SOME VANN FORMULAS REVEALED

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.

http://www.axisandallies.org/forums/index.php?topic=40290.msg1684908#msg1684908

And apply it to price units according to their strength. √((P100)/(S6))=C

I did not get through as well as you put:  √((P100)/(S6))=Cost

It was more a matter of trials with higher and lower costs to determine designer’s right price POV:

@Baron:

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 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:

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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.

@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.

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

It is a different formula : avgPN^2 compared to P^2N

Now, which one is more accurate?

3 Infs D2 23^2= 18 compared to 2^23= 12

11 A2 vs 9 D3 gives almost 50%-50%

11^22 vs 9^23
242 vs 243

OR

112^2 vs 93^2
44 vs 81

I think you put the square on the wrong figure…

The Larrymarx formula is more accurate of course. Lets use that.

Baron, how did you get the 1.61 factor in your formula that takes into account number of hits?

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)

Also I have a question, how come for combined units you take the average value for example your carrier example, I would make the power value 10 on defense (8 for fighters +2 for carrier), but instead you took the average (8+2)/2=5. Same with the cost, you went with avg between 16 and 20 (18) but I would calculate hte value for a unit like this:

OOB CV with double fighters
Cost: 36
Power (defense): 10
Hits: 4

I get value of 1.63 which makes sense, it’s better than the DD.

I also have doubts on how we can use these formulas because they state that two infantry are better than a tank (both on offense OOB), not taking into account movement which is wrong according to AACALC

Do you use a A2 D2 C6 Submarine?

How can you get 1.5 for surprise strike?

2.5 maybe… 3…

The formula is 36*…
Not same as yours

A Battleship A6 D6, 2 hits, which always hit the mark what is the point?

nobody uses Vann anymore they use the Larrymarx formula :roll:

@Dauvio:

I MADE A MISTAKE ON THE FIRST FORMULA PEOPLE. IT SHOULD BE THIS.

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 N^2*P=S
And just for fun you can try these formulas also. S/N^2=P. √(S/P)=N
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.

Knowing this, does it changed the way you use blocker or picket Infantry?

Punch formula ? for 3 Inf+1 Fg A3+A3 A6, 4 units =10?  vs 3 Infs D6, 3 hits = 9

4^21.5 = 24   vs 3^22 = 18

The second formula seems to show a clear advantage for attacker, as seems the case.

AACalc:

Overall %*: A. survives: 72.1% D. survives: 23.3% No one survives: 4.6%

1 Fg 2 Infs A5 vs 2 Inf D4

3^21.67 = 15   vs 2^22 = 8, ratio 15: 8 or 1.875 : 1

Less than before but better on Calc…
A. survives: 80.8% D. survives: 13.8% No one survives: 5.4%
But it is working as a fight to death.
Which would not be the case for exchanging 1 TT.

See this other thread:
@Baron:

So, as a rule of thumb, if the enemy can bring 2 aircrafts in addition to the same number of Infantry picket, then you are toasted. Right?

2 Fgs & 3 Infs^2 * A9/5 = 25*1.8 = 45

3 Infs^2 * D2 = 18

It is more than double value of picket stack.
45 vs 18 = 5 : 2 ratio

But, if there is only 1 additional plane in attack, it is workable for defender?
(1A3+3A1)^2 *A6/4 = 16 * 1.5 = 24

24 vs 18 = 4 : 3 ratio

So, whenever the attacker get only 4:3 ratio or less, the defender should try it.

Is it a right way to apply your formula?

Here we go again.

I really wish this would die out I’m sick of seeing it pasted everywhere

@generalTrible:

I really wish this would die out I’m sick of seeing it pasted everywhere

contribute to the discussion or just leave the thread.

@generalTrible:

I really wish this would die out I’m sick of seeing it pasted everywhere

In addition, the moderator Panther, thanks to him, deals with this issue by regrouping all threads in this sub-forum.

Vann was new conscript and spammed similar posts and PM everywhere, and he got a full load of negative reactions, of course. But, I think he learned the lesson.

Aside from the messenger, the message was still relevant. It get to underlying maths relations between units and the A&A dice combat process with hit and value points. Before the code was plainly revealed the only way to figure was on AACalc and just between 2 units.

This give the strength to cost of units on the same scale basis.
Now, to what extent this can help the decision process in a game, that is for Vann to explain, since he pretends that this changed his way of playing the Classic game.

Sorry for you, but these threads are in the right place now and maybe tell more than meets the eyes.

@Dauvio:

I MADE A MISTAKE ON THE FIRST FORMULA PEOPLE. IT SHOULD BE THIS.

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 N^2*P=S
And just for fun you can try these formulas also. S/N^2=P. √(S/P)=N
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.

@Genghis:

I also have doubts on how we can use these formulas because they state that two infantry are better than a tank (both on offense OOB), not taking into account movement which is wrong according to AACALC

The Vann or Baron-Larrymarx formulas only tell that on same IPCs basis, buying 2 Infs (4.00) will give better odds on AACalc than 1 Tank (3.00).

Vann, you need to explain how it can guide purchasing mix of units like:
        Baron-Larrymarx                     PUNCH           STACK formula (Kreuzfeld & Vann, quote and link above)
4 Infs 44.00 / 8.00 = 16.00 / 32.00       A4 D8  4 hits     4^21= 16  /   4^22= 32
3 Artillery 34.50 = 13.50                       A6 D6   3 hits     3^22= 18  /   3^22= 18
2 Tanks 23.00 = 6.00                            A6 D6   2 hits     2^23= 12  /   2^23= 12
1 Tk 3.00 & 2 Infs 24.00=11.00/19.00    A5 D7  3 hits    3^21.67= 15 / 3^22.33= 21

The Stack formula gives the right strength of each mix.
Much accurate than both Punch and Baron-Larrymarx (which is misleading for Inf vs Artillery, if you multiply by number of units).

Vann, does it requires to calculate the average number of all units purchase with Baron_Larrymarx?
    Baron-Larrymarx                     PUNCH           STACK formula (Kreuzfeld & Vann, quote and link above)
4 Infs 44.00/4= 4.00 / 8.00                 A4 D8  4 hits     4^21= 16  /   4^22= 32
3 Artillery 34.50/3 = 4.50                    A6 D6   3 hits     3^22= 18  /   3^22= 18
2 Tanks 23.00/2 = 3.00                       A6 D6   2 hits     2^23= 12  /   2^23= 12
1 Tk & 2 Infs (3.00+24.00)/3 = 3.67    A5 D7  3 hits    3^21.67= 15 / 3^22.33= 21

This say the best attack will be 4.50 with 3 Artillery followed by 4 Infantry 4.00 then mixed group.

First example, if I buy 1 1942.2 Carrier A1 D2, 1 hit (0.184 / 0.367) and 2 Fgs (1.08 / 1.44)
So Offence would give (0.184 +1.08+1.08)/3 = 0.78
and Defence would give (0.367+1.44+1.44) = 1.08

But this is dubious for Carrier…

Another example, if I buy 1 G40 Carrier (0 / 0.736) and 2 Fgs (1.08 / 1.44)
So Offence would give (0+1.08+1.08)/3 = 0.72
and Defence would give (0.736+1.44+1.44) = 1.21

And this is dubious too for G40 Carrier because of 0 value but 2 hits …

Maybe, if it is only use to add up units to get an average of potential strength might be OK.

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