G40 VANN FORMULAS RESULTS

@Baron:

I tried to apply your formula to a special case.
For instance, the defensive picket made usually by Russia to prevent Germany’s blitzkrieg while retreating main force behind this front line.

Usually, you need to commit 1 ground unit, as much as possible the chespest: 1 infantry.

But your formula seems to show that it can be more cost effective to put 3 Infs, even if it costs 9 IPCs to inflict more casualty to the attacker.
At 1 or 2 units, it keeps the same ratio for the investment (1.25) but beginning with 3 units the stack get stronger per IPC invest  (2.00).
Often, the picket Inf brings no result except blocking but if you block and get 1 casualty or more, it is far better.

So, does this formula is showing a better use of unit in this tactictal retreat?

Simple answer is no, it does not. For two reasons, 1, your goal with the scirmishers is not to inflict dammage, but to prevent blitzing. So the purpose is different. And the other reason is covered below.

Longer answer is: The formula does only give the strength of the stack, you need a different formula to figure out what damage that will result in. If the stack will die anyways (like your example) it might be that adding the 2 extra inf not will inflict the needed 6 ipc of damage to the germans attacking it.

On an extra note:

@Baron:

But your formula seems to show that it can be more cost effective to put 3 Infs, even if it costs 9 IPCs to inflict more casualty to the attacker.
At 1 or 2 units, it keeps the same ratio for the investment (1.25) but beginning with 3 units the stack get stronger per IPC invest  (2.00).
Often, the picket Inf brings no result except blocking but if you block and get 1 casualty or more, it is far better.

It actually shows that a bigger stack is more costeffective than a smaller. So if you have 50 units, it it better to have them in 1 big stack, rather than 2 smaller. it is a more costeffective way of fighting :) But I guess everybody already knew that ;)

Thing about tanks costing 5 is that the side that wants to attack will just buy tanks.

I don’t understand why everyone still wants to debate this mess. First of all you are all way off course. His formula was based on Classic not on G40 so the numbers are all off to begin with. The 2 games are vastly different in almost all respects so even if the costs and values were the same the numbers would still be bogus. Throw in the others here who want to change the values of units instead of debating the formula which was based on a game which none of you are talking about in the first place and based on OOB values to begin with. So…WHAT THE SAM HELL ARE ALL OF YOU WASTING YOUR TIME HERE FOR?!?

Put your stupid calculators away and learn how to play the game using your intelligence and creativity. This game was created to be played between people, not machines. If you want to talk about changing the values then go to the House Rules section where there are already several threads to discuss that.

This game is actually a lot of fun to play. Try not to forget that while you are staring at your calculators.

carrier and bomber spam kind of reduces the fun for me

@GeneralHandGrenade:

This game is actually a lot of fun to play. Try not to forget that while you are staring at your calculators.

Still trying to come to grips with the fact that I agree with a Canadian on something…

@GeneralHandGrenade:

I don’t understand why everyone still wants to debate this mess. First of all you are all way off course. His formula was based on Classic not on G40 so the numbers are all off to begin with. The 2 games are vastly different in almost all respects so even if the costs and values were the same the numbers would still be bogus. Throw in the others here who want to change the values of units instead of debating the formula which was based on a game which none of you are talking about in the first place and based on OOB values to begin with. So…WHAT THE SAM HELL ARE ALL OF YOU WASTING YOUR TIME HERE FOR?!?

Put your stupid calculators away and learn how to play the game using your intelligence and creativity. This game was created to be played between people, not machines. If you want to talk about changing the values then go to the House Rules section where there are already several threads to discuss that.

This game is actually a lot of fun to play. Try not to forget that while you are staring at your calculators.

I’ve stressed this in another thread.

@Kreuzfeld:

@Baron:

I tried to apply your formula to a special case.
For instance, the defensive picket made usually by Russia to prevent Germany’s blitzkrieg while retreating main force behind this front line.

Usually, you need to commit 1 ground unit, as much as possible the cheapest: 1 infantry.

But your formula seems to show that it can be more cost effective to put 3 Infs, even if it costs 9 IPCs to inflict more casualty to the attacker.
At 1 or 2 units, it keeps the same ratio for the investment (1.25) but beginning with 3 units the stack get stronger per IPC invest  (2.00).
Often, the picket Inf brings no result except blocking but if you block and get 1 casualty or more, it is far better.

So, does this formula is showing a better use of unit in this tactictal retreat?

Simple answer is no, it does not. For two reasons, 1, your goal with the scirmishers is not to inflict dammage, but to prevent blitzing. So the purpose is different. And the other reason is covered below.

Longer answer is: The formula does only give the strength of the stack, you need a different formula to figure out what damage that will result in. If the stack will die anyways (like your example) it might be that adding the 2 extra inf not will inflict the needed 6 ipc of damage to the germans attacking it.

On an extra note:

@Baron:

But your formula seems to show that it can be more cost effective to put 3 Infs, even if it costs 9 IPCs to inflict more casualty to the attacker.
At 1 or 2 units, it keeps the same ratio for the investment (1.25) but beginning with 3 units the stack get stronger per IPC invest  (2.00).
Often, the picket Inf brings no result except blocking but if you block and get 1 casualty or more, it is far better.

It actually shows that a bigger stack is more costeffective than a smaller. So if you have 50 units, it it better to have them in 1 big stack, rather than 2 smaller. it is a more costeffective way of fighting :) But I guess everybody already knew that ;)

I might widen my line of questioning then.
Simply put, your formula specific changes when reaching 3 Infantry (for 9 IPCs), like the start of an exponential curve (there is a square operation in the formula x^2), makes me wonder if there  is some circumstances in which a stronger picket of 3 Infs is more potent.

Probably if your totally outwhelmed, in any case your picket will only roll once, but if limited number of units are involved maybe there is a threshold of enemy units in which throwing 3 Infs get you more than a single roll on defense and you get the opportunity to make more casualty on enemy before the decisive battle.

Is it possible?

Why are you guys still discussing this? Didnt we already decide that we aren’t interested? Or am I nuts?

After showing many shortcomings on Vann formula, Kreutzfeld compared with his own formula (which can be more easily use on game without using AACalc, to measure two stacks strength).

Then I tried to showed or validate some tactical combat (for a different optimal tactical retreat) implications from his formula which cannot be implied by Vann formula either.

If someone said he does not want to talk about pratical impact of measuring combat values, it does not mean everyone is clueless. And I cannot see why it was not a correct line to investigate an idea.
Aside some different combats values thrown in (which may condamned this thread to HR even if this was not OP intent) because Vann formula is still able (or unable) to point a few obsolete or weak units in OOB roster.

I would never have think about a possible different way of optimizing a tactical retreat if this specific comparison about mathematical formulas had not been push forward.

And don’t tell me TripleA players never check odds on BattleCalc before sending their final moves in PBF.
:-D

@Baron:

I might widen my line of questioning then.
Simply put, your formula specific changes when reaching 3 Infantry (for 9 IPCs), like the start of an exponential curve (there is a square operation in the formula x^2), makes me wonder if there  is some circumstances in which a stronger picket of 3 Infs is more potent.

Probably if your totally outwhelmed, in any case your picket will only roll once, but if limited number of units are involved maybe there is a threshold of enemy units in which throwing 3 Infs get you more than a single roll on defense and you get the opportunity to make more casualty on enemy before the decisive battle.

Is it possible?

I guess it would be possible to construct some examples where stronger pickets might be better. But it would require some limitations on your opponent.

If we assume that germany and ussr are picketing each other on the east front. And we assume that they are both strong enough to deadzone the area between their main stackes. And we also assume that they have 3 or 4 areas where then can scirmish. And we also assume that most of the short range luftwaffe are tied up west and cant participate, only the two german bombers can, and 1-2 fighters. If you then put out 3 inf in each area, germany would have to send in at least 3 inf + bomber to reliably take the terr. So, if you are able to picket back with 3 inf and ussr plane, you might be able to force an increase in the losses to scirmishing on the east front. germany would very quickly run out of inf, and would have to use mechs instead. This could be very favourable for the soviet. Therefore the german might go for only attacking 2 of the terrs with 2 planes and 2 infs instead of picketing all 4.  But then, you are preventing the german from getting income from 2 of the terrs and you only have to pay with 1 extra inf in each of the two areas that does get hit. So you can picket right back with the red air force and some infs.

So in this very spesific situation, you might want to picket with 3 infs. However, if germany have 2 planes for each terr (so 8 in total), instead of 1 for each, then this picketing strat is getting worse.

Others might be able to think of other scenarios where having more troops scirmishing is beneficial.

This thread is still here also !!!

I also see VANN DANN still can go on site here but is banned from speaking.

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?

Thats why you use the Larrymarx formula to solve these issues.

@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?

@Imperious:

Thats why you use the Larrymarx formula to solve these issues.

For now, this is Kreuzfeld formula that I’m applying here.

Someday, there maybe a way to use both but for now it is two different beasts.

And the Baron-Larrymarx formula does not help, not accurate or too many calculations to get to something.

Kreuzfeld formula is simpler for a F-2-F game, and few numbers.

Kreuzfeld formula.

As long as its not named after a member… better.

@Imperious:

Kreuzfeld formula.

As long as its not named after a member… better.

For now, it is the case all Vann, Kreuzfeld, Baron and Larrymarx are members.

If you have an idea for a more suitable name for Baron-Larrymarx, I’m opened to it, as long as others agree.

I cannot deny Vann, Larrymarx then me filiation (or line of succession) to this Baron-Larrymarx formula.
But Kreuzfeld bring his own much earlier. And it is a different beast, for a different purpose.

You guys are forgetting something important: SIZE MATTERS

The back and forth nature of A&A battles means that very slight advantages will snowball into huge advantages when you scale up the number of units. To demonstrate, I pulled up a battle calculator and tried throwing infantry against half their numbers in tanks (stacks with equivalent values).

Infantry     Tanks       Attacker wins     Avg swing    Total value     % swing
   2               1            55%                   0.1                12               0.8
   4               2            60%                   1.2                24               5.0
   8               4            66%                   4.2                48               8.8
 16               8            74%                  11.6               96              12.1
 32             16            83%                  29.4              192              15.3
 64             32            92%                  68.3              384              17.8
128             64            98%                 147.5              768             19.2

You start with what is nearly a fair fight at the beginning and wind up with an overwhelming advantage as you draw out the battle and increase the number of turns over which the advantage is played out. In contrast, if the battles are only for one round, the % swing rises only to 4.166% (1/24) and then stays there no matter how large the stacks are.

This, combined with my earlier assertion that units are almost always better in mixtures means we really should be looking at how to determine the relative worth of stacks and mixtures of units as opposed to individual units. Units mean nothing by themselves - they always must be analyzed in context.

I propose analyzing different mixtures and quantities of units to determine their worth in attacking vs. stacks of units we already know to be strong on defense - infantry, destroyers, fighters and carriers (because they carry fighters). A compete analysis will increase the size of the defender’s stack if the attacking units are slow because the defender will “see it coming” and have more time to turtle up.

@larrymarx:

The back and forth nature of A&A battles means that very slight advantages will snowball into huge advantages when you scale up the number of units.

And speaking of formulas, the point mentioned by Larrymarx ties in nicely with Lanchester’s Square Law, a differential equation which models the attrition effects of modern combat involving long-range weapons.  As I understand it, the equation basically states that the rate of attrition is proportional to the square of the number of weapons which are shooting, and therefore that any numerical advantage by one side will increase exponentially as the battle progresses.

Yep Marc,
The original thread started with this Lanchester’s Square Law, then found a specific formula for stacks of A&A units.

I made it on AACalc then I revised numbers by applying this formula derived from above Stack formula:
√(P2 / P1) = N1 / N2

To get break even (meaning 50% vs 50% odds) number of unit ratio for different  Power relative to each other:

Power  1
vs 2 = 14 units :10 units  (140:99)
vs 3 = 19:11 (189:109)
vs 4 = 2:1

Power 2
vs 1 = 10:14  (99:140)
vs 3 = 11:9 (109:89)
vs 4 = 14:10 (140:99)

Power 3
vs 1 = 11:19 (109:189)
vs 2 = 9:11 (89:109)
vs 4 = 15:13 (149:129)

Power  4
vs 1 = 1:2
vs 2 = 10:14 (99:140)
vs 3 = 13:15 (129:149)

So, if you want to see if your on the right side, find the average Power and compare your number  of units with the ratio above.

For example, you have 3 Tank and 1 Inf vs 2 Inf 1 Art.
Avg less than 3 compared to 2.
4 units vs 3 units 4:3

The table for 3 vs 2 say 9:11, so, if you drop to 2 tanks vs 3 units during combat resolution, you know  you are below 50% odds of survival. You may then retreat, or try your luck.