TWO PLUS TWO IS FOUR?
By Erwin Ephron
If you’re old enough to recall drilling on those impossible multiplication tables, you’re probably too old to remember your name. But cheer up. Neuroscience can now explain how life can be beautiful and math can be ugly.
A recent New Yorker article asks “Are our Brains wired for Math?” The answer is “no.” The human brain learns and remembers by broad association. To remember Cousin Diana I think of “princess.” Nicholson in China Town connects to my grandson Jake. That amazing kind of memory is ill-suited for arithmetic which requires its data not be connected to irrelevant information. That’s why much of math has to be learned by rote. What does 7 x 8 call to mind except the answer you can’t remember?
We all know dyslexia is a difficulty with words, but few of us are aware of dyscalculia which is a difficulty with numbers. Media, a business of numbers, has its share of discalculics. I speak as patient, not physician. Read on and see if you need treatment too.
How would you answer this head-bending email from a young media buyer? “A national cable rep tried to sell me an “equivalized” CPM guarantee. But for 15’s, he would only guarantee half the reported rating. Now I understand the need to weight the ad impact of a 15 vs. a 30, but I’ve considered this a planning not a buying adjustment. The audience for both is the same, so shouldn’t they be counted as the same?”
He seems to have a point. But the seller’s rating adjustment is for cost not impact. Since national cable sells a 15 for half the price of a 30, the 15 second audience is entered at half its weight in the calculation to produce an equivalent 30 CPM. This lets us compare schedule CPMs regardless of the mix of units.
But we can sympathize with the buyer since agency planners do not adjust 15’s when calculating impressions or Reach/Frequency. As equal opportunity mathematicians, we should ask why.
THE READER-PER-COPY TRAP
Here’s a math error I used to make in calculating magazine readers-per-copy -- until Pete Walsh of Telmar straightened me out.
If eighty percent of a magazine's readers read in-home copies where the readers-per-copy is 2.5 and 20% of readers read public place copies where the readers-per-copy is 50, what is the magazine’s average readers-per-copy?
The math seems simple. (80% x 2.5 + 20% x 50) divided by 100% = 12 readers-per-copy. Public place reading certainly boosts a magazine’s readership.
But the calculation is wrong. Somehow we’ve used only readers. How can we get readers-per-copy without using the number of copies? Here is the right way:
If the number of readers is one million, eighty percent, or 800,000 read in-home copies with a readers-per-copy of 2.5. This accounts for 320,000 copies (800,000/2.5 = 320,000). The other twenty percent or 200,000 readers read public place copies with a readers-per-copy of 50. This accounts for 4,000 copies (200,000/50 = 4,000). So in total we have 1,000,000 readers and 324,000 copies. Dividing total readers by total copies the answer is 3.1 readers-per-copy, not 12.
Today it’s fairly common in planning to acknowledge consumer inattention by reducing a TV schedule’s audience for viewers who don’t see the advertising.
For example, we might reasonably estimate that 65% of a Nielsen reported commercial minute audience will actually see our brand’s message. The error is in conveniently applying that 65% adjustment to the schedule’s reach. It’s wrong because it ignores frequency.
If 65% of the audience sees the advertising with each exposure, then each additional exposure increases their probability of seeing it. The numbers are 88% of people exposed twice will see it, and 96% of people exposed 3 times will see it. That means for any substantial TV schedule, the “sees the message” reach adjustment will be far smaller than the adjustment for audience. Most of the 35% loss will be in frequency.
IT CAN LEAD TO CUBISM
If you feel you’re
a bit discalculic, don’t worry, other famous people are also. Historians
tell us the young Picasso had it bad. He tended to see numbers as real figures
-- the number 1 was a person standing, 2 was someone praying, the number 8
was his plump Aunt Pepa.
- April 7, 2008 -