Using Statistics to Accurately Measure Gravity in Genshin Impact
Рет қаралды 703
Күн бұрынIn a previous video, I measured Genshin's gravity to be 20.85 m/s^2. While it appeared to be pretty accurate, I want to formally check if it really is accurate. In this video, I analyze my previous experimental data consisting of a height vs time graph using statistics to determine the best gravitational acceleration that most accurately models the data, then check if there's a statistically significant difference between that value and my assumed 20.85 m/s^2 acceleration with a two-tailed t-test.
I go over and explain these topics: curve fitting, hypothesis testing, type I errors, p-values, levels of significance, and t-tests. While there is quite a bit of math behind it, I do my best to ensure that most people can conceptually understand the topics. I especially go in-depth about the hypothesis testing topics.
Previous video: "Measuring Gravity in Genshin Impact" by @CountSacke
• Measuring Gravity In G...
Scientific Method Explained: "Analyzing Theorycrafting from a Scientific Perspective | Genshin Impact" by @CountSacke
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• Analyzing +150 Million...
#statistics #physics #genshinimpact #gamephysics
#curvefitting #hypothesistesting
Chapters:
0:00 Introduction
1:03 Best Fit Coefficient (Curve Fitting)
6:27 Hypothesis Testing and the P-Value
13:55 Significance Level
17:27 Statistical Analysis (t-Test)
21:14 Results and Analysis
25:04 Conclusions and Recommendations
Genshin Impact Name: Keacs
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Song 1: "Dvalin Is Landing!" by @HOYOMiX
• Dvalin Is Landing!
Intro Music: "Triumphant Step" by @CountSacke
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Song 2: "Island of Crystal and Pearl" by @HOYOMiX
• Island of Crystal and ...
Song 3: "Cogitation of Epochs" by @HOYOMiX
• Cogitation of Epochs
Song 4: "Resonance of Khvarena" @HOYOMiX
• Resonance of Khvarena
Song 5: "Ondulations du rythme" by @HOYOMiX
• Ondulations du rythme
Song 6: "Foregone Depiction" by @HOYOMiX
• Foregone Depiction
Song 7: "A Pensive Sigh" by @HOYOMiX
• A Pensive Sigh
Song 8: "Into the Perilous Labyrinth of Fog" by @HOYOMiX
• Into the Perilous Laby...
Song 9: "Rondeau des fleurs et des rapieres" by @HOYOMiX
• Rondeau des fleurs et ...
Song 10: "Invokation Game" by @HOYOMiX
• Invokation Game
Song 11: "Ex Favilla Incendi" by @HOYOMiX
• Ex Favilla Incendi
Song 12: "Realms of Amnesia" by @HOYOMiX
• Realms of Amnesia
Song 13: "Coronation of Providence" by @HOYOMiX
• Coronation of Providence
Song 14: "Pilot's Rest" by @HOYOMiX
• Pilot's Rest
Outro Music: "Radiant Voyage" by Count Sacke
• "Radiant Voyage" by Co...
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@ingang8817 3 ай бұрын
When you have no resin left :))))
@CountSacke 3 ай бұрын
Haha, I suppose. I’m actually a player with a lot left to do in Genshin so it doesn’t really apply to me that much.
@ingang8817 3 ай бұрын
@@CountSackeIt's fun to see you discover these things in GI XD
@hndc5435 3 ай бұрын
Why not just calculate the speed of a sunsetia falling from a tree? Just outside Montstat
@CountSacke 3 ай бұрын
HAHAHA. Could have been my Isaac Newton moment lol. In all seriousness, that method is a little problematic because you have to spend the time to measure the height the sunsettia falls from. It would also be subject to the same level of error that my previous method had. Though you now make me wonder if items fall at the same acceleration as players lol
@roozeveltfox 4 ай бұрын
ahaha I feel like a video like this brings out the Reviewer #2 in people. 😂 I think this is pretty neat tho! I appreciate the scicomm (mathcomm? statscomm?). The only thing I'd be caught up on is the average height. 4 to 5 feet?? Sheeeeeeesh!
@CountSacke 4 ай бұрын
HAHAHA. Well it's fine. I consider the critical comments as an informal version of peer review or academic defense. If I can't really defend myself against a critique or answer a question, it would be reasonable to think that I probably did get something wrong. (As long as the comment seems "reasonable"). Anyway, thank you :) It's nice to know that you found this interesting. Really makes my day! On a Side note: I think this video is more of a statcomm because of its heavy focus on the statistics and data analysis side of things (but then I guess arguably that means it is technically mathcomm... oh well...). There wasn't a lot of science or physics mentioned, only some terms but not explaining them.
@niom9446 4 ай бұрын
VERY BIG POG WOW VIDEO CONTENT
@CountSacke 4 ай бұрын
Haha thank you :)
@slacker.. 4 ай бұрын
There is no gravitational acceleration, its just pure and consistent velocity.
@CountSacke 4 ай бұрын
No, the player does accelerate at least for a short bit, I pointed this out in the previous video. You can literally see that isn’t true based on that the data points appear to curve as time increases. In fact, any semblance of a “curved” trend (or even sudden jump) means acceleration. The player does accelerate at least for a short period, 0 to about 22 m off the ground is where I’ve determined how long it takes to accelerate. Anything higher than 22 m would result in the player reaching the terminal velocity and hence no acceleration. You could use multiple linear regression of the form y=B2x^2+B1x+B0 with given data points then apply the t-test to statistically determine that B1 (initial speed) and B0 (initial height, which is defined as zero based on how the coordinate system is set up) are very close to zero and insignificant while B2 (the acceleration term) is much larger and cannot be removed. If you really don’t believe me, try drawing a straight line with the displacement vs time graph, you’ll find it’s not a very good match.
@slacker.. 4 ай бұрын
@@CountSackeI am not doing the testing myself but i respect the efforts you put in.
@primary4075 4 ай бұрын
Bro just use linear regression for a video, bruh...... Btw, should't it be exponential distribution for the acceleration until terminal it reach terminal velocity for better distribution fit. From exponential dist, you can change it to normal distribution then u can start using linear regression. You just violated the assumption or linear regression that is data normality.
@CountSacke 4 ай бұрын
I didn't use linear regression of the form y = B1x + B0 because we already know B0=0 (I hope I don't need to prove that it takes 0 seconds to fall 0 meters). I just didn't want to include it into my fitted curve. As far as I have studied from my courses, I have no idea how you can force B0 to be a specific value with linear regression. This is why I went with the form y = Bx. Yes, I know just doing linear regression would be 1000x faster and I had to go through more math to get the equations in this video (even though they're technically the same exact form), but, I wanted to show how the equations would be obtained using the least-squares method (in fact, you could use the same method to obtain the linear regression equations, just change beta into a vector containing B1 and B0 and vector x into a matrix with 1's in the first column and x's in the second). For your remark about the exponential behavior to account for the terminal velocity, that was something I initially assumed in my previous video and is to be covered in the next video when I find the correct terminal velocity. I did derive an equation for the velocity and height as functions of time using differential equations in my previous video. A bit of a spoiler for my next video, so up to you if you want to keep reading: I've found that the exponential nature was not observed when plotting the displacement vs time graphs; it gave me inaccurate times and heights. When I used the simpler kinematic equations (those of linear nature), the times actually came out to be much more accurate. It also struck me that it's a lot easier to program the kinematic equations than the differential equations for it. Genshin's movement doesn't strike me as something that uses forces for movement, it feels more simple, so it's not that surprising to see that it probably just uses the kinematic equations for movement. Hope that clarifies things for you :)
@primary4075 4 ай бұрын
@@CountSacke yes, that definitely did clarify very clearly.
@CountSacke 4 ай бұрын
@@primary4075 I can’t really tell if you’re being sarcastic or not :/
Genshin Impact
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