Lanchester square tabletop theory

[chapter master 454]

I've heard numerous times about this lanchester square or something that is something like '3 units are 3 times as effective' or something however I can't see it too well. Now as someone who uses math-hammer only for slight things (frag missles and such) this seems silly, if my opponent can pop one he can pop 2 and he can certainly pop 3, target redundancy doesn't negate systematic annilation (Pop a target, move on, pop a target, move on, rinse and repeat) and while I've tryed 3 land raiders and 2 predators I have not seen this square work too well.

 

First case: 3 land raiders (one of each variant) should therefor be 3 times as effective according to this law, however as I stated this was met when all three were systematicly destroyed.

 

Second case: if 3 preds is 3 times as effective, how come my three were (a dakka and two combis) not as effective as they should be therefor the rule doesn't apply here ether.

 

not sure if I am just changing the variants is whats wrong but so far I haven't seen the rule kick in so why do I hear of it so much with tri-vindicators and tri-thunderfire cannons. Something isn't adding up so could someone please point out where this rule even came from and how it is applied and what evidence is supplied to support this rule of '3 units equals three times the power of the unit itself'

[minigun762]

not sure if I am just changing the variants is whats wrong but so far I haven't seen the rule kick in so why do I hear of it so much with tri-vindicators and tri-thunderfire cannons. Something isn't adding up so could someone please point out where this rule even came from and how it is applied and what evidence is supplied to support this rule of '3 units equals three times the power of the unit itself'

 

Here is the wikipedia article on the law, if you haven't read it yet.

http://en.wikipedia.org/wiki/Lanchester....27s_Square_Law

 

You'll notice that it does have some limitations, but in essence what its saying is that:

1 unit (often a vehicle in 40k) will take N resources to kill

2 of the same units will take NxN resources to kill

 

While its hard to see the actual math at work on the tabletop, the idea still holds up. Lets take a situation in a vaccum.

If you only take a single Land Raider and I have a single Multi-Melta Land Speeder, I have to commit a certain amount of resources towards killing it and you have a certain amount of resources to stop me.

Now if you have 2 Land Raiders and I have the same single MM Speeder, your proportionately much safer because its much more likely that you will be able to stop my single speeder before I can kill both of your Land Raiders. Since you have 2x the firepower and I have to kill 2x the units, you are 4x as durable.

 

Now you could argue that you're using more points then I am and you got to double your units while I stayed the same and you would be correct, but none of that means that the rule isn't appropriate or true. If I take a 2nd Speeder, the equation would again be balanced. If I took 3 extra Speeders, then the Land Raiders would be on the losing side of the equation (proportionately) because I have twice doubled up my firepower where you have only doubled yours.

 

See this comment on the wiki page:

It does not apply to whole armies, where tactical deployment means not all troops will be engaged all the time

This is a prime example of why the rule is hard to see on the table top as a whole. Variables like deployment, use of reserves, the composition of the rest of your army and terrain all complicate the situation.

 

For most people, the take away message is that of redundancy. It is usually proportionately harder to kill 2 of something then it it to kill 1 and the reserve is also true, it is proportionately easier to kill 1 of something when you have 2 of the counter unit.

[Deus de Mortalis]

It really has no practicality for 40k, because any information you can gleam from it is pretty obvious (or should be) to any 40k general worth his salt.

 

In the strictest sense of the law, it is saying that 11 marines are 1.21 times better than 10 marines, all else being equal (11x11 vs 10x10). In 40k however, there is a HUGE advantage to shooting first, which would more than make up for the perceived advantage from Lanchester's Law, because it violates one of the key assumptions. Also if you have a unit of 10 devastators, 4 with lascannons, and 6 with bolters, they will cream the same exact combat-squaded version of the squad because they can more easily take out the enemy heavy weapons doing the majority of the killing. In fact 40k violates all of the assumptions that gives the law any predictive value. Really the only place where it works out is in close combat between units of homogeneous composition fighting at the same initiative.

 

Basically what we can gleam from the law is that you want localized advantages of force in your games of 40k. If there are two squads of marines 18 inches away from each other, you would want to assault one with an overwhelming force rather than assault both at the same time.

 

For most people, the take away message is that of redundancy. It is usually proportionately harder to kill 2 of something then it it to kill 1 and the reserve is also true, it is proportionately easier to kill 1 of something when you have 2 of the counter unit.

 

I disagree on that point. The law deals with the relative concentration of forces in any one area of the battle that are able to engage each other. It isn't that 3 defilers are a whole lot harder to beat than 1 defiler, it is 3 units are a whole lot harder to beat than 1 unit, without respect for what those units are, if they are the same, or if they are completely different.

[minigun762]

For most people, the take away message is that of redundancy. It is usually proportionately harder to kill 2 of something then it it to kill 1 and the reserve is also true, it is proportionately easier to kill 1 of something when you have 2 of the counter unit.

 

I disagree on that point. The law deals with the relative concentration of forces in any one area of the battle that are able to engage each other. It isn't that 3 defilers are a whole lot harder to beat than 1 defiler, it is 3 units are a whole lot harder to beat than 1 unit, without respect for what those units are, if they are the same, or if they are completely different.

 

I agree and disagree with that point. By loading up on a particular type of unit, usually with a particular type of stat line or defensive bonus, you are hoping to overwhelm (either locally or as a whole) the opponent's ability to deal with that unit. Vehicles are the most common example because they are immune to small arms fire, which can severly limit what weapons may be used against them. High T models (Wraithlords) are another for the same reason.

 

Using your example, I would say that 3 Defilers in one location could be harder to kill if you can overwhelm their ability to deal with walkers (only 2 Meltaguns to counter for example) where as 1 Defiler, 1 Vindicator and 1 group of 10 Chaos Marines (all approximately the same point cost) might be easier to kill because the opponent has more options to use against them (Melta on Defiler, Kraks on Vindicator and Flamer/Bolters on CSM).

 

Of course now we're kind of taking the conversation in a different direction and talking about "spamming" which is what makes certain armies (150+ Ork Boyz hordes and 12+ AV12 vehicle IG armored companies) so difficult to beat.

[Deus de Mortalis]

I agree and disagree with that point. By loading up on a particular type of unit, usually with a particular type of stat line or defensive bonus, you are hoping to overwhelm (either locally or as a whole) the opponent's ability to deal with that unit. Vehicles are the most common example because they are immune to small arms fire, which can severly limit what weapons may be used against them. High T models (Wraithlords) are another for the same reason.

 

Using your example, I would say that 3 Defilers in one location could be harder to kill if you can overwhelm their ability to deal with walkers (only 2 Meltaguns to counter for example) where as 1 Defiler, 1 Vindicator and 1 group of 10 Chaos Marines (all approximately the same point cost) might be easier to kill because the opponent has more options to use against them (Melta on Defiler, Kraks on Vindicator and Flamer/Bolters on CSM).

 

Of course now we're kind of taking the conversation in a different direction and talking about "spamming" which is what makes certain armies (150+ Ork Boyz hordes and 12+ AV12 vehicle IG armored companies) so difficult to beat.

 

Your example isn't based on the square law though, it is based on your interpretation of how best to maximize the balance of power in your favor. There is also the problem that simply taking units doesn't make you work towards maximizing your gains with the square law. If you march 3 defilers up the center of the board along with the rest of your army, you are hoping that your army is the superior fighting force 1 on 1 and you aren't doing much to work Lanchester's law in your favor. Also in some cases 3 defilers are going to be more powerful and in other cases other stuff will be more powerful relative to the enemy force in that position. It is not about what units there are, it is about their power relative to the opponent's forces. Two whirlwinds are going to hurt a platoon of guardsmen, but 2 whirlwinds and a devastator squad are going to hurt them more, last longer, and possibly win against them by a margin greater than what a single devastator squad would be able to achieve. Also 30 scouts with CC weapons are going to be about even with 10 terminators, but those same 30 scouts are going to demolish a 5 man terminator squad with few casualties, and do the same thing to another 5 man squad of terminators because now the scouts have a great relative advantage even though in the end they end up fighting the same guys. It is an argument against combat squading (but far from making it a bad idea).

[chapter master 454]

Well the law does hold some credit if the whole thing is about duribility, my 2 raiders (Phobos and a redeemer) had gone through several matchs and while brutally wounded and hurt they were still active and blasting anything in range so duribility does increase. The problem I cans see is that with a game of random chance the law will rarely apply visually on the table unless conditions are met, I mean facing 12 lascannons from devastors and a further 6 from tacticals and a further 6 from sternguards then obviously I am going to lose my land raiders faster than I can put them on the table however if only one exists among heavy bolters then the law may appear somewhat.

 

Well anyway thanks for clearing this up for me, quite greatful that I now know what this thing is!

[Rogue]

If I can chip in, I think that Lanchester's sqaure law is simpler than it's being made out to be here.

 

In blunt terms, if one predator is useful, 2 predators operating in tandem are not twice as useful, but four times as useful. Three predators would be nine times as useful and so on.

 

In effect, your preds (or whatever) are doing twice as much damage, but also take twice as long to kill. Twice as much damage for twice as long means you cause four times as much damage. With three preds, it'd be three times as much damage for three times as long, for around nine times as much damage overall...

 

Imagine this really artificial scenario:

 

I have two tanks. You have four, but they're spread out and will fight as single units. Each is 100% intact.

My tanks engage one of your tanks. In an engagement, a single tank can inflict 50% damage in one minute. After one minute, your tank is dead (having taken 50% damage from each of my tanks, total of 100% damage), and mine are each at 75% (having manouvered to take half the incoming fire each, so the 50% damage you cause is split).

I engage your second tank. Again, I kill it, and you cause 50% damage, split two ways. My tanks are now each at 50%.

I engage your third tank. It dies, my tanks are now at 25% each.

I engage your fourth tank. Everyone dies.

 

Over the course of the engagements, my two tanks haven't just killed two of yours, they've killed four (my two tanks squared).

 

This maintains some relevance on the tabletop, where good manouvering, and good target selection can lead to a similar, overwhelming firepower, situation.

 

One example could be an entrenched tank with heavy weapon support (this kind of combined arms approach prevents the law operating as precisely as described above). If you wheel one tank out of cover each turn, you might nail the tank, but you'll probably get popped by the supporting heavy infantry. It might take two or three turns to destroy the enemy armour, costing you a tank a turn. On the other hand, if you move all your tanks out of cover, you'll almost certainly nail the enemy tank in a single turn, lose one tank to return fire, and move back into cover next turn. Same amount of damage caused to him, much less damage caused to you.

 

Hope that helps.

[Frosty the Pyro]

The square rule works by saying the offensive power time the defensive power equals actual power. the square rule assumes "damage" is evenly spread, and we all know thats not how it works. As an infantry example it assumes you dont remeove a single model of your 10 man squad of space marines untill it has taken all 10 unsaved wounds. We know this isnt how it works at all. 2 tanks are not 4 times stronger than one tank, but it IS more than twice as strong. A closer principle would be a reducing sum. thus 2 tanks would make 2+1=3 times the power, 3 tanks would be 3+2+1=6 times the power, 4 as 10 (4+3+2+1) and so on. This however also assumes that the offensive ability of the oposition remains constant, which is also hardly the trueth, if having more tanks means the enemy just brings more power to bear then your closer to a single rule (if they can kill both your tanks in one go then your 2 tanks are realy only twice as powerfull as one tank, as there is no survivabiilty increase). If having more tanks means you take out their anti-tank faster then you start getting closer to the square rule, or sometime even greater. In general though the reducing sum bit seams to be closer to what happens. Of course with the amount of chance, and the fact tanks (and most other models) esentialy work on a 1 life point system, means its fluctuates widely.