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Math on Widow Mines -- How STLife Dodged the Shots

Forum Index > StarCraft 2 Strategy 1 2 3 4 5 6 7 8 9 10 11 12 13 All
 
 Lone   March 19 2013 22:17. Posts 7
Profile # 
Hi everyone!

Sorry if this is in the wrong section, I fit it as best as I could. I'm pretty new here.
Anyways, I'm a regular over on the Bnet forums, and recently I posted some calculations I had on widow mines. However, being the Bnet forums, it was largely ignored, despite having significant merit and getting claim from the few people who did respond.

This is a primarily math based post, so bear with me.

Here's my transplanted post.

This little tidbit came to my attention during the recent MLG, and I decided to try to crunch some numbers in order to fully understand what it means in terms of gameplay.
I noticed in particular during Flash vs Life that Life was able to run through a number of Flash's minefields while only taking a few shots, far fewer than he should have.

The Theory:
Essentially, units are able to run through widow mine's attack radius without activating them due to the 1.5 second delay on the widow mine's activation.
After a unit leaves the mine's radius without activating the mine, the mine chooses a new target and attempts to "lock on" to that unit. It repeats until it finally locks on and fires.

So, widow mines have a lower "effective radius" than actual radius.

The Math:
I based my calculations on chord lengths using the following formula:
Chord Length = C = 2sqrt((r^2)-(d^2))
I then solved for d, getting:
d = sqrt((r^2)-(C/2)^2),

Which we can plug r=5 into, so my final formula became:

d = sqrt(25-(C/2)^2),
Where:
d = distance to Mine at closest point on chord (AKA Effective Radius)
C = unit speed*1.5.


Unit speed is calculated as range units traveled over 1 ingame second. So if you take your unit speed and multiply it by 1.5, you get the distance a unit can travel within a widow mine radius before activating the mine.

I bolded d because it's the most important, as we'll see soon.

For example, if we take Speedlings on creep, which have a C value of 9.163, we can do the following:
sqrt(25-(9.163/2)^2) = 2.002, or just 2.
This means that speedlings must travel on a chord which comes within 2 range of the widow mine in order to activate it before exiting the mine's range.

What this means in terms of Gameplay:
I hope that by now you're starting to understand what I'm getting at...

Based on the speed of the unit traveling over the mine, a mine has a radius in which the unit must pass in order for the mine to activate. I dubbed this radius "effective radius"

Let's again look at Zerglings, which have an above calculated d value of 2.
What that value means is that a speedling on creep, when traveling in a straight line through a mine's radius, must pass within 2 range of the mine in order to activate it.

And this is why Life was able to seemingly magically take Zero damage from mines. He likely realized, consciously or subconsciously, that if he attacked with the proper formation and using a move command, he could get mines to lock onto Zerglings which would not pass within 2 range of the burrowed mines. Once the first wave passed, the mines attempt to lock onto units based on proximity, so the chances of one locking onto a Zergling which just entered it's radius were near minimal. That led to a cascading "mine confusion" where they could not lock onto any unit for long enough to activate. More on this in the below bolded section.

Other unit examples: (All values in effective widow mine ranges):
+ Show Spoiler +

And here's a picture representation of the idea:
[image loading]

It's not a lot of leeway for most units, but speedlings, mutalisks and banelings are very able to run right over minefields without taking many, if any, hits for this very reason.
Furthermore, as pointed out by Terranic, once the first wave gets through the mines, the mine will start to select units based on proximity.
Given that, the very close units will already be halfway over the mine's radius. Meaning that they need to travel 5 range units in 1.5 seconds, which nearly all of the above mentioned units are able to do.
Any unit then traveling over the mine with a speed of at least 3.33(...) will be able escape the mine prior to activation, creating a cascading effect in which the mine is never able to activate and instead repeatedly changes targets.


Here's a graphic of this vital idea:
+ Show Spoiler +
- Credit to Mitosis for this excellent graphic!
And another:
+ Show Spoiler +
- Credit to Ahli for another sweet graphic, and Prplppleatr for analyzing it!

Of course, all of this only applies to units traveling in a straight line over the mine. However, this is relatively simple to do, as a move command will achieve this effect.

Conclusion:
Properly leading with well positioned units in muta-ling-baneling packs can allow a player to run over a minefield with near impunity. Use it if you can. It's a cool tactic.

And that's all for now.
Comments? Questions? Concerns?

Best of luck to you all,
Lone

MOD EDIT:
Here is Morrow's version from: http://www.teamliquid.net/forum/viewmessage.php?topic_id=403618&currentpage=3#49

On March 18 2013 14:15 MorroW wrote:
how widow mine works
they lock onto a target. first one who enter within 5 range OR best unit (which is basically the closest unit to the widow mine)
once they lock into a target it begins channeling for 1.5 seconds (ingame)

if the unit leaves the 5 range, dies or player manually switches target during the channeling period - the widow mine repeats the process


so this is why mines sometimes dont attack, sometimes kill terran and sometimes kill zerg
so lets say you run in with zerglings against marines and a widow mine. the widow mine locks onto the first zergling who enters.
if the zergling dies to marines, it changes target and has to wait another 1.5 sek, if that ling dies to marines it changes target etc. so it appears not to be attacking at all.
if the zergling runs past the widow mine, behind the marines for example it switches target as well (the target has to be within 5 range the entire lockdown process)

as terran
so in a fight, you basically as terran ideally want to switch targets between the zerglings until the banelings enter range and then you target the bane and let the mines be.
second option is to stay with the marines, burst down as many lings as you can, and hopefully (and probably) you will kill all zerglings which were targetted automatically by the widow mines before they finish channeling and then banelings enter and you target the mines onto the banes

as zerg
as a zerg player, you know that your first zerglings will be targetted, so use your frontal line in move command behind the terran army and attack with the rest of your zerglings normally. if you do this just right (and terran doesnt) the mines will all fire on your lings that are behind his bio army and kill everything he got


widow mines appear random at the first glance of it. but the more you play around with them the more you realize how much you (as terran or zerg) can manipulate them and make them do exactly what you want them to. its not a user friendly unit at all because of how it can completely backfire using widow mines where as a siege tank you know will do a certain amount of damage. things like this is really beautiful and what is making bw a very different game from sc2. in bw there were tons of "OP" units that crushed your opponent or did close to nothing or killed yourself where as in sc2 its much more predictable whats expected of a unit because the complexity of it its not very deep

i think the widow mines are slightly too strong right now. but if your a zerg reading this i hope it helped abit how to make the widow mines turn against the terran instead of raping everything you got

Last edit: 2013-03-21 06:50:40
Old Post

 
 reikai   United States. March 19 2013 23:04. Posts 307
Profile # 
+ Show Spoiler +
Et Ducit Mundum Per Luce. :T:
Old Post

 
 Surili   United Kingdom. March 19 2013 23:12. Posts 1077
Profile Blog # 
Could you possibly make an image to help me understand? I'm pretty dim.
"It is not a mistake to have strong views, it is a mistake to have nothing else." - Andrew Weston * * * Masters Protoss on EU.
Old Post

 
 SongMeister   United States. March 19 2013 23:26. Posts 18
Profile # 
damn lone, this is some serious stuff.... very nice work!
Old Post

 
 StagaDish   United States. March 19 2013 23:26. Posts 9
Profile # 

On March 19 2013 23:12 Surili wrote:
Could you possibly make an image to help me understand? I'm pretty dim.


^
This sounds like very useful information, but also very confusing for ppl with low math skillz. An image is a cool idea. Also video showing how this works (or when it doesn't - like when unit moves too slow or in the wrong path over mines).

Might be a lot to ask, but it sounds like you're on to something really important here! Put some effort so everybody could understand it easily :D

gl!
And thanks in advance
Practice Makes Perfect
Old Post

 
 AveSharia   United States. March 19 2013 23:33. Posts 60
Profile # 

Given that, the very close units will already be halfway over the mine's radius.


I think that's the most important point in the whole piece. Lead with lings, and the even the slower stuff that follows won't get hit.

Also, if I'm not mistaken, the Flash v Life engagement occurred off creep (http://bcove.me/gt7scsrw, 13ish minutes*). So this statement:


He realized that if he attacked from the correct angle, he could get mines to lock onto Zerglings which would not pass within 2 range of the burrowed mines.


...seems a bit misleading. The range should probably say 3.5.

* EDIT: The mines were actually at the edge of the creep, so the effective radius is going to fall between 2 and 3.5.
Last edit: 2013-03-19 23:38:10
Old Post

 
 jrkirby   United States. March 19 2013 23:33. Posts 507
Profile Blog # 
This is huge! A lot of people might have thought the widow mine is OP, but if you can micro against it like this, that has huge implications for all the terran matchups.
Last edit: 2013-03-20 02:36:07
Old Post

 
 hzflank   United Kingdom. March 19 2013 23:34. Posts 1068
Profile # 

On March 19 2013 23:12 Surili wrote:
Could you possibly make an image to help me understand? I'm pretty dim.


I cannot make an image, but I can explain it without any math.

A widow mine picks a target that comes within it's range. If it is a slow moving target it will fire at it. If it is a fast moving target it will only fire if the targeted unit gets very close to the mine. A widow mine can only have on target at a time.
Old Post

 
 mvdunecats   United States. March 19 2013 23:46. Posts 38
Profile # 

On March 19 2013 23:26 StagaDish wrote:

Show nested quote +



^
This sounds like very useful information, but also very confusing for ppl with low math skillz. An image is a cool idea.

No images to contribute, but imagine a circle. Now draw a line segment that is inside the circle. The longest line segment that you can have inside the circle is one that crosses through the center. The further the line is from the center, the shorter the line segment will be. The extreme case for the shortest line segment possible is a line that is tangent to the circle.

The widow mine is the center of that circle. People will instinctively think that they need to stay outside that circle to avoid damage from the widow mine. But because of the arming delay for the widow mine's attack, you can enter that circle as long as you get back out fast enough.

So going back to that mental image of line segments going through the circle. How quickly you can move from one end of the line to the other depends on how long the line is (the longer the line, the longer it takes to move that far) and how fast the unit is (a faster unit can cross a fixed length line in less time than a slower unit). A faster unit can run closer to the widow mine and still be safe.
Old Post

 
 Ahli   Germany. March 19 2013 23:50. Posts 107
Profile # 
The widow mine has a unit radius of 0.5 that is added to the range. Because the widow mine is burrowed, units can move across it. So it's actual range is 5.5.
Last edit: 2013-03-20 00:12:20
Try my Arcade map "Dia blo - Mortal Shroud" or "Temple Siege 2". :)
Old Post

 
 Chernobyl   Brazil. March 19 2013 23:50. Posts 100
Profile # 
Very good post.

Is far better than simply qq about a new unit.

For me, hots is amazing, and the widow mine is a very entertaining unit.
Old Post

 
 Rannasha   Netherlands. March 19 2013 23:59. Posts 2263
Profile Blog # 
Fear my mad MS Paint skills:
[image loading]
The black dot is the w-mine, the black circle the edge of the trigger range (radius 5). Suppose a unit passes by over the dark gray line, then the light grey line indicates the "effective radius".

The numbers in the first post are the maximal effective radii for various units to still trigger the mine (that is, the mine fires before the unit exits the radius 5 circle). The faster the unit, the closer it can pass by the w-mine without getting hit.
Such flammable little insects!
Old Post

 
 Ahli   Germany. March 20 2013 00:09. Posts 107
Profile # 
I made an Example image with Speedlings on creep not activating mine.

The ling in the south enters the range first, but leaves it. This allows the rest of the speedlings to directly travel over the mine.
Last edit: 2013-03-20 00:10:58
Try my Arcade map "Dia blo - Mortal Shroud" or "Temple Siege 2". :)
Old Post

 
 Miotonir   Poland. March 20 2013 00:10. Posts 66
Profile # 
This is somewhat true when the target is moving quickly but for targets that are slow the effectiveness of the mine is higher... so for example a stimmed marine might dodge the bullet , but non stimmed will not altho going trough same path ... It is perfect then for all matchups because a ling has higher chance of avoiding the mine ... while a zelot has lower since it has higher hp and slower movement speed.
Old Post

 
 ensign_lee   United States. March 20 2013 00:38. Posts 1017
Profile # 
Holy crap. What a high quality post.
Old Post

 
 Arghmyliver   United States. March 20 2013 00:39. Posts 660
Profile Blog # 
Wow dude - that's some sick mathematical insight! As a calculus veteran I say - major props!
Now witness their attempts to fly from tree to tree. Notice they do not so much fly as plummet.
Old Post

 
 _fool   Netherlands. March 20 2013 00:42. Posts 166
Profile # 
What's really cool about this post is that even without grasping the full math, I immediately got your point. Good job OP!
Why can't I select Team Grubby as my favorite progaming team? :)
Old Post

 
 Pufftrees   March 20 2013 00:44. Posts 2306
Profile # 
Simple elegant math leading to excellent insights! What is this the 15th century?

Nice job
Chance favors the prepared mind.
Old Post

 
 StagaDish   United States. March 20 2013 00:51. Posts 9
Profile # 
Lone, we might have to call you "The DeWidower" from now on...
Practice Makes Perfect
Old Post

 
 Targe   United Kingdom. March 20 2013 00:53. Posts 1719
Profile Blog # 
Awesome! Maths!
Nice job on interpreting it, I wouldn't have thought to work out a radius that is the closest you can get without activating, I guess the counter to this strategy is to manually target the mines on units further from the mine (after the initial ling).
Zelniq - you can avoid this DDoS problem if you increase your RAM. there is website to download more rams search TL to find it | Wax: fuck i forgot people can't read | Coach Park: We need miracle. We will make the miracle. Expect us and love us.
Old Post

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