The Shokz Guide, Starcraft 2 Guide

Widow Mine Math

Lone over on Teamliquid had a great post about the math of Widow Mines and if it’s possible to run past them with out triggering them.

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),
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 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.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):

  • Mutalisks: 4.0
  • SpeedBanes on creep: 4.1
  • Speedlings off of creep: 3.5
  • Speedbanes off of creep: 4.5
  • Roaches W/Glial on creep: 4.1
  • Roaches w/Glial off creep: 4.4
  • Charging Chargelot: 2.1
  • Phoenix: 3.85
  • Hellion: 3.85
  • Stimmed units: 4.3

And here’s a picture representation of the idea:

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:

- Credit to Mitosis for this excellent graphic

- 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.

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?

Another follow up to this topic by Marrow

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

Source: Teamliquid

  • RiotZ #240 @ NA

    This would make sense competitively, if you knew what the widow radius was, and where it was planted, but if you had that info, why not just suicide a cheap unit to initiate cd, or snipe it altogether.

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