Quick and dirty battle calculations

[Jennifer]

I’ve found that generally speaking if I have 1 or 2 infantry more then the defender and a superior force of tanks and planes the attacker will win.

I’m NOT saying equal forces, which is what I think you are saying I am intending.

For instance, if you have 15 infantry, 7 tanks, 5 fighters, bomber and are attacking 14 infantry, 4 armor, 3 fighters you have the advantage, even if the punch is close.    The punch only has a difference of 3 in attacker’s favor, but the odds of the entire battle are overwhelmingly in the attacker’s favor!  97% of the time the attacker should win that engagement.

Sure the defending infantry and fighters are stronger than their attacking counter parts, but each hit makes a larger impact on their next round’s ability to defend then each hit against the attacker does.

But if you don’t have the calculator, how would you see this?  Well, as I said, make sure you have almost the same or more infantry as the defender and you out number him in tanks and planes and odds are, you’ll win the engagement.  After all, if you just glanced at the numbers, without realizing the underlying impact of how the dynamic of the battle will probably shift in subsequent rounds, you may think the attack isn’t wise.  And if you were desperate for units it might not be, since odds are you’ll be reduced to 5 tanks, 5 fighters and a bomber.  That’s where the economic aspects of the game come into play and that’s a different discussion.

But as a rule of thumb, it seems to work out well that if you have more or equal infantry to the defender, you have more tanks and more planes than the defender, then you will win the engagement.  Margin is flexible, after all, if you have double the infantry or triple the tanks then you would expect a larger margin then if you only had 20% more.

[Crazy Ivan]

:-)
Quick and dirty;
I look at how many tanks and planes I have attacking and divide by 3. that is how many hits I predict they will make.
Infantry; divide by 10 if attacking, by 6 if defending, (Of course if Artillary and matching Inf are in the battle, divide by 6 when in the attack).
  I pretty much do this in my head, (which at my age may not be a good thing anymore) but it seems to come out pretty close to the end results after all the die have been thrown, hmm yes, even those that went across the room! :-P

[Jennifer]

Yea, but Ivan, that’s LL estimating. :P  I am just saying, look at the stacks, if you have the same or more infantry and you out number his tanks and planes, then odds are you will win as the attacker.  Otherwise, you probably will lose.  Requires no counting, no arithmetic or any calculators.

There’s no counting because being off by one or two isn’t a factor.  If he has 7 stacks of 9 infantry and you know you have 200 infantry available, you don’t have to count. :P  If he has 7 stacks of infantry nad you only have 5 stacks, then you don’t have to count either, you know you’re going to get wholloped good.

[Magister]

OK. Any hints to quick-and-dirtify necessary German coastal defences ?
If needed, I’ll get from my archives some sets of numbers to make your heads spin… each area with different numbers of planes that can reach for each side, tanks that can or cannot pour through breach (depending on whether German counterattack seals EEU or not), two levels of US threat to WEU (‘normal’ with one set of transports, or double if disrupting the shuck) etc. etc.

[Jennifer]

Have more infantry then America and England can possibly bring to attack, make sure you have an AA Gun present and try to keep your fighters in the territory most likely to be attacked since your armor can’t attack Karelia from W. Europe.

[HolKann]

as much inf as this easy formula: # defending inf = attacking land units + attacking air units + BB attacks + 1/2/3, depending on how safe you wanna play), complemented by an AA ofcourse. Every 2 ftr in defense allow you to reduce the inf stack by roughly 3.

[Jennifer]

Well, a little less, Holkann, because the English and American forces cannot attack together, so you can break up their hard hitting units, I think.

[Magister]

@HolKann:

as much inf as this easy formula: # defending inf = attacking land units + attacking air units + BB attacks + 1/2/3, depending on how safe you wanna play), complemented by an AA ofcourse. Every 2 ftr in defense allow you to reduce the inf stack by roughly 3.

Thanks, this is roughly OK to the safe side for ONE power threatening (since one can assume landings use 50% inf and 50% arty/tanks). I’d apply it, say to defend Italy vs US alone.
For TWO powers in 1-2 it ignores the major multi-attacker’s disadvantage - so it’s MUCH “too safe”, so it foregoes the chance to hold more land still safely enough. Two equal forces need 1.4x defense, not 2x. If forces are unequal, it’s biased towards the larger force.
And if some landing threats combine with an already existing land force which is inf-heavier (Allied Karelia+landing to German EEU) ?

It’s understandable if I try to hold WEU, Germany and EEU as long as feasible without excessive risk…

Then such calculations give the 50% midpoint, which may be deterrent enough for marginal landings (say two-wave WEU defended only by lots of inf; no planes to be caught there). But for Germany one needs 1% to 10% at most. How to conceive of such safety margins ‘quick-and-dirty’ without getting to gross excesses of forces (say 0.01% for Germany to fall) increasing risks elsewhere ?

[HolKann]

You know you’re asking to calculate something complex with simple methods. If you want a safety margin between 1 and 10%, you’ll need a calculator, there’s no other way; there are too many variables to make a simple rule with such precision.
Btw, the formula was indeed for a ±40% margin against one attacker. For double attackers: guess what you’ll have left after the first attack and detract that from the formula. If you want to be safer, throw in more inf, it’s the only simple way. Nobody can tell you how many you would need exactly, so just throw in as many as you think needed +1. That one inf won’t make or break the game.

[Guest]

Quick battle calculation (if not already covered):

Total Attacker “attack” points + number of units = a number
Total Defender “defense” points + number of units = another number.

If one of those numbers if more than 20% greater than the other, that side is the likely winner.  When it gets over 50% greater it is a “safe” battle.

To calculate the points:

of units times what you need to roll to hit with it.

Example:
Attacking with 10 INF, 2 ART, 3 ARM, 2 FIG
Defending with 14 INF, 1 ART, 4 ARM

Attacker points is (8x1)+(4x2)+(5x3)  8+8+15 = 31
Defender points is (15x2)+(4x3)        30+12  =  42
Then add the number of units present to each
31+17=48 for attacker
42+19=61 for defender

Checking against a sim, the odds for the battle are:
Sim concurs that attacker has only a 15% chance to win that fight.

[Trusty Sapper]

Thankyou all, esp Magister and ncsswitch.
I’ll run your two methods through a dozen or so simulations and see which does best
Trusty

[Mazer Rackham]

Hey TS.

There is no accurate quick and dirty method, but there are several components you should look at.

1. Count - How many units on each side.  This is the most important metric generally speaking.

2. Punch - As you mentioned, add up the hits-on values (divide by six for expected hits).

3. Skew - The balance within a force that has lower hits-on values protecting higher hits-on values.

Consider this fight: 10inf 10tnk vs. 20 inf.

Count: oCount = 20, dCount = 20
Punch: oPunch = 40, dPunch = 40

So counts and punches are equal.  But the 10inf 10tnk will annhilate the 20inf due to skew (72% win for attacker).  Early in combat, the attacker is losing 1’s while the defender is losing 2’s.

Any quick and dirty method that doesn’t take skew into account won’t be accurate.

Some sample battles for you to look at:
The Baltic UK1 - Run the battle with 2ftr 1bmr vs 1tra 2sub 1des.  Then add a sub or tra for the Germans and watch what happens.  That battle can teach you a lot about tactics (force composition).

Frindo UK1 - Run 3inf 1ftr vs. 2inf 1ftr.  Add an inf or two to watch the changes.

Holler if you want more.

Peace

[uffishbongo]

Skew is an important concept, but unfortunately, it’s hard to quantify.

The most accurate battle-predicting statistic that I know of is to add up your starting punch, plus your punch after taking 1 hit, plus your punch after taking 2 hits, etc, all the way down to when your force is wiped out.  For instance, if you have 2 inf 2 tanks attacking this statistic would be 8+7+6+3 = 24; for 4 inf defending it would be 8+6+4+2=20.  This statistic shows the advantage of skew.  Also, it can account for attacking transports and/or the “free” hit on battleships; for example, an attacking force of 1 BB 1 tran would have 4+4+4=12.  Unfortunately this takes a while to calculate, especially for medium- to large-sized forces.

If there’s a faster way to calculate skew, I’m not aware of it (but would love to be!)  Punch and count can be calculated much faster.  Based on these, the most accurate predictor comes from multiplying punch times count.  Punch times count tends to be a pretty good predictor unless the forces are highly skewed; for unskewed to moderately skewed forces it will pretty much always tell you who’s favored.  In most situations the way that I account for skew is just by noting that it’s there and mentally saying “ok, this side is actually a little better than the punch and count would indicate”.

Then of course you can always do the expected-outcome calculation where you run through a battle in your head, and for each round assume each side gets the expected number of hits, and see what happens.  The nice thing about this is that it does account for skew, plus you can do it reasonably fast.  Unfortunately the round-off errors can pile up, but it’s still a decent indicator overall.