This a revised version derived and adapted to G40 2ed units roster **from Vann formula**.

It has no pretense about game-play 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 near-same 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 **~~Baron-Larrymarx~~ formula completed on effective cost vs combat points ratio:

Refence unit cost^2*actual unit Power*1 HitPoint/(actual unit Cost^2)*{1+[(nb hit -1)/1*1.618034] }= 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)/1*1.618034] }= offense or defense factor* *based on cost*

To 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)/1*1.618034] } / 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)= **3.00**

**Mech Infantry** A1 D2 M2 C4 would get

Offense factor:

36*(1/4^2) = **2.25**

Defense factor:

36*(2/4^2)= **4.50**

**Artillery** A2 D2 M1 C4

Offense & Defense factor:

36*(2/4^2)= **4.50**

**Infantry** A1 D2 M1 C3

Offense:

36*(1/3^2) = **4.00**

Defense:

36*(2/3^2) = **8.00**

**AIRCRAFTS:**

**Fighter** A3 D4 C10, 1 hit

Offense factor:

36*(3/10^2) = **1.08**

Defense factor:

36*(4/10^2) = **1.44**

**Tactical Bomber** A3 D3 C11, 1 hit

Offense & Defense factor:

36*(3/11^2) = **0.89**

**Strategic Bomber** A4 D1 C12, 1 hit

Offense factor:

36*(4/12^2) = **1.00**

Defense factor:

36*(1/12^2) = **0.25**

**Combined 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)= **5.88**

**Mech Infantry & Artillery** A4 D4 C8, 2 hits

Offense factor:

36*(2/4^2) = **4.50**

Defense factor:

36*(2/4^2)= **4.50**

**Tactical Bomber & Tank** A7 D6 C17, 2 hits

Offense factor:

36*(3.5/8.5^2) = **1.74**

Defense factor:

36*(3/8.5^2)= **1.50**

**Tactical 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)= **1.14**

**WARSHIPS and Transports:**

**Transport and Destroyer** A2 D2 C15, 1 hit

Offense & Defense factor:

36*(2/15^2) = **0.32**

**Classic Transport** A0 D1 C8, 1 hit

Defense factor:

36*(1/8^2) = **0.5625**

**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 **1.33**

**Destroyer** A2 D2 C8, 1 hit

Offense & Defense factor:

36*(2/8^2) = **1.125**

**Cruiser** A3 D3 C12, 1 hit

Offense & Defense factor:

36*(3/12^2) = **0.75**

**1942.2 Carrier** A1 D2 C14, 1 hit

Offense factor:

36*(1/14^2) = **0.18**

Defense factor:

36*(2/14^2) = **0.37**

**1942.2 Carrier Full Fighters** A7 D10 C34, 3 hits

Offense factor:

~~36*(1/14^2) = ~~**0.18**

36*(3/10^2) = **1.08**

36*(3/10^2) = **1.08**

2.344/3= **0.78** to be revised, need to be below 0.74 but just above 0.72

36* (7/3)/(34/3)^2 = *0.65* Avg (0.78+0.65)/2= **0.72**

Defense factor:

~~36*(4/10^2) = ~~**1.44**

36*(4/10^2) = **1.44**

36*(2/14^2) = **0.367**

3.247/3= **1.082** to be revised need to be below 1.00 but above 0.94

36* (10/3)/(34/3)^2 = **0.93**

**G40 Carrier** A0 D2 C16, 2 hits

Offense factor:

36*[0/ (16^2)] * 2.618034 = **0**

Defense factor:

36*[2/ (16^2)] * 2.618034 = **0.736**

**G40 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 = **0.873**

Defense 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 1.33

10/4 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) = *1.21*

**G40 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 = **0.964**

Defense factor:

9/2 C37/2 2 additionnals hit/2

36*[4.5/ (18.5^2)] * 2.618034 = *1.239*

9/4 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) = *1.02*

**G40 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 = **0.783**

Defense factor:

8/2 C38/2 2 additionnals hit/2

36*[4/ (19^2)] * 2.618034 = *1.044*

8/4 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) = *0.84*

**Battleship** A4 D4 C20, 2 hits

Offense & Defense factor:

36* 4 / (20^2) * 2.618034 = **0.94**

**Battleship flag ship** A4 D4 C24, 3 hits

Offense & Defense factor:

36* 4 / (24^2)* (1+2*1.618034) = ***1.06**

Real factor according to AACalc simulation: Fg A3 36(3/10^2) = **1.08**

Sound 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) = **2.88**

**Mech 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)= **3.56**

Now, 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)= **3.57**

This 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 = **1.44**

36* 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 1.13

If 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) = **1.06**

Or maybe at 22 IPCs?

36* 4 / (22^2)* (1+2*1.618034) = **1.26**

And you get a similar factor with 15 IPCs 2 hits Cruiser.

36* 3 / (15^2) * 2.618034 = **1.26**

It 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.**