Kreuzfeld, Baron-Larrymarx, and VAN FORMULAS summery.

Larrymarx formula is the only one that accounts for everything

Do you remember how you discovered it back then when there was no AACalculator or Combat calculator invented?
For that time, it was clearly a breakthrough to make some tactical decision based on a more accurate odds calculation.

This is getting historical. Got to keep my eye on this thread. Hey which formula is better ?

VANN DAMM ?

KREUZFELD ?

LARRYMARX ?

I need to know by tonite. Have a game.
Man I’m Gettin confused

/-&=1.5. :+<=.8  1.5=<>   :? :?

Stack formula… coming from Kreuzfeld and others. Vann says he knew it too.

Metapower of a stack= Number of units^2 * avg combat Power

That  is the most useful for a F-2-F game. IMO.

Unless Vann get to explain how to use Vann formula or table  in F-2-F.

For purchase, the Punch formula seems enough because we intuitively try to maximize combat points and hits.
In addition, Artillery unit is a very safe way to maximize both attack and defense.
In Classic time there was no such unit, hence the famous Don’s Infantry-push mechanic was predominant.
AA50, Tank at 5 IPCs is a very best for attacker.
Now, with C6 Tank, it is when you need speed.
It is never optimal compared to M1 unit and MI is still better on defense and get M2.
You have to ask : do I really need to buy these 2 Tanks?
I can buy 1 StB (mobility+Punch), 3 MIs (speed&def), 3 Arts (max attack) or 4 Infs (max defense).
I believe that’s why StBs are so popular as the higher puncher.

Maybe it is the Tac Bomber which increase the interest for Tank vs MI.

Ya but how does the beanie inf rate using all these formulas ?

baron-larymarx shows STB as 1 on offense, and two tanks as 3.92. For tanks I used P=6, C=12 and H=1
P=power, C=cost, H=hits. For STB, P=4, C=12, H=1

value = 36P/(C^2)*(1+(H-1)(1.618))

Also tanks has better offense than MI but worse defense than MI according to baron-larymarx.

@SS:

Ya but how does the beanie inf rate using all these formulas ?

They maybe ingnoring you, but we both know that the “Battleing Beanie Bastards of Bastogne” are some pretty Bad Boys……

@Genghis:

baron-larymarx shows STB as 1 on offense, and two tanks as 3.92. For tanks I used P=6, C=12 and H=1
P=power, C=cost, H=hits. For STB, P=4, C=12, H=1

value = 36P/(C^2)*(1+(H-1)(1.618))

To compare both units, for same IPCs basis like 12 IPCs, there is nothing to add or change.

It is: Tank A3 D3 M2 C6
offense & defense factor: 36*3/(6^2)= 3.00

compared to
Strategic Bomber A4 D1 C12, 1 hit
Offense factor:
36*(4/12^2) = 1.00

So Tank are three times stronger.

On AACalc, 1 bomber vs 2 Tanks:
A. survives: 7.3% D. survives: 85.4% No one survives: 7.3%
And odds diminish for Bombers if you increase numbers like 6 bombers vs 12 Tanks
A. survives: 0.1% D. survives: 99.9% No one survives: 0%

@Genghis:

Also tanks has better offense than MI but worse defense than MI according to baron-larymarx.

True, for the same IPCs basis, like 3 MIs vs 2 Tanks (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

However, this does not consider when MIs can combined arms with Artillery:
Mech Infantry & Artillery A4 D4 C8, 2 hits
Offense factor:
36*(2/4^2) = 4.50
Defense factor:
36*(2/4^2)= 4.50

3 MIs+3 Arts will always beat up 4 Tanks.
But, you cannot be fast with Artillery.
If you planned long terms attack, always destroys MIs first, then Artillery or retreat before your Artillery power is destroyed.
That way, you may reinforce with fresh MIs and Infantry in retreating TT.

Here is where I revised the table for OOB units:
@Baron:

@Baron:

Here is the table based on Baron-Larrymarx formula completed on effective cost vs combat points ratio:
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 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)/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)= 3.00

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:
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+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) = 2.88

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.

@SS:

Ya but how does the beanie inf rate using all these formulas ?

Tank is 3.00 strength factor for offense or defense.
But, on same IPCs basis, Infantry (4.00) remains better to win a fight.
And Artillery (4.50) or Infantry+Artillery (5.88) is much better.

Infantry A1 D2 M1 C3
Offense:
36*(1/3^2) = 4.00
Defense:
36*(2/3^2) = 8.00

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

@Loose:

@SS:

Ya but how does the beanie inf rate using all these formulas ?

They maybe ingnoring you, but we both know that the “Battleing Beanie Bastards of Bastogne” are some pretty Bad Boys……

So Bad Assterd  true. I did get a reply but they forgot to factor in the +1 on A D do to they can fly up.

@SS:

@Loose:

@SS:

Ya but how does the beanie inf rate using all these formulas ?

They maybe ingnoring you, but we both know that the “Battleing Beanie Bastards of Bastogne” are some pretty Bad Boys……

So Bad Assterd  true. I did get a reply but they forgot to factor in the +1 on A D do to they can fly up.

Learning to fly will be part of the third ed. formula code with a special camo attack for paratroopers +1A surprise strike with hiding in bushes so they cannot be found in a contested TT. So no need for a +1D.
:wink:

@Baron:

@SS:

@Loose:

@SS:

Ya but how does the beanie inf rate using all these formulas ?

They maybe ingnoring you, but we both know that the “Battleing Beanie Bastards of Bastogne” are some pretty Bad Boys……

So Bad Assterd  true. I did get a reply but they forgot to factor in the +1 on A D do to they can fly up.

Learning to fly will be part of the third ed. formula code with a special camo attack for paratroopers +1A surprise strike with hiding in bushes so they cannot be found in a contested TT. So no need for a +1D.
:wink:

SWEET !  :-D

yes tanks are 3 times stronger on offense then bombers but that doesn’t take into account the fact that bombers can reach everywhere in the turn after they are built whereas tanks often take at least two turns and don’t have the flexibility of hitting sea units as well.

The Stack formula coming from Kreuzfeld, Ozymandiac and Vann has been modified to take accounts of 2 hits units.

@Baron:

@Kreuzfeld:

@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 think I also said that it was dependent on what other ships you had available. Subs isn’t best if you only have subs. I would expect the optimal ratio for subs vs other ships would be between 40 and 60 % of your fleet.

if you have no fleet, then you would be correct.

lets ssume you have 2 CV + 4 ftr, + 2 DDs + 2 subs.   I will count the CV as 2 units.  For your fleet so far, you have 26 pips and 12 hp. if you buy 6 subs, you will have 38 pips and 18 hp. if you buy 10 subs, you will have 34 pips hand 20 hp.

with sub
342020 = 13600
with DD
381818 = 12312

So, as you can see, the sub will be better for your metapower. It will also give you a better lossdistribution.

But, I think your point is interessting. I think this formula can be used to figure out what you want to buy. Just calculate your metapower and hp, and figure out what units  you should add. This can be extremely nice russia, germany, japan and USA.

This need a few Edits to be correct:
lets assume you have 2 CV + 4 ftr, + 2 DDs + 2 subs.   I will count the CV as 2 units.
For your fleet so far, you have 26 pips and 12 hp.
If you buy 6 Destroyers (D2= +12Def pips), you will have 38 pips and 18 hp.
If you buy 8 subs (D1= +8Def pips), you will have 34 pips hand 20 hp.

with Submarines:
342020 = 13600

with Destroyers:
381818 = 12312

But applying avg pips of stack to follow the formula almost to the letter, this give:

with Submarines:
(34/20)2020 = 34*20 = 680

with Destroyers:
(38/18)1818 = 38*18 = 684

And, considering Carrier being 1 unit for 2 hits, to apply this stack formula to the letter:
with Submarines:
(34/18)2020 = 755.6

with Destroyers:
(38/16)1818 = 769.5

So, in lasts 2 cases, you get a better defense with Destroyers compared to Subs purchase.
This contradict your initial thesis.

This rise a question: how consider the number of units compared to hits in this formula?

75 Cruisers Attack 3 vs 40 Battleships D4, 2 hits

Cruisers 225 pips, 75 hits vs BBs 160 pips and 80 hits

Cruisers
3* 75^2= 16875

Battleships
4* 80^2 = 25600,  too high!!!
Or
4* 40^2 = 6400,  too low!!!

But AACalc gives a pretty even match still win by Cruisers:
Overall %*: A. survives: 53.4% D. survives: 46.2% No one survives: 0.4%

Maybe the formula need this addition (1.618034) on hits or rolls for all 2 hits units
Battleships
*4 [(401.618034)^2] = 16755**
So, this seems to work.
However, IDK the derivative formula…

So, the complete Stack formula would be :
**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)] = Metapower**

For instance, comparing these 2 fleets on defense:
2 CV + 4 ftr, + 2 DDs + 10 subs
(16 hits + 2*1.618034)^2 * 34 pips/18 units = 698.9

2 CV + 4 ftr, + 8 DDs + 2 subs
(14 hits + 2*1.618034)^2 * 38 pips/16 units = 705.6

And this confirmed that adding DDs brings more defense metapower.

But not that much.
And this returns to the tricky Subs, DDs and planes triangle.
If attacker brings a lot of planes, Subs but no DDs, defending Subs will not protect the fleet core from air attack.

ENIGMA_Vann formula_Cost vs Odds_Roster charts_D6_D8_D12_D10.xls