World of Warships – Captain’s Academy #38 – Dispersion, Horizontal, Vertical and Sigma

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Sigma? Horizontal dispersion? Vertical dispersion? If you’ve got questions about this, then I’ve hopefully got some answers you. After banging my head on a desk for 6 days, I think I can finally provide you with a rather accurate picture of how dispersion works in World of Warships.

If you have questions, please leave them in the comments section below.


  1. Gamesghost CL55 Cleveland

    I still dont know what is Sigma means….

    I am such a idiot.

  2. Hello dear sir!

    Nice video, I like videos where you dig deep into the game mechanics!
    But I have to say, that you forgot one important thing in your Excel calculations. You have put the following in numbers:
    If you assume that the dispersion is the same, horizontal and vertical, the hits form a circle if they impact at a 90° angle. But the angle of the shells is different for every ship, e.g. the NC has higher arcs than the Amagi and therefor a bigger angle to the water surface. The hitpattern you showed for Amagi and NC is a projection of this circle onto the water surface. The trajectory of the Amagi’s shots ist more flat and so the projected ellipse is longer. This effect is reflected in the numbers in your Excel sheet (flatter angles mean more difference if you alter the gun elevation one degree).
    But here is the point you missed: If you shoot at a ship, these circles are not projected onto the water surface, but onto the side of the ship (belt and superstructure), which is more or less at an 90° angle to the water. If you consider this, the projections look very different and a flatter arc should mean a better (or atleast not worse) shot dispersion.
    You are calculating how far the shots would fly until they hit the water, but you have to calculate the difference in the height above the waterline at the position of your target. This is the number, that determines if a shot overshoots the ship or even the armored belt and becomes a miss or an overpen.
    So while your arguments are valid as long as you make trials with >1000 shots at water, you forgot the influence of a ship as a target.
    I hope my argumentation is understandable (english is not my mother tongue…) and I hope for answers and(or further questions. Maybe I forgot something! ^^

    Greetings from Berlin!

  3. Awesome video, thanks dude! Could you maybe do this with CRUISERS? I would LOVE to know how shell weight and velocity effects the many 203mm guns! I got my Zao VERY recently, and haven’t played her live just yet, but in the training room, I FELT like I could aim for a SPECIFIC PIXEL from 15+ km, and hit it at least 6 times out of 10! But Zao has higher velocity shells than any other IJN cruiser, and actually has the HEAVIEST 203mm shells in the game, at 342 pounds – so I gotta wonder, how does the Zao’s vertical dispersion compared to something like the Atago or Ibuki?
    iChase Senpai; WHAI U NO TALK OR TEST ABOUT SCHARNHORST?! She has the lightest AND Higest Velocity shells of ANY ship classified as a BB! I know she has a 2.0 Sigma – but I REALLY wonder about her vertical dispersion!

  4. wait…so why 420s have worse vertical dispersion compared to 406s when its got the heavier shell?

  5. One question: Do the accuracy modules that reduce dispersion reduce both the vertical and horizontal dispersion or just the horizontal??

  6. I LOVE these sorts of videos! Because I am an auto didactic, I tend to learn things incredibly quickly – if the subject interests me, and I retain VERY SPECIFIC knowledge about anything I am interested in! That is why I am able to just kist off the shell weights and velocities for almost every Cruiser and DD gun in the game, and many BBs too (at least from T6 up, I don’t care so much about low tier specifics), I know the general penetration curves by heart for MANY guns and shells, and I know SPECIFIC traits, like USN AP not automatically ricocheting until 70 degrees Angle (or was it 68? Oh well) – That German BB secondaries GET 1/4 Caliber HE pen while literally EVERY other shell in the game is 1/6 caliber HE pen – effectively giving the German 105mm secindaries have THE SAME HE PEN – as NORMAL 152mm HE, the 128mm guns have 1mm less HE pen than Normal 203mm guns, and the 150mm secondaries have a MASSIVE 38mm HE pen!

    All while the 105s fire off 17.9 rounds oer minute with a 9% fire chance! The few times I have ran into FULL secondary build (BFT+Demo Expert+AFT+IFHE +Manual Secondaries) Bismarcks from 8km or less, when in a cruiser, was a DEATH SENTENCE! Literally nothing I could do but try to run away, and die in the process. I really wish WG would fix thay 1/4 cal secondary HE pen… I get it for the main guns, but secindaries with better HE pen than cruisers is ridiculous, especially when said cruisers are throwing much larger and heavier shells.

  7. You think that maybe, just maybe, it would be a good idea to make it plain and simple to understand? The only thing i was able to get from this was that IJN BBs have the same horizontal accuracy across ranges. When it came to “the teradrop shape”, you made it SO much mroe complicated than it actually is. in “Lame mans” terms, the Amagi has higher velocity rounds, therefore, has a much more flatter arc than the North Cal, which has low velocity, and whose rounds have a much higher arc. This means, that thanks to RNG putting your rounds off from the center point, the Amagis rounds are much more likely to go long or fall short due to the flatter arcs, whereas the NCs rounds are coming down rather than at the target. Having a 3d model would make explaining that a whole lot easier.

    I suppose a practical way to explain it would be, take a coin, set it at a 45 degree angle on a table, and bring your eyes down to table top, the coin is now an oval shape, this represents the Amagis teardrop, only, sideways. Then bring your eyes up about 20cm’s off the tabletop, and you can notice that the coin is retaining more of the circular shape rather than the oval shape. Thats the NCs teardrop. Because theyre coming from above, the circle is more of a circle than the Amagis oval.

    Aside from that, this was like taking a lecture at a university for a subject i am no good at.

  8. Xannari Ferrows

    The use of a bell curve here glosses over the way probability never uniformly decreases or increasing in this kind of situation. Instead, should be used.
    This is a graph charting the overall probability of a single electron being anywhere on the board, demonstrating quantum probability using the Copenhagen interpretation of quantum mechanics in the double slit experiment. Now if ships had one gun, a bell curve would be fine, but they have many guns, so though not quite perfect, this graph is still a better approximation of what the actual graph would look like

    Also sub-octavian is correct. The definition of what Sigma is, is the factor of the decay of the probability of which any given shell can spread any given distance away from the original distance specified. However, this is not based on some arbitrarily fixed distance. It is based on the percentage of maximum possible dispersion. The probability gradient along the vertical axis is also affected by moment-to-moment shell speed. This is a logical consequence of how the change in angles of any one reference point to another is more significant when one can set into their final position earlier. When travelling more parallel to the water as well, any super tiny change in angular trajectory initially is more likely to have a massive impact on the final position of the shell, while the same kind of trajectory toward the middle or end will have minor to no impact at all

    This is also a consequence of Sigma being applied to any given shell upon being fired from the guns, meaning faster shells will be more affected by smaller probabilities, and slower shells needing much longer of a time for those changes to have an impact, after which their target occupies a much larger visual angle relative to it, thus wont be affected nearly as much as the same change. Shells rest when they are at their resting orientation, when just approaching the shell ceiling. Faster shells reach their resting orientation faster, thus fall into rest faster

    I need to learn to summarize

  9. Great Vid! It would be an interesting exercise to plot shot patterns for all the BBs to confirm which is truly the most accurate.

  10. Angel33Demon666

    Hi Chase, very good work here, I have a couple of comments and questions to ask:
    1. On your plot about the ‘standard error’, if I am not mistaken in understanding, your shells can exceed your maximum dispersion (which is the green bar) right? That seems odd…
    2. As for sigma, I think I have a better explanation. I’d say that the normal distribution is constrained to the sigma value, and the edges of the constrained normal distribution are the edges of your dispersion ellipse i.e. The maximum dispersion, the shape of that constrained sigma value is then overlayed horizontally, which gives us our dispersion distribution. (I wish I could add graphics to YouTube comments), but basically if you overlay a 1.5 sigma constrained distribution and compare to a 2.0 sigma distribution, the middle peak is much ‘sharper’, this can be quantified further using the ‘Full Width Half Maximum’. Furthermore, I feel the FWHM gives a much better explanation of how the dispersion actually is that if it is available, we should use it to describe horizontal dispersion.
    3. For vertical dispersion, I’d like to know if there is a distribution curve that we know about for that.
    4. Also, I’d like to know where we can find the data ourselves, it seems like Wargaming is shooting themselves in the foot by not explaining game mechanics and releasing data. I have no idea why they do this…
    5. Regarding vertical dispersion, a shell with flatter shell trajectories have more chance of hitting the target due to the trajectory right? I feel like that may or may not be a significant factor, I haven’t done the maths to know how high the shell is when it passes where the ship is.
    6. Finally, I’m curious to know about the dispersion on cruisers and destroyers.
    And once again, very good work Chase, I look forward to having some of the above questions answered 🙂

  11. simple trig and projectile physics gj, i didn’t have time for the data

  12. Have you tried turning your internet off and on again?

  13. Thank you iChase, that was some serious research there, never though of that system.

  14. Let me simplify this.. There are 3 dimensions… X,Y and Z. When a ship has tight sigma in all 3 dimensions, you hit a lot.

  15. ArticulatedHypernova

    Weird way to calculate vertical dispersion.

  16. Joeseph Hunnicutt

    Oh no I’m a day lait

  17. Joeseph Hunnicutt

    I always thought Sigma was the most important

  18. Excellent video, I fell asleep at 8:13.

  19. Excellent quality upload, you’ve gained a subscriber just on that 1 vide. Good work, thank you.

  20. Someone need to make a TL;DR lol

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