The Caliber of a Book of Orders (or Ad Server)

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.”

If the cross-section’s area is large (Caliber is high), then many possible futures exist. The company will have many options and choices. Options give rise to optimization for the company. High Caliber companies will have high sustainability since they will have many options. If a company has low Caliber then it has fewer options. Low Caliber companies have low sustainability and have less ability to tolerate change in the environment.

I think the newer name for Entropy fits very well, especially with my notion of the Caliber of a Book of Orders. In past blogs I called this macro state Entropy. The value of a Book of Orders is the product of it’s Profit and the Caliber associated with the collection of Orders given a supply of Goods.

The same concept applies to ad servers, one of my favorite topics. How do you calculate the Caliber of an ad server? Answer: Look at the distribution of sales by customer. Caliber is calculated directly from this distribution. Here is a graph of Caliber given the number of ads shown on an ad server. For a business to be valuable, it needs both Profit and Caliber and it’s world with many possible futures. The higher the Caliber the easier the system (Book of Orders) can produce Profit even with client base disruption. High Caliber business is resilient and lower risk.

The graph to the right above, startled me. It shows that anytime an ad server gives ALL the business to a single customer Caliber goes to zero! The only value of this exchange is pure profit. But company equity (Sales multiple) is at a minimum! Any business with a single client has low sustainability, very high risk and very low Book Value.

Years ago I helped design ad servers that could pick the “best” number of ads to display. “Best” was always the ad set that produced maximum profit. The above graph tells me that we were wrong! If Caliber = Sustainability then the “BEST” number of Ads should produce the maximum sustainable profit. It seems to me that Caliber can be used to make a more “Intelligent” ad server. One that makes profit now and produces company equity. The Caliber is the factor ad servers can use to make decisions that properly weight profit and equity.

I have recently read a number of articles discussing customer concentration of a business. The general topic was the sales discount for companies with high customer concentration. Everyone agreed that concentration is bad but they offered no calculus for the discount. One said that a Sales discount of 30% is appropriate when customer concentration exists. Maybe Caliber is a way to calculate this discount.

Further work needed

The potential value of an ad server is constrained by traffic supply Y. Adding some supply parameters to our calculus is necessary. The total supply of traffic to our ad server has cost, risk of disruption and sustainability. Traffic volume is an obvious constraint. My goal is still to use the basic thermodynamic model of a heat engine to describe ad servers and Books of Orders. For the Carnot engine:

ΔQ = T x Caliber

Where ΔQ is the value produced, T is the Temperature of the market.

1. What is T? (the thermodynamic temperature of the business?)
2. How does the Caliber of supply constrain the overall Caliber of the business?

While also considering the Wissner-Gross formula:

F = T ∇Caliber(τ)

Where F is a force, T is the ‘strength of belief’ and ∇Caliber(τ) is the gradient of the Caliber over some future time tau.