I just tried to addressed to the one of the main complaint about Japan’s power in Anniversary and claimed that having Japan with that power is not a must for maintaining balance but happy to see different income distirbutions with No’s or not.
G40.2 1942.2 Formula to balance cost and combat points for customized units

This a revised version derived and adapted to G40 2ed units roster from Vann formula.
It has no pretense about gameplay strategy or tactic.
All the implications of this formula are yet to be discovered.One purpose is to get an idea of the relative strength of a given unit in relation to its combat value and IPCs per hit ratio. It says if you get enough or too much for your bucks.
Mainly, it provides a single number as guideline to determine if at a given cost (same IPCs basis) and a given power such custom units of yours is either in the upper or the lower hand of the spectrum. Of course, it is more fruitful to compare similar type of units.
The benchmark has been fixed upon the Tank A3 D3 C6 at a offense & defense factor of 3.00
Same number as attack and defense combat values but for other units it varies.From highest to lowest offense or defense factor, you get:
8, 5.88, 4.50, 4.00, 3.00, 2.33, 2.25, 2.00, 1.74, 1.50, 1.44, 1.17, 1.14, 1.13, 1.08, 1.00, 0.89, 0.75, 0.25, and there is more.When 2 units have nearsame factor, it means that on AACalc with same IPCs basis, these units will be even and near 50%50% odds of survival against each other. But, you no more need to make simulations to get the relative strength of your costum units. Just file in the number you have in mind and compare with similar units.
I provided an example of an HR Mechanized Artillery A2 D2 M2 C5 custom unit at the end of this table.
Is this stronger or weaker than an OOB Tank? Does is it a better defense than an OOB D3 Tank?
Does combined arms remains within other OOB combined arms?You will get an accurate idea with this.
@Baron:
Here is the table based on ENIGMA (Vann) formula
BaronLarrymarxformula completed on effective cost vs combat points ratio:
Refence unit cost^2actual unit Power1 HitPoint/(actual unit Cost^2){1+[(nb hit 1)/11.618034] }= offense or defense power*hit factor
For a 6 IPCs Tank as reference unit, it means 36 multiplier
For all 1 hit units, you use : 36 Power/(cost^2) = offense or defense factor* based on cost
For 2 hits and 3 hits unit : 36 Power/(cost^2) {1+[(nb hit 1)/11.618034] }= offense or defense factor* based on costTo get the cost of a 1 hit unit for a given factor of reference: √(36*Power of unit / Offence or defence Factor)= Cost.
For a 2 hits unit for a given factor of reference:
√(36*Power of unit {1+[(nb hit 1)/11.618034] } / Offence or defence Factor)= Cost.For combined arms and multiple units you have to average both combat points per unit and cost per unit.
Then you can add it into the formula.Tank is the basic reference and gives also 3.00 offense and defense factor based on cost (same as attack or defense points).
Tank A3 D3 M2 C6
offense & defense factor: 36*3/(6^2)= 3.00Mech Infantry A1 D2 M2 C4 would get
Offense factor:
36*(1/4^2) = 2.25
Defense factor:
36*(2/4^2)= 4.50Artillery A2 D2 M1 C4
Offense & Defense factor:
36*(2/4^2)= 4.50Infantry A1 D2 M1 C3
Offense:
36*(1/3^2) = 4.00
Defense:
36*(2/3^2) = 8.00AIRCRAFTS:
Fighter A3 D4 C10, 1 hit
Offense factor:
36*(3/10^2) = 1.08
Defense factor:
36*(4/10^2) = 1.44Tactical Bomber A3 D3 C11, 1 hit
Offense & Defense factor:
36*(3/11^2) = 0.89Strategic Bomber A4 D1 C12, 1 hit
Offense factor:
36*(4/12^2) = 1.00
Defense factor:
36*(1/12^2) = 0.25Combined ARMS:
Infantry & Artillery A4 D4 M1 C7, 2 hits
Offense factor:
36*(2/3.5^2) = 5.88
Defense factor:
36*(2/3.5^2)= 5.88Mech Infantry & Artillery A4 D4 C8, 2 hits
Offense factor:
36*(2/4^2) = 4.50
Defense factor:
36*(2/4^2)= 4.50Tactical Bomber & Tank A7 D6 C17, 2 hits
Offense factor:
36*(3.5/8.5^2) = 1.74
Defense factor:
36*(3/8.5^2)= 1.50Tactical Bomber & Fighter A7 D7 C21, 2 hits
Offense factor:
36*(3.5/10.5^2) = 1.14
Defense factor:
36*(3.5/10.5^2)= 1.14WARSHIPS and Transports:
Transport and Destroyer A2 D2 C15, 1 hit
Offense & Defense factor:
36*(2/15^2) = 0.32Classic Transport A0 D1 C8, 1 hit
Defense factor:
36*(1/8^2) = 0.5625Submarine 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 1.33Destroyer A2 D2 C8, 1 hit
Offense & Defense factor:
36*(2/8^2) = 1.125Cruiser A3 D3 C12, 1 hit
Offense & Defense factor:
36*(3/12^2) = 0.751942.2 Carrier A1 D2 C14, 1 hit
Offense factor:
36*(1/14^2) = 0.18
Defense factor:
36*(2/14^2) = 0.371942.2 Carrier Full Fighters A7 D10 C34, 3 hits
Offense factor:
36*(1/14^2) = 0.18, need to be below 0.74 but just above 0.72
36*(3/10^2) = 1.08
36*(3/10^2) = 1.08
2.344/3= 0.78 to be revised
36* (7/3)/(34/3)^2 = 0.65 Avg (0.78+0.65)/2= 0.72Defense factor:
36*(4/10^2) = 1.44need to be below 1.00 but above 0.94
36*(4/10^2) = 1.44
36*(2/14^2) = 0.367
3.247/3= 1.082 to be revised
36* (10/3)/(34/3)^2 = 0.93G40 Carrier A0 D2 C16, 2 hits
Offense factor:
36*[0/ (16^2)] * 2.618034 = 0
Defense factor:
36*[2/ (16^2)] * 2.618034 = 0.736G40 Carrier A0 D2 C16, 2 hits with 2 Fgs A6 D8 C20, 2 hits
Offense factor:
6/2 C36/2 2 additionnals hit/2
36*[3/ (18^2)] * 2.618034 = 0.873Defense factor:
10/2 C36/2 2 additionnals hit/2
36*[5/ (18^2)] * 2.618034 = 1.454 have to be below 1.44 but above 1.125 and just below 1.3310/4 C36/4 1 additionnal hit considered as whole unit
36*[2.5/ (9^2)] = 1.111
Until further investigation, I believe this average is better: (1.454+1.111)/2= 1.28
Or avg Defence would give (0.736+1.44+1.44) = 1.21G40 Carrier A0 D2 C16, 2 hits with 1 Fg & 1 TcB A7 D7 C21, 2 hits
Offense factor :
7/2 C37/2 2 additionnals hit/2
36*[3.5/ (18.5^2)] * 2.618034 = 0.964Defense factor:
9/2 C37/2 2 additionnals hit/2
36*[4.5/ (18.5^2)] * 2.618034 = 1.2399/4 C37/4 1 additionnal hit considered as whole unit
36*[2.25/ (9.25^2)] = 0.947
Until further investigation, I believe this average is better: (1.239+0.947)/2= 1.093
Or avg Defence would give (0.736+1.44+0.89) = 1.02G40 Carrier A0 D2 C16, 2 hits with 2 TcBs A6 D6 C22, 2 hits
Offense factor :
6/2 C38/2 2 additionnals hit/2
36*[3/ (19^2)] * 2.618034 = 0.783Defense factor:
8/2 C38/2 2 additionnals hit/2
36*[4/ (19^2)] * 2.618034 = 1.0448/4 C38/4 1 additionnal hit considered as whole unit
36*[2/ (9.5^2)] = 0.798
Until further investigation, I believe this average is better: (1.044+0.798)/2= 0.921
Or avg Defence would give (0.736+0.89+0.89) = 0.84Battleship A4 D4 C20, 2 hits
Offense & Defense factor:
36* 4 / (20^2) * 2.618034 = 0.94Battleship flag ship A4 D4 C24, 3 hits
Offense & Defense factor:
36* 4 / (24^2)* (1+21.618034) = 1.06
Real factor according to AACalc simulation: Fg A3 36(3/10^2) = 1.08Sound very good…
This last example confirmed that the formula is right on!!! :mrgreen: :mrgreen: :mrgreen:
HR unit examples:
Mech Artillery A2 D2 M2 C5 gives +1A to Inf or MI
Offense & Defense factor:
36*(2/5^2) = 2.88Mech Infantry & Mechanized Artillery A4 D4 M2 C9, 2 hits
Offense factor:
36*(2/4.5^2) = 3.56
Defense factor:
36*(2/4.5^2)= 3.56Now, is it the end of Tank purchase? Not if you restrict Blitz to Tank only.
Or, add a combined arms with Tank and Mech Artillery.
That way, Tank will remain interesting.Here is what it can be:
Tank giving +1D to same Mechanized Artillery above A5 D6 M2 C11, 2 hits
Offense factor:
36*(2.5/5.5^2) = 2.98
Defense factor:
36*(3/5.5^2)= 3.57This means that you get a similar attack factor because it cost 1 less IPC than 2 Tank.
And an higher defense factor per cost than Tank but similar to MI+MechArt.
Meaning that these 2 units defending @2 for 9 IPCs has same power per cost than 2 units defending @3 for 11 IPCs.
Another example for Naval, a 2 hits Cruiser at 14 or 15 or 16 IPCs to replace OOB Cruiser?
Cruiser A3 D3 C???, 2 hits
Offense & Defense factor:
36* 3 / (14^2) * 2.618034 = 1.4436* 3 / (15^2) * 2.618034 = 1.26
36* 3 / (16^2) * 2.618034 = 1.10
Do you want it better than a Battleship A4 D4 C20, 2 hits at 0.94?
Weaker than a Destroyer? A2 D2 C8 at 1.13If you want this progression SS>DD>CA>BB, then you go for 16 IPCs.
Now rise the question of an OOB obsolete BB…
But, you can change for a 3 hits BBs… of very similar strength to Cruiser, but 3 hits give more latitude for strafing enemy’s fleet:
Strong Battleship A4 D4 C24, 3 hits
Offense & Defense factor:
36* 4 / (24^2)* (1+2*1.618034) = 1.06Or maybe at 22 IPCs?
36* 4 / (22^2)* (1+2*1.618034) = 1.26And you get a similar factor with 15 IPCs 2 hits Cruiser.
36* 3 / (15^2) * 2.618034 = 1.26It remains up to the designer to choose among these possibilities.
HTH
P.S. To get the cost for a given factor of reference:
√(36*Power/Strength of offence or defence Factor)= Cost. 
to be honest, all I do to get an idea of how good a unit is at offense or defense is calculate the offense power divided by the cost and the defensive power divided by the cost. So tank is 3/6=0.5. Infantry is 2/3=0.66. I also consider hits per cost so tank would be 1/6 = 0.17 and infantry is 1/3=0.33. This shows that infantry is better than tanks at defending on a one to one basis.
I did that for every unit and I found that the air force is by far much more powerful than navy when it comes to what you get for your money. The reason is that bombers can compete with loaded carriers (Bombers on offense is 0.25 and loaded carrier on defense 0.28, bombers hit/cost is 0.08 and CVs 0.11). But air force has versatility. Bombers can hit any boats, strategic raid, attack big stacks with a huge range of 7. However navy has the advantage of being able to tip carriers and BBs so in the case of carrier spam next to an adjacent controlled territory where the defending planes can land, the defender can simply tip all the carriers and destroy any attacker. And the ability to heal is another factor to consider outside of the math.
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.
If you look at the math you will see there is no offensive tool to deal with spam of loaded carriers. that’s why you usually see two big fleets in the pacific and nobody wants to attack because the attacker will lose. Similar to AandA Classic when both sides had huge stacks of infantry (there were no artillery back then and tanks defended on 2s) and this resulted in a stalemate. Here it’s the same: nobody wants to attack a fleet unless they have a big stack of bombers that outnumber the carriers.

The Larrymaxx formula since it takes into account the subs , combined arms , and 2 hit BB makes it superiour by far.
All hail the Larrymaxx formula!

@Imperious:
The Larrymaxx formula since it takes into account the subs , combined arms , and 2 hit BB makes it superiour by far.
All hail the Larrymaxx formula!
Could it be ??? Naw ! :?
Hail Hail Hail Hail Hail Hail Hail Hail Hail

Hello Baron, now with your formula I see, why you suggested 15IPC instead of 14IPC for our cruiser A3 D3 2 hits.
It brings it closer to the rate of destroyers. (15IPC = 1,26)8)

Hello Baron, now with your formula I see, why you suggested 15IPC instead of 14IPC for our cruiser A3 D3 2 hits.
It brings it closer to the rate of destroyers. (15IPC = 1,26)8)
Now you said it, I saw it too.
This might help make comparative analysis between various units OOB and customized.It is much easier to compare two numbers than rolling many simulations on an AACalc.
Things remains relative to the OOB Destroyer.For instance, the 2 hits Cruiser idea help me bring it into a balanced fit with a G40 Redesign (Philadelphia Experiment, cost structure 569121518) roster:
Destroyer A2 D2 C6, 1 hit.
Offence & defence factor:
36*2/6^2 = 2So I can use a Cruiser A3 D3 C12, 2 hits
Offence & defence factor:
36*3/12^2 * 2.618034= 1.96I deliberately choose a lower 569121518 cost structure for warships.
I might have keep Cruiser A3 D3 C9, 1 hit
Offence & defence factor:
36*3/9^2 = 1.33But it was so weak compared to Destroyer that I preferred this 2 hits Cruiser.
This formula is not that bad. It doesn’t solve everything but help make some choices.
For instance, I have a Fighter in this roster which is A2 D2 M4 C6, 1 hit which always target enemy’s plane first, then AAA, then casualty selection as usual.
Based on the formula, it the same as Destroyer.
Offence & defence factor:
36*2/6^2 = 2I can say that this ability maybe somewhat similar to the AntiSub capacity of DD.
Maybe, maybe not.
All that the formula reveals is that Tank are better for the cost and DD (1.125) vs Fg (Off 1.08 / Def 1.44) in OOB are quite similar.
So this seems correct that Fg in this Experiment get a similar combat factor compared to Destroyer as the case OOB.Now, if I look at the Tactical Bomber A3 D2 M4 C7, 1 hit of this experiment…
Offense factor:
36*(3/7^2) = 2.20
Defense factor:
36*(2/7^2) = 1.47It is a bit better on Offense and weaker on defense. Now, you can judge if it can compare with OOB for Fg vs TcB analysis.

@Imperious:
The Larrymaxx formula since it takes into account the subs , combined arms , and 2 hit BB makes it superiour by far.
All hail the Larrymaxx formula!
It is BaronLarrymarx formula,
Larrymarx breaks the Vann code (which Vann still courteously provided in the player’s help while we were working at it),
I standardized number in reference to Tank 3 and expanded the formula and basis to include other cases like 1942.2 Full Carrier, 2 hits or 3 hits warships and combined arms.
Without the basic code, I would not have been able to push forward, hence the Larrymarx named.@Dauvio:
It came to my attention that one of my formulas are already out there that I discovered 30 years ago.
http://www.axisandallies.org/forums/index.php?action=profile;u=185969 has also discovered the formula P^2*N=S
And just for fun you can try these formulas also. S/P^2=N. √(S/N)=P
P=POINTS
N=NUMBER OF UNITS
S=STRENGTH OF ONE KIND OF UNITS IN A TERRITORY
This formula should replace the punch formula. It is much better then the punch formula.Now the next formula is (P100)/(C^26)=S
P=POINTS
C=COST
S=STRENGTH OF THE UNIT BASED ON COST
With this formula you can also price units according to their strength. √((P100)/(S6))=C
This formula is for points. (S*(C^2*6))/100=PFor better results for some of these formulas, have all your units cost ten times then what they are. These are some of the VANN FORMULAS I came up 30 years ago.
If you have any questions about these formulas, please ask.

Here is the final numbers missing for G40 Carriers, there is probably a small difference compared to 50%50% AACalc for defense because defense points are lost that way for 2 Fgs: 0,2,6,10 /2 = 0, 1, 3, 5 and not 0, 0, 3, 5 as I made in this formula.
G40 Carrier A0 D2 C16, 2 hits
Offense factor:
36*[0/ (16^2)] * 2.618034 = 0
Defense factor:
36*[2/ (16^2)] * 2.618034 = 0.736G40 Carrier A0 D2 C16, 2 hits with 2 Fgs A6 D8 C20, 2 hits
Offense factor:
6/2 C36/2 2 additionnals hit/2
36*[3/ (18^2)] * 2.618034 = 0.873Defense factor:
10/2 C36/2 2 additionnals hit/2
36*[5/ (18^2)] * 2.618034 = 1.45410/4 C36/4 1 additionnal hit considered as whole unit
36*[2.5/ (9^2)] = 1.111
Until further investigation, I believe this average is better: (1.454+1.111)/2= 1.2825G40 Carrier A0 D2 C16, 2 hits with 1 Fg & 1 TcB A7 D7 C21, 2 hits
Offense factor :
7/2 C37/2 2 additionnals hit/2
36*[3.5/ (18.5^2)] * 2.618034 = 0.964Defense factor:
9/2 C37/2 2 additionnals hit/2
36*[4.5/ (18.5^2)] * 2.618034 = 1.2399/4 C37/4 1 additionnal hit considered as whole unit
36*[2.25/ (9.25^2)] = 0.947
Until further investigation, I believe this average is better: (1.239+0.947)/2= 1.093G40 Carrier A0 D2 C16, 2 hits with 2 TcBs A6 D6 C22, 2 hits
Offense factor :
6/2 C38/2 2 additionnals hit/2
36*[3/ (19^2)] * 2.618034 = 0.783Defense factor:
8/2 C38/2 2 additionnals hit/2
36*[4/ (19^2)] * 2.618034 = 1.0448/4 C38/4 1 additionnal hit considered as whole unit
36*[2/ (9.5^2)] = 0.798
Until further investigation, I believe this average is better: (1.044+0.798)/2= 0.921 
Ok so I’m confused how am I supposed to apply the VannBaronLArrynx formula? What do I do with the 1.454 number? And where is the derivation for the formula? Or is it just madeup?

Ok i understand it but I don’t get how you got your 1.61 factor for the baron formula with hits.

@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 5050% 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 5050 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 + (21) *1.618034}
If 3 hits, it gives … * 4.236068 {1 + 3.236068}
 {1 + (31) *1.618034}
HTH

@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: AntiSubmarine Attack 1 Defense 1 presurprise 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 569121518 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,
AntiSubA1D1,
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 M68 C5, 0 hit,
SBR 1 hit A1 dmg 1D6Fighter
A2 D2 M46 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 M46 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) = 1.47Antiaircraft 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.

@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 5050% 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 5050 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 + (21) *1.618034}
If 3 hits, it gives … * 4.236068 {1 + 3.236068}
 {1 + (31) *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.

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 + (31) *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


500 Battleships ? Must be nice !

@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 5050% 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 5050% 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 5050 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 + (21) *1.618034}
If 3 hits, it gives … * 4.236068 {1 + 3.236068}
 {1 + (31) *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 5050% odds,
819 dmgd BBs A4 D4, 1 hit vs 400 BBs A4 D4, 3 hits, near 5050% 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=BatInfArtAArtArmSubSSubDesFigJFigCruBomHBomCardBatTra&ool_def=TraBatInfArtAArtArmBomHBomSubSSubDesCarCruFigJFigdBat&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 5050% 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 + (31) 1.618034} = 1.45
144/420.25 * 4.236068 = 1.4515
OR
364/20.5^2 * {1 + (31) *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 5050% 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 5050% 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 5050% 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 5050% 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 F2F, 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 5050% 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 5050% 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 5050% 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 5050% 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 5050% 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 5050% 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 5050% 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 5050 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 + (21) *1.618034}
If 3 hits, it gives … * 4.236068 {1 + 3.236068}
 {1 + (31) *1.618034}
HTH
What battlecalc did you used for the for the different strength units??? The A&A battlecalc only calculates battleships.

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.