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erigold13261 · 1 year ago

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[Okay finally finished my mathing lol. Gonna copy and past stuff into here. It's a lot so I will put my TLDR before the cut, but if you want to see how I got to my conclusion then feel free to read my work]

Alright, this post is just gonna be me realizing I keep fucking up at math. Well not messing up at the math part, but messing up on how I want it to be applied to the power. It’s more just talking through my thought process and why I think certain power percentages wouldn’t work for me. I’ll try to make a last paragraph explaining whatever I come up with in simple terms and put it right up here for people who don’t want to see math lol.

TLDR:

-Pre-revolution NSR starting out had about a 95-5% split of total power produced between Megastar-Lesser artists at around a 65% power output. Hypothetically, Megastars were producing 617.5 units of power (308.75 units per Megastar) per citizen, while Lesser artists were making 164.5 units of power (3.25 units per Lesser) per citizen. This is at a population of 1 million, Megastar count at 2, and Lesser artist count at 10.

-Revolution time NSR had about a 65-35% split of total power produced between Megastar-Lesser artists at around 47% power output. Hypothetically, Megastars were producing 305.5 units of power (61.1 units per Megastar) per citizen, while Lesser artists were making 164.5 units of power (.583 units per Lesser) per citizen. This is at a population of 2 million, Megastar count at 5, and Lesser artist count at 300.

-Post-revolution NSR had about a 52-48% split of total power produced between Megastar-Lesser artists at around 78% power output. Hypothetically, Megastars were producing 405.6 units of power (81.12 units per Megastar) per citizen, while Lesser artists were making 374.4 units of power (.7488 units per Lesser) per citizen. This is at a population of 2.25 million, Megastar count at 5, and Lesser artist count at 500.

[I am going to warn you, it is a lot to read. It is also written in a way that it's more me thinking out loud than super academically written. Also I decided to post screenshots of my math instead of copy and past the text because I color-coded my math a bit and reference that in the writing.]

Okay, so here’s what I ended up doing when it came to the power output math. I was changing the math around to figure out roughly what I wanted the pre-Revolution power output to be between the Megastars and the combined force of the lesser nsrtists. I did a lot of math to try and figure this out but honestly I am really indecisive of what I want the power output percentage to be.

At first I did the entirely wrong set of math. Before I changed what I was originally going to say, I was going to have the Megastars only produce 10-15% more energy than the Lesser artists. However, for some stupid reason my math showed that I made the Lesser artists make up a total of 10-15% of the total energy output. Meaning that instead of producing 10-15% MORE energy, I actually made calculations where the Megastars made up 85-90% of the total 47% output number.

That would mean out of the 47% of total EDM power output, the Megastars were making up 39.95-42.3% of power and the Lesser artists were making up 4.7-7.05% of the total power. I realized this is technically the wrong math only because I had initially wanted the Megastars to be making 10-15% MORE than the Lesser artists.

Because of this realization, I ended up making a small formula that I thought would have fixed this problem (only to now realize this is also not what I was going for). I ended up with the formula 100=x+(x-___).

The 100 represents the total amount of power being produced (this would later be used out of the 47% total power output). The x represents the number I wanted the Megastars to have but didn’t know what it was yet. Finally the minus blank spot was what I knew I wanted the “percent more” to be that the Megastars had over the Lesser artists.

So in my first instances of 100=x+(x-10) and 100=x+(x-15), I thought that this would mean I was making the stance that the Megastars would be making 10-15% more energy than the Lesser artists, but this isn’t the case.

Anyway, what I ended up doing was figuring out what the x would be and technically what a y would be. y in this case would be y=(x-___). I don’t know why I struggled with this part but I did so much I just put the equation into google and got my answer as seen below with the like peach colored text.

x=55 and x=57.5 were the ranges for the Megastars percent of the total power output. While the 7=42.5 and y=45 would be the ranges for the Lesser artists percent of total output.

From here I divided all these numbers by 100, along with the initial 47% so that I can get their decimal versions and turn those into the actual percent of total power they are contributing.

So for the Megastars I did .55*.47=.2585. Then I multiplied that by 100 to get the percent, meaning that on the low end, in this example, the Megastars make up 25.85% of the actual 47%.

I did the math again for the rest of the numbers, but honestly I could have just got the range of the Megastars and then subtract those percentages from the 47% to get the range of total power the Lesser artists were producing. So 47-25.85=21.15. That means that the Lesser artists total power output, in this example, is 21.15% out of the total 47%.

I then went on to do this for a few other versions of ranges because I initially felt that the peach ranges above put way too much emphasis on the Lesser artists. I don’t know why but I wanted the Lesser artists to be a bit less in their power so it is justified to have Megastars in the first place.

This led to quite a few trial and error math problems as I didn’t realize I could work backwards until after I had done most of this math. I also just had fun doing the math so it wasn’t a bother.

Anyway, this blue version shows (at the time what I thought) was the Megastars making 30-45% more power output than the Lesser artists.

For some reason I still didn’t like that. The levels seemed too close to me for some reason, so I went and did a more drastic number at 80-95% range.

However, the major problem with this yellow range is that it makes the Lesser artists almost powerless. They wouldn’t be making anywhere near enough power to make up for the less performances that the Megastars have and would have made my whole District Music Life post pointless.

(I do kinda see this being the earlier range for the NSRtists like a couple years ago though honestly)

I still wanted the Lesser artists to be making enough of an impact that without their presence, the Megastars would actually have to pick up their shit and do more work. They are supposed to be pretty even but still have enough impact.

At least that is what I think now. I went on to lower the range a bit to this version with 60-75% afterwards.

For some reason I started to like this but changed my mind and went with a new range that I was going to pick last night, but now I am changing my mind.

This range being 75-85%.

Anyway, this was all well and good when I was doing it last night, except that all of these percentages are not what I originally wanted.

I originally wanted the Megastars to be making 10-15% MORE energy output than the Lesser artists. What I ended up doing was figuring out the different ranges of the TOTAL energy output.

I know it’s confusing, it is confusing to me too a bit. But if we look at the green percent range I think I can explain what I mean. I’ll just use one set of numbers in the range actually to make it easier to explain.

The TOTAL output of energy is 47%. The split between that 47% is 41.13% and 5.87%. Megastars make a total energy output of 41.13% and the Lesser artists make a total energy output of 5.87%.

Now if we look at the total as 100%, as that is 100% of the power being made, that means the Megastars are making 87.5% of the total energy output and the Lesser artists are making up 12.5% of the total energy output.

Now, the whole reason why I even started doing this math was so that I could figure out what 10-15% MORE energy output would be like (I’ll just stick to 10% for now to make it simpler). When I say this, and everytime I did say this beforehand, I wasn’t thinking of it in a way that if one is making 30% energy then the other is making 40% energy.

No, instead I was thinking of it as, if one is making 100 units of energy, then the other would be making 110 units of energy. That is 10% more energy. However, that doesn’t really work honestly in all my math and I didn’t realize that at all until after I made all this math.

If we turn the percentages into true units I think I can figure out what it would be. For some reason I am having a hard time working this math when it comes to using only percentages.

Now that I know that my first math based on an equation gives me numbers like this. I was able to make up a new equation that would let me figure out what truly the Megastars would be making vs the Lesser artists if the Megastars were making 10% more power than the Lesser artists.

I needed to do this into units which I could then later turn into a percentage. Instead of starting off with 100, I instead started off with the total 47%. x is what the Megastars will produce while (x-.1x) are what the Lesser artists will produce. .1x is 10% of what the Megastars are making, so taking the number the Megastars are making (x) and subtracting it from what the Lesser artists are making (.1x) would give me the 10% difference while making it all add up to 47 units. y in this case would also be (x-.1x)

So with this idea, the only way that the Megastars would be producing 10% more power than the Lesser artists would be if the Megastars produced 24.47% of power out of 47% (which is 52.64% of all power production) while the Lesser artists make 22.26% out of the total 47% (which is 47.36% of all power production).

To me, this actually seems like a good proportion only AFTER the revolution happens (proportion meaning the 52.64-47.36 split, not the actual output of power unit numbers). Before the revolution happens though, I do think that the power of the Megastars should be a lot greater than the power of the Lesser artists but still have enough of an impact that if the Lesser artists stopped playing it would have been a catastrophe for the city.

So, long story short, I think the power ratings would be something like this.

-Early years of NSR had the Megastars making 92.5-95% of total power while the Lesser artists made around 5-7.5% of the total power. I can see the actual output of power being about 55-65% for a small while (as EDM would have been a new-ish genre) which then slowly settled down to the 47% we see in game.

-By the time of the revolution happening, the Megastars are making up 65-72.5% of the total power while the Lesser artists are making 27.5-35% of total power. This is when the actual output of the power being made was stuck at 47%.

-After the revolution, probably about 2-3 years afterwards, I would say the Megastars are making 52.64% of total power while the Lesser artists are making 47.36% of the total power. The actual output of power would probably be at least 65-75%. And that is at the very least, I can see the actual output being as high as 85-90% of actual power output.

Now I want to see what these numbers would look like if they were of equal standing. I am just going to use these numbers for each. 95-5 split at 65% power for pre-revolution. 65-35 split at 47% power for revolution, and rounding the numbers at a 52-48 split at 78% power for post revolution (just to make it more simple).

Actually, I realize now that it would be extremely difficult to compare these numbers in their entirety because the numbers alone do not represent accurate percentages. Or at least these percentages literally cannot be compared at face value.

This is because these numbers do not take into account the growth of Vinyl City or NSR at the time. They come from completely different time periods.The pre-revolution is around the start of NSR which could be anywhere from 7-10 years ago in my version of it (closer to 10 years ago most likely). On the other hand, the post-revolution would be only 2-3 years after the revolution happened. I don’t think there is a way to really compare these numbers as is without going into the hypothetical maximum energy output (or max energy output needed to run the whole city) that would have been needed at that time in Vinyl City’s life.

So, going into this, the smallest population needed to be classified as a city (most of these numbers I am going to use are probably US approximations) would be 50,000 inhabitants. Research shows that between 200,000 and 500,000 would be like an average city population (at least in the US), and then a large city would be 400,000 and 1,500,000. With really anything over 1,000,000 being seen as a metropolis.

For Vinyl City, I see the city itself as being already on the medium to larger size when the Goolings were ruling the city. So by the time NSR becomes a company, I can definitely see the city being more on the large size. Let’s say, when NSR came to power, the city was around 1,000,000 pre-revolution.

By the time the revolution happened, about 8-10 years later (let’s just round to 10), the city would have definitely gone through a major expansion. Especially as now there would have been a major influx in power production and entertainment because of NSR. However, I kinda see it as a logarithmic growth as the introduction of NSR and the first like 3-5 years of the company really brought a lot more people into the city which then the growth slowly lessened by the time of the 10 year mark. Which is in line with the average city growth that I’ve been seeing in my research (at least in the US, however this research might also be bringing in the pandemic in their research which accounts for the slow in growth).

Because of this, I can see the city becoming extremely big by the end of the decade. To me, 2 million would not be big for some reason, however, that is because I am comparing the number to other larger and more established cities that I know (such as New York City, I was going to also do California but I bailed when LA didn’t have totally accurate census records around the 1950s).

At first I was thinking that just doubling the population wouldn’t be that amazing, especially for a city that is so important like Vinyl City. I realized my error though when I found out I was looking at New York as a whole and not just New York City. Using the annual growth rate from that I actually think it would be an amazing feat for Vinyl City to have doubled its population in only 10 years. It’s not impossible as some other cities are currently on this kind of trajectory. I still think a majority of this growth happened in the first 3-5 years while the last few years have seen a major decrease in growth. Anyway, that goes to say that I think Vinyl City would have a 2,000,000 population at the time of the revolution.

And with that being said. Vinyl city having a slower population growth by the time of the revolution, into the new decade, now needs to be thought of. The average population growth is like .4%, so I honestly think (with how big 10% is by the end of the decade) Vinyl City could be heading towards 4-5% population growth. Still a lot, but also not as much as before. Vinyl City did just have a revolution, however, things are getting better in the city because of said revolution. I think I will go with a 4% growth rate over a 3 year period. This would mean during the time of the story, Vinyl City would have a population of 2,249,728 post revolution.

Now that we have the populations to work with, we need to figure out the average electricity usage of a person. I’m gonna look pretty much only at the US consumption of energy because almost all of these other numbers and statistics come from the US. It’s also because I plan to use statistics from 2000 and 2010, and the power consumption of Malaysia at that time doesn’t seem to fit what I think Vinyl City could possibly have needed/used. This is taking into account the whole country which I plan to address when I do my math.

Mtoe= Millions of tonnes of oil equivalent. This is the energy consumption of all fuel, not just electricity. I’m also just gonna average all this stuff out since I don’t think it is really possible to separate individual energy consumption from company energy consumption. I mean realistically they both need energy, the only difference is that I am going to make my calculations based on consumption per person so the numbers might actually be skewed somehow (I don’t know if they would be higher or lower honestly, but it is something to take into consideration).

There’s also the fact that the website I am using for energy consumption (World Energy & Climate Statistics-2023) does have a breakdown in energy consumption where you can tell how much of a certain energy was used (in our case the electricity consumption is what we will be looking at). However, the NSR world is a world based on music and music being electricity/power. So If I find a good average of how much electricity is used for the world (which I think that website has), I am probably going to either double or triple that number since this world would be using electricity far more than other modes of energy consumption (I doubt it’s FULLY electricity. Heck I might just swap the biggest energy method and make that number electricity. We’ll see when we get to that point).

Okay, let’s just use the 4,500 kWh per year per person since I feel like that would be a realistic energy consumption with how the NSR world presents itself.

Actually. Nevermind. I was going to try and attempt a really complex calculation of all of this information, however, I do not think I know exactly how it would work. I tried to figure out how to find the relationship between kWh and population using the information of the United States and Malaysia, but it was too difficult for me. The two formulas that I found above also did not help and whenever I did try to do some kind of calculation I got a solution that Vinyl City consumed more energy than the entirety of our world, which is obviously wrong. The electricity calculation is just too much for me to do.

So instead I am going to just look up what other cities (or in this case it is countries) have for power consumption and use that. I’m going to try and keep the per capita around 3,500-4,500 kWh as I think that is a reasonable consumption of power given the information I had already found.

Here are some countries that I think have a potentially relatively similar power output to Vinyl City.

These seem fine. I couldn’t find any other countries that had similar populations to what I was looking for and could not find any information on cities that could have helped me. The problem I am having is that I have no idea how to convert the kWh per capita into the total power consumption using the population. I’m not expecting absolute accuracy, but I can’t even get close to the GWh/y number.

At first I tried multiplying the kWh per capita by the population and then converting that into GWh/y, but that doesn’t get me anywhere near the total power consumption. I think the reasoning for this is that the per capita number is only taking into consideration people (or like the average person) and not taking into consideration companies and stuff like that (which I think the total power consumption is).

There is also the idea that I am just doing all of this wrong and there is either a formula or a conversion that I am completely missing out on. Which is entirely the case.

The whole reason I even went into this energy consumption problem was because I wanted to figure out a legitimate measure of power that Vinyl City would have produced in a certain year (pre-rev., rev., post-rev.) so I could take my percentages I got earlier and find an average or per capita (not the word I am looking for) version of the percentages to make them equal.

To me, having the percentages of different time periods of power output doesn’t do much unless you can accurately compare them. Otherwise that is like comparing $50 from a century ago to now. They have completely different meanings to them. 30% of energy output pre-revolution is not the same as 30% energy output post revolution. I just don’t know how to actually get the information needed to find out what the true values would be.

I was initially going to try and make up a single number to calculate my percentages, but that would be more like comparing different cities in the same year than the same city in different years. Then I was going to try and use the Central Limit Theorem because I believe you use that when comparing statistics that come from data with different sample sizes, however that alone was too complex for me to even try. Which is why I started going down the electricity rabbit hole, but the major problem for me was not knowing how electrical conversions work, and not being able to find any good sources of City or Country examples of electrical consumption for large populations because I kept getting websites on prices for electricity or how to figure out my own personal electricity consumption. It was fairly difficult to find sources that would allow me to analyze large portions of electricity data that weren’t hidden behind a paywall or hidden in over 500 pages of other texts that went way above my knowledge level of what was going on.

I’m gonna try one more time to find a solution to me figuring out how to properly compare those percentages that I got. This is all gonna be hypothetical so that I don’t have to keep researching stuff.

I’m going to take the populations of Vinyl City I made, divide them by 1,000, and then make that number the total output needed to give everyone in Vinyl City the proper amount of power.

I think I finally figured this out and that this is the correct way to show the correlations between the three different time periods. Having the per capita numbers means that I now know how much energy was produced for one person in the population.

So what all this data basically boils down to, is that Pre-Revolution Megastars were producing the most power out of the three time periods (617.5 units), then they slowly dipped down a pretty big deal (305.5 units) but are now making their way back up to a slightly respectable power output (405.6 units). They are still not near what they were originally at though as they still perform mainly EDM and EDM at this time is still an oversaturated market. Newer additions of other genres, plus more incorporations of other genres that the Megastars add in, is allowing the Megastars to slowly work their power output back up but are still making up the majority of power output.

The Lesser artists started off at a dismal 32.5 units of power. Barely anything. This is because there were so few artists at the time that even if they were playing the “new” EDM genre, it wasn’t enough to outperform the Megastars present at the time. However, they took a big leap up to 164.5 units of power by the time of the revolution, making up more than half of what the Megastars were making on their own at 374.4 units of power (mainly because of the vast amount of artists now in this section, technically if we figured out a number of artists, it would most likely show that the individual lesser artist is making less power output at the time of the revolution compared to the lesser artists at the time of the start of NSR as a company). Finally, the Lesser artists’ energy basically doubled in output in the span of 3 years. Not only because even more artists were signed on, but now there is a much greater variety of artists playing all kinds of genres. Still, with heavy elements of EDM still saturating the genre of Lesser artists, they are not making as much energy as the Megastars even though they vastly outnumber them.

That last part is actually something to look into. We know there are 5 Megastars (technically more because of like 1010 and Sayu Crew, but I’m just gonna keep it to 5). There is no real way to factually calculate how many Lesser artists there are with this information, so I will give hypotheticals. (Lesser artist numbers are not actual numbers, but just to give an example).

What this information shows us is that at the start of NSR, both Lesser artists and Megastars were producing the most energy per performer. As the music scene became very saturated because of EDM being basically the only genre, more performers were needed to get the same power output. The output drastically died down during the revolution and technically stayed low after the revolution, but it did also rise a bit in the upcoming years. Having output that did rise along with a lot more artists did allow the energy output to become stable. It most likely will continue to grow for as long as new artists are introduced and the genre scene stays varied. If that stays the case then both the power output in general and for individual performers should continue to rise as the years go by.

It is also worth to note that these hypothetical power outputs for the artists are averages. So technically Eve could be making the most power out of all the Megastars while DJSS is slacking in the energy output they are giving. I’m not gonna actually go into real detail about who I think produces the most power because that would then go into schedules and stuff. Just know that the energy output here doesn’t take into consideration how many times an artist plays.

So, as an example, in the pre-revolution stage, 1010 could be making more power than Eve only because they perform a lot more than her, while she makes more power per show. If 1010 played the same rate as Eve, their energy output would be drastically lower than hers, and vice versa with her output being drastically larger if she performed as much as them.

All of this to say, NSR power output has gone through a lot of changes.

TLDR:

#nsr #no straight roads #eritalks #noart #put way too much effort into this #but it was honestly a lot of fun #frustrating at time #but i figured it out eventually #:3

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