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 Author Topic: SOME VANN FORMULAS REVEALED  (Read 1621 times)
Baron Munchhausen
A&A.org Battleship

Posts: 4445

Dreaming of all possibilities...

 « Reply #30 on: August 27, 2017, 02:07:51 pm » 0

OK, I found he used a 420 IPCs basis/100.

If I use Infantry as the basic reference: 420 IPCs/140

If all these units have the same 3 IPCs cost, here is what you would get for:

1 Movement Force
Infantry= 1.00 Attack, 2.00 Defense, 1.00 HP
Artillery= 1.50 Attack, 1.50 Defense, 0.75 HP
Infantry/Artillery= 1.71 Attack, 1.71 Defense, 0.86 HP

2 Movement Force
M-Infantry= 0.75 Attack, 1.50 Defense, 0.75 HP
Tanks (Original)= 1.80 Attack, 1.20 Defense, 0.60 HP
Tanks (Revised)= 1.80 Attack, 1.80 Defense, 0.60 HP
Tanks (1940)= 1.50 Attack, 1.50 Defense, 0.50 HP

Tank (Original) A3D2/MI A1D2= 1.33 Attack, 1.33 Defense, 0.67 HP
Tank (Revised) A3D3/MI A1D2= 1.33 Attack, 1.67 Defense, 0.67 HP
Tank (1940) A3D3/MI A1D2= 1.20 Attack, 1.50 Defense, 0.60 HP
Artillery + MI A4 D4, 2 hits = 1.50 Attack, 1.50 Defense, 0.75 HP

_______________________________________ _______________________________

It is also possible to use the Enigma formula with a small addition to get the relative strength between each unit:
36*Power*HP/cost^2= Strength factor
And since it is all 3 IPCs basis 3^2 = 9, a
simpler formula of Enigma for  3 IPCs: 4*Power*HP = Strength factor

1 Movement Force
Infantry= 1.00 Attack, 2.00 Defense, 1.00 HP
36*1*1/9= 4.00        36*2*1/9= 8.00
Artillery= 1.50 Attack, 1.50 Defense, 0.75 HP
36*1.5*.75/9 = 4.50
Infantry/Artillery= 1.71 Attack, 1.71 Defense, 0.86 HP
36*1.71*.86/9= 5.88

2 Movement Force
M-Infantry= 0.75 Attack, 1.50 Defense, 0.75 HP
36*.75*.75/9 = 2.25     36*1.5*.75/9 = 4.5
Tanks (Original)= 1.80 Attack, 1.20 Defense, 0.60 HP
36*1.8*.6/9 = 4.32    36*1.2*.6/9= 2.88
Tanks (Revised)= 1.80 Attack, 1.80 Defense, 0.60 HP
Simplified formula: 4*1.8*.6= 4.32
Tanks (1940)= 1.50 Attack, 1.50 Defense, 0.50 HP
4*1.5*.5= 3.00

Tank (Original) A3D2 + MI A1D2= 1.33 Attack, 1.33 Defense, 0.67 HP
4*1.33*.67= 3.56
Tank (Revised) A3D3 + MI A1D2= 1.33 Attack, 1.67 Defense, 0.67 HP
4*1.33*.67= 3.56      4*1.67*.67= 4.48
Tank (1940) A3D3 + MI A1D2= 1.20 Attack, 1.50 Defense, 0.60 HP
4*1.20*.60=  2.88     4*1.50*.60= 3.60
Artillery + MI A4 D4, 2 hits = 1.50 Attack, 1.50 Defense, 0.75 HP
4*1.50*.75= 4.50

_______________________________________ __________________________________

So, when on the same IPCs basis, the underlying factors in Vann and now Enigma formula was simply:
Power*HP* ( 36/cost^2) = Strength factor
Assuming Power and HP can be a fraction from reference unit.
Above, I choose Infantry A1 C3, 1 hit as reference unit.
And *36 or *4 was simply a factor to get whole number results for Tank C6 and Inf C3

This give for each ground unit, without this little multiplying factor, these attack and defense factors:

Ground units:
1 Movement Force
Infantry= 1.00 Attack, 2.00 Defense
Artillery= 1.125 Attack, 1.125 Defense
Infantry/Artillery= 1.47 Attack, 1.47 Defense

2 Movement Force
M-Infantry= 0.5625Attack, 1.125 Defense
Tanks (Original)= 1.08 Attack, 0.72 Defense
Tanks (Revised)= 1.08 Attack, 1.08 Defense
Tanks (1940)= 0.75 Attack, 0.75 Defense

Tank(Original) A3D2 + MI A1D2= 0.89 Attack, 0.89 Defense
Tank(Revised) A3D3 + MI A1D2= 0.89 Attack, 1.12 Defense
Tank(1940) A3D3 + MI A1D2= 0.72 Attack, 0.90 Defense
Artillery + MI A4 D4, 2 hits = 1.125 Attack, 1.125 Defense

These values allows to easily compared with Infantry A1 D2 to know below or above Infantry strength a given unit is.

Eventually, it will be possible to derivate this formula from Stack formula (based on Lanchester's Laws).

_________
Aircrafts:
Fighter A3 D4 C10, 1 hit becomes *3/10 in Inf basis=
0.90 Attack 1.2 Defense, .30 HP
Strength factor: .90*.30= 0.27 Attack, 1.2*.30= 0.36

Strategic Bomber A4 D1 C12, 1 hit becomes *3/12 in Inf basis=
1.00 Attack 0.25 Defense, .25 HP
Strength factor: 1.00*0.25= 0.25 Attack, 0.25*.25= 0.0625

Tactical bomber A3-4 D3 C11, 1 hit becomes *3/11 in Inf basis=
0.82-0.91 Attack 0.82 Defense, .273 HP
Strength factor: .82*.273= 0.224 .91*.273= 0.248 Attack,
0.82*.273= 0.224 Defense

Combined Arms:
Tactical Bomber & Tank A7 D6 C17, 2 hits becomes *3/17 in Inf basis=
1.235 Attack 1.059 Defense, 0.353 HP
Offense factor:                   Defense factor:
1.235*0.353 = 0.436      1.059*0.353= 0.374

Tactical Bomber & Fighter A7 D7 C21, 2 hits becomes *3/21 in Inf basis=
1.00 Attack 1.00 Defense, 0.286 HP
Offense factor:                   Defense factor:
1.00*0.286= 0.286                0.286

WARSHIPS:
Submarine A2 D1 C6, 1 hit becomes *3/6 in Inf basis=
Regular: 1.00 Attack 0.50 Defense, 0.5 HP
Surprise strike: 1.50 Attack 0.667 Defense
Offense factor:                   Defense factor:
1.00*0.5= 0.500     0.50*0.5= 0.250
Surprise strike:
1.50*0.5= 0.750     0.667*0.5= 0.333

Destroyer A2 D2 C8, 1 hit becomes *3/8 in Inf basis=
0.75 Attack 0.75 Defense, 0.375 HP
Offense factor:                   Defense factor:
0.75*0.375= 0.281    0.281

Cruiser A3 D3 C12, 1 hit becomes *3/12 in Inf basis=
0.75 Attack 0.75 Defense, 0.25 HP
Offense factor:                   Defense factor:
0.75*0.25= 0.188    0.188

1942.2 Carrier A1 D2 C14, 1 hit *3/14 in Inf basis=
0.214 Attack 0.418 Defense, 0.214 HP
Offense factor:                   Defense factor:
0.214*0.214 = 0.046   0.418*0.214= 0.092

1942.2 Carrier Full Fighters A7 D10 C34, 3 hits *3/34 in Inf basis=
0.618 Attack 0.882 Defense, 0.265 HP
Offense factor:                   Defense factor:
0.618*0.265 = 0.164   0.882*0.265= 0.233

G40 Carrier A0 D2** C16, (2 hits = **1.618034) *3/16 in Inf basis=
0.00 Attack 0.607 Defense, 0.303 HP
Offense factor:                   Defense factor:
0.00*0.607 = 0.00   0.607*0.303= 0.184

Battleship A4 D4 C20, 2 hits, (2 hits = **1.618034) *3/20 in Inf basis=
0.971 Attack 0.971 Defense, 0.243 HP
Offense factor:                   Defense factor:
0.971*0.243 = 0.236                 0.236

Both values for 2 hits Carrier and Battleship are correct since you can use Baron-Larrymarx values /4 and gets the number above.

So, based on this quoted table, it is easy to see how in Classic time, the Infantry Push Mechanics was king.
Artillery unit becomes the offense unit par excellence when paired with Inf.
But Revised Tank, get a similar attack and defense value compared to Artillery in itself.

There is probably many other things to analyse.
For instance, comparing Revised Tank A3 D3 C5 to Mech Inf A1-2 D2,
M-Infantry= 0.5625Attack, 1.125 Defense
Tanks (Revised)= 1.08 Attack, 1.08 Defense

MI is twice weaker on offence and of similar defence 1.125 vs 1.08.
So, introducing MI required the change to a C6 Tank as we know it.
Tanks (1940)= 0.75 Attack, 0.75 Defense
And MI now is still weaker on offence, but stronger in defense, as we prefer for an Infantry-like unit.
 « Last Edit: August 27, 2017, 08:26:35 pm by Baron Munchhausen » Logged
Baron Munchhausen
A&A.org Battleship

Posts: 4445

Dreaming of all possibilities...

 « Reply #31 on: September 06, 2017, 05:12:06 pm » +1

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 (P*100)/(C^2*6)=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. √((P*100)/(S*6))=C
This formula is for points. (S*(C^2*6))/100=P

For 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.

I found how you can get the main part of Vann formula or Baron-Larrymarx according to a specific unit as benchmark.

I took the Fighter A3 D4 C10 and I wanted to convert into Tank A3 D3 C6 as benchmark (Baron-Larrymarx formula).

Then I saw what I did.

Power (of attacking Fighter): A3 * C6 (cost of Tank)/C10 (cost of Fg) * 1 Hit Point *C6 (cost of Tank)/C10 (cost of Fg) = 1.08
You can reduce this equation because (cost of Tank)*(cost of Tank)/ (cost of Fg)*(cost of Fg) is same to
(cost of Tank) IPCs^2 / (cost of Fg) IPCs^2 and give a simple ratio.

C6^2*A3/C10^2 = 1.08
36 squared IPCs *3 Power * 1 Hit /100 squared IPCs = 1.08 Power*Hit Point

This explained what is hidden in Baron-Larrymarx formula:
Offence or defence strength factor= 36*Power/Cost^2.

The whole Enigma formula is
Refence unit Cost^2*Power of the actual unit*1 HP/Cost of the actual unit^2

So, the Basic offence or defence strength factor result (1.08, in this case) is express in Power*Hit Point
1^2*Power (of a given unit)*1 hit/Cost (of this same given unit)^2

And this formula can be adapt according to any benchmark, for instance a 1 IPC unit:
1*3*1 hit/10^2 = 0.300

And this is a very small number. That's why Vann formula:
Strength= (Power*100)/(Cost^2*6)

So, 16.667*1*3*1 hit/10^2 = 0.5
And this would provide the Fighter strength attack factor based on an hypothetical benchmark unit of √16.667 = 4.0825 IPCs.
A 5 IPCs revised Tank in Vann formula gives a Strength : 16.667*3*1 hit/5^2 = 2.00 power*hit

 « Last Edit: September 06, 2017, 07:44:06 pm by Baron Munchhausen » Logged
Dauvio Vann
A&A.org Artillery

Posts: 196

 « Reply #32 on: July 01, 2018, 08:58:41 pm » 0

For house rules, this is a good way to price your units, and to give them a proper attack, and defense for your dice.

It's good for tweaking your game.
 « Last Edit: July 19, 2018, 10:25:00 pm by Dauvio Vann » Logged
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