SOME VANN FORMULAS REVEALED

I’m much open to hit.

As you probably see, the 36* factor was meant to make easier calculation with the second edition A&A Tank A3 D3 C6.
(Your formula is less functional as it is with 100* factor.)
It reveals easier to add things up like Infantry 4/8, Art 4.5/4.5, Mech 2.25/4.5, Tank 3/3 and some others like bombers 1 /0.25.

Based on the limited example in my last post, I believe it is the way to go.
Add up all units strength, then get the average. But this probably works only if you have the same IPCs basis to compare to stack.

If you get 3 Infs A1 (4.00) against 2 Tanks D3 (3.00), it seems to say that 3 Infs is better.
But 3^21= 9  vs 2^23= 12
And Calc gives: A. survives: 32.3% D. survives: 62.8% No one survives: 4.9%
Probably the Stack formula work for all situations while this Baron-Larrymarx has limited values in game.

In addition, you need to learn a different set of values above the usual units values.
This is not very practical.

I think Stack formula (Kreuzfeld or zergxies?) is both useful for optimizing purchase and comparing stack strength.
Here is the thread where it appears in G40 forum:
Method for Estimating the Outcomes of Large Battles
http://www.axisandallies.org/forums/index.php?topic=39526.msg1640769#msg1640769
@Ozymandiac:

@zergxies:

@Ozymandiac:

Interesting difference between your ideas is that HolKann claims the number of units is more important than the power; while your calculations show metapower is a multiplication of power and the number of units so they are symmetrically important.

I think my results support HolKann’s.� Given that metapower = units * power = units^2 * avg(power), I think it’s safe to say that the number of units is more important metapower than power is, and in fact, this shows you how much more important it is.� And also how skew doesn’t add much :)

I like the term skew much more than distribution; I spent forever trying to come up with a better word and this eluded me!

Pft why didn’t I think of that (numbers^2). Thanks, that’s it.

A sub A2 with sneak attack is the same as a unit A3 without a sneak attack.

I found it with AACalc simulations too thanks, I corrected this point.
How do you find it?
I also use AACalc for D1 first strike value of Sub to be D1.33, and since 36*1…/6^2= 1… but IDK it can be 1.30.

If there is another way to get the strength, tell me please.

I think standard stack formula or AAcalc is better for battle outcome predictions while Vann-Baron formulas are excellent at predicting what a new house rule unit should cost or what the current units should cost when using a unit as benchmark.

@Ozymandiac:

@Kreuzfeld:

Ususally, subs is the most costeffective unit to buy for defence.

I’m not following this. Suppose I have 48 IPCs and want to buy a defensive fleet.
-I buy 8 subs, receive metapower=881=64.
-I buy 6 destroyers, receive metapower=662=72.

Aren’t destroyers the units with a higher metapower and as such better as defensive units?

I see they also use this Metapower formula to get an optimized purchase.
And it is confirmed by AACalc.
If there is 24 IPCs to spend on Inf, Art, MI and Tank, it will be easier to decide since in case of combined arms, you can add it too.

8 Infs             A8 D16    8 hits     8^21= 64  /   8^22= 128   tot.: 192
6 Artillery       A12 D12   6 hits     6^22= 72  /   6^22= 72    tot.: 144
4 Tanks          A12 D12   4 hits     4^23= 48  /   4^23= 48     tot.: 96

1 Tk & 6 Infs   A9 D15    7 hits    7^21.29= 63.2 / 7^22.14= 104.9  tot.: 168.1
2 Tk & 4 Infs   A10 D14  6 hits    6^21.67= 60.1 / 6^22.33= 83.9    tot.: 144
3 Tk & 2 Infs   A11 D13  5 hits    5^22.2= 55 / 5^22.6= 65             tot.: 120
3 Art & 4 Infs   A14 D14  7 hits    7^22= 98 / 7^22= 98                 total: 196

1 Tk, 3 Art, 2 Infs            A13 D13 6 hits  6^22.17= 78.1 / 6^22.17= 78.1  tot.: 156.2
1 Tk, 2 Art, 1 MIs, 2 Infs  A12 D13 6 hits  6^22 = 72        / 6^22.17= 78.1  tot.: 150.1
1 Tk, 1 Art, 2 MIs, 2 Infs  A10 D13 6 hits  6^21.67= 60.1 / 6^22.17= 78.1  tot.: 138.2
1 Tk, 3 MIs, 2 Infs            A8 D13 6 hits  6^21.33 = 47.9 / 6^22.17= 78.1  tot.: 126

Even with such low 24 IPCs, it seems rather complex to sort out these numbers.
Unless having a few tables with various combinations, it only points out that it is cumbersome and also, Artillery with combined arms clearly gives better offensive.

It might help choose but the Punch formulas might be enough in this case.

Probably the things were different in Classic time with Tank A3 D2 C5.

So, this formula seems more useful when calculating odds between two stacks.

its ok Vann helsing.

This is why nobody uses the Van formula and now they use the Larrymarx formula. Thanks for everything!

@Genghis:

I think standard stack formula or AAcalc is better for battle outcome predictions while Vann-Baron formulas are excellent at predicting what a new house rule unit should cost or what the current units should cost when using a unit as benchmark.

I think the same.

Stack formula replace AACalc for mental calculation.

The Baron-Larrymarx based on Vann tables are better for evaluating if a given cost is correct or not.

What about finding a more accurate name for this formula?
Something like Enigma formula to decode A&A combat and cost structure.
Any idea?

the correct cost of cruiser and BB are 10 and 18 according to baron-larymarx formulas and using OOB DD values as benchmark.

@Genghis:

I have used the baron formulas that take into account the hits in order to come to the following conclusions:

Taking the benchmark DD value of 1.125 as the basic ship: Cruiser should cost 9.79 IPCs and BB should cost 18.28 IPCs. Alternatively a BB with 5/5 stats should cost 20.43 IPCs. (Assuming special abilities of ships are equal)

@Genghis:

the correct cost of cruiser and BB are 10 and 18 according to baron-larymarx formulas and using OOB DD values as benchmark.

I cannot agree more.
All these 3 units are very similar in the A&A roster: surface vessel warships, able to fight all naval or air units.
So, the basic assumption was to keep the same benchmark, here the better one of DD, in a way increasing the cost (and BB or Cruiser are among the most expensive ones) will not change their attack and defense factor.

So, the way to keep offense & defense factor 1.1125 is DD 8$, CA 10$ and BB 18$.

But, then you may ask, why not use the usual decrease of strength as you get for ground units?

Infantry A1 D2 C3 (4.00/8.00) & Subs A2 D1 C6  (2.00/ 1.00) double cost, 4 times weaker
Artillery A2 D2 C4 (4.50)        & DD A2 D2 C8 (1.1125) double cost, 4 times weaker
Tank A3 D3 C6 (3.00)            & Cruiser A3 D3 C12 (0.75) double cost, 4 times weaker
? ? ?                                      & Battleship A4 D4 C20, 2 hits (0.94)

That allows for the fodder tactic, lower combat value have much off/def factor because low cost per hit.
If you wish to keep it, you may put Cruiser at 11 IPCs while keeping BB at 20 IPCs.
Cruiser C11: 363/11^2= 0.893
Cruiser C10: 363/10^2= 1.08

At 10, it would follow the ground unit decrease rule, but BBs are so prohibitive that you cannot really desire this luxury item without affecting your fleet strength compared to 2 Cruisers. Even if from pure offense factor compared to Art or Art+Inf, Tank is weaker; it is still more affordable (than BB) for low economy Powers, have speed and have special blitz ability.

At 11, Cruiser can play the part of having a weaker strength factor than a fodder unit (Destroyer) but, because 11 IPCs make for better affordable unit than BB for most of low economy Powers. So, it is not as best as BB, you can still put a better punch unit in SZ than DD.

Unfortunately, the double cost for warships cost structure is strongly impregnated.
11 was not a well round number compared to 12 or 10.
10 is a fine number, but Larry (in addition to not changing the cost structure progression) wanted that Battleship remains a viable purchase and not a totally obsolete unit.
And he never consider to reduce BB cost to 18, even if 18 was 6 times Infantry cost or 3 Tanks cost.
Battleship C18, 2 hits: 36* 4 / (18^2) * 2.618034 = 1.16

I also suggested elsewhere, instead of a double cost per combat points, *a 1.5 cost multiplier.
That would have give a more practical and affordable roster from odds in pure combat POV:

Submarine A2 D1 C5 (4.5 rnd up)  362/5^2= (2.88/ 1.44)
Destroyer  A2 D2 C6    362/6^2=(2.00)
Cruiser      A3 D3 C9    363/9^2=(1.33)
Carrier     A0 D2 C12, 2 hits 36 2 / (12^2) * 2.618034 = (1.31)
Battleship A4 D4 C15, 2 hits 36* 4 / (15^2) * 2.618034 = (1.68)

From Sub to BB, the same strength curve of decrease then increase for Battleship occurs, as OOB.
But, now being at 9 IPCs, Cruiser becomes a kind of luxury (as Tank) some Powers may purchase because not willing to place all their eggs on a Battleship. And, to increase the similarity, you may make it a M3 faster warship.

However, making a little change in cost for Battleship, it would fit into a constant decrease pattern.
Battleship C18, 2 hits: 36* 4 / (18^2) * 2.618034 = (1.16)

yes but battleships doesn’t only have two hits as ability. It also has ability to soak hits and then heal, which cruisers don’t have. This isn’t taken into account in the formulas. (Assuming the BB survives the combat). that’s why I think it’s OK if the strength factor decreases all the way to BB.

I believe it too.

At the bottom of this post, wodan put a few numbers to get the strength of Classic, Revised and G40 Tank.
Is there any maths genious who can sort out the equation he used?
IMO, it may be near Enigma formula.
Thanks.

@wodan46:

@Veqryn:

KEPT the tank at the pre-revised stats of 3-2-2-5

Hmm.

For 20 IPCs
4 Tanks=12 Attack, 8 Defense, 4 Hits
5 M-Infantry=5 Attack, 10 Defense, 5 Hits

For 21 IPCs
3 Artillery, 3 Infantry=12 Attack, 12 Defense, 6 Hits
7 Infantry=7 Attack, 14 Defense, 7 Hits

Interesting.  That actually works a lot better.  Tanks are still clearly the best way of projecting offense, but M-Infantry are better at securing territories.  Artillery/Infantry are the best all around force, but move slower, and Infantry have the best defense/health, but have pathetic attack and move.

Also, M-Infantry are going to be really bad for Invasions, as when transported, they are the same as Infantry, but take up the better slot of the Transport and cost more.

In fact, the full statistics are below:

1 Movement Force
Infantry=1.40 Attack, 2.80 Defense, 1.40 HP
Infantry/Artillery=2.40 Attack, 2.4 Defense, 1.20 HP
2 Movement Force
M-Infantry=1.05 Attack, 2.10 Defense, 1.05 HP
Tanks(Original)=2.52 Attack, 1.68 Defense, 0.84 HP
Tanks(Revised)=2.52 Attack, 2.52 Defense, 0.84 HP
Tanks(1940)=2.10 Attack, 2.10 Defense, 0.70 HP
Tank(Original)/M-Infantry=1.88 Attack, 2.35 Defense, 0.94 HP

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:
36PowerHP/cost^2= Strength factor
And since it is all 3 IPCs basis 3^2 = 9, a
simpler formula of Enigma for  3 IPCs: 4PowerHP = Strength factor

1 Movement Force
Infantry= 1.00 Attack, 2.00 Defense, 1.00 HP
3611/9= 4.00        3621/9= 8.00
Artillery= 1.50 Attack, 1.50 Defense, 0.75 HP
361.5.75/9 = 4.50
Infantry/Artillery= 1.71 Attack, 1.71 Defense, 0.86 HP
361.71.86/9= 5.88

2 Movement Force
M-Infantry= 0.75 Attack, 1.50 Defense, 0.75 HP
36*.75*.75/9 = 2.25     361.5.75/9 = 4.5
Tanks (Original)= 1.80 Attack, 1.20 Defense, 0.60 HP
361.8.6/9 = 4.32    361.2.6/9= 2.88
Tanks (Revised)= 1.80 Attack, 1.80 Defense, 0.60 HP
Simplified formula: 41.8.6= 4.32
Tanks (1940)= 1.50 Attack, 1.50 Defense, 0.50 HP
        41.5.5= 3.00

Tank (Original) A3D2 + MI A1D2= 1.33 Attack, 1.33 Defense, 0.67 HP
41.33.67= 3.56
Tank (Revised) A3D3 + MI A1D2= 1.33 Attack, 1.67 Defense, 0.67 HP
41.33.67= 3.56      41.67.67= 4.48
Tank (1940) A3D3 + MI A1D2= 1.20 Attack, 1.50 Defense, 0.60 HP
41.20.60=  2.88     41.50.60= 3.60
Artillery + MI A4 D4, 2 hits = 1.50 Attack, 1.50 Defense, 0.75 HP
41.50.75= 4.50

So, when on the same IPCs basis, the underlying factors in Vann and now Enigma formula was simply:
PowerHP ( 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: 1.000.25= 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:
1.2350.353 = 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:
1.000.286= 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:
1.000.5= 0.500     0.500.5= 0.250
Surprise strike:
1.500.5= 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:
0.750.375= 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:
0.750.25= 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:
0.2140.214 = 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:
0.6180.265 = 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 231.618034/16= 0.607 Defense, 31.618034/16= 0.303 HP
Offense factor:                   Defense factor:
0.000.607 = 0.00   0.6070.303= 0.184

Battleship A4 D4 C20, 2 hits, (**2 hits = 1.618034) 3/20 in Inf basis=
431.618034/20 = 0.971 Attack 0.971 Defense, 0.243 HP
Offense factor:                   Defense factor:
0.9710.243 = 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.

@Baron:

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:
36PowerHP/cost^2= Strength factor
And since it is all 3 IPCs basis 3^2 = 9, a
simpler formula of Enigma for  3 IPCs: 4PowerHP = Strength factor

1 Movement Force
Infantry= 1.00 Attack, 2.00 Defense, 1.00 HP
3611/9= 4.00        3621/9= 8.00
Artillery= 1.50 Attack, 1.50 Defense, 0.75 HP
361.5.75/9 = 4.50
Infantry/Artillery= 1.71 Attack, 1.71 Defense, 0.86 HP
361.71.86/9= 5.88

2 Movement Force
M-Infantry= 0.75 Attack, 1.50 Defense, 0.75 HP
36*.75*.75/9 = 2.25    361.5.75/9 = 4.5
Tanks (Original)= 1.80 Attack, 1.20 Defense, 0.60 HP
361.8.6/9 = 4.32    361.2.6/9= 2.88
Tanks (Revised)= 1.80 Attack, 1.80 Defense, 0.60 HP
Simplified formula: 41.8.6= 4.32
Tanks (1940)= 1.50 Attack, 1.50 Defense, 0.50 HP
        41.5.5= 3.00

Tank (Original) A3D2 + MI A1D2= 1.33 Attack, 1.33 Defense, 0.67 HP
41.33.67= 3.56
Tank (Revised) A3D3 + MI A1D2= 1.33 Attack, 1.67 Defense, 0.67 HP
41.33.67= 3.56      41.67.67= 4.48
Tank (1940) A3D3 + MI A1D2= 1.20 Attack, 1.50 Defense, 0.60 HP
41.20.60=  2.88    41.50.60= 3.60
Artillery + MI A4 D4, 2 hits = 1.50 Attack, 1.50 Defense, 0.75 HP
41.50.75= 4.50

---

So, when on the same IPCs basis, the underlying factors in Vann and now Enigma formula was simply:
PowerHP ( 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: 1.000.25= 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:
1.2350.353 = 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:
1.000.286= 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:
1.000.5= 0.500    0.500.5= 0.250
Surprise strike:
1.500.5= 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:
0.750.375= 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:
0.750.25= 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:
0.2140.214 = 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:
0.6180.265 = 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:
0.000.607 = 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:
0.9710.243 = 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.

@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=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.

If you have any questions about these formulas, please ask.

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 PowerHit 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^2Power of the actual unit1 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:
131 hit/10^2 = 0.300

And this is a very small number. That’s why Vann formula:
Strength= (Power100)/(Cost^26)

add an arbitrary 1001/6= 16.667…
So, 16.667131 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 : 16.66731 hit/5^2 = 2.00 powerhit