Sholip Profile Blog Joined March 2014 Hungary 420 Posts #1



The fact that Phoenixes can infinitely kite certain other units due to their high speed and their ability to attack while moving has been known for a long time. The question is, which course should the Phoenixes follow so as to take no damage.



Let's take the speed of the Phoenix as v, the speed of the chasing unit as u. The Phoenix wants to keep a distance of d from the pursuing unit. Without detailed mathematical demonstration, the result is that the Phoenix should move along a circle of the radius



So I've been looking through forums about how to micro Phoenixes against different units perfectly. Since I did not find any satisfactory answer on the topic, I decided to do the math myself and calculate how exactly Phoenixes should be microed theoratically. Here is what I found.The fact that Phoenixes can infinitely kite certain other units due to their high speed and their ability to attack while moving has been known for a long time. The question is, which course should the Phoenixes follow so as to take no damage.Let's take the speed of the Phoenix as, the speed of the chasing unit as. The Phoenix wants to keep a distance offrom the pursuing unit. Without detailed mathematical demonstration, the result is that the Phoenix should move along a circle of the radius v*d/sqrt(v^2-u^2).

This will cause the chasing unit to move along a circle concentric to the Phoenix's, but with the radius



This will cause the chasing unit to move along a circle concentric to the Phoenix's, but with the radius u*d/sqrt(v^2-u^2).

Furthermore, the chasing unit's phase must be delayed by



Furthermore, the chasing unit's phase must be delayed by alpha = acos(u/v)

(where acos is the arcus cosine function), which also means that the direction in which the Phoenix is facing and the direction in which the chasing unit is facing should always form an angle of alpha.

In case of range-upgraded Phoenixes vs. Corruptors, the values for radii and angle are as in the figure:

+ Show Spoiler +



For those who don't believe me, here are two things. First,

You may say, OK, this is theory, but real game is another thing. The two, however, actually coincide perfectly in this case. To prove this, I made a tiny test map and tested it, and, hey presto!, the test results were perfectly as predicted.

Here is a video demonstration:



(where acos is the arcus cosine function), which also means that the direction in which the Phoenix is facing and the direction in which the chasing unit is facing should always form an angle of alpha.In case of range-upgraded Phoenixes vs. Corruptors, the values for radii and angle are as in the figure:For those who don't believe me, here are two things. First, here is a short document with the exact mathematical derivation of the above formulae. I tried to be as clear as possible, but it contains some more serious maths (well, no rocket science, but still not the most basic things). However, I suggest you DO read it, even if you skip the maths, because it is a very thorough document; this post here is merely an extract from it.You may say, OK, this is theory, but real game is another thing. The two, however, actually coincide perfectly in this case. To prove this, I made a tiny test map and tested it, and, hey presto!, the test results were perfectly as predicted.Here is a video demonstration:



As you can see, the Corruptor exactly follows the circle it is supposed to, and never ever damages the Phoenix.

I concede, this micro cannot be used in real game to kill enemy units, because the opponent will not let that happen and at least pulls away his unit, but if you start your microing in the right direction, and you can maintain it for two-three volleys, you can actually gain a significant lead.



Anyway, I have some other topics related to of math in SC2; if you find this one interesting, I will upload more. As you can see, the Corruptor exactly follows the circle it is supposed to, and never ever damages the Phoenix.I concede, this micro cannot be used in real game toenemy units, because the opponent will not let that happen and at least pulls away his unit, but if you start your microing in the right direction, and you can maintain it for two-three volleys, you can actually gain a significant lead.Anyway, I have some other topics related to of math in SC2; if you find this one interesting, I will upload more. "A hero is no braver than an ordinary man, but he is brave five minutes longer. Also, Zest is best." – Ralph Waldo Emerson