Minimum offensive firepower to overcome defense

  • '21 '20 '19 '18 '17 '16

    Does anyone have a quick and dirty formula for calculating how much firepower is necessary to take a territory given a certain amount of defensive firepower?

    Marsh

  • '19 '17 '16

    No. Use the calculator. No amount is exactly 100% though.


  • Yes.

    TLDR Version :  (number Attacker units needed for 50% chance) = (Number of Defender units) * SQRT ( ( Average Defender Strength) / (Average Attacker Strength))

    My formula is exact and easy to prove correct when you attack with only units of one type, against only units of a different type ( like inf v inf, inf v tanks, inf v ftrs, etc). I am a mathematician, I can send you the proof if you don’t trust me.

    If average Defence  power is 2, and average attack power is 1, then  you need Sqrt(2) (1.141 number of units to win the attack 50%

    I have made some calculations. If you assume you attack with only units with strength 1, and the defenders have only units of strength 2,3,4, then the number of units needed to have 50% chance of taking the terr is as follows;
    1 v2 -> (sqrt(2)  =) 1,41… This means that 141 infs will have less than 50%, while 142 has more than 50% against 100 infs defenders.
    1v3 -> (sqrt(3) = )1.73…  This means that 173 infs will have less than 50%, while 174 has more than 50% against 100 tanks defenders
    1v4 -> (sqrt(4) =) 2 . So 200 infs have exactly 50% chance of winning against 100 planes.
    2v4- > (sqrt(2)  =) 1,41… This means that 141 art will have less than 50%, while 142 has more than 50% against 100 ftr defenders.

    The main advantage of the attacking infs is that they lose less of their combatstrenght when taking losses, than defenders does. This is why they need fewer dice than the defendes.

    Lets assume that the defender has the highest average strength (it the attacker has the highest, just switch it around)
    The quick and dirty formula will then be :
    strenghtratio = (Defenders Average Strength) / (attackers average strength)
    Number of units needed for 50% to win for the attackers will then be:
    #Numbers needed = SQRT(Strength Ratio) * (#Number of Defender units)

    This will change depending on the “structure” of the strength, however it will not be a Huge change. The more diverse, the better the force is.  A force defening force of 50% inf and 50% FTRs  is better than a defending force of 100% tanks.  So depending on Who I judge to have the better designed force, I add some Strength to that side when I calculate the average strength

  • '21 '20 '19 '18 '17 '16

    Thanks Kreuz!

    Out of curiosity, how do you factor in “free” hits (i.e., an undamaged battleship) and AA guns?

    Marsh

  • '21 '20 '19 '18 '17 '16

    @ShadowHAwk:

    I generaly calculate it having 1 hit for every 6 attack power.
    Sure it isnt perfect but it can be done easy at a table.

    Shadow, appreciate the response.

    That tells me the number of hits I can expect on the first round, which is useful information. However, it doesn’t tell me how many units I need to win at a certain percentage. Kreuzfeld is on the right track for my question.

    Thanks!

    Marsh

  • '21 '20 '19 '18 '17 '16

    @simon33:

    No. Use the calculator. No amount is exactly 100% though.

    Simon, appreciate the response. I was actually looking for something along the lines of what Kreuz posted.

    Marsh


  • I do them manually for shorebombartment. A free hit from a battleship will just remove a defender unit.
    2 AA will remove an attacking plane.
    Then I calculate the strenghtratios.

    The AAs are interesting, since they will be taken as hits, and therefore will count in the number of defender unit calculation.

    In bigger battles, you can usually just say that a BB is worth 2 dice (since it only fire once), while the AA is worth 4 dice (since it kills planes). Then you can calculate the Average Attack Strength as  (# dice in the first round) / (#units in the first round). This will include the battleship for the dice, but not for the units.

    As a quick and dirty method, this should work fine.

    One fun thing to notice tho; 2:1 in number of units will ALWAYS have at least 50% chance of winning (ofc assuming they can all hit eachother).

  • '21 '20 '19 '18 '17 '16

    Interesting.

    Thanks again!


  • Variation of that question: For it’s not only firepower, how many straw to burn should be within the attacking army? As Kreuzfeld already stated, the quality of the lost units is crucial for the firepower (and for the foregoing campaign, as I had to learn…).
    Something like “deploy at least 50% of the number of defending units as affordable victims”?  Or even 100%? It depends on the own firepower though…


  • @ShadowHAwk:

    Unless you can do square root calculations without a calculator ofcourse ( i surely cant )

    You dont really need to, all you need is a ballpark.

    If I tell you
    Sqrt(1,25) = 1,12
    SQRT(1,5) = 1,22
    SQRT(2) = 1,41
    SQRT(3) = 1,7
    SQRT(4) = 2

    Now, if you just rememberthose, you can easily guess how many units you need. You don’t actually have to calculate anything, you can just use it to get a feel for the strength.  You can just go : hmmm If I put my stack next to his, can he attack? I got 60 units, how many does he have? He has 90…. opps better not do that then. Or he has 70… hmm maybe I should, or does he have too many tanks and planes among those 70?.. hmm 30 planes and tanks,… better not do that then.

    If you really just want to do a short calc to get more familiar, you could count and approximate average strength and use the table from above. You will usually just have to figure out which ratio you are cloesest to among the ones in the list. The difference between 1.22 and 1.12 is rarely more than a couple of units. (unless the stacks re 50+ ofc)
    So defender has 40 units, with avg strenght of 2,3 and I can attack with avg strength of 1,4. Then the ratio is about 1,5- 1.7, I should then have more than  (if its 1,22) 55 units, bud do not need more than 65 units to have the minimum attack.

    I use it as a tool to get a feel for the combatpowers of stacks , to better evaluate my position. For me it is all about NOT having to calculate. Whenever oyu check stacks, you count number of units and number of eyes anyways. The most supprising insight this will give  to many is that you need only about 1,41 to win when inf is attacking inf.

  • '21 '20 '18 '17

    add your total attack power and total hit points

    add up their total defensive power and total hit points

    When you exceed them by a combined total  (hit points plus attack power) of 8 or more, you are very likely to win (55+%)
    If you exceed them by 16 or more, it will be a wipeout, and casualty choosing/preserving forces) is your primary goal

    If the ##s are equal, as far as total hits and total power, then it is a 50/50 battle.

    These calculations are best done on the fly and I use estimating to evaluate the chances of success each turn.

    Using a true calculator doesn’t take special rules into account (such as that the attackers carriers do not attack and thus do not lose him any attack power but can absorb hits, has won me several major battles) and it is not permitted in tournaments, its not particular fair or time thoughtful, and it doesn’t reveal any more information than on the fly addition

  • '21 '20 '19 '18 '17 '16

    @ShadowHAwk:

    You wanted quick and dirty right, just repeat the process in case there are any defending/attacking units left. Basicaly you asume the average hits from both sides and then continue.
    It is also usefull to determine if you should press the attack or retreat, sometimes it is better to leave 2 tanks standing then to expose your 10 tanks to a counterattack

    Unless you can do square root calculations without a calculator ofcourse ( i surely cant )

    I already know how to do what you’re suggesting. And yes, I can do square root calculations without a calculator.

    Marsh


  • @Baron:

    Bumped.
    Please, Wittmann or Panther, move this thread into Player help.
    Thanks.

    Done - Thank you for bringing it up.

  • '17 '16

    @Kreuzfeld:

    Yes.

    TLDR Version :  (number Attacker units needed for 50% chance) = (Number of Defender units) * SQRT ( ( Average Defender Strength) / (Average Attacker Strength))

    My formula is exact and easy to prove correct when you attack with only units of one type, against only units of a different type ( like inf v inf, inf v tanks, inf v ftrs, etc). I am a mathematician, I can send you the proof if you don’t trust me.

    If average Defence  power is 2, and average attack power is 1, then  you need Sqrt(2) (1.141 number of units to win the attack 50%

    I have made some calculations. If you assume you attack with only units with strength 1, and the defenders have only units of strength 2,3,4, then the number of units needed to have 50% chance of taking the terr is as follows;
    1 v2 -> (sqrt(2)  =) 1,41… This means that 141 infs will have less than 50%, while 142 has more than 50% against 100 infs defenders.
    1v3 -> (sqrt(3) = )1.73… This means that 173 infs will have less than 50%, while 174 has more than 50% against 100 tanks defenders
    1v4 -> (sqrt(4) =) 2 . So 200 infs have exactly 50% chance of winning against 100 planes.
    2v4- > (sqrt(2)  =) 1,41… This means that 141 art will have less than 50%, while 142 has more than 50% against 100 ftr defenders.

    The main advantage of the attacking infs is that they lose less of their combatstrenght when taking losses, than defenders does. This is why they need fewer dice than the defendes.

    Lets assume that the defender has the highest average strength (it the attacker has the highest, just switch it around)
    The quick and dirty formula will then be :
    strenghtratio = (Defenders Average Strength) / (attackers average strength)
    Number of units needed for 50% to win for the attackers will then be:
    #Numbers needed = SQRT(Strength Ratio) * (#Number of Defender units)

    This will change depending on the “structure” of the strength, however it will not be a Huge change. The more diverse, the better the force is.  A force defening force of 50% inf and 50% FTRs  is better than a defending force of 100% tanks.  So depending on Who I judge to have the better designed force, I add some Strength to that side when I calculate the average strength

    @Kreuzfeld:

    @ShadowHAwk:

    Unless you can do square root calculations without a calculator ofcourse ( i surely cant )

    You dont really need to, all you need is a ballpark.

    If I tell you
    Sqrt(1,25) = 1,12
    SQRT(1,5) = 1,22
    SQRT(2) = 1,41
    SQRT(3) = 1,7
    SQRT(4) = 2

    Now, if you just remember those, you can easily guess how many units you need. You don’t actually have to calculate anything, you can just use it to get a feel for the strength.  You can just go : hmmm If I put my stack next to his, can he attack? I got 60 units, how many does he have? He has 90…. opps better not do that then. Or he has 70… hmm maybe I should, or does he have too many tanks and planes among those 70?.. hmm 30 planes and tanks,… better not do that then.

    If you really just want to do a short calc to get more familiar, you could count and approximate average strength and use the table from above. You will usually just have to figure out which ratio you are cloesest to among the ones in the list. The difference between 1.22 and 1.12 is rarely more than a couple of units. (unless the stacks re 50+ ofc)
    So defender has 40 units, with avg strenght of 2,3 and I can attack with avg strength of 1,4. Then the ratio is about 1,5- 1.7, I should then have more than  (if its 1,22) 55 units, bud do not need more than 65 units to have the minimum attack.

    I use it as a tool to get a feel for the combat powers of stacks , to better evaluate my position. For me it is all about NOT having to calculate. Whenever oyu check stacks, you count number of units and number of eyes anyways. The most surprising insight this will give  to many is that you need only about 1,41 to win when inf is attacking inf.

    This table below is also derived on Kreuzfeld formula.
    It might help visualize all he is talking about 1.41, for instance.

    Lanchester’s Tables for Axis and Allies 2nd Edition

    I made it on AACalc then I revised numbers by applying this formula derived from above Stack formula:
    √(P2 / P1) = N1 / N2

    | Avg Power
    1
    1.5
    2
    2.5
    3
    3.5
    4
    4, 2hits
    | 1
    1.00
    0.82
    0.70
    0.63
    0.58
    0.53
    0.50
    0.31
    | 1.5
    1.22
    1.00
    0.87
    0.77
    0.70
    0.65
    0.62
    0.38
    | 2
    1.41
    1.15
    1.00
    0.89
    0.82
    0.76
    0.70
    0.43
    | 2.5
    1.58
    1.29
    1.12
    1.00
    0.91
    0.85
    0.79
    0.50
    | 3
    1.73
    1.41
    1.22
    1.10
    1.00
    0.93
    0.87
    0.53
    | 3.5
    1.87
    1.53
    1.32
    1.18
    1.08
    1.00
    0.94
    0.58
    | 4
    2.00
    1.62
    1.41
    1.26
    1.15
    1.07
    1.00
    0.62
    | 4, 2hits
    3.33
    2.64
    2.30
    2.00
    1.87
    1.73
    1.62
    1.00

    | Avg Power
    1
    1.5
    2
    2.5
    3
    3.5
    4
    4, 2hits
    | 1
    1:1
    9:11
    12:17
    5:8
    4:7
    9:17
    1:2
    3:10

    |
    1.5
    11:9
    1:1
    13:15
    7:9
    12:17
    9:14
    5:8
    3:8
    | 2
    17:12
    15:13
    1:1
    9:10
    9:11
    3:4
    12:17
    3:7
    | 2.5
    8:5
    9:7
    10:9
    1:1
    10:11
    5:6
    4:5
    1:2
    | 3
    7:4
    17:12
    11:9
    11:10
    1:1
    19:20
    13:15
    9:17
    | 3.5
    17:9
    14:9
    4:3
    6:5
    20:19
    1:1
    20:21
    4:7
    | 4
    2:1
    8:5
    17:12
    5:4
    15:13
    21:20
    1:1
    5:8
    | 4, 2hits
    10:3
    8:3
    7:3
    2:1
    17:9
    7:4
    8:5
    1:1

    |

    |

  • '17 '16

    Extended Lanchester’s Tables for Axis and Allies 2nd Edition

    I made it on AACalc then I revised numbers by applying this formula derived from above Stack formula:
    √(P2 / P1) = N1 / N2

    | Avg Power
    0.5
    1
    1.5
    2
    2.5
    3
    3.5
    4
    4, 2hits
    5
    | 0.5
    1.00
    0.70
    0.58
    0.50
    0.45
    0.41
    0.38
    0.35
    0.22
    0.32
    | 1
    1.41
    1.00
    0.82
    0.70
    0.63
    0.58
    0.53
    0.50
    0.31
    0.45
    | 1.5
    1.73
    1.22
    1.00
    0.87
    0.77
    0.70
    0.65
    0.62
    0.38
    0.55
    | 2
    2.00
    1.41
    1.15
    1.00
    0.89
    0.82
    0.76
    0.70
    0.43
    0.63
    | 2.5
    2.24
    1.58
    1.29
    1.12
    1.00
    0.91
    0.85
    0.79
    0.50
    0.70
    | 3
    2.45
    1.73
    1.41
    1.22
    1.10
    1.00
    0.93
    0.87
    0.53
    0.77
    | 3.5
    2.65
    1.87
    1.53
    1.32
    1.18
    1.08
    1.00
    0.94
    0.58
    0.84
    | 4
    2.83
    2.00
    1.62
    1.41
    1.26
    1.15
    1.07
    1.00
    0.62
    0.89
    | 4, 2hits
    4.58
    3.33
    2.64
    2.30
    2.00
    1.87
    1.73
    1.62
    1.00
    1.41
    | 5
    3.16
    2.24
    1.83
    1.58
    1.41
    1.29
    1.20
    1.12
    0.70
    1.00

    | Avg Power
    0.5
    1
    1.5
    2
    2.5
    3
    3.5
    4
    4, 2hits
    5
    | 0.5
    1:1
    12:17
    4:7
    1:2
    4:9
    5:12
    5:13
    5:14
    2:9
    5:16
    | 1
    17:12
    1:1
    9:11
    12:17
    5:8
    4:7
    9:17
    1:2
    3:10
    4:9
    |
    1.5
    7:4
    11:9
    1:1
    13:15
    7:9
    12:17
    9:14
    5:8
    3:8
    5:9
    | 2
    2:1
    17:12
    15:13
    1:1
    9:10
    9:11
    3:4
    12:17
    3:7
    5:8
    | 2.5
    9:4
    8:5
    9:7
    10:9
    1:1
    10:11
    5:6
    4:5
    1:2
    12:17
    | 3
    12:5
    7:4
    17:12
    11:9
    11:10
    1:1
    19:20
    13:15
    9:17
    7:9
    | 3.5
    13:5
    17:9
    14:9
    4:3
    6:5
    20:19
    1:1
    20:21
    4:7
    5:6
    | 4
    14:5
    2:1
    8:5
    17:12
    5:4
    15:13
    21:20
    1:1
    5:8
    9:10
    | 4, 2hits
    9:2
    10:3
    8:3
    7:3
    2:1
    17:9
    7:4
    8:5
    1:1
    17:12
    | 5
    16:5
    9:4
    9:5
    8:5
    17:12
    9:7
    6:5
    10:9
    12:17
    1:1

    |

    |

  • Disciplinary Group Banned

    There’s not such a thing because the die rolls vary.  :-( :-( :-(


  • Hey guys, this formula is really useful. I would love to see the proof for this. It’s not that I don’t trust you, I just want to see how you derived it, thanks!

    -GK


  • Ok so I tested manually 141 infantry attacking 100 infantry defending and the results was 12 infantry left standing on the attacks vs 0 on the defense. AAcalc gives this result as well.

    Shouldn’t the remaining infantry be the same on both sides if the battle is supposed to be exactly 50:50 according to the table/formula?


  • I find that this works exceedingly well with the well known Larry -Marx formula. Its well known.


  • Larry Marx has nothing to do with battle estimation, it’s for evaluating HR units and comparing unit to one another.

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