@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}
If 3 hits, it gives … * 4.236068 {1 + 3.236068}
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,
http://calc.axisandallies.org/?mustland=0&abortratio=0&saveunits=0&strafeunits=0&aInf=&aArt=&aArm=&aFig=&aBom=&aTra=&aSub=&aDes=&aCru=&aCar=&aBat=101&adBat=&dInf=&dArt=&dArm=&dFig=&dBom=&dTra=80&dSub=&dDes=&dCru=&dCar=&dBat=80&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,
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 = 1.4391
800 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 = 1.0707
737 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 = 1.1029
466 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 factor0.18
36* 4 / (46.6^2) * 2.618034 = 0.1736
OR
36* 4 / (46.6^2) * 2.6 = 0.1724
So, 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)] = Metapower
466 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=200 704
737 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=1 048 576
187 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=102 400
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
819 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