Simple Combat – Lanchester's Linear Law

Sholip

Hungary422 Posts

August 18 2014 18:01 GMT

Hi everyone! This topic is about a very simple combat model, which is called Lanchester's Linear Law. I've actually been quite curious about the existence of a formula that could describe the result of an engagement in Starcraft II, so I decided to examine its possible applications to the game. Detailed description below:

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TL;DR: If two homogeneous armies engage so that only a certain amount of units can attack at a time on both sides, e. g. in a choke point, then the outcome of the battle is decided by the armies' size multiplied by their relative unit strength multiplied by the number of units that can attack at a time. Whichever army has this value higher, wins the fight. Hence it is called the army's strength.
This theory works fairly well in real conditions as well.
More about Lanchester's Laws on Wikipedia.

Available in pdf format here.

As always, feedback is appreciated!

P.S. A post on Lanchester's Square Law coming soon.

Previous projects:
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Imbalanced Hatcheries
The Effects of Worker Pairing
Perfect Micro with Phonixes
Floating to the Gold Base

Socup

190 Posts

August 18 2014 18:48 GMT

In other words, have a larger force engage a smaller force, engage a force that has to go through a choke while you are spread out so more of your force can attack at once.

hellokitty[hk]

United States1309 Posts

August 18 2014 18:50 GMT

Aka force fields good unit.

GDI

United States69 Posts

August 18 2014 19:03 GMT

Could you imagine someone pausing the game before every fight to do this formula?

Grumbels

Netherlands7031 Posts

August 18 2014 19:06 GMT

You should do marines vs zerglings and how ranged units scale better than melee ones.

loft

United States344 Posts

August 18 2014 19:19 GMT

On August 19 2014 04:06 Grumbels wrote:
You should do marines vs zerglings and how ranged units scale better than melee ones.

DPS Density... cause marines can clump up so well in tight spaces compared to other units (Tanks, roaches, stalkers)

Or ... area DPS... not sure what to call it.

linuxguru1

110 Posts

August 18 2014 19:26 GMT

On August 19 2014 04:03 GDI wrote:
Could you imagine someone pausing the game before every fight to do this formula?

Sorry to step on any dreams but, there are only 3 pauses allowed per player per game.

Nerski

United States1095 Posts

August 18 2014 23:19 GMT

Stuff like this is interesting to read, just from a if your a thought kind of person.

Though what's really impressive to me and what makes top players top players, is they've played enough and had enough experince that regardless of these formula they instinctively know the probable outcome without the math. Even knowing that outcome they can find ways to overcome small deficits in that math through micro to turn what should be an engagement where say 2 zealots survive, into an engagement where 2 zerglings survive instead.

It's stuff like this that at times can make any game an amazing spectator sport. Also why I frown face units that take the player out of the driver seat and give way to pure math vs math battles.

Master of DalK

Canada1801 Posts

August 18 2014 23:21 GMT

I'm loving all the math that you've been putting together. I'm making sure to try and keep a note of these for when I cast :3

vult

United States9400 Posts

August 18 2014 23:24 GMT

#10

Wow cool research! Thanks for all the hard work you do!

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