Thanks for sharing Dauvio.
I found the way to calculate the increase of Strength per unit based on cost when such unit have 2 or 3 hits.
And apply it to price units according to their strength. √((P100)/(S6))=C
It was more a matter of trials with higher and lower costs to determine designer’s right price POV:
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 say if you get enough 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, 1.143, 1.125, 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 costum 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 Baron-Larrymarx formula completed on effective cost vs combat points ratio:
For all 1 hit unit, you use : 36 Power/(cost^2) = offense or defense factor*
For 2 hits and 3 hits unit : 36 Power/(cost^2) {1+[(nb hit -1)/11.618034] }= offense or defense factor*
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 offense and defense factor (same as attack or def point)
Tank A3 D3 M2 C6
offense & defense factor: 36*3/(6^2)= 3
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
Defense:
36*(2/3^2) = 8
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) = 0.893
Strategic Bomber A4 D1 C12, 1 hit
Offense factor:
36*(4/12^2) = 1
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) = 1.744
Defense factor:
36*(3/8.5^2)= 1.495
Tactical Bomber & Fighter A7 D7 C21, 2 hits
Offense factor:
36*(3.5/10.5^2) = 1.143
Defense factor:
36*(3.5/10.5^2)= 1.143
WARSHIPS:
Submarine A2 D1 C6
Offense:
36*(2/6^2) = 2
36*(2.33/6^2) = 2.33 surprise strike
Defense:
36*(1/6^2) = 1
36*(1.17/6^2) = 1.17 surprise strike
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) = 0.750
1942.2 Carrier A1 D2 C14, 1 hit
Offense factor:
36*(1/14^2) = 0.184
Defense factor:
36*(2/14^2) = 0.367
1942.2 Carrier Full Fighters A7 D10 C34, 3 hits
Offense factor:
36*(1/14^2) = 0.184
36*(3/10^2) = 1.08
36*(3/10^2) = 1.08
2.344/3= 0.781 to be revised, need to be below 0.736
36* (7/3)/(34/3)^2 = 0.654
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
36* (10/3)/(34/3)^2 = 0.934
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
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
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
Battleship A4 D4 C20, 2 hits
Offense & Defense factor:
36* 4 / (20^2) * 2.618034 = 0.9425
Battleship 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) = 1.08
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) = 2.880
Mech Infantry & Mechanized Artillery A4 D4 M2 C9, 2 hits
Offense factor:
36*(2/4.5^2) = 3.556
Defense factor:
36*(2/4.5^2)= 3.556
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.
Another example, 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 0.9425?
Weaker than a Destroyer? A2 D2 C8 at 1.125
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