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Subject: Lanchester's Laws, force to space ratio, and tactical wargame scenarios rss

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Michael Dorosh
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Simple question to the forum - can anyone direct me to discussions of the application of Lanchester's Laws and the principles of force-to-space ratios to the design of tactical wargame scenarios?

Do the principles apply?

The reason for the question is I am wondering how map size and order of battle inter-relate and if there are valid scientific principles that could be applied. If so, have these been discussed in depth anywhere specifically at the "modern" (i.e. 1939-present) tactical level?

I know for example that Don Greenwood (IIRC) commented at least once about unrealistic "piece density" in Squad Leader scenarios. I think this is another way of saying that force to space ratios may have been modelled unrealistically in his opinion, at least some of the time. (His phrase was something like "squads and guns behind every bush and rock.")

I'm not necessarily thinking about discussions of typical company, battalion, regimental "frontages" as I've seen what the manuals say and have access to some textbooks and primers on basic tactics. I'm more interested in a more general scientfic study, such as:

http://en.wikipedia.org/wiki/Lanchester%27s_laws

and

http://en.wikipedia.org/wiki/Force_concentration

but with the notion of tactical scenarios specifically in mind. i.e. can one devise a formula for game map size, squads, tanks and come up with an optimal set of parameters? (I'd think no on the face of it, since you're excluding morale, terrain, weather, etc.)

Interested in your thoughts as well.
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Jur dj
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Trevor Dupuy is really keen on Lanchester, so you might check out his modelling work. I only have read Understanding War, but there might be a book in which he goes even deeper into the model and Lanchester equasions.

Not sure applying scientific principles will get you very far in what I see more as a craft or an art. I have the feeling that in practice there was a wide variation in densities. Not so much by choice as by accident and expedience. My approach would be to take an empirical approach and look at as many situations you are trying to recreate and derive realistic densities from them.

Maybe David Rowland. The Stress of Battle: Quantifying Human Performance in Combat can provide some of the answers you see.

So good luck!
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Confusion Under Fire
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I would also say no as you point out there are other factors to consider. Take a game like Combat Commander where the map size is fixed for every scenario yet the number of units can range from a single figure to 20 or so units per side. Because a scenario has less units does not make the scenario any better or worse, just different.
Most tactical wargames give the Russian nation more units so nationality is also something to consider.
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Seth Owen
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jurdj wrote:
Trevor Dupuy is really keen on Lanchester, so you might check out his modelling work. I only have read Understanding War, but there might be a book in which he goes even deeper into the model and Lanchester equasions.

Not sure applying scientific principles will get you very far in what I see more as a craft or an art. I have the feeling that in practice there was a wide variation in densities. Not so much by choice as by accident and expedience. My approach would be to take an empirical approach and look at as many situations you are trying to recreate and derive realistic densities from them.

Maybe David Rowland. The Stress of Battle: Quantifying Human Performance in Combat can provide some of the answers you see.

So good luck!


This is probably the most exhaustive attempt at this: http://www.amazon.com/Numbers-prediction-war-history-evaluat...
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Nick Hawkins
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In his (excellent) book 'Simulating War' Phil Sabine discusses the limitations of simple force ratio approaches like the 'Lancaster Law'. I think he's a little bit too dismissive but who am I to judge? I'm not a professor of military simulation techniques…

In short, 'Lancaster's Law' is a useful first order approximation but no more than that as it applies to an idealised steady state combat situation that seldom applies in real warfare.
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Michael Sommers
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Michael Dorosh wrote:
Simple question to the forum - can anyone direct me to discussions of the application of Lanchester's Laws and the principles of force-to-space ratios to the design of tactical wargame scenarios?

Have you checked Google Scholar? A search there of "force to space ratio lanchester" turns up some papers that may be appropriate. Interestingly, the same search on plain Google turns up this thread on the first page.
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Fred Thomas
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Pages 77-78 of Defense at Low Force Levels give the following thresholds for battles in central Europe.

max attack density (shoulder space) 10 km/division
max defense density (shoulder space) 15
hold density (above this the advance is slowed) 25
minimum density (below this the advance is faster) 40
breakthrough density (below this the attacker enters exploitation) 60

It seems like the best Lanchester fit is the logarithmic one, in which your losses are proportional to your own force's size and independent of the force ratio. (So your forces exponentially decay like radioactive isotopes whenever they are exposed to the enemy's lethality. Most CRTs are thus unrealistic.)

Putting the Art Before the Force

Lanchester's Square Law in Theory and Practice
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Matt Jolly
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wargamer55 wrote:
jurdj wrote:
Trevor Dupuy is really keen on Lanchester, so you might check out his modelling work. I only have read Understanding War, but there might be a book in which he goes even deeper into the model and Lanchester equasions...

...Maybe David Rowland. The Stress of Battle: Quantifying Human Performance in Combat can provide some of the answers you see.

So good luck!


This is probably the most exhaustive attempt at this: http://www.amazon.com/Numbers-prediction-war-history-evaluat...


All,

I think that most of Dupuy's work is a little dated, and I am also a bit unsighted as to some of the data he uses for his analysis of pre-WW2 conflict, but it's a good read, and reasonably well explained. I prefer http://www.amazon.com/Understanding-War-History-Theory-Comba... myself of Dupuy's work. But I still think that Rowlands' work is a bit more definitive. I have heard both men speak, and found myself convinced by both.

I would add though that force to space ratios (as opposed to force ratios) are less well covered by either, and I think must be better covered elsewhere, although off the top of my head I can't think where; Sabin mentions it, in Simulating War and Lost Battles.

You might find more stuff of interest here: http://www.ismor.com/archive.shtml too....

As for Lanchester's square and linear laws, I don't see these as separate, but rather mathematically the same equation with variable powers. In effect, the square law (and any power greater than 1) is suggesting that quantity is more important than quality, powers of less than 1 suggest quality is more important, and my guess is that different forces try to adopt tactics which push the powers in their direction; higher if you have a lot of men, lower if you have good kit.... but I can't find a reference for that at all.....

Cheers,

Matt

[Edit: Added ISMOR reference]
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Fred Thomas
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After some obsessive Google searching, I found a copy of Liddell Hart's 1960 article on the subject. His conclusions were that NATO required a tactical minimum density of one division per 40 km at the front and a strategic minimum total force ratio of 2 to 3.
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Pelle Nilsson
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These lines from that Rowland review were interesting:

Quote:
In defending against a 3:1 attack, the average rifleman will inflict 0.5 casualties on the attackers whereas a MG will inflict 4 casualties;

1 in 8 riflemen will cause 4 casualties, and the other 7 none;


Perhaps something to consider when making man-to-man combat games, even if the effect will average out in squad-based games.
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Michael Dorosh
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pelni wrote:
These lines from that Rowland review were interesting:

Quote:
In defending against a 3:1 attack, the average rifleman will inflict 0.5 casualties on the attackers whereas a MG will inflict 4 casualties;

1 in 8 riflemen will cause 4 casualties, and the other 7 none;


Perhaps something to consider when making man-to-man combat games, even if the effect will average out in squad-based games.


The Combat Mission games have a feature that track "kills" and it is interesting to see how the stats play out. While they do have 1:1 modelling, currently they only track stats for squad-sized units, and individual vehicles. I will pay more attention to this, but it does seem - realizing we are talking about a game and not reality - that battles often hinge on one or two well-placed/slash/lucky units that rack up more enemy casualties than their companions. I think I know what S.L.A. Marshall would have to say about the above - that 1 in 4 riflemen were "natural fighters" and more disposed to fight, but I wonder if there isn't something to suggest that in any fight, sometimes you just get one or two units into the right spot at the right time to do maximum damage for a fleeting second or two also.
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Martin McCleary
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this is correct.

We observed this phenomena repeatedly at the National Training Center during the Cold War; select tank crews would identify "key hole" positions and kill large numbers of the enemy. These were your "aces". Historically these are the Wittmans's, etc. They are few in number but have a high situation awareness and can use the terrain to maximum advantage. The air force has had the same phenomena since the beginning of air combat - the "ace". Per the book "The Ace Factor" 5% of the pilots do 40% of the killing if they survive their first 5 missions. So what we find is that in almost any environment land, sea, air, there are relatively small percentages that possess similar characteristics and are able to inflict large numbers of casualties. But you need numbers to generate depth in a formation as quantity has a quality all its own so to speak.

As to the force ratios I can't comment on the math but frankly everything is driven by terrain and you can only pile so much in one place. Units are given boundaries for a reason and they adjust to the ground at hand.

One of the things Combat Mission illustrates is that even if you have a platoon formation properly arrayed they can't all always see the same targets so the total fire generated by the unit is variable based on the ground. This is also compounded - in reality - by the ability of small unit leadership to get the elements in the right place and have them generate sufficient fire volume and accuracy.
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Lawrence Hung
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Quote:
that 1 in 4 riflemen were "natural fighters" and more disposed to fight


Quote:
5% of the pilots do 40% of the killing if they survive their first 5 missions


Can I project that what Ayn Rand said about the world is true then?
 
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Jur dj
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Lawrence Hung wrote:
Quote:
that 1 in 4 riflemen were "natural fighters" and more disposed to fight


Quote:
5% of the pilots do 40% of the killing if they survive their first 5 missions


Can I project that what Ayn Rand said about the world is true then?


You can always project... there's room enough for that in psychology

But maybe the 5% of pilots are not the same as the 25% of riflemen, or the 1% of entrepreneurs, or the 1% of artists.

And maybe not all the people who project Ayn Rand's ideas unto themselves are the ones she's talking about.

Maybe Ayn Rand wasn't part of any 1%?
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Martin - skill makes for 80-20 laws rather than bell curves around average performance (which chance without skill produces). Lancaster is hopeless, both the linear and the square, which were meant to reflect single man and firepower integration fighting respectively.

But all the idealizations and even training results overpredict combat effectiveness of common weapon systems, and drastically underpredict actual fighting times. The average weapon system never takes out an equal amount of enemy combat power over its entire service life, let alone doing so in one short tactical combat, as all such idealizations predict.

To see that this must be so, consider all combat power fielded by both sides in the whole war. Assume that one side is annihilated completely - more than actually happens - and that the fight is close enough that only a modest part of the winner's force survives as still effective - again the worst loss result that could ever actually happen. Then the forces taken out are nearly equal to but slightly less than total forces fielded. But the total forces fielded are the forces doing the taking out. Ergo, over both forces combined, the average whole war enemy force accounted for by one increment of combat power is less than the force inflicting it. Some weapons can do more than that only if others do less. For realistic losses over whole wars, a lot less - like around half.

This means that a rifleman who takes out one enemy rifleman is already a large outlier on the above average side of the scale - over the entire war.

Since industrial strength heavy weapons, using gobs of ammo each, account for most actual casualties, it is even more extreme than that for the maneuver arms up front, whom are first and foremost the targets of most of that industrial firepower.

Tactical games and training reinforce a myth of prowess which tries to reassure the men in such maneuver elements that they matter and can keep themselves safe as well as effective by fighting with skill and bravery. But this is, objectively, mostly a way to fool those men into running insane risks for meager returns in terms of any actual effect they typically have on the enemy. "Join the army and be a target - you will be shot or shelled within a week without ever seeing the enemy, let alone hurting him", is nit a great recruitment speech. But for the average poor bloody infantryman, it is accurate, with almost mathematical certainty.

FWIW...
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