CAUTION: DANGEROUS CURVES

Formula Reach and Frequency is a Rough Approximation.

By Erwin Ephron

There's nothing as dumb as belonging to a cult. Subordinating your God-given intelligence to some shop-worn absolute.

Unless you're a media wonk and the cult is "reach and frequency."

But, how good are our R&F estimates and how did R&F's come to take over the media business?

In 1963, the very first issue of the Journal of Advertising Research contained an article by an obscure French researcher, Jean-Michel Agostini. It was titled, "How to Estimate Unduplicated Audiences." Agostini called his discovery of the mathematical relationship between media vehicle pair-duplication and schedule reach, Agostini’s Law. It was a revelation.

At the time, calculating R&F's was like designing fancy hats for rich women. A small group of media research "hot shots" at agencies, handcrafted estimates based upon probabilities, experience, spit and judgment. These custom-made R&F's were useful, but inconsistent. Different analysts produced different numbers for the same schedule, and the same analyst produced different numbers at different times. With Agostini, a small boy with survey data and a calculator could do an R&F in a matter of minutes, and it would not vary with the next calculation.

Although by day I worked for Nielsen, I had read Agostini's paper as a graduate student in Advertising Research at NYU. Agostini's Law, I reasoned, could be applied to Nielsen television data, where it could revolutionize the business and make me a hero. Could, but wouldn't, I soon discovered. Nielsen thought the idea was dangerous.

At first I felt Nielsen was suppressing Agostini to protect their special analysis income, like Standard Oil did with the car that runs on water. But the dull fact was Warren Cordell, Nielsen's head statistician, did not have much use for formula techniques, nor did Art Nielsen, Sr. I should have remembered the words of Lord Kelvin, stamped in gold-leaf on the cover of each Nielsen report: "If you can measure that of which you speak, you know something of your subject..."

In spite of Nielsen's refusal, R&F formulas soon grew like the ivy. In the next 10 years, Agostini's Law was bettered by Metheringham's formula (developed by Dick Metheringham of FCB London), Beta Binomial (the work of Jerry Green and Steve Stock of MarketMath), Modal and the Lambda function (which I believe they made into a movie). These were refinements. It was Agostini's Law and the computer, which transformed a cottage industry into a power tool.

Today's computer printouts give our reach and frequency estimates the aura of mathematical certainty in a business where not even rates are certain. But how good are the R&F's we use?

The formulas are generalizations from a limited number of observations so the "fit of the curve," is never perfect. And then there's the sampling error of the survey data to which the formula is applied. Fit and sampling errors may or may not cancel out, which makes the total margin for statistical error greater. (It's like an American playing the Tokyo market, where fluctuations in the value of shares are compounded by fluctuations in the value of the Yen.)

Sampling error is known and error tables are included in each survey report. We can examine "fit of the curve" error by comparing survey to formula R&F calculations. The net is, mathematically, R&F's are not certain, but they are pretty good.

But in the real world, planning error dwarfs these errors. We plan TV by prototype, using average day part ratings and average day part duplication patterns. The errors in R&F estimates introduced by the differences between the planning averages we use and the plans we execute are enormous and can't be forecast.

As a result, only very large differences (i.e., a reach difference of 10-15%, between plans), are likely to happen. Given this ambiguity, media planners over-use R&F's. They use its mystery to confuse clients, and its authority to coerce them. They use R&F's to stop the discussion and get their own way.

That's what is called "blowing smoke." And the numbers are more suited to Sitting Bull than Bill Gates. The Sioux count "One, two, many," sounds suspiciously like the media count "one, two, three or more."

- March 1, 1992 -
Originally published in Inside Media

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