I have two posts up about Lanchester's Laws and attrition modeling on my games blog (1,2). The third post is in the works, but life is not cooperating with my blogging schedule lately.

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Comment by Robert Cleary on August 5, 2010 at 8:35pm
Of course, as we have seen with events like the Battle of the Bulge the role from sync to async can change quickly.
Comment by Robert Cleary on August 5, 2010 at 8:29pm
As stated:
One of the references I gave (Perry) discusses what he calls the "fractal" attrition model, which is a very (VERY!) abstract representation of space and the ability of forces to move about and take advantage of that space, and this might be considered a type of asynchronous combat.

Gaining the advantage (the upper hand) would seem to be the goal of asynchronous warfare. It is highly facultative (I love that word) and represents the movement and alignment of those elements in the battle space with the objective of disrupting and dispersing the enemy forces. Synchronous would be those elements with a static set of goals whose job is to keep designated areas of the front stable while the real action is occurring somewhere else.
Comment by Dan Eastwood on August 5, 2010 at 3:46pm
I see what you are getting at with asynchronous combat, but I don't know that I could draw a line between synchronous and asynchronous. This would seems to depend on the scale of the game or simulation, and what is asynchronous at low-level/high-detail might be synchronous at a larger scale. I'll have to give this more thought.

One of the references I gave (Perry) discusses what he calls the "fractal" attrition model, which is a very (VERY!) abstract representation of space and the ability of forces to move about and take advantage of that space, and this might be considered a type of asynchronous combat. At least that's my interpretation of it (which is dangerous since I can't claim to fully understand it), and it ends up as another exponent in his equation. One of the pitfalls with this sort of model is that it tends to demonstrate the fact, but loses all the details of what it means. In your France 1940 example, the Germans might get a larger exponent than the French to represent their mobility advantage. Looking at it from the other "side" of the problem, I see the Germans have a larger exponent, but (with no other knowledge) I don't know why - mobility is only one factor that might result in the advantage.

More ... but maybe I'd better get back to work now. ;-)
Comment by Robert Cleary on August 4, 2010 at 9:39pm
As you have stated:
If you wanted your game to be very abstract you might remove those details from the game and instead build the exponents into a Combat Results Table. OR, you might leave the details in the game, and let the non-linear results develop naturally.
This may be out of left field but I always considered a battle to be made up of two fundamental behaviors: synchronous combat and asynchronous combat. Regarding your suggestion of creating an abstract CRT (which will host the combat-exponent value range), this may be a means of resolving synchronous battle results (e.g., WWI style trench warfare) while a more Object-Oriented approach would handle the asynchronous combat.

I threw a out a lot of terms, so I want to be clear that I consider synchronous warfare as those points of friction when two large forces are in contact and are applying pressure equally (like a cold and warm front on a weather map). My definition of asynchronous warfare is not confined to Guerrilla warfare but those aspects of battle in which one opponent attempts to gain the initiative and exploit the weakness of another and delivers the killing blow. What happened to France in 1940 would be a good example. On paper the belligerents could have bogged down into another static front (if the Germans had evenly distributed their forces). But, the Germans concentrated their mobile forces and executed a death blow to the French army by performing an excellent a asynchronous maneuver.

Also, my reference to Object-Oriented is not related to programming but to simply mean “less abstract”.

A bit long winded but I hope my points are clear.
Comment by Dan Eastwood on August 4, 2010 at 3:03pm
Hello Robert!

>Regarding your reference to "Guerrilla warfare: "...in setting such as Iraq and Afghanistan, it is much easier for insurgent to find US targets than is it for the US to find insurgent targets." I believe this supports the Square Law.

Agreed. That's why I stressed that Lanchester's Laws are NOT just a function of range, but of many factors.

>How that variance occurs will depend on a host of parameters (unit quality, supply, weather, etc). The goal for the attacker is to reach the magic number (2) while the defender is striving for (1).

You pretty much have it right. Just recall that these exponents are describing the results of combat arising from those parameters you describe, rather than values that can be assigned (at least, not in real life). If you wanted your game to be very abstract you might remove those details from the game and instead build the exponents into a Combat Results Table. OR, you might leave the details in the game, and let the non-linear results develop naturally.
Comment by Robert Cleary on August 3, 2010 at 8:44pm
Before I call it a night:

You state: "In application of Lanchester's Laws to historical data, it is generally found that some mix of the Linear and Squared Laws is the rule, not one or the other exclusively."

Such a concept could be applied to game design also. One idea I had some time ago was the use of "network" combat. For example: if two units attack the same enemy unit sequentially, the enemy would concentrate its defenses against the first, then against the second. This would result in a linear result which are handled by most wargames. If both attacking units work in perfect sync then the defending unit will equally split it's defenses resulting in a square law advantage for the attackers.

Now here is my idea: we do not live in a perfect world so the exponent of the combinded attack will vary from 1 to 2. How that variance occurs will depend on a host of parameters (unit quality, supply, weather, etc). The goal for the attacker is to reach the magic number (2) while the defender is striving for (1).

I have not yet put this to the test but maybe your articles will inspire my participation.
Comment by Robert Cleary on August 3, 2010 at 8:30pm
Regarding your reference to "Guerrilla warfare: "...in setting such as Iraq and Afghanistan, it is much easier for insurgent to find US targets than is it for the US to find insurgent targets." I believe this supports the Square Law. By carefully choosing their targets, a guerrilla force will swarm exposed elements of a larger force and render devastating results.
Comment by Robert Cleary on August 3, 2010 at 8:20pm
Hello Dan,

Just came upon your posts on attrition modeling. Thanks in advance for your work. I'll read through them and post any comments that may come to mind.

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