This is usually not a concern for countries with a fertility rate slightly below the replacement level, like France, which has maintained a fertility rate of approximately 1.7 - 1.8 children per woman in recent years. That fertility rate means France’s population may decrease slightly during the next few decades, barring immigration. However, it’s a serious concern for South Korea, which currently holds the world's lowest fertility rate at 0.72 children per woman.

If this rate remains constant, South Korea's population could halve before the end of the century1.

There are numerous reasons cited to explain this very low fertility rate: the financial cost of raising children, economic pressures, housing and education costs, and women’s concern with their careers. Given most of those reasons are of an economic nature, it’s not surprising that the South Korean government has chosen to address the issue through economic measures, spending more than 200 billion in the past 16 years towards that end.

Being the skeptic that I am, I decided to check the validity of those economic arguments in explaining low fertility by focusing on a particular group of people who are not financially stressed, don’t worry about the cost of raising an additional child, and don’t have problems affording housing and education for as many children as they desire: billionaires.

For this analysis I’ll focus on South Korean, French and German billionaires. France has a somewhat high fertility rate for a wealthy country, which makes the comparison with South Korean billionaires interesting, while also boasting a large number of billionaires. Germany, on the other hand, has a fertility rate of 1.5 children per woman, falling between South Korea and France2.

The samples

I established the following rules in order to select a good sample of billionaires.

• All living individuals listed as billionaires in the respective Wikipedia entries for each of the three countries are considered for inclusion.

• Many billionaires place a high value on their privacy for understandable reasons, so those for whom no information on the number of children could be found were not included in the sample3.

• Didn’t include anyone bellow the age of 43 because younger people have probably not reached their completed fertility4.

• Didn’t include billionaires who hold the nationality of a country yet have spent the majority of their lives, particularly their formative years, outside that country5. The sample is supposed to be a good representation of the general population of the country in terms of culture.

• Did not include widowers of billionaires, but did include children of billionaires even if they themselves do not appear in a billionaire’s list.

• I also included billionaire families, whose individual members do not necessarily meet the billionaire threshold on their own. These are families (meaning siblings, cousins) who collectively own billions (e.g. the Hériard-Dubreuil family, majority owners of Rémy Cointreau group, valued at more than 9 billion euros).

The purpose of including close family of billionaires and billionaire families is to have a larger sample of very rich people, especially people under 70 years old, who were raised in the same families as billionaires and experienced the same absence of economic hardship. Billionaires tend to be old for obvious reasons, and I wanted to have as many younger people on the sample as possible.

Also, billionaire families include individuals whose net worth is not billions, but only hundreds of millions. They are in the same category as billionaires from the point of view of not having economic constraints when deciding to have children. Yet, because they belong to very prominent families that have preserved their wealth for more than one generation, public information on these individuals is more accessible than on other individuals with hundreds of millions of dollars/euros6. This enabled me to enlarge my sample.

The results

The next chart compares the fertility rates for the general population against the rates for billionaires under the age of 70 in each of the three countries.

The chart reveals some clear patterns.

• In all three countries, the general population rate is considerably lower than the billionaire’s rate. The gap ranges from 1.11 in France to 1.32 in South Korea.

• The fertility rates of billionaires and the general population follow the same order across the countries. France is highest, South Korea is lowest, with Germany in the middle.

• The gaps between Korean billionaires and German/French billionaires, and between the South Korean general population and the French/German population are very similar. This is especially true when comparing Germany and South Korea.

This first point supports the economic arguments for low fertility: billionaires have a significantly higher fertility than the general population in all three countries.

But the third point is the most interesting one in order to understand South Korea’s situation. Korean billionaires have a significantly lower fertility than their French and German peers.

The values of the fertility gaps between South Korean billionaires and French or German billionaires are 0.71 and 0.62 respectively. Those same values for the general population are 0.92 and 0.64, a wider but similar range.

This suggests the existence of a factor, specific to South Korea, a non-economic issue that lowers fertility for both Korean billionaires and the general population.

I should mention that I used a six-year TFR average7 as the fertility rate for each country. Using this average provides a good estimate of the expected number of children for individuals who have recently completed their reproductive years. In fact, if I had used a broader year range the effect would have been a slightly higher Korean general population fertility rate, but a narrower gap between that rate and Germany’s and France’s rate.

In order to make that TFR average comparable to the billionaire’s fertility rate, I considered only billionaires between 43 and 69 years of age, an age bracket close to the one the TFR average is estimating. The next chart shows the decline in fertility when comparing this group to billionaires aged 70 and above.

As you can see in the graph, in Germany and South Korea older billionaires have higher fertility rates, and South Korea shows the largest decline in its billionaire fertility rate. This points again to the existence of a non-economic factor lowering the fertility of all South Koreans.

I don’t want to speculate on what that non-economic factor is. At least not on this post. My goal with this post is to show that economic factors are not the only important ones producing the current collapse of fertility in much of the world.

In the case of South Korea, I think any amount they spend to try to increase fertility will probably be wasted money and have very little effect. And with more and more countries joining the very low fertility group, it might be wise for their governments to think twice before spending billions to little effect.

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Disclaimer: I found out much more about the rich and famous than I ever wanted to know while researching this, but since I’m a very private person and I don’t like sticking my nose in the lives of others I’ve decided to forget each and every personal detail about the lives of these billionaires. Seriously. I’m very good at forgetting things so I expect not to remember anything about any scandals, inheritance fights, and all the other stuff in a few weeks. Maybe a few months.

I explained how the number of review ratings in Rotten Tomatoes (the sample for this analysis) should influence how much an estimated AS, estimated from review ratings, should deviate from RT’s Audience Score produced from all ratings.

I then pointed out that the deviation from the expected AS is very large for some shows with a large sample, a large number of public review ratings, and interestingly the deviation for those shows seems to indicate their AS in the Rotten Tomatoes site if too high compared with the Audience Score estimated from review ratings.

Finally, I remarked on how most of those suspicious shows are Disney shows.

What I didn’t mention in that previous post is that there is, or at least was until 2019, another production company associated with Marvel Entertainment and therefore with Disney. That company is Marvel Television.

For a brief description of Marvel Television I’ll quote Wikipedia:

Marvel Television was an American television production company responsible for live-action and animated… television shows and direct-to-DVD series based on characters from Marvel Comics… The division was transferred to Marvel Studios from Marvel Entertainment in October 2019 and was folded into the former two months later.

To be sure, Marvel Television hasn’t produced new shows after 2021 M.O.D.O.K. and Hit-Monkey, and up until that time it had produced more than 15 shows, all of them based on Marvel’s properties.

Those Marvel Television shows were produced by a different team than the one producing Marvel Studios shows. The Marvel Television shows usually credit as executive producers Jeph Loeb and Joe Quesada, with credit sometimes also for Karim Zreik, Jim Chory, Alan Fine and Stan Lee. The Marvel Studios shows credit as executive producers a different team of people usually headed by Victoria Alonso, Kevin Feige and Louis D'Esposito.

These were two different companies who happened to be owned by the same entity and worked with the same intellectual properties, Marvel’s properties.

Let’s take a look at the list of shows produced by Marvel Television. You’ll notice some of them were broadcast after 2019, but those shows were ordered in 2019 and produced by the same Marvel Television production team.

• Agents of S.H.I.E.L.D. (2013–2020)

• Agent Carter (2015–2016)

• Daredevil (2015–2018)

• Jessica Jones (2015–2019)

• Luke Cage (2016–2018)

• Legion (2017–2019)

• Iron Fist (2017–2018)

• The Defenders (2017)

• Inhumans (2017)

• The Gifted (2017–2019)

• The Punisher (2017–2019)

• Runaways (2017–2019)

• Cloak & Dagger (2018–2019)

• Helstrom (2020)

• M.O.D.O.K. (2021)

• Hit-Monkey (2021)

A few of those shows I’ve mentioned before. marvels_agents_of_shield S06 and marvels_helstrom S01 were included in my lists of shows in the upper tail of the distribution of audience scores (AS) and the lower tail respectively. In fact all Marvel Television shows broadcast in 2019 or later were included in the sample of 343 TV shows used for my previous analysis.

Why am I interested in these shows ? Because they are the closest in terms of subject matter and intended audiences to the Marvel Studios shows whose audience scores I found suspect. They were produced by a different production team but were based on the same Marvel properties as the Marvel Studios shows.

So just like I did in my previous analysis, I calculated a distribution of audience scores differences, this time for all Marvel Television shows for all seasons.

Even though it’s a small number of shows (just 34) you can see that the distribution of AS differences is a normal distribution, with a Skewness value of -0.42, standard deviation (σ) of 10.09, and its platykurtic.

Most important though is the value of it’s mean. The mean for this distribution of AS differences is 1.5, much closer to zero than the mean for the previous distribution of AS differences.

As I discussed in the first article, when doing the first analysis I decided on a cut-off value of at least 50 review ratings in order to avoid shows where just a few reviews could skew the analysis, and in fact shows with few review ratings tend to have higher absolute AS differences as I demonstrated in the second article. So in order to test the strength of this finding I calculated the distribution of AS differences for Marvel Television shows again, this time only for shows with 100 review ratings or more. It increases a little bit but not much: 2.32.

This mean AS difference, whether it’s 1.5 or 2.32 percentage points, is close enough to zero and so to what I would expect if nobody was gaming RT’s audience score system. The mean AS difference I calculated for the original 343 TV shows of my previous analysis, 5.99 percentage points, is not.

Cui bono

When I said the difference between Marvel Studios shows and Marvel Television shows is having been produced by different teams from different companies I neglected to mention another important difference. All those suspicious Marvel Studios shows were broadcast by Disney+, but none of the Marvel Television shows were broadcast by Disney+. They were broadcast by Netflix, FX, ABC, Fox, Hulu and Freeform.

Granted, ABC, FX and Freeform are networks owned by Disney Entertainment, and yet they are different companies with their own management teams.

If a show has bad reviews and low viewership that is a problem not just for the production company but also for the network who bought the streaming rights to that show. And in the case of Hulu, Netflix, etc.. that doesn’t seem to have any correlation with shows having suspicious audience scores, but in the case of Disney+, well….

In closing

With this I rest my case. What I think happened and I’ve tried to prove in these series of posts, is that one or more people inside Marvel Studios - and maybe other people in other Disney properties - intentionally gamed Rotten Tomatoes’ audience score system for their own benefit. Maybe. I’ll let you to decide whether I’ve made a convincing case for it or not.

I don’t think I’ll be doing many more posts focused on the entertaining industry in the future, so if you liked this series of posts I’m very happy that I managed to pique your curiosity and entertain you, but you might want to take a look at my other posts before deciding whether you want to subscribe.

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To sum up that post, I estimated the audience score for 343 TV shows using Rotten Tomatoes’ public reviews (ratings with a corresponding review) and got a distribution of Audience Score (AS) differences between RT’s audience score and my estimated audience score for each show.

Those AS differences follow an unsurprising normal distribution, but some TV shows do seem to have a very peculiar value for AS difference and some unusual characteristics. I focused on the shows Obi-Wan Kenobi S01 and Ms Marvel S01 in the previous post and in this post I would like to present some more data in order to get a clearer picture of what’s going on with Rotten Tomatoes’ audience scores.

If you read the previous post you might remember I mentioned the fact that obi_wan_kenobi S01 and ms_marvel S01 have a very large number of review ratings, and how unusual I thought that was considering their AS difference. I’ll show the upper tail and lower tail of the AS distribution again before explaining why.

The bigger the better

Why do I mention the fact that obi_wan_kenobi and ms_marvel are the shows with the larger number of review ratings in the upper and lower tails ? Because the bigger the sample, review ratings, the better I would expect that sample to reflect the true distribution of all ratings.

The only shows in the lower or upper tail with a number of review ratings approaching that of obi_wan_kenobi and ms_marvel (4853 and 1950) are the_idol and vampire_academy (939 and 1073), but they have an AS difference of -21 and -12 respectively. With many more review ratings obi_wan_kenobi and ms_marvel have an AS difference of 29 and 35 respectively.

So obi_wan_kenobi S01 and ms_marvel S01 already look suspicious, but I want to make sure my conjecture that bigger samples mean smaller AS differences is true. Here I graphed the absolute difference in audience score for each show (if AS difference is -6, then absolute AS difference is 6) against the number of review ratings for that show.

That graph doesn’t show a very clear picture of what I’m trying to figure out, mostly because the_lord_of_the_rings_the_rings_of_power is an outlier in terms of number of review ratings, even though its AS difference is “only” 8. Here’s the same graph without the_lord_of_the_rings_the_rings_of_power.

As you can see, most of the dots are very close to the Y axis (absolute difference close to zero) or very close to the X axis (small number of review ratings, but always 50 or more). I took the liberty of coloring the dots that clearly diverge from that pattern: in green TV shows from the lower tail and in red TV shows from the upper tail. The one green/red dot is actually two dots almost on top of each other.

As you can probably guess, the one of green dot corresponds to the_idol S01. And the 10 red dots are these shows, from right to left:

• ms_marvel S01 (Disney)

• obi_wan_kenobi S01 (Disney)

• hawkeye S01 (Disney)

• the_falcon_and_the_winter_soldier S01 (Disney)

• the_witcher S02 (Netflix)

• game_of_thrones S08 (HBO)

• willow S01 (Disney)

• wandavision S01 (Disney)

• the_wheel_of_time S01 (Amazon)

• she_hulk_attorney_at_law S01 (Disney)

If you know a thing or two about the streaming and television industry you might realize that a pattern is starting to emerge.

Looking at the last sixth show on that list, I was reminded of the time in 2019 when game_of_thrones S08 came out and my first thought was “I’m so happy that it ends and people will stop bugging me about watching it“, but soon I noticed a certain unhappiness in those same people that had been bugging me about watching it. Season 8 of game_of_thrones seems to have been very divisive among its enduring audience and I’m tempted to think that divisiveness might have something to do with my AS estimate being so different from RT’s AS (16% vs 30%). So in order to check if there was something suspicious not just with season 8 of game_of_thrones but with the show in general I estimated the AS from review ratings for all seasons of game_of_thrones, from S01 (broadcast in 2011) to S07 (2017). These are RT’s AS and estimated AS for those 7 seasons:

• S01: RT 96%, estimated 92%, AS difference is 4.

• S02: RT 96%, estimated 93%, AS difference is 3.

• S03: RT 97%, estimated 93%, AS difference is 4.

• S04: RT 97%, estimated 96%, AS difference is 1.

• S05: RT 90%, estimated 81%, AS difference is 9.

• S06: RT 92%, estimated 88%, AS difference is 4.

• S07: RT 81%, estimated 69%, AS difference is 12.

I still feel a bit worried about the fact that AS differences increase from the first seasons to the last seasons. But only a little bit.

About the_witcher S02 (broadcast in 2021), it turns out that the_witcher S01 (broadcast in 2019) is part of the sample of 343 shows, and so I can check the AS difference for the_witcher S01. It’s zero. RT’s audience score is 90% and my estimated audience score for 8911 review ratings is 90%.

Leaving aside game_of_thrones and the_witcher, all other shows from the red dots list except the_wheel_of_time are Disney shows. That seems odd. Is there something unusual about Disney ?

This is the distribution of AS differences for all Disney TV shows.

The two shows in the extreme left of that graph are the_proud_family_louder_and_prouder S01, which I’ve already talked about, and the_proud_family_louder_and_prouder S02 which has a very similar distribution of ratings curve as S01 (zero from 1.5 stars to 4 stars). Even if you don’t take out those two shows that distribution looks very lopsided.

Something you might have noticed when I described the studios that produced or broadcast the 343 shows in the sample is that I considered ABC as a separate studio from Disney. In fact Disney is a very large entertainment conglomerate with many divisions and subdivisions, and one of those divisions is ABC Entertainment. Other divisions are Lucasfilm, the producer of obi_wan_kenobi, and Marvel Studios, the producer of ms_marvel, hawkeye and the_falcon_and_the_winter_soldier.

The next table lists all Marvel Studio, Lucasfilm and Disney shows in the sample.

All audience score differences in red have a one standard deviation from the mean or more, and all shows in red were produced by Marvel Studios and broadcast by Disney+. Notice that shows from Disney (but not Marvel Studios nor Lucasfilm) mostly have a negative AS difference and many of them have an AS difference close to zero.

All audience scores from 60% upwards are considered good (red striped popcorn bucket) by Rotten Tomatoes. All audience scores below 60% are considered bad (green striped toppled popcorn bucket) by RT. If you were a Disney executive, how low would Rotten Tomatoes’ audience score need to be for you to worry about the viewership or profitability of your show? According to RT, every Marvel Studios show in the sample, every show from 2019 to this day except she_hulk_attorney_at_law, has an RT audience score of 80% or more.

With everything I’ve said thus far, I think it’s time to formalize what I think might be happening with Rotten Tomatoes’ audience scores.

The hypotheses

Hypothesis 1: Rotten Tomatoes is altering audience scores knowingly at the request of studios (or streaming services, or show’s producers).

Hypothesis 2: Some studios (or some streaming services, or some producers) are gaming Rotten Tomatoes’ rating system for some shows, and Rotten Tomatoes honestly doesn’t know this gaming happens or intentionally ignores it.

Hypothesis 3: I’m reading too much into this. It’s normal that the estimated AS for review ratings is different than the one for all ratings, and some TV shows will deviate a bit too much from the mean.

I’ll try to tackle hypothesis 2 before talking about hypothesis 1.

One thing that bothered me from the moment I saw the distribution of AS differences was the fact that the mean of the distribution was so high at 6 percentage points. Or at least to me that seemed high. It seemed reasonable that review ratings were not a perfect sample of all ratings but I was expecting a distribution of AS differences with a mean of 1, -1 or maybe 2.

While checking subsamples of the main sample I noticed the distribution of AS differences for shows from the CW and Peacock_NBCUniversal was definitely different than the distribution for all shows. Its mean is 1.7. That mean is closer to what I would have expected before starting my analysis.

This is probably a good moment to mention that Rotten Tomatoes is owned by the CW (WBD) and NBCUniversal (Comcast).

If I had used a 1.7 mean in the previous analysis, the upper and lower tails table would be this.

hawkeye S01 now shows up in the upper tail. No surprises there. But it’s interesting that several season 2, season 3 and season 4 shows are now included in the upper tail of that table. This gives us a chance to test Hypothesis 2, assuming some studios are gaming RT systematically, by looking at several seasons of the same show.

Take the_morning_show for example. Season 2 has a 29 percentage points difference between RT’s AS and the estimated AS. But season 1 is also part of the sample and it’s AS difference is just one percentage point (91% vs 90%). It seems a bit unlikely that someone went to the trouble of adding fake ratings for S02 in order to increase its audience score but didn’t do the same for S01.

Here’s a table with all seasons for another couple of those shows in the upper tail.

You’ll notice there are still no CW and NBCUniversal shows in the upper tail, but there are some HBO shows (westworld, the_undoing).

In order to test the hypothesis that the absence of CW and NBCUniversal shows in the upper tail is just a coincidence I checked for CW or NBCUniversal shows in the upper tail defined by just one standard deviation from the mean (AS difference of 15 or more) instead of two standard deviations. It turns out that good_girls S02 (NBC Universal) and manifest S04 (NBC Universal) are the only shows that are more than one standard deviation over the mean produced by either the CW or Peacock_NBCUniversal. In fact, Manifest was originally an NBC show, but Wikipedia says:

The series was added to Netflix shortly before it was canceled and immediately topped the viewing charts, persuading Netflix to renew Manifest for a fourth and final season

So, by the time manifest S04 was released it was no longer an NBC show, it was a Netflix show. That means that just one show from the CW or Peacock_NBCUniversal is in the upper tail of the distribution of differences, even taking the most generous definition of the upper tail, and it has 57 review ratings so it barely qualified to be considered in this analysis.

To me that doesn’t look like a coincidence. It seems that a show being produced by a studio with no direct relation to Rotten Tomatoes increases the chances of that show having a suspicious Rotten Tomatoes’ audience score, higher than the estimated audience score, and for some studios it’s a dramatic increase. And that would refute Hypothesis 1. If some studios or producers are gaming RT they would probably be aware it’s not in their best interest to mess with a company controlled by their own employer.

Is Hypothesis 2 correct? Are some producers or studios gaming Rotten Tomatoes’ rating system for some shows? I think I’ve presented all the evidence available, at least all the evidence publicly available, for you to make your own judgement.

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Tunelyz World | Insights Visualized

Renewables : Wind Capacity Around the Globe In 2022

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3 years ago · Khalil Gdoura

IRENA doesn’t just coordinate and promote the adoption of renewable energy, but also collects a wealth of information on renewable energy from its more than 160 member countries.

The focus for this article is on solar and wind energy as they are by far the two most important non-conventional (not hydro-power) forms of renewable energy and instead of just comparing the installed capacity for each country we decided to compare the density of installed solar and wind for each country. And by density I mean MW of installed capacity per each 1,000 square kilometers of area.

Here you can see a graph of wind capacity density for 164 countries.

Notice how Belgium, Denmark, Germany, the Netherlands and maybe even the UK have a much higher density than all other countries in the world. The fact that those are very windy countries is probably a factor in that high density.

And here is the same graph but for solar capacity density.

Countries with a very high density in this last graph, much higher than the rest of the world, are Belgium, Germany, Israel, Japan, the Netherlands, South Korea and Taiwan. And as you can see several countries have a high density of wind and solar: Belgium, Germany and the Netherlands, all of them in Northern Europe.

This made me wonder if I should look more closely at Northern Europe.

The previous map highlights all the 23 countries that we will consider for this analysis, most of them part of Northern and Central Europe and one of them, namely Italy, part of Southern Europe. More on Italy later.

The amount of solar radiation on a particular area depends on latitude and cloudiness (or lack thereof), and that means even though Central and Northern Europe are considered as temperate regions of the world they don’t get much solar radiation. The latitude of Central Europe is equivalent to that of Southern Canada, Mongolia or Patagonia. And having higher or lower solar radiation is a very important variable in how much electricity a solar cell will produce.

There’s no solar cell that will produce electricity 24 hours a day simply because the sun doesn’t shine 24 hours a day. And it should come as no surprise that all solar installations produce less than 50% of their nameplate capacity, usually much less, because they can’t generate during the night. That real production which is a factor of nameplate capacity is called capacity factor, and different technologies for producing electricity have different capacity factors which can also vary depending on fuel availability and other factors.

Now that we have a grasp of what a solar capacity factor means, let’s talk about the solar capacity factor for the those 23 Europen countries mentioned above. I’ll call them the Europe 23 from now on. The low solar radiation experienced by those countries would make me expect a low solar capacity factor, and that’s exactly the case. The average solar capacity factor for the Europe 23 is 10.28%. Not only that, but the average for the 8 countries with the largest capacity is just 9.98%.

The sunny countries

Now let’s take a look at another list of countries, 10 countries whose combined population is a little less than 400M people compared with the approximately 420M people of the Europe 23, and the solar capacity factor for each of these new 10 countries.

What these countries have in common is that they are sunny, or at least large parts of these countries are very sunny, and that explains why they have much higher capacity factors as shown on the table, with the average being 30.04%.

Now, let’s make a thought experiment. Suppose those 164,240 MW of solar capacity built in the Europe 23 had been built in the sunny countries instead. What difference would that make?

Assuming nothing else changes (cost of permitting, construction, etc… is the same), and assuming the capacity factor of the sunny countries remains the same even though their total installed capacity would grow approximately 10X, those 164,240 MW would generate around 284,300 GWh additional to the 146,980 GWh generated during 2021, because of the difference between a 10.28% capacity factor and a 30.04% capacity factor.

To put it another way, if those 164,240 MW of solar capacity had been built in the sunny countries, or equivalently sunny regions of the world, instead of the high latitudes regions of Europe that capacity would produce around 431,300 GWh instead of 146,980 GWh.

This is a back of the envelope estimate and should be taken with a big grain of salt. In particular, if 164,240 MW of solar capacity were added to the current solar installed capacity of the sunny countries that would mean increasing their solar capacity around 10 times, and there might not exist enough demand for that energy. Or there might not be enough coal-fired plants to close down if the objective is to reduce CO2 emissions.

To give some perspective on that number, total electricity production in the European Union was 2,785 TWh in 2021. The hypothetical 284,300 GWh that could be produced if the Europe 23 had the same capacity factor as sunny countries do would be 10.21% of that total. That is a large part of the total.

Even if we make the same comparison against the whole world - world electricity production is approximately 26,823 TWh - the hypothetical 284,300 GWh would be 1.06% of the world total. Not a trivial amount of energy.

Is it a good idea to keep building solar capacity in cloudy and high latitude areas of the world ?

A note on Italy

The reason to included Italy as part of the Europe 23 even though it’s not part of Northern Europe is because from the point of view of were its solar capacity is installed it partially looks Central European rather than Southern European. The 8 northern regions of Italy account for 38.4% of installed capacity, the 6 central regions (Tuscany, Marche, Lazio, Umbria, Abruzzo, Molise) account for 24.8% of capacity, and the 6 southern regions account for 36.8%.

Compare this geographic distribution to that of Spain, a country with a similar latitude, where 76.6% of installed solar capacity is in the South. And it’s no wonder then that Italy’s solar capacity factor is 12.7%, not much higher than the 10.28% average for the 23 European countries included in this analysis.

Think of the inclusion of Italy in the Europe 23 not because of it’s latitude but because of it’s low solar capacity factor. And think of the geographic distribution of solar capacity in Italy as a smaller scale example of the situation in the whole world.

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Which was a retweet of this original tweet from January 2022 by the user India in Pixels, showing a map of India with stark differences in the percentage of students enrolled in the humanities between Indian states, some states having more then 50% enrollment while others have less than 5%.

Browsing through the replies to those tweets I noticed that many of them attempted to explain those differences, and the majority of those explanations fell within these groups:

1. People in the North just want to get a government job or even be politicians, and a humanities diploma is required for a government job.

2. There’s a correlation between high enrollment in humanities and lower income level, and that probably means causation in one direction or another. Specially in relation to Uttar Pradesh and Bihar, both states with a very high percentage of students in the humanities according to those tweets, while at the same time being the two poorest states of India in per capita terms.

3. It’s the result of social pressure in the South. And family pressure. Humanities are looked down upon in the South.

4. It’s just the effect of engineering colleges in the South having many students from the North. There are just more engineering colleges in the South.

Not being Indian and therefore not having much context, my reply to that tweet was:

In fact, I thought that 1.6% for Telangana was so incredibly low compared to states like Jharkhand and Bihar that it might be worthwhile to take a look at the data used to support the idea that Northern Indians prefer the humanities while Southern Indians concentrate on technology studies and try to weigh the validity of the explanations offered in those reply tweets.

But before I dive into the data, let me add that the original post by India in Pixels provides a much more nuanced analysis of the graph and in fact is part of a thread with a whole set of graphs, not just for students enrolled in humanities but also technical courses, science, commerce. My intention was to take a look not just at enrollment in the humanities but also in other areas in order to better understand the context of these enrollment figures.

What’s the source for the data that was used to produce those maps and how did I get my hands on it ?

The education enrollment data for India comes from the National Sample Survey site from the Indian Ministry of Statistics and Programme Implementation. I downloaded the Household Social Consumption: Education, NSS 75th Round Schedule-25.2 :July 2017-June 2018 which is the same data mentioned as the source for the original tweet, and took a look at it myself. The households participating in the survey were randomly selected based on a sampling procedure. There were a few extra steps involved before I could actually work with the data (install the Nesstar data browsing program, export) but I won’t bore you with the details.

Also, the survey is divided into several blocks with each block focusing on a particular aspect of households. The block I mostly used for this analysis is the one concerned with education, consisting of persons between the ages of 3 and 35 who were studying at the time of the survey.

But before digging into the survey data I took a look at a few very large households in order to get a better understanding of the data before doing any analysis.

Here’s the first such household with 14 persons between the ages of 3 and 35 who are studying some course.

As you can see most students fall into the upto class X category for Course attending, which is to be expected given that 97% of Indian children between 3 and 15 years old are enrolled in those classes. And I should mention that the Course attending and Enrol basic course fields of this database are the ones that I’ll be focusing on during this whole analysis because they are the ones that answer the questions “how many students are enrolled in the humanities?“ and “how many students are pursuing humanities degrees?“

Let’s check another very large household now.

You can see there that humanities as a Course attending value can be a graduate course or a higher secondary course. In fact students attending a humanities course are for the most part enrolled in a graduate or higher secondary course (92%) but they can be enrolled in any of these courses:

• Secondary

• Higher secondary (49%)

• Diploma /certificate course (upto secondary)

• Diploma /certificate course (higher secondary)

• Diploma /certificate course (graduation and above)

• Graduate (43%)

• Post-graduate and above (7%)

And that makes me wonder if most students pursuing courses in the humanities are actually in higher secondary (grades or classes 11 and 12) courses, not in tertiary education or pursuing a diploma. In order to understand what is it that high secondary education students are engaged in I graphed the values for Course attending for all students enrolled in higher secondary education.

That graph reflects the fact that there are three core streams for higher secondary students to take in India: Humanities, Science and Commerce. And if I understand the university entry system in India correctly, the fact that a student chose a particular core stream does not preclude studying subjects related to another core stream or obtaining a diploma related to another core stream.

So including students in higher secondary education who chose the humanities stream in “students enrolled in the humanities“ category does not make sense. Not if you are interested in what course enrollment means in terms of the Indian job market in general, government jobs in particular, economic development of India, and the science and research output of India.

For what is worth, Bihar has a 59% higher secondary enrollment in humanities and Telangana has a 5% enrollment in the same stream. And yet when it comes to diploma, graduate and post-graduate enrollment only 30% of students in Bihar choose the humanities and only 1.3% of students in Telangana choose the humanities.

That 1.3% is pretty close to the 1.6% reported in the original tweet (maybe the 1.6% includes law), but the 30% for Bihar is far from the 70.5% reported. In fact I made a table of enrollment in the humanities for diploma, graduate and post-graduate courses considering 29 Indian states and union territories, and it shows much less of a difference between the North and the South of India than what the original tweet reported.

Compared to the original figures the percentages in this table exhibit some important differences:

• There is no state where a majority of students are enrolled in the humanities.

• There’s still a clear difference between enrollment in the North and the South although a much smaller one. And the area of India with the highest enrollment in humanities doesn’t seem to be just the North in general but the Northeast in particular.

• Jharkhand and Bihar are not the states with the highest enrollment in the humanities. The three states with the highest enrollment are all in the Northeast of India, including Assam. And even if we ignore Arunachal Pradesh, Tripura and Meghalaya because they were not considered in the original tweet, Jharkhand goes down to second place and Bihar goes down to third place tied with Rajasthan.

• The geographic divide between North and South is not so clear anymore, with Goa and Gujarat having a 4% enrollment in the humanities which is in the same range as the Southern states.

Still, the percentages for enrollment in the humanities for the states with the highest enrollment (Northeast India) seem to be around 25 to 30 times greater than the percentages for the states with the lowest enrollment (Andhra Pradesh and Telangana). And 20 to 25 times greater for Bihar and Uttar Pradesh.

Is this the whole story?

Relative to what

The percentages of students enrolled in diploma, graduate and post-graduate humanities courses still seem very high for several states. However, these percentages are relative to the total enrollment in any diploma, graduate, or post-graduate course.

If 40% of enrolled students are studying humanities out of a total student body that represents only 1% of the population of studying age, say 17 to 26 years, it would be inaccurate to claim an 'excess' of humanities students. Instead, I would say there’s too few people studying for any kind of degree across all areas.

This lead me to the question: what is the percentage of the population between the ages of 17 and 26 enrolled in diploma, graduate and post-graduate humanities courses in relation to the total population within that age group?

I chose the age bracket of 17 to 26 years old because 95% of all students currently enrolled in diploma, graduate and post-graduate studies belong to that age bracket. Here’s the answer:

As can be seen in the previous table Bihar and Uttar Pradesh are now in the 10th and 14th position for highest enrollment of students in the humanities respectively. And now their percentages are just 10 to 12 times greater than the percentages for the states with the lowest enrollment, Andhra Pradesh and Telangana.

There’s still a clear difference between North India and South India but more nuanced than what it seemed before. There are two areas with high enrollment in the humanities now, Northeast India as we saw before, and the extreme North of India: Jammu & Kashmir, Himachal Pradesh and maybe Uttarakhand. Also Delhi and Rajasthan have high enrollment but in the case of Delhi I think it’s safe to assume that being the capital of India it makes a lot of sense for Delhi to have a lot of demand for humanities degrees.

Now would be a good time to take another look at the idea that there’s a correlation between humanities high enrollment and lower income level for Indian states, and for that I graphed the percentage of enrollment in humanities against income per capita (USD PPP) for all the 29 states and territories that I’ve been working with.

I also added a red line eyeballing the tendency that I see in that graph and which matches the correlation value between enrollment and income per capita calculated for those 29 states and territories: -0.32. That is a low but not insignificant correlation, and it doesn’t say by itself what direction the correlation goes. Is it really the case that humanities high enrollment has a (mild) negative effect in the level of income, or maybe it’s just the fact that poverty and few job opportunities motivate people to study anything that might get them a job?

Humanities as a job ticket

In order to cast some light on that last question I calculated the same correlation for all the values of Course attending in the survey.

Some of those correlations seem consistent with the view the STEM studies in general are needed for economic growth but some of them don’t. First, the best correlations are for commerce, management and medicine, none of which I would consider part of STEM.

Second, at least one STEM subject, science, has a small negative correlation with income per capita while the other two, IT/computer and engineering, have a low and medium positive correlation respectively.

But what especially caught my attention is that education has a negative correlation very close to the negative correlation of the humanities.

That seems to lend support to the idea that studying humanities courses is for a lot of people in India a way to get a government job, and education seems like a second best option. This is also supported by the fact that the correlation between male enrollment in education courses and income per capita is a negative -0.38, even stronger that the correlation for all enrollment (male and female).

I hope this post has shed at least some light on this subject, particularly on the validity of the first and second group of tweet replies mentioned earlier. I intend to follow up in the next few days with a few data backed observations on group number four of tweet replies (“engineering colleges in the South having many students from the North“) and maybe a few more observations drawn out from the survey, which is really a treasure trove of information on India. [Edit: here’s the follow-up]

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I noticed some of these youtubers mentioned some very well known ratings and reviews aggregator sites, especially Rotten Tomatoes (RT for short), when discussing the popular reception of a movie or TV show, and sometimes not just to provide context for their video review but actually casting doubt on the veracity of the ratings scores provided by Rotten Tomatoes.

This puzzled me a bit. Being a popular youtuber doesn’t necessarily make you the most objective TV critic, and yet the numbers guy in me felt a bit uncomfortable about their questioning of a score mechanism, and yes I call it a mechanism, which at first sight seems so simple and transparent. Simple and transparent should mean trustworthy.

The Rotten Tomatoes’ scores that worried me are audience scores, not critics’ scores since I don’t consider myself to be qualified to question a group of critics’ objective opinions about a TV show, but I do consider myself to be competent enough to look for whatever data is publicly available for some TV shows and check whether Rotten Tomatoes’ audience scores for those shows make sense.

And the public data that is available are audience reviews left by users of Rotten Tomatoes for movies and TV shows, not all ratings left by users of RT. So I started digging into the audience reviews data for a sample of TV shows, trying to figure out a way to corroborate RT’s audience scores, and I focused on TV shows instead of movies because they are easier to check for technical reasons.

If you don’t care much about my criteria for choosing the sample of TV shows and already know how RT calculates audience scores for TV shows, then skip the next two sections and go straight to Calculating my own audience score ratings.

The sample

The sample I chose consists of 343 TV shows. Some of those shows are actually different seasons of the same show, such as Cobra Kai. Cobra Kai season 2 came out in 2019, s03 in 2021, s04 in 2021, and s05 in 2022, so those 4 seasons count as 4 shows and each of them has its own audience score in RT and its own reviews. From now on when I talk of a TV show I’m actually talking of a certain show for a certain season.

If you are wondering why I didn’t mention Cobra Kai s01, it’s because I limited the year in which shows were broadcast to a range from 2019 to 2023. Before 2019 there were fewer shows made by Disney and Apple (Apple TV+ didn’t exist) and that made those years less interesting than the last 5 years.

I’ve uploaded the list of shows to GitHub in case you want to take look at the whole list, and if you do you might realize there are not many small little known shows in that list. That is because another consideration in choosing my sample of shows was to include only shows with at least 50 public reviews, in order to avoid shows where just a few reviews could bias the analysis. That means a show like Wellmania with only 16 public reviews as of today doesn’t get included, despite the fact that RT says it has 50+ ratings because RT counts even ratings without a corresponding public review.

I restricted the sample to TV shows in the most popular genres, trying to include all shows in those genres in order to avoid cherry picking while at the same time limiting the genres so the sample didn’t grow too big. That means not including any sports dramas, no “unscripted” shows, no “reality” shows, no docuseries, no shows in languages other than English, no anime, and most important of all… NO musicals.

Finally, I restricted the sample to shows produced and broadcast by these studios or streaming services: ABC, Amazon, Apple, CW, Disney, HBO, Hulu, Netflix, Paramount, Peacock/NBCUniversal. These are not just the biggest producers of TV shows for the American market but most of the World.

All data for the shows in this sample I obtained during the third and fourth weeks of June 2023. And a note on naming of the shows. Throughout this article I’ll use the normalized Rotten Tomatoes names for shows, meaning I’ll prefer the_lord_of_the_rings_the_rings_of_power to The Lord of the Rings: The Rings of Power.

Next, I’ll explain a few things about RT’s ratings and reviews. If you are already familiar with those and know how RT calculates audience scores for TV shows, then skip the next section and go straight to Calculating my own audience score ratings.

How does RT calculate the audience score for a TV show?

RT takes all the ratings from all the users who rated that show and calculates the percentage of users that rated the show 3.5 stars (on a scale of 0.5 to 5 stars) or higher.

So, for these made up ratings for an unnamed show:

We’ve got 4 ratings: 2 stars, 5 stars, 3.5 stars and 3 stars, and so the audience score would be 50% because two out of four ratings are 3.5 stars or higher. And there’s definitely something wrong with the captain’s hair.

In that example all four ratings were left by users who also left a review, but in real life a lot of users just leave a rating for a TV show without writing a review, and those ratings without a review are also considered by RT when calculating the audience score.

From now on, when I talk about review ratings I mean ratings that are public because they have a corresponding review.

Calculating my own audience score ratings

Rotten Tomatoes does something very sensible when you browse through all the reviews for a TV show. It shows you reviews with their corresponding 0.5 to 5 star rating but doesn’t show you ratings without a review, even though all ratings are considered when calculating the audience score. Since my goal was to check whether there was something fishy with audience scores for some TV shows, I thought that a good way to do that was to calculate the audience score not from all the ratings for a show - which RT doesn’t publish - but from those ratings that are public because they have a review.

Of course estimating the audience score from the ratings of (public) reviews is not perfect. I can only estimate what fraction of all user ratings are review ratings for a show, because RT does not show the exact total of all ratings for a show, but a rough estimate says it’s usually between 15% and 50%. That should be a good sampling of all the ratings assuming nothing biases that sample, such as users who leave a review being more likely to rate a show lower than all users who rated that show or more likely to rate a show higher. In general, any change in the distribution of ratings between review ratings and all ratings will produce a difference between RT’s audience score and my estimated audience score.

What do I mean by distribution of ratings ? This.

As you can see from the graph most shows are hated by a lot of people, loved by a lot of people, or both.

If the distribution of ratings for my sample (review ratings) is different from the real distribution of ratings, the one only RT knows, then almost certainly my estimated audience score will be different from RT’s audience score. How much different?

Here is a (made up) case were the difference is zero:

And here is a case where the difference is 8 percentage points (73% vs 65%):

And here is a case where the difference is 14 percentage points (83% vs 69%):

The larger the difference in audience scores the more dissimilar the ratings distribution curves, real and estimated, will need to be.

How different are the audience scores that I estimated from RT’s audience scores?

This is the distribution of differences (AS differences) for all the TV shows and seasons that I used as my sample, with each bar representing how many shows have that much of a difference, positive or negative. Technically, it’s a histogram. For instance, the zero difference bar (in light blue) has a value of 13 indicating that 13 TV shows have zero difference between the audience score that I estimated from public review ratings and the audience score that RT gives for those shows.

Assuming there is no bias in the review ratings compared to all ratings the previous graph should show something close to a normal distribution centered on the bar for zero difference. But it doesn’t.

It shows that most estimated audience scores are lower than RT’s audience scores. That is what positive values for difference indicate, while negative values for difference indicate estimated AS that are higher than RT’s AS.

The average (mean or μ) for that distribution is a 5.99 percentage points difference, so for the “average” show my estimated audience score is 6 percentage points lower than RT’s audience score (e.g: 80% vs 74%).

That seems unusual if there is no bias in the review ratings.

I’m not implying that every show with a positive difference in that graph has a suspicious audience score in RT. I’m also not implying that all shows with a positive difference greater than the mean (greater then 6) have a suspicious audience score in RT. But that distribution taken as a whole does look a bit fishy, so I decided to keep digging.

Given the mean and standard deviation for this distribution, I would expect around 15.9% of all TV shows to have an estimated AS difference bellow -2.66 and around 15.9% of all TV shows to have an estimated AS difference above 14.64.

This is a good way to visualize why:

Actually, 50 shows out of the total of 343 have a difference of 15 or more and 39 shows have a difference of -3 or less, as shown here:

Now let’s take a closer look at those shows in the upper tail and the lower tail of the distribution of AS differences, the ones in the red bars of the previous graph.

As I’ve mentioned before, I decided on a cut-off value of at least 50 review ratings in order to avoid shows where just a few reviews could skew the analysis. Maybe most of those shows in the upper and lower tails of the distribution are close to the 50 review ratings threshold and that explains why they have such a large AS difference ?

When it comes to the lower tail, the shows for which I estimate a higher audience score than RT, that seems to be the case, with an average of 225 review ratings per show and a third of shows having 75 review ratings or less.

But for the upper tail the picture is not so clear. The average is 419 review ratings per show, and only 18% of those shows have 75 review ratings or less.

So shows in the lower tail are smaller. Smaller than all shows - the average number of review ratings for all shows is 481 - and much smaller than shows in the upper tail. And that was to be expected. What is unexpected is that shows in the upper tail are somewhat big.

Upper tail, lower tail and review ratings curves

I did a similar check for two standard deviations from the mean, a more extreme lower tail and upper tail, and the average number of review ratings in the more extreme lower tail is now 239 while the average number of review ratings in the more extreme upper tail is now 863. This is very odd.

These are the shows in both tails with more than 75 review ratings.

You’ll notice that generally the absolute values for AS difference for the upper tail are higher than those for the lower tail. This is to be expected considering the mean of the distribution of AS differences is 6. marvels_agents_of_shield S06 is just as far from the mean (26 - 6 = 20) than ginny_and_georgia S01 (-14 - 6 = -20).

A few shows stand out in that table due to having a higher number of review ratings, being very far from the mean, or both: ms_marvel S01, obi_wan_kenobi S01, the_handmaids_tale S03, gotham_knights S01, ginny_and_georgia S01, superman_and_lois S01, the_idol S01, the_proud_family_louder_and_prouder S01, vampire_academy S01.

But the ones in the upper tail are much farther away from zero, not just the mean, than the ones in the lower tail, meaning the difference between RT’s audience score and my estimated audience score is much higher for those shows than it is for ginny_and_georgia (-14), superman_and_lois (-15) and vampire_academy (-12). I’ll leave those three shows for later, and concentrate now on the remaining five shows: ms_marvel, obi_wan_kenobi, the_handmaids_tale, the_idol and the_proud_family_louder_and_prouder.

Remember the distribution of ratings curves we saw before ? Let’s take a look at the distribution of ratings curves for obi_wan_kenobi S01, the_handmaids_tale S03 and a few other shows.

I purposefully didn’t tag each of the 6 shows in that graph. The estimated AS for obi_wan_kenobi and the_handmaids_tale are 34% and 35% and I graphed the curves for them and for the other four shows with an estimated AS within 4 percentage points of obi_wan_kenobi and the_handmaids_tale. Can you pick the curves for obi_wan_kenobi and the_handmaids_tale in that graph ? Here are the 6 shows.

If my AS estimations are wrong for obi_wan_kenobi and the_handmaids_tale then there must be something very unusual with the review ratings for those two shows as compared with all ratings, and if there is something very unusual with the review ratings of those two shows then I would expect the distribution of ratings curves for them to look very different from the other four curves. You can see in the table that the other four shows have much smaller differences between the estimated AS and RT’s AS, so the estimated curve and RT’s all ratings curve should be similar.

Another way of stating the previous paragraph is, if I’m pretty confident that la_brea’s estimated curve is close to RT’s curve because there is a small AS difference, then I’m pretty confident that la_brea’s review ratings are a good representation of all ratings for la_brea. And if the_handmaids_tale’s review ratings are a bad representation of all the_handmaids_tale’s ratings then why would its curve, a curve constructed from review ratings not all ratings, look similar to the one from la_brea ?

There is a problem with the argument I just made and it’s this. If review ratings for a show are biased compared to all ratings for that show it doesn’t follow that the review ratings curve must be unusual. But in the previous graph the curve for the_handmaids_tale S03 is the one tagged “show F“, which is one curve you probably picked, and that might be related to review ratings of the_handmaids_tale being a bad sample.

Let’s now look at the curves for a couple of shows on the lower tail.

Among the 9 shows in the previous graph are the_proud_family_louder_and_prouder S01 and vampire_academy S01, and they both have an estimated AS of 56%. Can you pick the curves for those two shows ?

Assuming that you picked show A and show F, notice how those curves not only have values close to zero from the 2 star rating to the 3.5 star rating but also have a higher value for the 0.5 star rating than all the other shows. What those two curves seem to imply is that those two shows are very divisive for their audience, with almost all review ratings being 0.5 or 5. That seems to me like good evidence that the sample of review ratings is a little biased compared with all ratings.

Here I repeat the same exercise with the_idol S01 (estimated AS 79%).

Asking the same question again seems unnecessary. Yes, show A is the_idol S01.

And now with ms_marvel S01 (estimated AS 45%) from the upper tail.

Show A is not ms_marvel S01. Show C isn’t either.

I won’t present any more curves graphs for now, and I’ll just mention that the graphs for ginny_and_georgia S01 and superman_and_lois S01 don’t show any unusual curve, and the curves for gotham_knights S01 and the_morning_show S02 are only a bit unusual.

To summarize, TV shows in the lower tail have an unusual review ratings curve for the most part, especially those with a larger AS difference. TV shows in the upper tail can be divided into an unusual curve group: the_morning_show and the_handmaids_tale, and a not unusual curve group: obi_wan_kenobi and ms_marvel. Yet obi_wan_kenobi and ms_marvel don’t just stand out for having a not unusual curve but also being the shows with the larger number of review ratings and a much larger AS difference than ginny_and_georgia or superman_and_lois.

Wrapping it all up

Considering all the data that I’ve seen until now, it’s difficult for me to dismiss the idea that there’s something very suspicious about Rotten Tomatoes’ audience scores for Ms Marvel S01 and Obi-Wan Kenobi S01. I can’t be 100% sure what it is simply because I don’t have access to all the data, meaning all the ratings for all users, for those shows. Only Rotten Tomatoes has all the data.

I posted a follow up article with some more analysis, especially focusing on Marvel Studios, so you can ponder whether Rotten Tomatoes’ audience scores are trustworthy or not.

And finally a note on statistics, for the statistically inclined. The average (mean or μ) for the AS difference distribution that I presented in this post is 5.99 percentage points difference and the standard deviation (σ) is 8.65. Skewness is -0.47 and goes to close to zero if TV shows with less than 120 review ratings are taken out of the sample. From the point of view of Kurtosis, the distribution is platykurtic.

And if you found this post interesting or at least entertaining.

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