For a long time now, I have been interested in modeling of businesses. In particular the SureHits business model of a click marketplace.
Ad Servers play a big role in the profitability of many media companies. Many of these media companies are niche companies with narrow audiences and have fewer advertisers than, say, a mega media company like Google. For these blogs, I am specifically discussing niche media companies where the number of eligible ads is small.
Ad Servers perform two functions that produce value The number one function is to produce Profit.
E. T. Jaynes renames Entropy to Caliber “As the possible World-lines in phase space-time of each mircostate and its known history come together at the present, they form a tube from which events emerge into the future. The area of the cross-section of this tube is the Caliber.”
Ad selection for n ads is NP hard When an ad server has n eligible ads for display for k available slots, the possible choices for ad sets becomes exponential.
It has been a decade since we used very simple models for ad serving. Even then, with simple models, we produced great results. I did not realize it then, but we were using simple Causal Inference to make our estimates.
Entropy and a Book of Orders In thermodynamics, Heat, Temperature, Pressure, Work and Entropy are the main ensemble of variables that describe how mechanical/cyclical engines operate. The second law of thermodynamics was a big deal when it was discovered. The models of the cycle of these engines sparked the industrial revolution. Example the Carnot Heat Engine. Chemistry and chemical engineering fields also enjoyed a boon of discoveries and applications and products. All these are bound and constrained by this notion of Entropy. Around the same time, late 1800s, Willard Gibbs ‘discovered’ the same Entropy in statistical models of the world. This statistical Entropy worked the same way as physical entropy. Later in the 1950s Claude Shannon ‘discovered’ Entropy at Bell Labs as it relates to communications (conveying information). This entropy also obeyed the second law. Again it was a boon to understanding and building communication systems of all kinds. I think that in the business world probabilistic models can be applied to model cyclic processes like click advertising and lead generation (supply and demand problems). Gibbs Entropy, I believe, can be used to understand the limits, constraints and optimizations of the process. I believe that these business cycles will indeed obey the second laws of thermodynamics. The ensemble of Variables in advertising: Profit, Profit Margin and Entropy are analogous to Work, Temperature and Entropy in engines. Humans seem to understand entropy well. We are constantly weighing options while we all seek our own utility. Acting to get more energy than we expend. We watch around us as once ordered things decay, rust, stop working, crumble. Famously, Claude Shannon at AT&T made the the connection between Entropy, bandwidth and information content. I have abducted his Theorem (actually others are calling it Gibbs-Shannon Entropy) and eagerly explore this same entropy as an oracle for decision making for optimal consumption, in this case, an optimum ad serving strategy. I think we can calculate the value of a Book of CPC advertisers using Entropy. The Book is the full collection of all your CPC client Orders. “Book” for short. Temperature of the Book T is the difference between Sales (RPV) and Cost (CPC). Total Book value = Sum of (Entropy x T) This concept applies to certain difficult marketing businesses. An example system is Ad Serving, the business of choosing the ads to place on web pages given a Book of Ad Orders X, an uncertain supply of page views, ad placement and ad responses Y, and an uncertain user demographic and context variables Z, where Z∈Y. Likewise applicable is the internet Lead business where a Book of Orders for Leads X is sold into an uncertain supply of Leads and lead disposition variables Y that also have uncertain lead demographic and source (context) variables Z, where Z∈Y. In these businesses the Book of Orders (Book for short) is a company asset. It fairly can be put on the company’s Balance Sheet as the predicted sum of profit from the full depletion of the Book. It presents the ability to generate revenue in the future. The marketer’s goal is to deplete this Asset and produce the most profit for the company from this asset. I propose that the value of this asset is proportional to the Entropy associated with the Book of Orders. The value of the Book is product of the associated Entropy H(X) and the expected gross profit of a sale (Sales TX – Cost of Sales WX – Cost of Goods TY). Value = ∑z H(X) ( ΔT – WX) analogous to Total Energy = Σ H(x) Δ T And here are some framework notations for a Book of Orders: Let us define the common parameters of Orders and of supply. The probability of a match for Order xi = p( xi | z) where z are the order selection variables in set of Z where Z∈Y. We know that the probability of a match is the probability that supply Y is in the same demographics, so p( xi | z) = p( Y|z). Probability of a match is based on supply. Txi is the price of Order xi. Let n be the quantity of the Order or the maximum acceptable quantity in a time period. And TY(z) is the expected Cost of an instance of the supply yi(z). Profit for a filled order = Revenue – Cost of Revenue – COGS= Txi – TY(z) – WX Y contains a set of response variables and Do variables that denote a sales funnel which form a Markov chain ( y1 –> y2 –> y3 …). Entropy associated with Order x = H(x) = n ∑x∈Y – p( Y|x ) logb p( Y|x ). Note that if an order falls outside of Y (x∉Y), the Entropy associated with x is zero and the order will have no value. Maximum entropy occurs when p(Y|x) = 1/2. Using log base 2 gives units of bits for the entropy. However, Jing Chen, in his paper “The Entropy Theory of Value” says that b is the number of producers of Y. hmm. Equity of an Order Equity is Energy. Relative Temperature is ΔT = TX – TY or the difference in sales and cost (gross profit). The Balance sheet Equity E that is generated by an new Order is E = ∑z H(xi) ( Txi – TY(z) – WX) or E = ∑z H Δ T or Equity = Entropy x Change in Temperature Likewise Equity is produced if Entropy increases while Temperature is held steady. E = T Δ H The per Unit value of a drawn lead or page-view is V(Y|x) = – log2 p( Y|x ) is the log likelihood of a match and is = the number of true/false questions needed, on average, to guess if a match for order x has occurred. Equity of more than one order – a Book Entropy of two Orders x1 and x2 = H(X) = H(x1 ,x2 ) In general, H(x1 ,x2 ) ≤ H(x1 ) + H(x2 ). This means the book entropy can be less than the sum of entropy for each order. Equality occurs when x1 and x2 are independent. When two Orders overlap they have mutual information I. H(x1 ,x2 ) = H(x1 ) + H(x2 ) – I(x1 ;x2 ) where I(x1 ;x2 ) is the Mutual Information of the two orders. By Chain Rule, the Entropy of three Orders = H(X) = H(x1 ,x2 ,x3) = H(x1 ) + H(x2 | x1) + H(x3 | x2 , x1) The chain rule offes an algorithmic approach to calculating the Entropy of a Book. The series has k calculations. Book Entropy of k Orders = H(x1,x1,x1,…, xk) Total Value of a Book of Orders = ∑x H(X(x)) (ΔT(x))
Intelligent Marketing Manifesto Effective marketing of products is the art and science of making decisions. Marketers make these decisions using past experience or data. The outcome of their decision is uncertain. The goal is to produce utility by either making their company more valuable by increasing the company Equity or, more greedily, to maximize net profit for the period. When the marketer is confronted with choosing between two options A or B, how should they decide? Obvious Answer: They Do A or B based on their model of the world. They have a formula which calculates the likely utility of each decision and they choose, or Do, the option with greatest utility. But, I argue, that this is not the correct approach. It seems obvious that the decision, Do A, or Do B, is the one with greatest utility. The correct approach to this decision involves Entropy H. A more realistic setting is a constant ‘flow’ of choices – a stream of decisions. The intelligent marketer wants to look into this uncertain future and ask, “how do I make each decision so that the Total effect of my decisions is to maximize utility over time?”. Each marketer is constrained by their inventory or by their standing orders (Book of Orders). It is the rarity of their collection of products or the rarity of fulfillment of standing orders that also drives the marketer’s ability to produce utility. The probability that A will occur is p(A). The Entropy of A, H(A) = – p(A) log p(A). An excellent measure of Rarity is 1 / H. Marketers often have many options, A to Z, for every decision. For ad servers the number of possible options can be extraordinarily large and ad placement decisions must be made very fast. Online auctions also present the marketer with bidding decisions that must be made in near real time when the product being purchased has extraordinarily large possible variations such as keywords or lead auctions. This blog’s goal is to offer the marketer methods to always make intelligent decisions. Intelligence here is using Bayesian updating to update their model of the world given new evidence (or conditions). Intelligence is about effectively managing inventory (Entropy) too. Intelligence is maintaining your system in its highest possible state of Entropy and depleting this Entropy in the most efficient, most profitable means possible given the uncertainty of supply. I believe gravity is an entropic force in nature. So imagine two bodies with mass in a space. The entropic force of gravity assures that the system’s entropy will decline as the two bodies are attracted together. Ultimately the force of gravity assures that the two masses merge and the entropy of the mass distribution in the system reaches it’s minimum. Erik Verlinde suggests that: “Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies.” Likewise I think that there are economic entropic forces at play in business and economics. Intelligent Rules of Marketing Rule 1. Intelligent decisions produce the most Utility per Entropy expended by a system. Corollary 1. When managing a book of standing orders (a Book) and two or more orders match an uncertain inventory, sell to the Order with the greatest Utility per Entropy expended from the Book. Each filled order will reduce or deplete the entropy of the Book. Each new order may add to the entropy of the Book. The total entropy of a Book of Orders is proportional to the Equity of the Book. Corollary 2 : In game play: If two different moves produce the same utility, choose the move that will result in the greatest freedom of action of future moves. Corollary 3: A high entropy book of orders will offer more matching options and will have higher value than a low entropy book with fewer matching options. The value of a new order is the Margin ÷ the Entropy it will add to the Book of Orders. Corollary 4: Rarity is Value. The rarity of an object causes the human mind to assign it more value than a less rare object. Rarity = 1 / Entropy Rule 2. When adjusting your model of the world, use Bayesian Updating. It is the best and you can do no better. Bayes Theorem. Rule 3. When choosing between two models of the world that equally fit the evidence (data), the least complex (the one with least assumptions) model is more likely correct. The best model maximizes: Data Fitness – Complexity. Rule 4. When making a decision where many variables seem to drive a probable outcome, use Do Calculus to predict the results. Directed Acyclic Graphical Models make good choices for a model of the world. These models can be learned from data using, in part, the Conditional Entropy (Mutual Information) among the variables of the data. In the future I hope to publish blogs on each of these ‘rules’. And as I do, I will link these updates on this page. Entropy is a vague concept for most people. I hope in these blogs I can, if not demystify, offer tangible reasons to use Entropy in your marketing decisions. Please add comments and suggestions for improvement. I need your help, input and corrections.
Part 3 – Estimating Lead Gen Revenue In the field of insurance, companies grow by building a collection of policies. This collection is called a Book. So an established and successful insurance agent will have a large Book of Policies. This Book defines the present value of the agent’s business.
Predicting consumer response In the previous post I discussed how it is possible to compress our knowledge of auto insurance lead consumers into a very compact model. A Bayesian Network, shown here,
People are hungry in Edmond, Oklahoma. It is our hope to provide a source of nutritious fresh food by serving local food banks.
The garden sits in the bottom of Chisholm Creek and shows great promise with great top soil and a nice flat 1/2 acre for cultivation.
For a long time now, I have been interested in modeling...
MediaAlpha is for sale. Quinstreet should buy them....
Ad Servers play a big role in the profitability of...
What a great year 2017 was for Tomatoes The weather...
People are hungry in Edmond, Oklahoma. There were times as a child that I was hungry. People don't get enough fresh vegetables. It is my hope to provide a source of nutritious fresh food to my community of local food banks, kitchens, friends and family.
The garden sits in the bottom land of Chisholm Creek and has great top soil and a nice flat 1/2 acre for cultivation. We have added a water well, irrigation and electricity.
The setting is my favorite reason to garden here. The old elm tree shades a nice sitting area from which to view the garden and the rich nature that comes and goes in the bottom.
For a long time now, I have been interested in modeling...
MediaAlpha is for sale. Quinstreet should buy them....
Ad Servers play a big role in the profitability of...
Even in prosperous Edmond, food banks do a steady business serving the poor. Most efforts are operated by volunteers. They almost always need help. Please give cash or volunteer.
Great examples:
Regional Food Bank: where you can donate or volunteer.
Other Options, Inc. in OKC
Project66 Community Food Pantry in Edmond