“Five Thousand Percent”


By Rob Cohen

Your enjoyment of this article will be enhanced if you take this 2-question survey before reading any further.

While I am skeptical that you took my advice, I have no way of preventing you from proceeding other than perhaps another gentle suggestion to take the survey if you haven’t already.

A certain pharmaceutical drug’s price-hike has caught the American public’s attention (and outrage) this week. Rather than discussing the story outright, however, the math teacher in me would like to call your attention to a particular feature of the way in which this story has been reported. The story, as I first heard of it, described Turing Pharmaceuticals CEO Martin Shkreli’s extortionate price increase of Daraprim by 5000%. With the mention of this figure, I switched gears from thinking as a concerned citizen to thinking as a concerned math teacher/tutor.

Having seen first-hand the struggles of hundreds of math students with percentages, I wondered what portion (percentage, if you like…) of literate American adults would immediately recognize that an increase of 5000% means that the increase is 50 times that of the original price*. I thought that it would be less than half, which brings us to why I decided to write this article in the first place. Thank you if you took the above survey, by the way. I completely commiserate with those who did not answer correctly, having seen very bright people of all ages struggle with the difficulties of proportional thinking. Congratulations if you did answered correctly.

The use of percentages is rather ubiquitous in adult life from grocery stores to restaurants to newspapers. Sometimes percentages help to simplify our understanding of various figures – like a good metaphor. When newscasters speak of 17% of a certain population, it is usually easier for us to process than if they gave us the raw number. It allows someone to think “17 out of every 100”.

In the case of this Daraprim story, however, the use of percentages serves more to obfuscate rather than to elucidate. 5000% simply sounds bigger than it is, and it takes advantage of the non-mathematically oriented. Rather than lament the mathematical knowledge of most Americans, I would say instead that the use of figures like this in the news represent manipulative or irresponsible journalism. “Over 50 times bigger” would make better sense to many more people.

Aside from my curiosity about the American public’s ability or willingness to “do math” while listening to/reading/watching the news, I was also curious to see if the 5000% figure was ubiquitous in the popular media coverage of this story. It was not. Here are my findings from the nation’s top ten most circulated newspapers.

What I will note below is where in the article the actual price is mentioned and where (if it all) an additional descriptor like 5000% is mentioned. Links for each article I used are provided below. I tried to be consistent in picking all of the news articles from September 22 (and as news stories, not editorials etc.), when it was first reported that the price would be lowered as a result of public backlash.

All of them mention the actual price increase from $13.50 to $750 (except for the Washington Post, which reported an increase from $18 to $750). In the interest of precision, the amount of this increase is exactly 54 and 5/9 times bigger the original value, which we can round up to 55 (5500%). I think that it is worth noting not only the choice by journalists to present this increase as a percent, but also the way in which they rounded the figure.

  1. The Wall Street Journal

“more than 50-fold hike”: 1st paragraph

actual prices: 2nd paragraph

 

  1. The New York Times

actual prices: 3rd paragraph

(no descriptors)

 

  1. USA Today

actual prices: 2nd paragraph

(no descriptors)

 

  1. LA Times

“5000% price hike”: headline

“raised the price… by more than 5000 percent”: 1st paragraph

actual prices: 4th paragraph

 

  1. Daily News

“750 price”: headline

“raise the price… by 5000%: 1st paragraph

actual prices: 2nd paragraph

 

  1. New York Post

actual prices: headline and 1st paragraph

“more than 4000 percent price increase”: 4th paragraph

 

  1. Washington Post

“over 4000% increase”: headline

“raised the price… from $18 to $750 or more than 4,000 percent”: 2nd paragraph

 

  1. Chicago Sun Times

“$750 pill”: headline

actual prices: first paragraph

(no descriptors)

 

  1. Denver Post

actual prices: 3rd paragraph

(no descriptors)

 

  1. Chicago Tribune

actual prices: 2nd paragraph

(no descriptors)

 

 

*a technical note on the semantics of percent:

When I first started thinking about this, I had some initial confusion with the way a percent increase could be expressed in language. I didn’t initially think that the following phrases were equivalent: “a 5000% increase”, “an increase of 5000%”, “an increase by 5000%”. The first two clearly mean that it is the amount of the increase that is 5000% of the original amount or 50 times, making the new amount 51 times bigger. The last one, “an increase by 5000%”, I thought could be interpreted as an increase by a factor of 5000%, which in turn would mean by a factor of 50. I now realize that despite any ambiguous language surrounding the percent increase, the # percent always refers to the increase as a percentage of the original. This semantic confusion further proves the inadequacy and inappropriateness of percentages in this case. I would never even think to interpret “an increase by 50%” or “increase by “100%” as increasing by a factor of those nubers.