@general-5-stars Today shall be the beginning of my journey!
G40.2 1942.2 Formula to balance cost and combat points for customized units
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Ok so I’m confused how am I supposed to apply the Vann-Baron-LArrynx formula? What do I do with the 1.454 number? And where is the derivation for the formula? Or is it just made-up?
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Ok i understand it but I don’t get how you got your 1.61 factor for the baron formula with hits.
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@Genghis:
Ok i understand it but I don’t get how you got your 1.61 factor for the baron formula with hits.
I was lucky on that one.
I compared on AACalc similar Attack 3 Defense 3 with 1 hit vs A3 D3 2 hits.
Knowing also that a A3 D3, 2 hits have a similar power 50-50% with A4 D4, 1 hit (was able to calculate).
When I compared these two numbers, it was around 2.60… times greater than off def factor of A3 D3 1 hit.
So, in my POV, it was close to 1+ golden number.I made an educated guess for the formula, and AACalc confirmed a few variations with A2 D2, 2 hits A3 D3, 2 hits and A4 D4 2 hits. It gave me near 50-50 each time. So it was OK.
The next step was to try AACalc with a 3 hits against Fg 1 hit, give me 50%-50% and it works.So, maybe this formula will no work for 4 hits units but I don’t see the relevance of creating such units for A&A.
…* {1+[(nb hit -1)/1*1.618034]}
If 1 hit, it simply gives …* {1 + 0}
1 +[(1 -1)/1*1.618034]If 2 hits, it gives … * 2.618034 {1 + 1.618034}
- {1 + (2-1) *1.618034}
If 3 hits, it gives … * 4.236068 {1 + 3.236068}
- {1 + (3-1) *1.618034}
HTH
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@Genghis:
The ability to tip carriers and BBs neuters the submarine first strike ability (So no need for DDs) and I have yet to play a game where a sub first strike actually worked (i think it happened once). And most of the time you don’t want to attack with air force as well because then his fighters can defend at 4 and hit your planes and you arent allowed to use subs as casualties. Meaning it’s most of the time beneficial to not put a DD in your fleet, just spam loaded carriers.
Only Fg+TcB stack seems to rivalize with G40 Full Carrier. Carrier were stronger so you can buy defenseless TPs. Otherwise, 2 big defensive stacks of Carrier cannot break the ties going offense unless willing to lose units for greater purpose.
I agree with you about this Submarine with no surprise strike.
So I suggested a second different variant with 2 hits Cruiser and 3 hits BB in G40 Redesign.
Subs is cheaper and always roll surprise. And in regular combat planes can still hit Sub without DD.
But all ships cost are modified…But, you makes me wonder about the impact of 2 hits Cruiser on Submarine, even at 5 IPCs the Surprise strike is still nerfed …
The cost structure put Carrier at 15 and make it less optimal, even with 3 Fgs on board.
http://www.axisandallies.org/forums/index.php?topic=36518.msg1682831#msg1682831ASAD: Anti-Submarine Attack 1 Defense 1 pre-surprise strike phase attack def @1
Air Base giving +2M, up to three scramble either Fg or TcB
Second version, 3 planes Carrier, 2 hits Cruiser and 3 hits BB, simpler interactions and 5-6-9-12-15-18 cost structure:
Transport, defenseless
A0 D0 M3 C7, 0 hit,
taken last, carry 1 Inf+1 any groundTransport working as warship (Military Armed TP being escorted by a few DEs)
A0 D1 M3 C9, 1 hit,
carry 1 Inf or MI +1 any ground unit (might help faster US deployment: MI+Tk)Defence factor:
36*1/9^2 = 0.44Submarine
A2fs D1fs M2 C5, 1 hit,
Stealth Move, No DD block, may Submerge after ASAD.
2Ds in Convoy SZOffense:
36*(3/5^2) = surprise strike 4.32
Defense:
36*(1.33/5^2) = surprise strike 1.92Destroyer
A2 D2 M2 C6, 1 hit,
Anti-SubA1D1,
1D in Convoy SZ
Offense and defense factor:
362/6^2 = 2.00
If ASA1D1 maybe worth +.5
362.5/6^2 = 2.50Escort Carrier (optional)
A0 D2 M2 C8, 1 hit,
ASA1D1 carry 1 plane,
No dice in Convoy SZ
Defence factor:
36*2/8^2 = 1.125Cruiser
A3 D3 M3 C12, 2 hits,
Shorebombard @3,
1D in Convoy SZ
Offence & defence factor:
36*3/12^2 * 2.618034= 1.96Carrier
A0 D3 M2 C15, 2 hits,
carry 3 planes, damaged Carrier carry 1 plane
No dice in Convoy SZ
Offense factor:
36*[0/ (15^2)] * 2.618034 = 0
Defense factor:
36*[3/ (15^2)] * 2.618034 = 1.26Carrier A0 D3 C15, 2 hits with 3 Fgs A6 D6 C18, 3 hits
Approximative Offense factor:
6/3 C33/3 2 additionals hit
36*[2/ (11^2)] *(1+2*1.618034) = 2.52Does not work.Approximative Defense factor:
9/4 C33/4 1 additional hit
36*[2.25/(8.25^2)] * 2.618034 = 3.129/5 C33/5 1 additional hit considered as whole unit
36*[1.8/ (6.6^2)] = 1.488
Until further investigation, I believe this average is better: (3.12+1.49)/2= 2.305Battleship
A4 D4 M2 C18, 3 hits,
Shorebombard @4,
1D in Convoy SZ
Offense & Defense factor:
36* 4 / (18^2)* (1+2*1.618034) = 1.88Strategic Bomber
A0 D0 M6-8 C5, 0 hit,
SBR 1 hit A1 dmg 1D6Fighter
A2 D2 M4-6 C6, 1 hit,
SBR A2 D2, always hit air first, then AAA
Can hit Sub without Destroyer presence
2Ds in Convoy SZ
Offence & defence factor:
36*2/6^2 = 2.00Tactical Bomber
A3 D2 M4-6 C7, 1 hit,
TBR A1 D1, dmg 1D6,
ASA1D1, can hit Sub without Destroyer presence
2Ds in Convoy SZ
Offense factor:
36*(3/7^2) = 2.20
Defense factor:
36*(2/7^2) = 1.47Anti-aircraft Artillery
A0 D1* M1 C3, 1 hit,- @1 vs up to 3 planes, 1 roll per plane max, each combat round.
It is not preemptive but a regular roll.
When fighting against 1 aircraft:
Defense factor:
36*(1/3^2) = 4.00
When fighting against 2 aircrafts:
36*(2/3^2) = 8.00
When fighting against 3 aircrafts:
36*(3/3^2) = 12.00
AAA (12.00) is stronger than Infantry (8.00) when defending against 3 planes but more AAA cannot hit the same unit, it has no offense value and don’t have the versatility of Fighter.
In fact, this formula cannot consider multiple hits from a single unit.Now I can compare the Strength of both Subs:
OOB
Submarine A2 D1 C6
Offense:
36*(2/6^2) = 2
36*(3/6^2) = surprise strike 3.00
Defense:
36*(1/6^2) = 1
36*(1.33/6^2) = surprise strike 1.33Submarine A2fs D1fs C5
Offense:
36*(3/5^2) = surprise strike 4.32
Defense:
36*(1.33/5^2) = surprise strike 1.92Compared to Destroyer, it remains clear that you will not use Subs as fodder on offence, the First strike will be helpful.
Also, on defense, you almost get a similar loss per cost, it might be a difficult decision whether submerging Sub for later or using it as fodder. - @1 vs up to 3 planes, 1 roll per plane max, each combat round.
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@Baron:
@Genghis:
Ok i understand it but I don’t get how you got your 1.61 factor for the baron formula with hits.
I was lucky on that one.
I compared on AACalc similar Attack 3 Defense 3 with 1 hit vs A3 D3 2 hits.
Knowing also that a A3 D3, 2 hits have a similar power 50-50% with A4 D4, 1 hit (was able to calculate).
When I compared these two numbers, it was around 2.60… times greater than off def factor of A3 D3 1 hit.
So, in my POV, it was close to 1+ golden number.I made an educated guess for the formula, and AACalc confirmed a few variations with A2 D2, 2 hits A3 D3, 2 hits and A4 D4 2 hits. It gave me near 50-50 each time. So it was OK.
The next step was to try AACalc with a 3 hits against Fg 1 hit, give me 50%-50% and it works.So, maybe this formula will no work for 4 hits units but I don’t see the relevance of creating such units for A&A.
…* {1+[(nb hit -1)/1*1.618034]}
If 1 hit, it simply gives …* {1 + 0}
1 +[(1 -1)/1*1.618034]If 2 hits, it gives … * 2.618034 {1 + 1.618034}
- {1 + (2-1) *1.618034}
If 3 hits, it gives … * 4.236068 {1 + 3.236068}
- {1 + (3-1) *1.618034}
HTH
How did you get the factor 1.618034 for double haul BB??? I got a factor 1.6. I used the battlecalc I had 800 bombers attack 500 battleships.
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In all my simulations, it was not exactly a 1.6 factor. As far as I remember, always slightly above.
Did you try it with 3 hits and 1.6 factor in a formula like:
…* {1 + (3-1) *1.6}
To see if you get nearer or farther than mine.The golden number have a few properties when making it square.
I will try to see if I can retrieve what simulations I exactly done.
This will help:
@Baron: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|
|
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500 Battleships ? Must be nice !
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@SS:
500 Battleships ? Must be nice !
Yeahh, totally not realistic!!!
But when crunching numbers and trying to get randomness out of the way, the higher the number on AACalc the better you get an accurate average.Basically, 8 bombers (or damaged BBs) are near even with 5 battleships.
In punch formula: 8 A4, 1 hit vs 5 A4, 2 hits are about 50-50% odds of survival.
As you can see, even with 10 000x battles, odds varies with low numbers:
Sim 1: A. survives: 49.5% D. survives: 44.1% No one survives: 6.4%
Sim 2: A. survives: 48.3% D. survives: 45.4% No one survives: 6.3%
Sim 3: A. survives: 49.5% D. survives: 44% No one survives: 6.5%
Sim 4: A. survives: 49.1% D. survives: 44.1% No one survives: 6.7% -
@Dauvio:
@Baron:
@Genghis:
Ok i understand it but I don’t get how you got your 1.61 factor for the baron formula with hits.
I was lucky on that one.
I compared on AACalc similar Attack 3 Defense 3 with 1 hit vs A3 D3 2 hits.
Knowing also that a A3 D3, 2 hits have a similar power 50-50% with A4 D4, 1 hit (was able to calculate).
When I compared these two numbers, it was around 2.60… times greater than off def factor of A3 D3 1 hit.
So, in my POV, it was close to 1+ golden number.I made an educated guess for the formula, and AACalc confirmed a few variations with A2 D2, 2 hits A3 D3, 2 hits and A4 D4 2 hits. It gave me near 50-50 each time. So it was OK.
The next step was to try AACalc with a 3 hits against Fg 1 hit, give me 50%-50% and it works.So, maybe this formula will no work for 4 hits units but I don’t see the relevance of creating such units for A&A.
…* {1+[(nb hit -1)/1*1.618034]}
If 1 hit, it simply gives …* {1 + 0}
1 +[(1 -1)/1*1.618034]If 2 hits, it gives … * 2.618034 {1 + 1.618034}
- {1 + (2-1) *1.618034}
If 3 hits, it gives … * 4.236068 {1 + 3.236068}
- {1 + (3-1) *1.618034}
HTH
How did you get the factor 1.618034 for double haul BB??? I got a factor 1.6. I used the battlecalc I had 800 bombers attack 500 battleships.
101 BBs A4 D4, 2 hits vs 80 BBs A4 D4, 3 hits, near 50-50% odds,
819 dmgd BBs A4 D4, 1 hit vs 400 BBs A4 D4, 3 hits, near 50-50% odds,
http://calc.axisandallies.org/?mustland=0&abortratio=0&saveunits=0&strafeunits=0&aInf=&aArt=&aArm=&aFig=&aBom=&aTra=&aSub=&aDes=&aCru=&aCar=&aBat=&adBat=819&dInf=&dArt=&dArm=&dFig=&dBom=&dTra=400&dSub=&dDes=&dCru=&dCar=&dBat=400&ddBat=&ool_att=Bat-Inf-Art-AArt-Arm-Sub-SSub-Des-Fig-JFig-Cru-Bom-HBom-Car-dBat-Tra&ool_def=Tra-Bat-Inf-Art-AArt-Arm-Bom-HBom-Sub-SSub-Des-Car-Cru-Fig-JFig-dBat&battle=Run&rounds=&reps=10000&luck=pure&ruleset=AA1942&territory=&round=1&pbem=819 dmgd BBs A4 D4, 1 hit vs 400 BBs A4 D4, 3 hits, near 50-50% odds,
/40 = 20.5 dmgd BBs A4 D4, 1 hit vs 10 BBs A4 D4, 3 hits,So such 3 hits BBs should cost 20.5 IPCs and will be even with a Fg D4 C10 which is known at strength factor1.44
36*4/20.5^2 * {1 + (3-1) 1.618034} = 1.45
144/420.25 * 4.236068 = 1.4515
OR
364/20.5^2 * {1 + (3-1) *1.6} = 1.44
144/420.25 * 4.2 = 1.4391800 dmgd BBs A4 D4, 1 hit vs 500 BBs A4 D4, 2 hits, near 50-50% odds,
/50 = 16 dmgd BBs A4 D4, 1 hit vs 10 BBs A4 D4, 2 hits,So, such 2 hits BBs should cost 16 IPCs and will be even with a Fg D4 C10 which is known at strength factor1.44
Battleship A4 D4 C16, 2 hits
Offense & Defense factor:
36* 4 / (16^2) * 2.618034 = 1.4726
OR
36* 4 / (16^2) * 2.6 = 1.4625
This last one is nearer.187 Cruiser A3 D3, 1 hit vs 100 BBs A4 D4, 2 hits, near 50-50% odds,
/10 = 18.7 Cruiser A3 D3, 1 hit vs 10 BBs A4 D4, 2 hits,So, such 2 hits BBs should cost 18.7 IPCs and will be even with a Fg A3 C10 which is well known at strength factor1.08
Battleship A4 D4 C16, 2 hits
Offense & Defense factor:
36* 4 / (18.7^2) * 2.618034 = 1.0781
OR
36* 4 / (18.7^2) * 2.6 = 1.0707737 Destroyers A2 D2, 1 hit vs 320 BBs A4 D4, 2 hits, near 50-50% odds,
/40 = 18.425 Destroyers A2 D2, 1 hit vs 10 BBs A4 D4, 2 hits,So, such 2 hits BBs should cost 18.425 IPCs and will be even with a Destroyers A2 D2 C8 which is well known at strength factor1.125
Battleship A4 D4 C18, 2 hits
Offense & Defense factor:
36* 4 / (18.425^2) * 2.618034 = 1.1105
OR
36* 4 / (18.425^2) * 2.6 = 1.1029466 Carrier A1, 1 hit vs 140 BBs A4 D4, 2 hits, near 50-50% odds,
/10 = 46.6 Carrier A1, 1 hit vs 14 BBs A4 D4, 2 hits,
So, such 2 hits BBs should cost 46.6 IPCs and will be even with a Carrier A1 C14 which is well known at strength factor0.1836* 4 / (46.6^2) * 2.618034 = 0.1736
OR
36* 4 / (46.6^2) * 2.6 = 0.1724So, I cannot tell from these various AACalc results which number is the accurate multiplier.
Sometimes 1.6 seems nearest the point, while other times it is 1.618034.
From an empirical POV and F-2-F, it can be easier to simply said 1.6 but from a derivative equation, which I don’t know, maybe it is PHI or golden number the correct multipler in this equation.If we try with this other equation.
Metapower = units^2 * power
N1 is nb of 1 hit units
N2 is nb of 2 hits units
(N1+ N2*1.618034)^2 * avg power [total power/(N1+N2 units)] = Metapower466 Carrier A1, 1 hit vs 140 BBs A4 D4, 2 hits, near 50-50% odds,
466^21 = 217 156
(1401.618034)^24= 205 253.9
(1401.6)^2*4=200 704737 Destroyers A2 D2, 1 hit vs 320 BBs A4 D4, 2 hits, near 50-50% odds,
737^22 = 1 086 338
(3201.618034)^24= 1 072 346.74
(3201.6)^2*4=1 048 576187 Cruiser A3 D3, 1 hit vs 100 BBs A4 D4, 2 hits, near 50-50% odds,
187^23 = 104 907
(1001.618034)^24= 104 721.361
(1001.6)^2*4=102 400800 dmgd BBs A4 D4, 1 hit vs 500 BBs A4 D4, 2 hits, near 50-50% odds,
800^24 = 2 560 000
(5001.618034)^24= 2 618 034.025
(5001.6)^2*4=2 560 000819 dmgd BBs A4 D4, 1 hit vs 400 BBs A4 D4, 3 hits, near 50-50% odds,
819^24 = 2 683 044
(4002.618034)^24= 6 702 167.1
(4002.6)^2*4=4 326 400
Here, the formula does not work for 3 hits units.Based on this Stack formula, I rather believe *1.618034, is a better multiplier to get equations results as similar as possible.
Also, it seems to work better when compared to @1, @2 and @3.However, the only case where the formula is exactly even is the one you bring for A4 1 hit vs D4, 2 hits.
800 dmgd BBs A4 D4, 1 hit vs 500 BBs A4 D4, 2 hits, near 50-50% odds,
800^24 = 2 560 000
(5001.618034)^24= 2 618 034.025
(5001.6)^2*4=2 560 000 -
@Baron:
@Genghis:
Ok i understand it but I don’t get how you got your 1.61 factor for the baron formula with hits.
I was lucky on that one.
I compared on AACalc similar Attack 3 Defense 3 with 1 hit vs A3 D3 2 hits.
Knowing also that a A3 D3, 2 hits have a similar power 50-50% with A4 D4, 1 hit (was able to calculate).
When I compared these two numbers, it was around 2.60… times greater than off def factor of A3 D3 1 hit.
So, in my POV, it was close to 1+ golden number.I made an educated guess for the formula, and AACalc confirmed a few variations with A2 D2, 2 hits A3 D3, 2 hits and A4 D4 2 hits. It gave me near 50-50 each time. So it was OK.
The next step was to try AACalc with a 3 hits against Fg 1 hit, give me 50%-50% and it works.So, maybe this formula will no work for 4 hits units but I don’t see the relevance of creating such units for A&A.
…* {1+[(nb hit -1)/1*1.618034]}
If 1 hit, it simply gives …* {1 + 0}
1 +[(1 -1)/1*1.618034]If 2 hits, it gives … * 2.618034 {1 + 1.618034}
- {1 + (2-1) *1.618034}
If 3 hits, it gives … * 4.236068 {1 + 3.236068}
- {1 + (3-1) *1.618034}
HTH
What battlecalc did you used for the for the different strength units??? The A&A battlecalc only calculates battleships.
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I used Transports and put TPs first in order of casualty.
So it worked like a 2 hits unit for Carrier A1 D2 or Cruiser A3 D3, and a 3 hits unit if paired with 1 Battleship.
If I want to recreate a G40 Carrier on offence, I put 2 TPs as similar to 1 Carrier. -
The on going discussion:
http://www.axisandallies.org/forums/index.php?topic=40520.msg1693864#msg1693864
on Transport with defense roll makes me wonder about actual combat strength of Classic Transport and an escorted TP:Transport and Destroyer A2 D2 C15, 1 hit
Offense & Defense factor:
36*(2/15^2) = 0.32Transport and Cruiser A3 D3 C19, 1 hit
Offense & Defense factor:
36*(3/19^2) = 0.30Classic Transport A0 D1 C8, 1 hit
Defense factor:
36*(1/8^2) = 0.5625I revised the opening post.
As comparison points, a Fighter A3 D4 C10 off/def is 1.08 / 1.44Destroyer A2 D2 C8, 1 hit
Offense & Defense factor:
36*(2/8^2) = 1.125Submarine A2 D1 C6
Offense:
36*(2/6^2) = 2.00
36*(3/6^2) = surprise strike 3.00
Defense:
36*(1/6^2) = 1.00
36*(1.33/6^2) = surprise strike 1.33You need to send 2 Destroyers to get a similar defense value with Classic Transport strength 0.5625:
Transport and 2 Destroyers A4 D4 C23, 2 hits
Offense & Defense factor:
36*(2/11.5^2) = 0.544Or make defenseless Transport a 4 IPCs unit:
Transport and Destroyer A2 D2 C12, 1 hit
Offense & Defense factor:
36*(2/12^2) = 0.50Now, if you want to introduce a Classic TP with the same strength of actual DD+TP combo 0.32:
You need to make TP cost 10,5 IPCs:
Classic Transport A0 D1 C10, 1 hit
Defense factor:
36*(1/10^2) = 0.36At 11 IPCs, it would be 0.30 though.
Transport defending A0 D1 would be interesting at a clean 10 IPCs.