Hi, thank you soo much for your kind words :) Most of my knowledge in calculus and statistics are from courses I took in college. From my experience, it's a lot more detailed than whatever I learned about statistics in high school (I haven't taken an AP course so I can't really say if it'll have the same depth or not). When I had calculus in high school, I didn't really notice that much of a difficulty spike between it and the college course. I find it rather difficult to recommend videos for statistics and calculus because I haven't really found any videos that hit the right level of complexity. From what I generally notice, videos are usually either too dumbed down or too difficult to understand. I find that the classroom setting is often what bridges the gap between these two levels of difficulty. @3blue1brown has a nice video series explaining the concepts of calculus, however, I have to admit that I understood his video series better after taking a calculus course.

Wow. It's cool to see that even after all this time, this thing still works :)

Lol, if you insist. I don't really know at what height the player dies from fall damage though.

Why not?

bcuz :DD

Nice to know you found it useful. Good luck on your exam :)

Well yes, but without using any elemental skills or just modifications to the player movement, all characters consistently fall with the same acceleration as I proved in the first video. That consistent value for gravity is what I measured.

It’s physics applied to a video game.

It’s great content, that’s what.

Ty for saying that :) Though, I’m not that surprised with the amount of subs I have. Educational Topics + Video Games is a more niche audience so it is what it is.

@@CountSacke As long as you’re happy :)

Of course if I had 1 million subs I wouldn’t be complaining in the slightest XD

Haha that's nice to hear :)

Sounds like an interesting topic. Though, charged shot arrows might be a little difficult to deal with because they can travel quite far in addition to having to figure out the vertical angle the player shoots in. I'll see what I can find out. Also, glad to hear that you enjoyed the video :)

Thanks :) I was very surprised with those low pity summons. I guess the Great Misfortune was because I couldn't get any Gorou constellations rip. That's just the way it is sometimes ; - ; I don't max ascend my characters because I'm doing it as a challenge. I want to feel a bit of difficulty especially when it comes to the Archon Quest so yeah. I miss out on some primogems in the Spiral Abyss but it doesn't really bother me that much.

Thank you :) To answer your question I think I should provide some context: the whole reason why I was measuring character speeds is because I wanted to use it to measuring distances. I didn't really consider sprinting speeds because I was unsure how to handle the acceleration that sprinting can cause and that sprinting has quite limited stamina. On top of that, trying to handle cases with both normal jogging and dashing sounds way to complicated and annoying to deal with. Overall, it just didn't look very attractive from the standpoint of calculating distances. For every other player who isn't interested in calculating distances, I haven't really considered that so I could probably revisit this topic sometime and determine the sprinting speeds just for fun. Though I would only be for when the player sprints at constant full speed.

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.

@@CountSackeIt's fun to see you discover these things in GI XD

Aww thanks :) Most of my Genshin Content is rather niche so yeah, it’s to be expected. In terms of who I ship him with, I have mentioned it in a video though from what I can tell, it’s usually one that people either dislike a lot or like it (in addition to it being that the other person I ship him with has an extremely popular ship).

@CountSacke Well, now I have a mystery on my hands. I don't remember you saying it in the video, hmm...

@@SparklilyCordiale Haha, I didn’t say it was in this video. It’s just in one of my videos.

@@SparklilyCordiale I mean, do you really want to know?

@CountSacke Oh you. What an evil genius. Your cunning scheme worked. I will now watch all of your videos. I was going to watch them anyway, but now I'm also intrigued :D

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

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.

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.

@@CountSackeI am not doing the testing myself but i respect the efforts you put in.

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 :)

@@CountSacke yes, that definitely did clarify very clearly.

@@primary4075 I can’t really tell if you’re being sarcastic or not :/

Haha thank you :)

Thanks for the compliments. It's great to know that there are people who are looking for these things. In terms of the actual data I've collected, now that you've mentioned it, letting people see the spreadsheet itself would be much more convenient for people. I'd be happy to share a view-only link to the spreadsheet I used. I'll put it as a pinned comment on this video.

I guess you could say that this is genshin's impact...

Haha thank you. Someone had to measure it eventually :)

Ty ty :)

If it makes you feel better, based on the actual player data, most of the times when people pulled a 5 star was at about 77 pity (that doesn't necessarily say if they got the character they wanted or not). It's worth mentioning that I based my calculations on just pulling ANY 5-star, not necessarily if the pull was the limited-time character. For the 50/50, you should expect that half of the time you win and half the time you lose which seems to be backed up by what you've said. Out of the 6 limited-time characters you mentioned you have, you lost 3 or 4 times which is about half of the time. As you obtain more and more 5 stars, you may sometimes lose or win the 50/50 more frequently than the other but in the grand scheme of things, it should be about half and half when considering a larger amounts of pulls.

Thank you, I'm glad you enjoyed :) Out of curiosity, what value for the gravitational acceleration did you calculate?

@@CountSacke I got 9.525m/s^2 which doesn't make the most sense. Also thank you for recommending other sources.

@@treetrunker573 Ah, I see. As far as I can tell, if you do measurements below 20 m heights or about 1.4s of falling, you don't need to consider air resistance and the terminal velocity. And, you're welcome :)

Slr. Yeah a pretty similar judgement scheme. Your method probably would be better for most people since it's mush simpler and quicker to do lol. I tried to account for the fact that different people care about different things and, well, ended up with a pretty big chart. In creating the chart, I guided myself based on this idea: don't make things too complicated that it's too hard to understand but not too simple that you lose too much important details.

Because it’s Anti-Nightcore

Hmmm, I'm not sure since there isn't really a simple substitute for the fortune slip. Maybe you could beat up treasure hoarders since she caught a criminal in her demo? For my rituals, I always like to find things that relate to the character. If anything, the fortune slip isn't the most related to Navia in the first place. It's more of just something I typically do when I want to wish for a character.

@@CountSacke I have just pulled Navia!! I’m so happy💝 I used some parts of your ritual, and it worked! 🫶🏻

@@Ms_Kocho Nice! Congratulations on getting Navia.

@@CountSacke Thank you💝

Thank you soo much. It means a lot to hear that you found it helpful :) Sorry for replying soo late btw ; - ;

@@CountSackeno it’s ok man I didn’t really care but thanks for replying ❤

PGJoey