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What kind of revenue numbers would justify Pinterest’s $200 million valuation? Atlantic writer Alexis Madrigal and others have used back-of-the-envelope math to explain this valuation. In his article, “Why Pinterest Is Playing Dumb About Making Money,” Madrigal puts Pinterest’s annual revenue at $45 million a year. Based on statistical modeling, I believe there is only a .25 percent chance that Pinterest is making that much money.

Considering all possible scenarios — not just the most optimistic ones — let me show you why and how much Pinterest earns.

Madrigal calculates Pinterest revenue from its only known source — affiliate fees from SkimLinks. “So, Pinterest has 10 million users,” writes Madrigal. “Let’s say that the average across all of them is that they buy items valued at $10 in a month through affiliate links on Pinterest. That’s $100,000,000 of sales for which Pinterest would get credit. That’s $3.75 million in monthly revenue, or $45 million of annual revenue.”

There are two problems with this calculation. One, no one verified whether Pinterest generates enough traffic to generate 10 million transactions per month. Two, revenue numbers based on broad assumptions have uncertainties that are not quantifiable. For example, how likely is it that each user is generating $10 a month?

Let’s look at the first problem. What kind of traffic should Pinterest generate to websites to deliver 10 million transactions per month? According to the Top 500 Guide: Profiles and Statistics of America’s 500 Largest Retail Web Sites Ranked by Annual Sales, the average conversion rate of website visits to sales is 4.3 percent. That means Pinterest must garner 232 million visits to result in 10 million transactions.

How does that compare to total traffic to all online stores? Data collected by Complete says online stores receive a total of 662 million visits a week, or 1,434 million visits a month. This means that in order to justify Madrigal’s estimates, Pinterest must account for 16.1 percent of all online retail traffic. That’s a tall order. According to Shareaholic, Pinterest only drives 3.6 percent of referral traffic. It is safe to say that Madrigal’s numbers grossly overestimate Pinterest’s page views, transactions, and hence its revenues.

Regarding the second problem with revenue models based on assumptions, let me clarify that it is not possible to avoid assumptions when it comes to privately held companies. However, we can start with smaller, more granular and better assumptions, and we can use statistical models to quantify the uncertainties in them. Instead of making such assumptions as 10 million transactions per month and $10 average transaction size, let’s build out a model from its components.

Sales from Pinterest links = Number of transactions/year X number of active users X transaction size

Pinterest revenue = Sales from Pinterest links X percentage of affiliate fees

Each variable in these two equations are unknowns that must be estimated. Instead of assuming an average value for these numbers, we estimate the low and high values that we’re 90 percent confident about. To be 90 percent confident about an estimate, we need to have a low and high value such that there is only 10 percent chance that the real value falls outside of the range.

Here are the numbers I used based on my research.

90 percent confident Low High Number of transactions per user per year 1 18 Number of active users 1,000,000 5,000,000 Sales per transaction $2 $18 Affiliate fee % 2% 4%

(Note: Pinterest has more than 10 million registered users. I generously estimated that they have one million to five million active users who click on product links and make at least one to 18 purchases a year.)

There are two advantages to this approach. First, we are estimating many smaller numbers. And secondly, we are quantifying our uncertainty in our estimates. As we gain more information about any one of the components, we can refine the estimates.

Once we have this range for each component, then we can calculate Pinterest’s revenue numbers using a statistical modeling method called the Monte Carlo method. It’s like imagining living your life 10,000 times to find out how many different lives have certain outcomes. For Pinterest, we’re trying to discover how many different scenarios yield different revenue numbers.

The results are stunning:

Thirty-three percent chance Pinterest makes more than $10 million a year Twenty-five percent chance it makes more than $12 million a year One percent chance it makes more than $36 million a year Less than .25 percent chance it makes the $45 million number quoted by Madrigal Considering all possible scenarios, the expected value of its revenue is just $9 million.

A $200 million valuation based on high revenue numbers that have such a low chance of being true is a risky bet. Clearly, the VC firms focused on the most optimistic scenario — regardless of its chances — and didn’t account for the entire spectrum of scenarios. But that’s business as usual in the Valley.

Rags Srinivasan is a management professional who specializes in strategic marketing. He recently published, “To Group Coupon or Not,” and he blogs at Iterative Path and tweets at @rags.

Featured image courtesy of Flickr user Mykl Roventine.