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Surprising statistical patterns on MIT OpenCourseWare's YouTube channel

Rauan Kaldybaev

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Statistical patterns on MIT OpenCourseWare’s YouTube channel

The current essay analyzes the number likes, dislikes, and views at MIT OpenCourseWare’s YouTube channel, where some of MIT’s courses are published. The essay looks at 95 courses. An interesting pattern is that some lectures typically have significantly more likes and views than the other lectures in the same course. In the course 22.01: Introduction to Nuclear Engineering and Ionizing Radiation, for example, the most popular lecture has 185 times more views than the median! And the number of views of the

-th most popular lecture in any of the surveyed courses is very accurately

(

≈0.97

) described by a power law

N≈+k

-γ

for some constants



, which are unique for each course, and

||<<k

. It turns out that the average value of

is roughly 1, which is reminiscent of Zipf’s law. This suggests that most of the views that MIT OCW’s YouTube channel gets come from “laymen” who randomly click the videos rather than students who methodically watch the videos one by one. This conclusion is confirmed by the fact that courses with loud names, such as Introduction to Nuclear Engineering and Ionizing radiation, have a higher variability of views than courses with modest names like Introduction to Solid State Chemistry. While loud names attract many laymen, courses with modest names are mostly viewed by students who systematically watch the lectures. The current essay also compares different majors. Materials science and physics courses were found to have a very high ratio of likes to dislikes, contrary to architecture and urban science & planning. The majors with the highest ratio of likes to views are Nuclear Science and Cognitive Science, and the most popular majors are math and computer science. The majors with the highest unevenness, or variability, in the number of views are Nuclear Science and Biological Engineering, which can be explained by the fact that their content has been “hyped up” by science fiction. As a final note, the reasons for choosing MIT OpenCourseWare as the subject of study (as opposed to, for example, EdX) were: (1) OCW is the largest of its kind, (2) MIT uses a particularly simple course naming system, (3) MIT OpenCourseWare’s YouTube channel is more popular than its competitors’.

Out[]=

Average ratio of likes to dislikes for different majors


Materials science	49.5
Physics	45.7
Cognitive studies	40.0
Biology	34.2
Management	32.4
Mathematics	32.2
Computer science	31.4
Economics	29.9
Chemistry	28.2
Aerospace engineering	27.3
Mechanical engineering	26.7
Chemical engineering	24.2
Nuclear science	21.5
Biological engineering	14.3
Planning	9.0
Architecture	6.4

Out[]=

Extracting the data

Before beginning to analyze the data, we need to first gather it. This step is quite trivial, so reading this section is not that important. Now, getting to the technical part, getVideos returns the list of links to all videos in a given playlist, and videoData returns the number of likes, dislikes, and views for a given video. Together, they can be used to determine the number of likes and and dislikes for all videos in a given playlist. And since lecture courses come in the form of playlists, we can use the functions to find the number of likes, disliked, and views (later called the data) for a given course. What then remains is to make a list of courses and run the program. And lastly, it must be noted that the two functions below only work in Kazakhstan because they assume that the language of the YouTube page is Kazakh. If you run this from somewhere else - Europe, the US, Asia, etc - you would need to figure out what keywords to use when parsing the HTML text. This can be done within 30 minutes by opening some random video and looking through the HTML code of the YouTube player. If the number of views is 47329, then in the HTML you should look for the number 47329. The structure of the page is the same for all videos, so it’s possible to deduce a general rule for finding the data on the video.

In[]:=

ClearAll[getVideos];getVideos[playlist_] := Block[  text = URLRead[playlist]["Body"], shift, truncatedText, marker = "\"title\":{\"runs\":[{\"text\":", markerLen, markerChars, antimarker = "\"YouTube TV\"", antimarkerLen, antimarkerChars, record = True, markerPositions, i, iHelper, j , markerLen = StringLength[marker]; markerChars = Characters[marker]; antimarkerLen = StringLength[antimarker]; antimarkerChars = Characters[antimarker]; shift = StringPosition[text, marker][[1, 1]] - 1; truncatedText = StringJoin@StringPart[text, shift + 1;;]; markerPositions = StringPosition[truncatedText, marker][[All, 2]]; Table[ If[StringPart[truncatedText, pos+1;;pos + antimarkerLen]  antimarkerChars, record = False]; If[record, iHelper = False; For[i = pos, True, i++, If[StringPart[truncatedText, i;;i + 2]  {"u", "r", "l"}, If[iHelper, Break[], iHelper = True]] ]; For[j = i, True, j++, If[StringPart[truncatedText, j]  ",", Break[]] ]; "https://www.youtube.com" <> StringJoin[StringPart[truncatedText, i+6;;j-2]], Nothing ], {pos, markerPositions} ]]

In[]:=

ClearAll[getVideoData];getVideoData[video_] := Block[  text = URLRead[video]["Body"], likesStart, i, dislikesStart, j, viewsStart, k , likesStart = StringPosition[text, "Басқа "][[1, 2]] + 1; For[i = likesStart, StringPart[text, i] ≠ " ", i++, Null]; dislikesStart = StringPosition[text, "басқа "][[1, 2]] + 1; For[j = dislikesStart, StringPart[text, j] ≠ " ", j++, Null]; viewsStart = StringPosition[text, "\"viewCount\":\""][[1, 2]] + 1; For[k = viewsStart, StringPart[text, k] ≠ "\"", k++, Null]; k--;  ToExpression@StringJoin@StringPart[text, viewsStart;;k], ToExpression@StringJoin@StringPart[text, likesStart;;i], ToExpression@StringJoin@StringPart[text, dislikesStart;;j] ]

List of courses


Extract data from YouTube channel

Here is the code that extracts the data from the YouTube channel:

In[]:=

ytData={#[[1]],getVideoData/@getVideos[#[[2]]]}&/@courseList;

In[]:=

ytData

Out[]=

{{15.S08,{{27696,560,15},{6025,132,2},{5405,98,1},{2839,45,0},{5993,144,1},{2417,45,1},{1988,36,1},{1523,23,5},{2431,39,0},{1442,27,0},{2505,45,1},{1117,21,0}}},

⋯93⋯

,{18.06,{{449693,28,27},{530250,3424,138},{1477620,2394,165},{1073601,14,113},{381643,471,58},{627942,604,61},{592047,272,52},{478821,1728,49},{433873,1214,43},{451852,15,44},

⋯16⋯

,{41720,658,4},{175605,14,9},{171605,33,16},{37280,621,4},{43984,583,15},{269526,756,29},{27089,428,1},{108989,401,10},{154218,809,6},{143023,0,8}}}}

large output

show less

show all

set size limit...

And since it takes forever to run, I’ve recorded the output it produces and copied it into the notebook like that, so that the code would not have to be executed every time:

ytData =

YouTube data

;

It must be noted that the data above was gathered in January 2021, so by the time you read the essay, the actual numbers might change. ytData is a list of the form {..., {name, {lec1, lec2, ... }}, ...}, where name is the name of a course and lec1 represents the first lecture in the course. lec1 is of the form {views, likes, dislikes}.

The student-layman model and Zipf’s law

Introducing the model

The first thing that we notice when looking at the number of views for the lectures in a given course is that the numbers are highly uneven. Here, for example, is the data for the course 6.172:

In[]:=

ListPlot[ReverseSort@ytData[[11,2,All,1]],PlotRangeAll]

Out[]=

Here, the vertical axis is the number of views and the horizontal axis is the lecture’s rank, with the most popular lecture being first, the second most popular lecture being second, and so on. The first lecture has 12.5 times more views than the median. And for the course 22.01, the ratio of the number of views of the most popular lecture to the median number of views is 185! It turns out that the number of times a lecture is viewed is very accurately described by a power law

N≈+k

-γ

for some constants



. For the course 6.172, for example, the law is

N≈-2.9·

+6.06·

-0.853

In[]:=

courseCKGModelPlot[11]

Out[]=

The coefficients

,k,γ

are determined using the method of least squares, in the log scale (see code at the bottom of the subsection). The model seems to be a good fit, and indeed, the value of

is 0.982. The model turns out to be accurate for all courses, as can be seen from the histogram of the values of

for the surveyed courses:

In[]:=

{courseslist,coursesklist,coursesγlist,coursesFVUlist}=Transpose[courseCKGModelFit/@Range[Length[ytData]]];

In[]:=

Histogram[1-coursesFVUlist,AxesLabel{"

",""}]

Out[]=

In[]:=

Median[1-coursesFVUlist]

Out[]=

0.973113

The median value of

is 0.97. Isn’t this amazing how accurate the model is?

Supplemental code


Interesting features

Things become even more interesting if we plot the histogram of the parameter γ in the approximate law

N≈+k

-γ

In[]:=

Histogram[coursesγlist,AxesLabel{"γ",""}]

Out[]=

In[]:=

{Mean[coursesγlist],Median[coursesγlist]}

Out[]=

{0.976588,0.967773}

This is a unimodal distribution centered at 1! This is exactly what we would expect from Zipf’s law, which tells us that the number of views under the

-th most popular lecture in a course should be

times smaller than the number of views under the most popular lecture. And the distribution’s shape is similar to the bell curve, which is also quite satisfying. Also, notice that most of the times,



is much less than

In[]:=

Histogram[courseslist/coursesklist,AxesLabel{"/k",""}]

Out[]=

Most of the times, the ratio

/k

is between -0.05 and 0.05. Also, since the distribution looks like a symmetric zero-centered distribution with a left tail, one might suspect that the departures from 0 are caused by some sort of noise, and that the “normal” value of  is zero.

Interpretation

The number of views a lecture has can be represented as a sum of two components: students, who pedantically watch all the lectures in order, and “laymen”, who click on the lectures either accidentally or because of their loud names. The number of student views stays constant from lecture to lecture, while the number of laymen views changes. Comparing that to the empirical law

N≈+k

-γ

, we would expect



to tell us the number of students, and

- the number of laymen. The constant γ controls how quickly the number of views decays with the lecture’s rank, which roughly translates to how quickly laymen get bored with the lecture content. This can’t be quite right because



is often negative, but still, it’s reasonable to think that



and

are somehow related to the number of students and laymen. The reason why γ often comes out negative is probably that the number of views actually falls off a bit faster than a power law.

In[]:=

ytData[[#,1]]&/@(Reverse@Ordering@coursesγlist)

Out[]=

{14.73,14.772,20.010J,16.01,6.832,15.S50,2.830J,8.962,22.01,5.112,6.01SC,18.650,16.687,20.219,18.217,9.00SC,6.042J,3.091,6.0002,6.450,6.172,15.S08,8.04,6.851,5.60,9.40,7.013,3.021J,6.858,18.S096,6.001,15.S12,6.262,6.S897,6.013,11.601,8.851,10.34,6.002,8.286,8.421,3.60,6.849,8.334,8.422,5.95J,6.451,18.086,2.003SC,7.012,6.890,18.01,8.333,8.821,14.01SC,8.05,6.033,8.591J,5.80,2.71,5.07SC,6.172,3.320,6.006,5.61,7.016,6.034,6.189,5.08J,6.041,18.085,8.03SC,9.04,18.065,18.03,6.868J,2.627,16.885J,6.003,6.02,18.02,15.401,18.03SC,3.054,7.014,15.031J,16.842,4.696,7.01SC,6.0001,6.046J,7.91J,18.06,5.111,2.003J}

This interpretation can be tested by looking at how the course’s γ constant relates to its content. In the list below, you can see courses sorted by their γ’s, with courses whose γ is largest coming first. The course with the highest γ is 14.73, The Challenge of World Poverty; the next course is again of major 14, Development Economics: Macroeconomics (it seems like there is something special about the major). The third course is 20.010J, Introduction to Bioengineering. All the three courses have very loud names that can be exciting and attractive to a wide audience. But now, look at the course 2.003J, whose view count is the most uniform. Its name is Dynamics and Control I, which means nothing to an average person. The next course is 5.111, which has the modest name Introduction to Chemical Science. A possible explanation for this phenomenon in the framework of the student-layman model is that people are attracted by some of the courses’ bright names but later leave the courses because they didn’t fulfil the high expectations. Courses with modest names, on the other hand, are watched by people who know what they are looking for and hence won’t change their mind in the middle of the course. And can we use the interpretation to explain why the approximate law is

N≈+k

-γ

and not, for example,

N≈+kExp[-γn]

? In other words, why are the numbers described by a power law? An explanation is that the number of laymen watching a particular lecture depends on how much views the lecture already has. The more popular the lecture is, the more popular it becomes - it’s like a snowball. And snowball-type processes are known to be described by power laws. Why does the exponent on average equal -1? Must be some feature of the YouTube algorithm.

Comparing courses

Max to median views

The previous section looked at the unevenness in the number of views of the lectures. Continuing on this topic, let us compare the courses by how the number of views of their most popular lecture relates to the median number of views. In other words, let us compare the courses by

Max[views]/Median[views]

, where views[[i]] tells us the number of views of the i-th lecture:

In[]:=

ClearAll[getMaxToMedianViews];getMaxToMedianViews[courseData_] := Block[{views = courseData[[2, All, 1]]}, Max[views] / Median[views]];

In[]:=

coursesByMaxToMedianViews=Reverse@Ordering[getMaxToMedianViews/@ytData]

Out[]=

{10,27,75,4,58,2,66,87,17,3,57,69,90,82,41,80,37,64,52,63,71,89,8,51,29,60,53,62,73,74,93,38,65,6,7,14,13,16,21,50,67,92,77,36,81,35,86,28,19,68,9,39,76,25,15,46,32,34,5,11,94,47,20,12,85,30,79,22,84,1,59,61,49,40,83,78,31,56,91,45,26,42,88,44,54,55,24,18,33,70,95,48,23,72,43}

In[]:=

ytData[[#,1]]&/@coursesByMaxToMedianViews

Out[]=

{22.01,20.219,6.001,18.217,14.73,3.091,6.01SC,5.112,18.650,8.962,6.006,6.832,16.01,3.60,8.04,5.60,6.849,14.01SC,8.851,18.03SC,2.830J,20.010J,16.687,6.851,6.858,6.262,2.003SC,6.042J,5.80,6.450,18.03,8.422,9.00SC,9.40,6.S897,5.08J,5.61,10.34,5.07SC,14.772,6.172,7.012,18.085,8.333,18.086,18.S096,6.451,6.890,11.601,2.71,15.S12,8.286,6.189,8.821,8.03SC,6.034,8.421,8.334,7.016,6.172,6.002,2.627,6.0002,18.065,6.013,8.591J,18.01,6.0001,6.033,15.S08,6.041,7.01SC,7.013,8.05,3.320,18.02,15.S50,6.003,16.885J,6.868J,6.046J,9.04,7.014,6.02,15.401,15.031J,3.054,16.842,7.91J,5.95J,18.06,3.021J,5.111,4.696,2.003J}

As previously, 2.003J: Dynamics and Control I comes as the course with the most homogenous stats. The most uneven course is now 22.01: Introduction to Nuclear Engineering and Ionizing radiation. Similarly to the result we got by comparing

, courses with loud names tend to have more uneven views than courses with modest names, although the exact ordering has changed quite a bit.

Total views

Let’s now assess courses’ popularity by comparing their total number of views:

In[]:=

ClearAll[getTotalViews];getTotalViews[courseData_] := Total@courseData[[2, All, 1]];

In[]:=

coursesByViews=Reverse@Ordering[getTotalViews/@ytData];

In[]:=

ytData[[#,1]]&/@coursesByViews

Out[]=

{6.006,18.06,18.01,18.03SC,6.034,18.02,18.S096,8.04,18.03,14.01SC,7.01SC,5.60,6.042J,2.003SC,6.041,6.002,6.0001,6.0002,15.401,6.046J,9.00SC,6.001,18.085,18.650,18.065,22.01,5.111,6.858,6.01SC,6.003,15.S50,7.012,8.05,7.014,14.73,5.112,6.450,8.333,18.086,16.885J,2.627,8.286,7.91J,6.262,6.851,7.013,6.033,6.868J,8.03SC,3.60,15.S12,6.451,6.849,16.842,5.07SC,8.962,7.016,8.422,2.71,6.189,6.832,8.591J,9.04,6.02,15.031J,5.61,6.172,6.013,8.421,8.821,16.687,20.010J,6.890,8.334,3.054,2.830J,6.172,14.772,3.320,10.34,2.003J,8.851,3.021J,16.01,5.08J,18.217,5.95J,5.80,9.40,20.219,6.S897,15.S08,11.601,3.091,4.696}

The most popular course is 6.006: Introduction to Algorithms, and the next most popular one is 18.06: Linear Algebra. These courses are relevant in fields like machine learning and IT, as well as a ton of other industries - probably that’s why they are so popular. Notice that the first seven positions are taken by math and computer science as the most “industrious” fields. The first non-math and non-CS popular courses are 8.04: Quantum mechanics I and 14.01SC: Principles of Microeconomics. The three least popular courses are 4.696: A Global History of Architecture, 3.091: Introduction to Solid State Chemistry and 11.601: Introduction to Environmental Policy and Planning. These are courses with very specific target audience and a comparatively limited practical application (apart from 3.091, which strangely has so few views). It is interesting that 6.S897, a computer science course, is the fifth least popular course, as CS is the most popular major. The explanation is probably that the course is very specific: its name is Machine Learning for Health Care, which is only going to attract a few narrow specialists. All in all, it can be seen that majors relevant in industry, such as computer science and math, are the most popular, while courses with a narrow target audience and comparatively limited practical applications get the least number of views.

In[]:=

{BarChart[getTotalViews@ytData[[#]]&/@coursesByViews[[;;7]],ChartLabels(ytData[[#,1]]&/@coursesByViews[[;;7]]),BarSpacing0.5,PlotLabel"Top 7 courses by the percentage of likes to views",ImageSizeMedium],BarChart[getTotalViews@ytData[[#]]&/@coursesByViews[[-7;;]],ChartLabels(ytData[[#,1]]&/@coursesByViews[[-7;;]]),BarSpacing0.5,PlotLabel"Bottom 7 courses by the percentage of likes to views",ImageSizeMedium]}

Out[]=





In[]:=

Histogram[getTotalViews/@ytData,40,PlotLabel"Total number of views",PlotRange{{0,2*

},All}]

Out[]=

Likes to dislikes

Having assessed the courses’ popularity, it would now be interesting to evaluate how enjoyable they are by comparing the total number of likes to the total number of dislikes they have. The idea is that the more exciting is the course, the higher is the ratio of likes to dislikes. There are of course some issues with this metric - for example, since there are far more laymen than students, the data we get will reflect the preferences of laymen - it’s still a fairly reasonable way to measure how exciting the course’s content is. So, here is the code:

In[]:=

ClearAll[getTotalLikes];getTotalLikes[courseData_] := Total@courseData[[2, All, 2]];ClearAll[getTotalDislikes];getTotalDislikes[course

Surprising statistical patterns on MIT OpenCourseWare's YouTube channel

Extracting the data

List of courses

Extract data from YouTube channel

The student-layman model and Zipf’s law

Introducing the model

Supplemental code

Interesting features

Interpretation

Comparing courses

Max to median views

Total views

Likes to dislikes

List of courses


Supplemental code
