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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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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.
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Aka force fields good unit.
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Could you imagine someone pausing the game before every fight to do this formula?
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You should do marines vs zerglings and how ranged units scale better than melee ones.
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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.
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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. 
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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.
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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
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Wow cool research! Thanks for all the hard work you do!
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EPT![[image loading]](http://i.imgur.com/W1XcG0F.jpg)
![[image loading]](http://i.imgur.com/N4H36KF.jpg)
![[image loading]](http://i.imgur.com/tvGbTeA.jpg)
