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Hi everyone, this topic is about Force Fields. In this one, I use maths based on Lanchester's Square Law to determine how you should split the enemy army with your Force Fields. The assumption is that you have a set of Force Fields, with which you can divide the enemy army in two parts. The details are here (quite some math again):
+ Show Spoiler +
The final conclusion is the following: in ranged battles, assuming Lanchester's Square Law is useable, you should try to cut the army exactly in half, unless you can't defeat even half of the army. Then you should Force Field away as many units as you can kill with your army and kill them while losing all your army (although using Force Fields to disengage and safely retreat is a wiser option in real conditions). Regardless of wheter you win or lose, you will trade as if your army had been at least twice as strong as it actually was (aka Force Field good unit).
This result raises other interesting questions as well. What happens if you can divide the army in 3, 4, ..., n parts? Do you have to perfectly split the enemy army in 3, 4, ..., n equal parts? Will that make your army 3, 4, ..., n times as strong? (I personally think it should not be linear, rather 3!, 4!, ..., n! maybe?) It would definitely be an interesting research topic, but rather tedious; if some of you should be interested in examining it, I am curious about the results. 
Pdf format here.
Anyway, opinions, criticism, etc.?
Previous projects:
+ Show Spoiler +
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I think is flawed . sometimes you have mostly melee units ( zealots ) and if you cut a MMM army in half it will damage you more since after you kill half army your zealots are stuck and the terran army keeps full dpsíng .
You can win the first battle and lose the second one since your dps will drop . Forcefields are pretty neutral in mid-late game. You can rly win battles only if you try to hit a timing. but even then what good player would allow you to perfeclty ff his army ? zergs will surround your army and terrans will pickup army in medievak and drop behind forcefields ...
edit : the maths behind your logic is cool but has no practical application. just like pure maths in general 
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On August 26 2014 07:12 xsnac wrote:
I think is flawed . sometimes you have mostly melee units ( zealots ) and if you cut a MMM army in half it will damage you more since after you kill half army your zealots are stuck and the terran army keeps full dpsíng .
This calculation is for ranged vs. ranged battles, so your point is not valid here. It is still true, though, what you say about Zealots.
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On August 26 2014 07:17 Sholip wrote:Show nested quote +On August 26 2014 07:12 xsnac wrote:
I think is flawed . sometimes you have mostly melee units ( zealots ) and if you cut a MMM army in half it will damage you more since after you kill half army your zealots are stuck and the terran army keeps full dpsíng . This calculation is for ranged vs. ranged battles, so your point is not valid here. It is still true, though, what you say about Zealots.
Is in a perfect scenario . but vs what ?
Zerg will surround you.
Protoss is imunne to ff ( since colossus ) .
You wont fight eighter vs terran with pure range units or you lose too hard to heavy marauder-viking style .
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On August 26 2014 07:20 xsnac wrote:Show nested quote +On August 26 2014 07:17 Sholip wrote:On August 26 2014 07:12 xsnac wrote:
I think is flawed . sometimes you have mostly melee units ( zealots ) and if you cut a MMM army in half it will damage you more since after you kill half army your zealots are stuck and the terran army keeps full dpsíng . This calculation is for ranged vs. ranged battles, so your point is not valid here. It is still true, though, what you say about Zealots. Is in a perfect scenario . but vs what ? Zerg will surround you. Protoss is imunne to ff ( since colossus ) . You wont fight eighter vs terran with pure range units or you lose too hard to heavy marauder-viking style .
What about early fights in PvP, where protoss only has gateway units and immortals?
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hmmm you did a lot of effort but its no useful information and not applicable to real gaming, try to focus on more important topics, good luck
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On August 26 2014 07:20 xsnac wrote:Show nested quote +On August 26 2014 07:17 Sholip wrote:On August 26 2014 07:12 xsnac wrote:
I think is flawed . sometimes you have mostly melee units ( zealots ) and if you cut a MMM army in half it will damage you more since after you kill half army your zealots are stuck and the terran army keeps full dpsíng . This calculation is for ranged vs. ranged battles, so your point is not valid here. It is still true, though, what you say about Zealots. Is in a perfect scenario . but vs what ? Zerg will surround you. Protoss is imunne to ff ( since colossus ) . You wont fight eighter vs terran with pure range units or you lose too hard to heavy marauder-viking style .
I think you can force engagements vs. Zerg where you can FF their army in half. Particularly with 2 base all-ins like the Soultrain, you can attack the third base and force the Zerg to defend with mostly Roaches and lings (those are melee units, but very fast so they may fit into the model). Of course there is the possibility to get surrounded, but rather often Protoss players manage to win with similar strategies, so it's not impossible.
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I think many people take these informative threads too seriously.
Sholip is only trying to use mathematical models to determine optimal plays. These are only models, and its application would be limited in a real battle.
If Sholip tried to factor in every variable (each unit, terrain, etc.) the equation would be way too complex.
However, they still provide some insight when making in-game decisions.
On topic, it seems intuitive that cutting the army 50/50 would be the best use of FF in a big fight. However, if we add in zealots to the mix, ideally you would want to cut off a smaller chunk to let your zealots engage in some units. If you cut off a larger chunk, those zealots might just melt too quickly to be of much use.
edit: great post Sholip. I really liked the pheonix one. Prior to your post, I would do a back/forth micro with them, but I would still take damamge. Now I try to run an arc as big as possible before I back off. Lets me save a couple phoenix after small engagements. Great advice!
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I also would like to add, the title seems too instructional. Perhaps it should be changed to "Optimal use of forcefields in big engagements" or something of that nature.
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On August 26 2014 08:26 Jett.Jack.Alvir wrote:
I also would like to add, the title seems too instructional. Perhaps it should be changed to "Optimal use of forcefields in big engagements" or something of that nature.
Yes, please!
+ Show Spoiler [How to Use Force Fields] +1. Click on Sentry. 2. Hit "F" or click on Force Field icon ![[image loading]](http://wiki.teamliquid.net/starcraft/images2/9/90/Force_field.gif) 3. Click on map.
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On August 26 2014 08:15 Jett.Jack.Alvir wrote:
I think many people take these informative threads too seriously.
Sholip is only trying to use mathematical models to determine optimal plays. These are only models, and its application would be limited in a real battle.
If Sholip tried to factor in every variable (each unit, terrain, etc.) the equation would be way too complex.
However, they still provide some insight when making in-game decisions.
On topic, it seems intuitive that cutting the army 50/50 would be the best use of FF in a big fight. However, if we add in zealots to the mix, ideally you would want to cut off a smaller chunk to let your zealots engage in some units. If you cut off a larger chunk, those zealots might just melt too quickly to be of much use.
edit: great post Sholip. I really liked the pheonix one. Prior to your post, I would do a back/forth micro with them, but I would still take damamge. Now I try to run an arc as big as possible before I back off. Lets me save a couple phoenix after small engagements. Great advice!
The thing is, all the previous posts from Sholip were great because although they were highly theoretical, the situation they modeled were still close enough to in-game situations to really be helpful in your everyday games. Here, the hypothesis are simply too strong, what's being modeled is too far from any kind of "real" in-game situation. So it's very nice work (which I enjoyed a lot !), just not as helpful/useful as the previous threads I think. But thanks anyway Sholip, it's always interesting !
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Didn't read through everything but isn't it obvious that if you cut the enemy army in half, that during the fight you have twice the army as your opponent?
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The maths is sound. However, it looks like you've made the assumption that all units have the same range. This is largely an incorrect assumption and can greatly vary how you want to cut up the army.
As an example, if you've got colossus vs Hydra, you want to cut the WHOLE army away, as you're using range to your advantage. I'm not totally sure that can be done mathematically, as you can't just average out the range of your army.
Zealot colossus fights require most, if not all of the army to me forced TOWARDS you, as the Zealots act as another layer of forcefields (I know that you have said that you have deliberately not included Zealots in your calculations, but I'm using them as 0 range units and colossus as 9 range units, you still can not really average out the range to 4.5!).
In all, if you're doing stalker vs stalker engagements, this method will work, but outside of that, there are more optimal ways of splitting the army.
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known for 4 years that cut the army in 1/2 is the best (especially vs Z with roaches&hydras). "No risk" P players are trying rather 1/4 than 1/2. More than 1/2 is deadly for P.
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well it obviously depends on how confident you are winning the battle, how many FFs you have, and whether you're trying to buy time or just smash him. if i have 6 sentries with full energy i will lay 4-5 in front and allow my colli free shots first, then engage later.
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