G40 OOB (0.632).
    But still more cost efficient.


  • The Strategic Bomber is just fine as it is. The only OOB unit that’s problematic is the Cruiser at 10 IPC.

    People buy Bombers because of their reach for both land and sea, numbers don’t quantity that value.

  • '17 '16

    @Imperious:

    The Strategic Bomber is just fine as it is. The only OOB unit that’s problematic is the Cruiser at 10 IPC.

    People buy Bombers because of their reach for both land and sea, numbers don’t quantity that value.

    Sorry IL but it is a totally different paradigm we were talking about.
    A game changer for Strategic bomber, no more A4 C12 M6.
    It is a much different dynamic and have way more interesting implications.

    Here is the link to this Redesign discussion:
    http://www.axisandallies.org/forums/index.php?topic=39384.msg1632453#msg1632453

    Soon, you will be able to playtest G40 both AA Cruiser C12 and bomber C5 on Triple A.

    This method is to compare between SBR values in itself.
    It cannot consider general combat values for sure.

    And a way to explain why some SBR method and values may be unbalanced even without a lot of gametests.

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