Penetration Confusion

From “Final Frontier for Wireless Hard to Break Through” in The New York Times: “In Botswana, cellphone penetration exceeds 80 percent, and in South Africa, it has topped 100 percent.”

Why does that sound wrong? We occasionally see percentages higher than 100, but those usually refer to growth rates (“iPhone sales up 150%”). In contrast, penetration implies a part of a whole. A fully penetrated market would be 100 percent penetrated.

So how does South Africa have cellphone penetration above 100 percent? Apparently, the answer comes from dividing the number of wireless subscribers by the population (49 million divided by 47.9 million as of 2008). There are more subscribers than people because some subscribers are double- or triple-counted because they have multiple subscriptions, such as one for a BlackBerry and one for an iPhone. A little Web searching indicates that this calculation is common for the wireless industry, and several countries have penetration above 100 percent.

The wireless industry probably started using penetration as a metric back when wireless phones were the size of bricks and the few people that had one indeed had exactly one. At that time, I doubt wireless executives dared to dream that people would one day carry multiple devices, and thus the traditional concept of penetration applied: Just divide the number of people with phones by the population, and you’ve got penetration that maxes out at 100 percent.

Many years later, the wireless industry is still using penetration—that part-of-the-whole metric—but no one knows what the whole should be. If we just use the population, we’ll get situations like South Africa where the part is bigger than the whole due to some people having multiple phones. However, at this point, changing the definition of the whole would be arbitrary: 100 percent penetration is when everyone has two wireless devices? Three?

Maybe the better answer is for the wireless industry to replace penetration with “wireless subscriptions per capita.” Botswana would get 0.8, and South African would have 1.02. Numerically, it expresses the same thing as the penetration metric, but it does not imply the part-of-a-whole relationship.

And since we’re on the subject, a few additional metrics would be helpful. For example, with penetration (or wireless subscriptions per capita), we don’t know whether Botswana’s 80 percent penetration is due to 20 percent of the population having four phones each or whether 80 percent of the population has one phone each. Something like “percentage of people with at least one wireless subscription” would help. From that and the already-known total number of subscriptions, we could calculate the average number of subscriptions per subscriber. Finally, we could multiply that number by the population without a subscription and, coming full circle, estimate the remainder of the market to be penetrated at that point in time!