YouTube-Differential-Analytics

Applied Mathematical Modelling

Faysal.El.Khettabi@gmail.com

This essay is a non-technical overview of some subjects related to my field of research, modeling big data using numerics and analytics. You don't have to be a mathematician to read it. If you have any questions or suggestions I'd be glad to hear from you.

We study the monetization problem faced by YouTube channels that provide a number of videos, presented via a wide range of annotations, to viewers that arrive over time. The goal of a channel is to design an optimal policy that maximizes the collected revenue from the enabled monetization process. Our motivation is to discuss a real-time dynamic profitability framework for this kind of on-line platform involving free charged viewer and monetized advertisers for its profitability.

Our hope is to foster a holistic and consistent quantitative framework to be empirically informative for the monetization process in the field of Connected Viewing by examining together elements and processes normally studied separately. This holistic and consistent design process for the monetization process in the field of Connected Viewing is presented in this essay using YouTube platform as an example.

Introduction:

Youtube explains "how to earn money from your videos" as completing three step:

What does monetize your video mean?

Monetization is a simple process that requires you to agree to YouTube's terms and conditions for advertising. Once you agree to the terms, you can allow ads to run with your videos, and YouTube will share of portion of the ad revenue with you. Certainly, there are social, cultural and economic determinants for an adequate monetization:

Some Scenarios

This process to make money sounds like a social casino, no earnings on your monetized videos may be a fact, You DO NOT make money based on the amount of views( function of the number of users watching your videos) you have. You make money based on user’s engagement with the advertisements where engagement means, for instance, the users are not skipping the advertisements when they are playing:

The network effect is subject to an audience that "watch what they want to watch, when they want to watch it" making a critical mass formation hard to achieve, i.e. the platform, the channels and the advertisers require a critical mass of viewers for growth to continue.

Some Solutions



Most Popular Videos in YouTube

A statistical analysis is conducted to decipher some numerical facts about categories and most popular videos in YouTube platform, see, YouTube Most Popular Videos: Learning Engagement With Bursting Velocity.

Thinking Mathematically: Numerics & Analytics:

The most important point of this essay, it's possible to mathematically model these processes:

into one unified dynamical system.

Although the users, interested by a specific video on YouTube, consist of a number of individuals, their aggregate interactions can be effectively modeled by a dynamical system that involves continuously varying variables related to the anticipated "Revenue per thousand impressions".

This system of equations describes, the changes over time that occur between the flowing capital and the monetization taking into consideration the users interaction frequency with the content (videos). This system offers a more quantitative, theoretical, and mechanistic approach to explanation and prediction of emergent characteristics generated by the processes:

This system of equations constitutes a simulation model to define how a system changes over time, given its current state (initial departure). Unlike analytical models, this simulation model provides the changes of system states ( real time dynamic profitability) that can be observed at any point in time based on specific inputs. This tool provides an insight, i.e. decision support tool to assess the involved processes.

Numerical Results:

In general, the expected revenue level of capital to be earned by a channel from its proposed videos is time dependent. This time dependent profitability function is generated implicitly by the active viewers on the YouTube platform and the presence of advertisement on viewed or streamed videos. We assume that the channel may experience a revenue loss that may occurs when these source of profitability (advertisement) are not monetized adequately (viewers continually are skipping them).

The profitability dynamics modeled by our system of differential equations are not generally solved in closed form. We use numerical solutions to solve some important scenarios to assess the profitability using a number of traffic intensities representing the "viewer interactions with the channel", considering that the viewer is freely skipping the adds, to model the monetization as is happening accordingly to a well-established expectancy function.

Our illustrative numerical simulations consider the traffic intensity and policy effect on the dynamics of the profitability. The traffic intensity is mainly related to how much the channel is considered by the viewers. The traffic intensity is a fundamental parameter to monitor the dynamics of the profitability ( when the traffic intensity is equal to zero, the dynamics of the profitability is simply defined as a null function).

The policy effect is considered as a two-variables function that is depending on the level of profitability and its first-order time derivative. We assume that more the channel is appreciated more advertisements are attracted with adequate monetization. The policy effect function is quantified as a decreasing function. More the profitability is higher, the perturbation on the future ones is minimized, future profitability is expected to rise or increase adequately.

Interestingly enough, the policy effect function should be crafted in response to viewer or audience engagement to boost the channel's earnings.

Qualitative Analysis.

We reduce our system of differential equations to two independent variables. In two-dimensional models, the temporal evolution of these two variables can be visualized in the so-called phase plane. Our reduced system of differential equations has two variables, Realized-Profitability and Expected-Profitability. The nullclines are very informative to conduct a qualitative analysis to answer some questions, questions related to the short/long term behavior of profitability given a number of conditions.

Plainly, nullcline divides the phase plane in two different regions: one where the rate of change of the respective variable is positive and one where it is negative. Phase portrait of our reduced system of differential equations: Figure below associated to a fixed policy effect function and variable traffic intensity.



Figure below, for a fixed traffic intensity, we change the parameters related to function policy effect. The four policy effect functions are sorted from the more noisy (policy 1) to less noisy (policy 4).



Quantitative Analysis.

We use a number of traffic intensities and using two different policy effect functions. A perfect policy effect function is adding no perturbation on the Expected-Profitability and a noisy effect function which is adding white noise perturbation on the Expected-Profitability. The flowing capital, the presence of advertisements on processed videos, is time variable and grows at a constant rate. The computed Realized-Profitabilities are in:

Realized-Profitability using variable traffic intensities under two policy effect functions to monitor the Expected-Profitability.

Realized-Profitability using bursting traffic intensities under diffrent policy effect functions to monitor the Expected-Profitability.

Discussion and Conclusion:

Adequate traffic intensity, the presence of viewers to watch videos, with enhanced policy effect, the presence of tools to leverage the monetization, enable substantial realized profitability for a channel in Youtube. Our framework shows a mathematical and numerical support to this statement using a number of simulations, general initial conditions and suitable inputs encountered in practice.

The potential application of our simulation tool is to provide an insight about how specific elements may effect the channel profitability by using traffic intensity, the shaped policy effect function and the nature of flowing capital, the presence of advertisements on processed videos, which is certainly time variable but not necessary growing at a constant rate. Our mathematical framework in which a wide range of models can been implemented has been developed together with efficient numerical algorithms to handle general cases.



Author scientific profile:

Statistics and Applied Mathematics for Data Analytics, Identify opportunities to apply Mathematical Statistics, Numerical Methods, Machine Learning and Pattern Recognition to investigate and implement solutions to the field of Data Content Analytics. Data prediction via computational methods to predict from massive amounts of data (Big Data Content). These methods included clustering, regression, survival analysis, neural network, classification , ranking, deep discrepancy learning .

Author: Faysal.El.Khettabi@gmail.com , Living in Vancouver, BC, Canada.
The MIT License (MIT) Copyright 1994-2017, Faysal El Khettabi, Numerics&Analytics, All Rights Reserved.