Jump to content

Search the Community

Showing results for tags 'for science'.



More search options

  • Search By Tags

    Type tags separated by commas.
  • Search By Author

Content Type


Forums

  • World of Warships - News and Information
    • News And Announcements
    • Updates and PTS
    • Developer's Corner
    • Community Volunteer Programs
  • Feedback and Support
    • Game Support and Bug Reporting
    • Player Feature and Gameplay Suggestions
    • Game Guides and Tutorials
  • General WoWs Discussion
    • General Game Discussion
    • Discussions about Warships
    • Player Modifications
  • Off Topic
    • Historical Discussions and Studies
    • Off-Topic
  • International Forums
    • Foro en Español
    • Fórum Brasileiro

Find results in...

Find results that contain...


Date Created

  • Start

    End


Last Updated

  • Start

    End


Filter by number of...

Joined

  • Start

    End


Group


Discord


Twitter


Website URL


Instagram


YouTube


Twitch


Skype


Location


Interests

Found 2 results

  1. This is an analysis to tackle the vertical dispersion from the dispersion tests done by LittleWhiteMouse. It is still an approximation due to limitations from the tools and plain RNG. If anyone that can point how to refine this analysis, feel welcome to do so. For those that don't know, Sub_Octavian explained long ago that there are three parameters that affect the shell's dispersion on the aiming plane: horizontal dispersion, sigma and a horizontal-to-vertical ratio. This analysis tries to find the latter. As a clarification, there are two different types of dispersion that people refer to when discussing vertical dispersion, as illustrated by this famous image by Sub_Octavian as "built on [aiming] plane" and "on water [plane]". My goal is to find the vertical dispersion on the aiming plane, not on the water plane, and I'll refer to that as "aiming vertical dispersion" to keep it clear. The idea of the analysis is quite simple: Pick the dispersion test from LWM's reviews. Measure the distance between the aiming plane (Fuso's center, 15 km range) and the leftmost point in her test. Check the angle that the shell hits the water using a ballistics calculator. Estimate the approximate aiming vertical dispersion by taking the tangent of that angle on impact with the distance of that point. The step 2 can be seen as following: And step 4 can be visualized as follows: It is also possible to do so with the distance between the aiming plane and the rightmost point, though I am not entirely sure how the game models the shot when the shell's target point is underwater. As usual practice, here are the assumptions of this analysis: LWM's stated parameters of her test: Fuso at 15 km, no camouflage, whether the ship being tested was using specific dispersion modules and the shots coming from right to left. The relation between horizontal and vertical being a constant value on the given dispersion stance. Fuso's length: 212.75 meters in game. The aiming plane is on Fuso's center, and is at the stated 15.00 km distance. The ballistics calculator's accuracy provides a decent approximation of the shell's angle on impact. The shell's flight between the aiming plane and the impact point is flat enough that we can treat it as a straight line. There is also a common belief that the relation between horizontal and vertical is constant for a given nation or dispersion formula. While it doesn't affect the analysis itself, it affects the interpretation of the results. The data and results are on this spreadsheet: https://docs.google.com/spreadsheets/d/1l9uOVRgiS8WNyFQXQZbu__XbWZypNJXIu3WUkWoZMLE/edit?usp=sharing , with the results from following the steps above being summarized as follows: , where the "Vertical ratio I" in green being the the estimate relation between horizontal and vertical on the upper half (radius) of the ellipse. For the full vertical size of the ellipse, multiply it by two. Important notes: Florida, Georgia and Thunderer use the battlecruiser dispersion formula (R*8.4 + 48). Warspite and Vanguard use a special British dispersion formula (R*10.3 + 51). P.E.F. uses a dispersion test from before the buff to the German dispersion formula (R*9.8 + 66) and has an exception on LWM's usual tests: because she got an unusually tight RNG, she ran additional shots and recorded the furthest point away from the center she could find. The first result (1) uses that furthest point, the second result (2) doesn't use it just as a comparison to how much RNG can mess with the analysis (a lot). Odin uses the post-buff German dispersion (R*10 + 60), shared with the Americans and the British. Bajie uses the Japanese dispersion formula (R*7.2 + 84). AL Sovetskaya Rossiya uses the American dispersion formula, while Lenin and Sovetsky Soyuz use the Russian formula (R*11.8 + 35) instead. The spreadsheet also has three other results from exploring the lower half of the aiming vertical dispersion (Vertical ratio III) and using the angle of impact if the shell hit the water at the aiming plane instead (Vertical ratio II and IV), the latter done to verify how the "flat trajectory assumption" affects the results. The result with the lower half deserves mention, as it shows the American BBs with a notably larger aiming vertical dispersion than they presented in the upper half, including the ones using the battlecruiser dispersion formula: Last, a reminder of the limitations and liberties taken that make these results an approximation: The LWM tests are subject to RNG not sending a shell at the highest/lowest point of the aiming vertical dispersion, as seen quite clearly on the P.E.F. test. Even if a ship from a given nation/formula shows a low ratio, it is possible that the nation/formula still has a much higher ratio than the analysis could find. Add to it that the number of tests per nation is small (at most 7 for IJN, counting Bajie as an Izumo clone), it is very likely that any given nation has a much higher ratio than seen above. The shell's trajectory isn't itself perfectly flat, making the use of the angle of impact an overestimation in the upper aiming half, and an underestimation in the lower half. The ballistics calculator used (https://jcw780.github.io/wows_ballistics/) isn't perfect. I know because the travel time listed doesn't match exactly for Yamato's case. The in-game UI tells that Yamato's AP takes 8.21s to hit the water at 15.00 km away; the ballistics calculator says it takes about 8.667s instead. As such, the angles used are themselves an approximation as well. If someone knows of a better ballistics calculator, or some other way to get the impact angle, please feel welcome to tell me. I've tried to use WoWstf's one (not enough granularity on distance for this test) and Proships.ru (Yamato's AP reaching 15 km at 27.64s, wth?!) and they aren't good enough for the task. And LWM, if you're reading this: Please tell me :(
  2. So, I haven't found someone mentioning a way to measure how much difference a 0.1 or 0.2 sigma makes, making it hard to say how any two BBs compare. Like Yamato vs Thunderer: how does that extra 0.2 sigma compare with the battlecruiser dispersion? I'm trying to quantify it and want to check if my assumptions are correct. First assumption is that the gaussian distribution as seen in images in the forums, such as the following: , is indeed the way WG uses the sigma parameter. If it is, then it is formally a truncated gaussian distribution, for which there are plenty of free statistical packages available, like "truncnorm" package for the R language. The second assumption is that the information given on the How it Works: Firing and Dispersion video is still accurate and up-to-date. More specifically, I assume that: the maximum horizontal dispersion is the diameter (not the radius) of the ellipsoid no shell falls outside the ellipsoid the maximum dispersion given in port is for when a target is locked on Third, that the dispersion formulas collected here by the community are also accurate and up-to-date. I'm relying on those formulas for determining the dispersion at different ranges for each ship. If all the above are correct, then we could try to measure accuracy by calculating at which distance from the center of your aim a given percentage, or set of percentages, of the shells will fall. Say, 75% of the shells falling within 50m for one ship at a 15km range and 60m for the other? The former ship can then be said to be more accurate at that range, as the majority of its shells will fall closer to where you actually aimed. This can be used to find how ships with different sigma values perform at each range, even if they have different dispersion formulas. Other percentages can be chosen, of course. To calculate that, I'm using the 'truncnorm' package mentioned above. More specifically, its 'qtruncnorm' function, which gives the distance that covers a given percentage area of the truncated gaussian distribution. In other words, at how many meters away from the center will a given percentage of the shells fall. So, we work with the following idea: use one of the distribution's tails, or halves, and assume that the game simply flips a coin to decide whether the shell will fly to the left or to the right of your aim the maximum distance from the center is half of the dispersion of the shot at that range, since the dispersion refers to the diameter of the ellipsoid, not the radius So, to measure how Yamato performs with the legendary module, I can code the following: sigma <- 2.1 range <- 5:26 modifiers <- 0.93*1.04*1.05*0.93 dispersion <- (84 + 7.2*range) * modifiers yamato <- qtruncnorm(0.75, 0, sigma) * dispersion / (2*sigma) names(yamato) <- c(5:26) , which includes the effect of the aiming module on slot 3 (-7% dispersion), the opponent using a camouflage (+4% dispersion) and the concealment mod on slot 5 (+5% dispersion), and the legendary module for Yamato on slot 6 (-7% dispersion). As far as I know, they stack multiplicatively, not additively. And Thunderer's code is as follows: sigma <- 1.9 range <- 5:26 modifiers <- 0.93*1.04*1.05 dispersion <- (48 + 8.4*range) * modifiers thunderer <- qtruncnorm(0.75, 0, sigma) * dispersion / (2*sigma) names(thunderer) <- c(5:26) Which gives the following result: yamato 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 29.34723 31.10807 32.86890 34.62974 36.39057 38.15140 39.91224 41.67307 43.43391 45.19474 46.95557 48.71641 50.47724 52.23808 53.99891 55.75974 57.52058 59.28141 61.04225 62.80308 64.56392 66.32475 thunderer 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 25.28905 27.64936 30.00967 32.36999 34.73030 37.09061 39.45092 41.81123 44.17154 46.53185 48.89217 51.25248 53.61279 55.97310 58.33341 60.69372 63.05404 65.41435 67.77466 70.13497 72.49528 74.85559 What do these numbers mean? For each range (between 5km and 26km here), it tells at how many meters from the center of your aim 75% of the shells will fall in the horizontal axis. For instance, shooting at a locked target at a range of 15km, 75% of Yamato's shells will fall up to about 47m away from where you aimed (to either left or right), while 75% of Thunderer's shells will fall up to almost 49m away. An equivalent way to interpret it is that, for a given rng roll (in this case 0.75, from between 0 and 1) when shooting their guns, the rng will make the shell fly 47m away from where you aimed if you're on the Yamato, and 49m away if you're on the Thunderer. The result suggests that Thunderer is more accurate than Yamato until about 11km; between 11km and 12km, Yamato starts surpassing Thunderer and becomes more accurate at 12km and above. This means the extra 0.2 sigma actually has a huge impact; the range at which the two ships have the same dispersion is 17.67km, but that extra sigma allows Yamato's shell to behave similarly to Thunderer's about 6km earlier than their dispersion curves would suggest. And here are the results of the tier X battleships, in 25%/50%/75% quantiles (commonly used in scientific articles): accuracyBBs 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Yamato 25% 8.281209 8.778081 9.274954 9.771826 10.268699 10.76557 11.26244 11.75932 12.25619 12.75306 13.24993 13.74681 14.24368 14.74055 15.23742 15.73430 16.23117 16.72804 17.22491 17.72179 18.21866 18.71553 Yamato 50% 17.449525 18.496497 19.543468 20.590440 21.637412 22.68438 23.73135 24.77833 25.82530 26.87227 27.91924 28.96621 30.01318 31.06016 32.10713 33.15410 34.20107 35.24804 36.29501 37.34198 38.38896 39.43593 Yamato 75% 29.347234 31.108068 32.868902 34.629736 36.390570 38.15140 39.91224 41.67307 43.43391 45.19474 46.95557 48.71641 50.47724 52.23808 53.99891 55.75974 57.52058 59.28141 61.04225 62.80308 64.56392 66.32475 Thunderer 25% 7.210110 7.883053 8.555997 9.228941 9.901884 10.57483 11.24777 11.92071 12.59366 13.26660 13.93955 14.61249 15.28543 15.95838 16.63132 17.30426 17.97721 18.65015 19.32309 19.99604 20.66898 21.34193 Thunderer 50% 15.152416 16.566642 17.980867 19.395093 20.809318 22.22354 23.63777 25.05200 26.46622 27.88045 29.29467 30.70890 32.12312 33.53735 34.95157 36.36580 37.78002 39.19425 40.60848 42.02270 43.43693 44.85115 Thunderer 75% 25.289052 27.649363 30.009674 32.369986 34.730297 37.09061 39.45092 41.81123 44.17154 46.53185 48.89217 51.25248 53.61279 55.97310 58.33341 60.69372 63.05404 65.41435 67.77466 70.13497 72.49528 74.85559 Conqueror 25% 9.155312 9.987613 10.819914 11.652215 12.484516 13.31682 14.14912 14.98142 15.81372 16.64602 17.47832 18.31062 19.14292 19.97523 20.80753 21.63983 22.47213 23.30443 24.13673 24.96903 25.80133 26.63363 Conqueror 50% 19.207531 20.953671 22.699810 24.445949 26.192088 27.93823 29.68437 31.43051 33.17665 34.92278 36.66892 38.41506 40.16120 41.90734 43.65348 45.39962 47.14576 48.89190 50.63804 52.38418 54.13032 55.87646 Conqueror 75% 31.903454 34.803767 37.704081 40.604395 43.504709 46.40502 49.30534 52.20565 55.10597 58.00628 60.90659 63.80691 66.70722 69.60753 72.50785 75.40816 78.30848 81.20879 84.10910 87.00942 89.90973 92.81005 Montana 25% 8.433330 9.199997 9.966663 10.733330 11.499996 12.26666 13.03333 13.80000 14.56666 15.33333 16.09999 16.86666 17.63333 18.39999 19.16666 19.93333 20.69999 21.46666 22.23333 22.99999 23.76666 24.53332 Montana 50% 17.723077 19.334266 20.945455 22.556644 24.167833 25.77902 27.39021 29.00140 30.61259 32.22378 33.83497 35.44615 37.05734 38.66853 40.27972 41.89091 43.50210 45.11329 46.72448 48.33567 49.94685 51.55804 Montana 75% 29.579428 32.268467 34.957506 37.646545 40.335584 43.02462 45.71366 48.40270 51.09174 53.78078 56.46982 59.15886 61.84790 64.53693 67.22597 69.91501 72.60405 75.29309 77.98213 80.67117 83.36021 86.04925 Ohio 25% 8.116246 8.854087 9.591927 10.329768 11.067608 11.80545 12.54329 13.28113 14.01897 14.75681 15.49465 16.23249 16.97033 17.70817 18.44601 19.18385 19.92169 20.65954 21.39738 22.13522 22.87306 23.61090 Ohio 50% 17.081352 18.634203 20.187053 21.739903 23.292753 24.84560 26.39845 27.95130 29.50415 31.05700 32.60985 34.16270 35.71555 37.26841 38.82126 40.37411 41.92696 43.47981 45.03266 46.58551 48.13836 49.69121 Ohio 75% 28.626925 31.229373 33.831820 36.434268 39.036716 41.63916 44.24161 46.84406 49.44651 52.04895 54.65140 57.25385 59.85630 62.45875 65.06119 67.66364 70.26609 72.86854 75.47098 78.07343 80.67588 83.27833 GK/Bourgogne 25% 9.571462 10.387117 11.202772 12.018427 12.834082 13.64974 14.46539 15.28105 16.09670 16.91236 17.72801 18.54367 19.35932 20.17498 20.99063 21.80629 22.62194 23.43760 24.25325 25.06891 25.88456 26.70022 GK/Bourgogne 50% 20.080601 21.791817 23.503034 25.214250 26.925467 28.63668 30.34790 32.05912 33.77033 35.48155 37.19277 38.90398 40.61520 42.32641 44.03763 45.74885 47.46006 49.17128 50.88250 52.59371 54.30493 56.01615 GK/Bourgogne 75% 33.353610 36.195918 39.038226 41.880534 44.722841 47.56515 50.40746 53.24976 56.09207 58.93438 61.77669 64.61899 67.46130 70.30361 73.14592 75.98823 78.83053 81.67284 84.51515 87.35746 90.19976 93.04207 Republique 25% 8.866522 9.622104 10.377686 11.133268 11.888850 12.64443 13.40001 14.15560 14.91118 15.66676 16.42234 17.17792 17.93350 18.68909 19.44467 20.20025 20.95583 21.71141 22.46700 23.22258 23.97816 24.73374 Republique 50% 18.660374 20.250563 21.840751 23.430939 25.021128 26.61132 28.20150 29.79169 31.38188 32.97207 34.56226 36.15245 37.74264 39.33282 40.92301 42.51320 44.10339 45.69358 47.28377 48.87395 50.46414 52.05433 Republique 75% 31.273234 33.938258 36.603281 39.268305 41.933328 44.59835 47.26337 49.92840 52.59342 55.25845 57.92347 60.58849 63.25352 65.91854 68.58356 71.24859 73.91361 76.57863 79.24366 81.90868 84.57370 87.23873 Kremlin 25% 7.530559 8.475885 9.421210 10.366536 11.311861 12.25719 13.20251 14.14784 15.09316 16.03849 16.98381 17.92914 18.87447 19.81979 20.76512 21.71044 22.65577 23.60109 24.54642 25.49174 26.43707 27.38239 Kremlin 50% 15.825857 17.812507 19.799157 21.785807 23.772458 25.75911 27.74576 29.73241 31.71906 33.70571 35.69236 37.67901 39.66566 41.65231 43.63896 45.62561 47.61226 49.59891 51.58556 53.57221 55.55886 57.54551 Kremlin 75% 26.413009 29.728685 33.044361 36.360036 39.675712 42.99139 46.30706 49.62274 52.93841 56.25409 59.56977 62.88544 66.20112 69.51679 72.83247 76.14814 79.46382 82.77950 86.09517 89.41085 92.72652 96.04220 , so you can compare how your favorite tier X BBs behave at each range and what you can expect when shooting their guns. For instance, how the gun behavior of GK and Bourgogne at 15km is the behavior of Yamato at 23-24km, and of Montana at almost 17km. Note that this result is for all non-american ships using the ASM1, the american ones using the artillery mod on slot 6 instead (-11% dispersion, no -7% dispersion from ASM1), and Yamato running both ASM1 and legendary module. If you want to see, say, how your secondary build BB will behave with the secondary mod on slot 3, or how Yamato/Montana/Ohio behave if running the reload module on slot 6 instead, I'll need to run it again with different modifiers. Also, for the german BB lovers there, you can see how the buff to american/british dispersion formula will affect GK by comparing with the Conqueror. Both ships have the same sigma value and access to ASM1. Anyway, I need to doublecheck if any of the assumptions behind it is wrong or inaccurate. If you found anything wrong above, point it away. And if you want to replicate it, I can prepare a script later on or help you get familiarized with the basics of R. Also, feel free to use the results as you wish; content creation, german buff analysis, build comparisons, etc.
×