Ranges: The definitive guide

Simpson Bart
Simpson Bart
Incursion Leader
Joined Aug 2012 Posts: 1,003
  Let me start by saying that these numbers are reverse deduced from the UI. As a result, some numbers may be off if Kixeye has fudged the UI, the display of ranges, and could be offset. As a result, I'm relying on YOU to test them out and raise the issues you have, I'll adjust the guide as needed.

  Also, there is some math involved. If you hate numbers, skip most of the post. If you like to play "by feel" then don't read at all. K? Let's go.

  Kixeye's War Commander is an isometric view game. This means that whole the game is 2D, but, instead of a top view, it is displayed as if you are looking at the table at an angle. This is much easier to write and easier on resources than 3D, and it looks better than 2D, hence its name of 2.5D.

  First, let's fin the ratio. If you place a L5 plasma turret in a base, it displays a range circle. For plasma, this is 1356 pixels wide and 678 pixels high. Plasma has a range of 479 in-game, so the correction factor for X is ~2.83 and the correction factor for Y is 1.415. Those of you more mathematically inclined, you may have recognized these, these are magic numbers. Respectively, one is the double of the other, and the smaller number is SQRT(2).

  This means that the display is twice wide as it is high, for once, so the range display is really an ellipse, whose equation we'll need later. The reason behind the SQRT(2) is a bit of a mistery. It could be a leftover from an initially 3D engine, it could simply be a cosmetic figure to zoom the combat from a math fan. Or, it could be the game is aligned by X and Y and then rotated 45 degrees. Either way, it's good.

  Let us test this theory of mine, shall we?

  First, a War Commander image:
image

  Nice. Now, let's test that 2:1 skew ratio:

image

  Squares. Circles. Now we're cooking. Let me straighten that for you:

image

  Theeere we go. Unfortunately, since I'm working raster, I'll have to measure in the skewed displayed version, because this much processing is blurring the edges.

  So the math goes like this:

  Plasma
  X: 1356 px, Range 479, X skew: 2.83
  Y:  678 px, Range 479, Y skew: 1.415

  Let us check our numbers:
  MGT:
  X: 976 px, skew 2.83, Projected range: 344.87
  Y: 488 px, skew 1.415, Projected range: 344.87
  Real range: 345.

  So we can safely say that measured range is reliably producing numbers both ways. Cool, so now we have the math to actively measure ranges.

  To simplify, we will reduce the game to 2D. This is done by reducing the game to 2:1 wide-wise. As a result, all buildings become square and isometrics is all but eliminated, with a universal correction factor of SQRT(2) (because it's at 45 degrees).
 
  A turret measures at 140 px by 70 pixels, which is to say that reduced to one side, it's 70x70, minus the isometrics. As a result, the actual space it eats up in range is:

  70 / 1.415 = 49.49. This is just under 50. Because I'm lacking info from Kix, my precision is limited to rounding errors, but however you round it, it is UNDER 50. Meaning, if a turret glued to another turret has 50 range on you it might launch. 49 will not, 51 will. I'm guessing 50 will, because my experience is Kix uses Round() and, unlike me, they probably have round numbers in definitions and round the UI, whereas I'm doing the reverse. If I were you, I'd go with 50 and assume 50 is a hit.

  A bunker measures 200 by 100, minus the isometrics, it's 100/100 with a correction factor of 1.415, so that becomes:

  100 / 1.415 = 70.71. This is OVER 70, meaning that if a turret is behind a bunker, it needs to have at least 70 in range to ice you. Again, rounding, etc. I don't know if it launches at 70, but it will launch if it has 71 on you and will not at 69. Again, limitations of the GUI.

  A wall is 42/21.

  21/1.415 ~= 15.

  Now, the smaller an object becomes, the less reliable the measurement of its size, because of anti-aliasing. I'm off by 1-2 pixels, so it could be 42/21, but it could be 38/19 as well. No matter, however, because:

  22 / 1.415 = 14.8

  It can't be more than 21 because at 22 it would be 44 wide and it isn't.

  So a wall is ~15 range. However, if the image is mathematically processed, it says 16. I tend to think it is right, as odd numbers in building sizes make very little sense. Keep this in mind when looking at ranges. There is little I can do, the game has some AA and the models have been processed.

  Hopefully, by this time the ranges Kix have set start to make sense to you.

  Plasma is 479.
  Hellfire is 475. (-4)
  Mega/Chal is 390 (-89)

  So, a hellfire can safely engage a wall next to a Plasma, but not the Plasma itself. However, at 89 reach advantage, the plasma can ice your mega from behind another turret. Also, it outreaches you from behind a bunker, as well. Not good news for tanks.

  Similarly, a RBT has a range of 548. Let's see how it compares to Hellfire (475). That's -73. A 73 reach advantage means that the RBT can ice you when behind a turret, and behind a bunker But a wall is pushing it.


====================

Compounding buildings

  When attacking a turret, it's a center versus center battle and it doesn't matter. Simple as could be. But, when attacking another building, this get complicated.

  Because attacking is done center to center, it's like a building has a "loss" around it of half its size. For example, if you put a turret behind another turret, the first turret has a 50x50 range size, so it eats 25 range in your direction. The other turret also has a 25 range penalty, so they neatly add up to one turret.

  But what of different buildings? Well, a bunker has a 70x70 footprint. So, when attacking a bunker, it has a 35 personal space around its core, which is added to the 25 the turret has. So, added up, it's 60 range. So in spite of the fact that the bunker is 70, the turret behind it only needs a 60 reach advantage to ice you.


   ,------,------- reach advantage is 25+35, half of 50 and half of 70
 _____ _______
|  |  |   |   |
|25|25|35 | 35|
|__|__|___|___|
   ^      ^-- Where you hit
   `----------Where the range is calculated



====================

Angles.

  You though this was straight up, didn't you?

  Attacking at an angle shouldn't matter on a unit versus turret combat, because the lines in any reasonable game is calculated as the distance between the centers of the sprites. So, at any angle, range holds true with careful programming.

  But what of attacking buildings at an angle, when there is a turret behind it? Well, now it kind if matters, because as the angle walks around, the square becomes a rhombus, and then a square again. So it varies from Size to size * SQRT(2) and back to Size.

  If, for example, you have a building that is not in front of the turret, but an angle, then the size of that building is larger, in straight range. It varies from straight-on (range) to 45 degrees (range * 1.415). With square buildings, that is.

  So:

  TT
  TT
  BB           TT: Turret
  BB           BB: Building
  ||
  ||
  ||
  UU           UU: Unit


 In this case, the ranges add up. But.


        TT
        TT
      BB
      BB
    /
   /
  /
UU


  Now it's the best angle. If BB is another turret, then its range eating power is no longer 50, but 70 diagonally. In fact, the equation itself is like this:

  S1 * SQRT(2) / 2 + S2 / 2 * SQRT(2) / 2

  Which simplifies as
  (Size1+Size2) / 2 * 1.4142

  The range is eaten by half of a turret's width (add Pitagora because it's angled) and half of the (building you attack)'s width, because you attack its center.

  For 2 turrets, the size is the same and it adds up to 1/2 turret+1/2 turret = 1 turret, or 50. Which is funny, because SQRT(2) * SQRT(2) is 2, so diagonally size is pixels, which is 71.

  If, for example, you have a turret and a bunker, you add up half of the turret (the other half is outside range) and half of the bunker (the other half is towards you), so you lose 50/2+70/2 = 25+35 = 60. If you attack diagonally, that's 60 * 1.4142, or 84.85. Again, not knowing how Kix rounds, but that is the general idea.

  So
    A turret has to outrange you by 60 in a straight line, but 85 diagonally behind a bunker.
    A turret has to outrange you by 50 in a straight line, but 71 diagonally behind a turret.

  Seems like a weird number, that's a lot of range. Who would outrange what by 85?

  Well, RBT outranges all tanks by 84. So no defense glued to a RBT is safe by tank. But people rarely stack their defense diagonally, and your angle needs to be perfect, and no rounding errors, so the reach is usually good.

===========

  Arbitrary angles

  With an arbitrary angle, math becomes so weird you can't really do in real time as you attack, so I'll restrict to a few nice rules.

  Best striking angle is always along the line determined by the centers of the two buildings. Stacked front to back, attack from the front. Diagonally, attack diagonally.

  When forced to attack from the side, the range difference is very small, and can only be achieved if the turret has the same range or outranges you by one. Anything more, and don't bother.

         TT
         TT
UU-------BB
UU       BB


  The range in this case, is varying from 50 (front) to 0 side, in a very round equation, so the edge is minimal. Because it follows a half moon graph, the range difference is very VERY small at around 90 degrees, a tank's width off center will not matter.


====================

Conclusions:

  The thick of it is this:

  When doing it yourself:

  * When computing ranges, measure the range in pixels, vertically, and divide by SQRT(2).
  * When hitting buildings, angle doesn't matter (shouldn't matter)
  * When stacking defenses, you need to outrange the attacker by 50 if you stack turrets, by 60 if you stack a turret and a bunker. When at an angle, you lose at these values, so put your range-y turrets at corners.

  When using:

  * RBT 5: 548
  * Mortar 5: 498
  * Plasma 5: 479
  * Cryo 5: 479
  * Hellfire: 468

  * Tank (Mega/Chal): 390 (warning: Paladin (385) and Behemoth (380) have a lower range)
  Vs RBT 5: 548 == -158. Don't even think about it.
  Vs Mortar 5: 498 == -118. Again, don't even think about it. Will put a hole through you if it has 2 turrets an a wall in front.
  Vs Plasma 5: 479 == -89. Tank can do 2 buildings in front. Can't do one, will get sniped from behind the laser. Will also get sniped diagonally. Basically, Plasma has a no-tank zone for itself and all adjacent defenses.
  Vs Hellfire: 468 == -78. Can hit behind a defense. Can NOT hit behind a defense, diagonally.

  * Hellfire (475 at L9)
  Vs RBT 5: 548 == 73. RBT will hit behind a turret, but not behind 2 turrets and is diagonally challenged. Will not hit behind a turret if there is a wall to target. But only just. So turret, turret, wall is safe if you hit the wall with L9 EHFs. Make sure you align correctly. You have about half a wall tolerance.
  Vs Plasma 5/ Cryo 5 == 4. A difference of 4 means that it will hit directly, but will NOT hit behind a turret, or even a wall. With 25 range lost by its base alone, even an ant will spoil it. So you can hit any turret near the plasma, unless you go over 80 degrees.
  Vs Hellfire 5 == -7. Will outrange safely, but make sure you don't order tanks in formation and target it explicitly. At that difference, half a tank will trigger the Hellfire.

  * Razorback has 410, so look at Tank and subtract 20 from the figures. Mortar and RBT still outrange it to Hell and back. Plasma has 69 reach advantage, meaning you barely hit diagonally from a plasma. Hellfire has a 58 reach advantage, meaning you can't hit in line, but CAN hit another turret diagonally. The error is less than a wall, so align yourself properly.

  And that's about it.

  Turrets are among the smallest buildings around, so get a bearing by that.

  A turret in front of another turret means 50 reach advantage.

TTTT_______________UU
TTTT               UU
        +<50


  A bunker is 60 reach advantage.

TTBB_______________UU
TTBB               UU
        +>70


A wall in front has approx 14. So a turret loses 25 and wall another 7, that's 32.

TTW________________UU
TTW                UU
        +<32


  To get diagonal figures, multiply by 1.4142.

  Building wise,
  Turrets are 50.
  Bunkers are 70, same as power plants, mines and oil pumps, and oil storage, BUT NOT METAL STORAGE. Metal is about half way between a turret and a bunker (~60). Probably because Kix hates COD sufferers. (Cod is OCD, but with the letters in order, as they should be, thank you very much).

  So there we have it. A UI reverse math of the range system. You can do your own from here, and see what hits what, and remember to apply all bonuses to base range.

  I eagerly await your proof of me being wrong.
  • Chris Land
    Chris Land
    Strike-force Captain
    Joined Sep 2012 Posts: 968
    Holy MIT Batman.  Well done!
    All the tools are there, you just have to be smarter than the tools your working with.
    me wrote:
    Hell lets just give all units the DPS of a water pistol, name the game Lazer tag and call it a day ...
  • Jason Gao
    Jason Gao
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    Joined Dec 2011 Posts: 1
    did your math teacher help you with this?
  • Ratcher
    Ratcher
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    You lost me at the fifth word...
    Ratcher - Just so you know what name to shout when i pummel your platoons into the ground and take all your resources.
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  • David Davidson
    David Davidson
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    Joined Nov 2012 Posts: 260
    I think this may very well be the best post on the forums. One thing I've noticed you missed, however (and that I think is possibly the most useful bit of information you could have pulled):

    What is the trigger range on a drone silo? I've heard from some people that it increases with upgrades and from others that it does not, I frankly never paid enough attention before to notice and don't have enough thorium yet to check for the next level.

    But whether it changes or not, having a solid number to go off of would be beautiful.
    "The very first essential for success is a perpetually constant and regular employment of violence." - Adolf Hitler

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  • Simpson Bart
    Simpson Bart
    Incursion Leader
    Joined Aug 2012 Posts: 1,003
    edited 27 Mar 2013, 12:39AM


    What is the trigger range on a drone silo? I've heard from some people that it increases with upgrades and from others that it does not, I frankly never paid enough attention before to notice and don't have enough thorium yet to check for the next level.

    But whether it changes or not, having a solid number to go off of would be beautiful.
       I work with GUI, so if the displayed range is off I'm off but (I'm skipping math since everyone complained) my level 3 drone silo has a trigger range of 600.

      You can do it yourself to your drone silo. Take a screenshot of the game, in full screen so the entire range fits in the screen. Measure the vertical span of the circle in pixels and divide by SQRT(2) or 1.4142.

      Also, it is slightly smaller than my Watchtower sniper, with a range of 410, +50% range, which is 615 by my math, and 615 by wiki. So I'm fairly confident in saying range of the drone silo is 600, the second best range in the game.

      I've been reviewing my post (this time with pen and paper) and a few things need to be reviewed, such as I never specified that I measured the circle's diameter instead of radius (what range really is) and some figures are off. No matter, however, as the ranges as numbers stand, it's only the names that are off. Once I make sure everything is OK and I get a hold of Mr Sharma so he can take a look I'll finalize the thing.

      I'll be correcting the numbers as soon as I am sure I didn't screw up again. Sorry about that. Ranges for turrets and stuff stand, but the size of the buildings have been overestimated.

      Since I've been reviewing, the range of a mine is 50.
  • WCZenMaster
    WCZenMaster
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    nice theory kixeye hopefully wont be mad
  • George Chalkias
    George Chalkias
    Strike-force Captain
    Joined Nov 2011 Posts: 835
    Engineer detected...Or Math professor/teacher detected..No thanks I dont have time to read it :S, anyway nice posting this guide with your effort time!
    Math f!ck logic..Omg
    Senior member of War Commander wikia.Photographer of special events in WC Wikia. 


  • thomaspoul
    thomaspoul
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    Give me a website name that i can download that game.
  • Spetsnaz722
    Spetsnaz722
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    this is great.  Best post i have read on the forums. Thanks for posting this!
  • TroyW
    TroyW
    Unicorn Overlord
    Joined Jan 2013 Posts: 3,760
    I read a similar thread and was confused then.  I asked a question in that one but have not gotten a response so I'm just going copy it over to this one since it is just about the core concept of what these two thread are about anyways.  Here it is :

    ok I'm lost.

    mlovolm said:
    UPDATED AGAIN:

    just some small informations,some ppl may not know these:
    +Turret Platform takes 82 range in each side of it
    +Bunker,Silo,Power Plant,Storages take 110 range
    +CC takes 180 range
    +Wall takes 22.5 range
    +Wall take 4 small grid,so that means,each grid take 5.625 range

    it means
    +if a lvl 5 Mortal,Napalm,Plasma is placed behind the other Turret/Building (MGT as example),lvl 3-> HF can destroy that Turret/Building without hited by the Turret

    +if a lvl 5 RBT is placed behind behind the other Turret/Building,lvl 6-> HF can destroy that Turret/Building
    *note:
    HF must stay in a Perfect Straight line,a Perfect 180 degree 
    take out a ruler and make a straight line pass through the center of Turrets,and HF must stay on that line
    HF lvl 6-> should be able to destroy the Turret without being hitted by RBT
    this is why:
    lvl 6-> HF's range is 468
    RBT's range is 466,after reduced by having a Platform in front of it




    I assume you mean by "takes" is reduces. And am I correct in interpreting this to mean that by placing an Item ( turret, bunker, wall....) in front of a turret its range is reduced by this Item when being attacked from across the Item on a straight center line?

    so what I have shown here?
    image


    And if this is right then why does this happen?

    I don't understand where these ranges are coming from you list:

    mlovolm said:
    actually,the range can be more than that,because i found this when using lvl 5 Cobra(263) to destroy Mortal in opposite side of lvl 5 Gun Turret(350)
    350-263=87

    its possible that Turret Platform take 100 range,Silo,Storage take more than it a bit,so,around 110 range

    p.s:61 views and 1 comment :))

    I don't understand where these ranges are coming from?

    Level 5 MGT is 345 not 350
    Level 5 Cobra is 286 not 263

    and it this second example the way its worded means your doing the opposite of what I think you were say  in the fist one. Worded this way but on the pic what your saying is your using cobras to attack the Napalm Turret opposite side of the MGT.  So on the left most range line??  But that can't be right.   But if you mean like what is shown in the pic and your attacking the Napalm Turret in front of the MGT on the reduced range line then ( If what I think you guys are say is true ) yes the level 5 cobra can destroy the NT without being hit by the MGT. 

    Again if true then what happens when the NT is destroyed? Does that remove the reduction which would easily put the Cobra's back in the FULL range (345) of the MGT?


    Oh I just realized in the pic the MGT is behind walls so does that mean the two lager range lines are both reduced by roughly 22 making them actually 323 not 345?

    WAR COMMANDER WIKIA

     Lead Administrator
  • Simpson Bart
    Simpson Bart
    Incursion Leader
    Joined Aug 2012 Posts: 1,003
      Well, there is something about the WC ranges that I do not understand. Namely, the fact that the UI seems to not match the stuff in the engine. It LOOKS like some units don't attack the center of the building. Because of this, things are weird to say the least.

      Your post is quite confusing, sorry, but I don't understand what the question is what with quotes not aligning right. So I'll try to blabber on.

      There are also other issues with the game, for example, some ranges have been fixed. I know my math may not be rock solid, but some things I KNOW have changed. For example, I am a long time E-Hellfire driver, and I know them by heart. I did L30s and L40s to fill a dumpster and EHF has never before been able to nuke the turret glued to a RBT - I just tested this as I am typing and I just did. Not only a turret, but the EHF can target a wall right in front of the RBT. This didn't happen before. RBT used to nuke me at least a turret in front, if not 2.

      So it is entirely possible the figures have been invalidated. It is also possible, and likely, that the GUI displays buildings and ranges and the engine does what it likes - which kinda explains why a building seems to not eat as much range in math than on screen.

      A L9 EHF outranges the RBT5 by a number (548-475=73) that seems to suggest that a turret (half-length) plus a wall (half-length) is > 73 (because I can target the center of the wall). This suggests that a turret is about 60+ each side, or 120+ wide. That means that plasma range (479) covers about < 4 turrets (3 and change since it takes a bit itself) but the red circle in game covers about 7. That suggest that a turret is about 479/7.5 = 63 WIDE, meaning 32 each side. With 32 and the wall making about 40, I should be wasted by the RBT a long time ago.

      The UI doesn't correspond to the engine, for whatever reason. And I'm not going to dig any deeper, because WC is a cluster**** and I'm going away.

      But numbers posted in your quote are incorrect. If a turret takes 82 on each side, then hitting though 2 turrets needs a 162 reach advantage. I posted:

       "[...]It also has a 160 reach over the Pals I have, meaning Plasma will ice a Pal from behind 2 turrets. This is also correct, as I tested.[...]"

      Tested, Plasma will ice a Paladin from behind 2 turrets, meaning that 2 turrets are smaller than 160. Pal has 319 at my level, Plasma has 479, that's 479-319 = 160.

      If you are unclear as to how ranges OFFICIALLY work, I refer you to my first schematic (look for "reach advantage is 25+35, half of 50 and half of 70")

      If you have a question (or more) try to put them in a more structured form so I know what I'm answering. All I got is that you initially misunderstood how ranges are shortened and then figured it out.
  • ITALIANFIGHTER
    ITALIANFIGHTER
    Incursion Leader
    Joined Feb 2013 Posts: 1,008
    edited 4 Sep 2013, 4:47PM
     The target is not a perfect center to any unit either so that also offsets true range. Your numbers are good, if not for the imperfect square and offset target center, we could really take advantage of the #'s. The offsets, and non square issue causes more math to be worked. I think every degree of half footprint is going to have a range difference depending on targets "true " center and offset square dimensions. I've been working on these issues not by numbers, but by the long process of true game physic's manipulating positions to try and get better perspective of range from 8 common degrees, but it is complicated. This is the only way to work out range cause these are not perfect square/rectangles, and each of the 4 corners would need to be at least same angle as opposing corners (left/right corners same. north/south corners same angle to each other), along with having a perfectly centered target per item.
  • Simpson Bart
    Simpson Bart
    Incursion Leader
    Joined Aug 2012 Posts: 1,003
      In theory, the firing center of a unit is the point it uses to rotate, else it will move to hit a target that was already in range. Which they sometimes do.

      There is also the issue of units having inconsistent range/detection/poor judgement. For example L10 EWHs can be directed to attack a turret. After they start, point them to another target that doesn't require moving. After that target is destroyed, they stay there, like the old target wasn't in range. Ordered to attack again, they do but don't move. Under these conditions, it's pretty hard to see what is going on.

      Like I said, I could go deeper, sniff the traffic, see what the orders are and how they move - but two things are holding me back:

      a) The game is buggy as heck and sometimes things don't reproduce
      b) They keep fiddling with it. I don't know if someone from Kix saw this and checked or if it's just a coincidence, but ranges have been changed since I first posted, and are now more consistent. This is good, but if they keep fiddling with it I
    I'm not going to get decent results.

      Soon, though, once things get a bit more settled I'll give it a go again, this time I'm going to do sanity checks before I go though the whole shebang. I'm gonna start using units in descending order of range to determine range, then check against the UI and adjust.
  • Blackbladiz
    Blackbladiz
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    Joined Jun 2013 Posts: 271
    This post is old and is it updated from when they redid the building spaces, they trimmed the size of some of the buildings. Also, even though I am good at math, I didn't really understand the equations but the information/explanation is what did it for me in understanding this. I don't know how, but I understand this. Thanks.

    Prizes: ERM, EHG, Gats, Egats, Valks, E Valks, HF, EHF, HS, E razors, Gladiators, Stingers, Dogs, Honey Badgers.

  • Brandan_M4
    Brandan_M4
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    Joined Apr 2013 Posts: 100
    I have to say, just by looking at my base and seeing turrets motars towers ranges useing the res circle plus multi tests, that the range changes when u are at a diff. Angle.u start to lose range around the sides and backs of the guns and towers, bunkers ect.
    Once a Night Wolf, always a Night Wolf.
  • Richard Ho
    Richard Ho
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    Joined Apr 2012 Posts: 126
    good write up but i dont think it applies in events or to KIx's bases cause the base defences are souped up.
  • D3L7A
    D3L7A
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    Joined May 2013 Posts: 1,792
    This post is old and is it updated from when they redid the building spaces, they trimmed the size of some of the buildings. Also, even though I am good at math, I didn't really understand the equations but the information/explanation is what did it for me in understanding this. I don't know how, but I understand this. Thanks.

    Holy bump.

    The original post is pretty awesome, though my head hearts from all the math. I hate math.

    The OP deserves a nobel prize for this!
    War Commander level: 29, Home Sector : 265.  Ater Honos Forum Officer
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  • BratB
    BratB
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    ^:)^  Simpson...for ya!!
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  • Kevin_L856
    Kevin_L856
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    Joined Nov 2013 Posts: 182
    Can i ask a question about this? I suppose turret is 50*50 and bunker is 71*71, if i put a RBT near a bunker and turrets as shown in the attached file, can i defend Lv9 hellfires from any angles? If not, any suggestions that can solve this problem? Dimension shown in file. 


  • Sixto_D6
    Sixto_D6
    Greenhorn
    Joined Feb 2013 Posts: 3

    Seriously a wealth of information! I love math just enough to follow you visually in my mind as I read your thread. I think I grasp now why when I arrange my platoon in an arch They have a better affect then in a straight line. At any rate I shall put these theories to the test and eagerly await the results. The only variable not assigned a value to measure and defeat would be the attack clock, guess Im on my own to figure out how to achieve victory in the time frame. Thank you very much for the time and effort you put forth on this thread. Glad to see there are still those willing to teach players wanting to excel in WC.

  • Manny The Man
    Manny The Man
    Incursion Leader
    Joined Oct 2010 Posts: 1,001

    I'm not a dedicated math mathematician, but this is indeed alot of information. However, alot of people are talking about different ranges of towers or units. Is there a simple conclusion that you can deduce from this information for people like me who don't understand or can't read it all.

    Are the ranges wrong?
    Are there aspects about ranges that we don't know about?
    Does Kixeye Know?

    In Short what does this information tell us?

    It's Manny! Manny The Man! :D


  • rheazhl
    rheazhl
    Greenhorn
    Joined Jul 2014 Posts: 1

    ok,go!!

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