March 14, 2013

Do You Spend $33 a Year On Bread Twist Ties?

I saw an article yesterday from Planet Money titled $10 Billion Bread Battle: Twist-Tie Vs. Plastic Clip

[note: the original Planet Money article has since been corrected]

$10 billion?   Really?   That seemed odd.  Not sure how there would be a $10 billion market for items that probably cost less than 1¢ each.    Lets say every single person in America, roughly estimated at 300 million people, eats one loaf of bread every day of the year we'd get 300 million x 1 loaf x 1¢ x 365 or 300,000,000 x 1 x .01 x 365 = $1,095,000,000 or $1 billion.   Clearly thats a gross overestimate since we don't eat a loaf of bread per capita daily.  But my gross overestimate is already 1/10th the number that NPR cited.    Looking at it another way if they're right and the $10 billion dollar figure is correct then that equates to about $33 per year per person, hence my article title.

Where did NPR get this from?   They said it came from a Business week article titled Twist-Ties vs. Plastic Clips: A $10.6 Billion Battle of Tiny Titans

The article originally said :

U.S. unit sales for packages of bread, rolls, buns, English muffins, and bagels for a recent 52-week period totaled more than 7.2 billion (yes, we still eat a lot of carbs, Dr. Atkins notwithstanding). If we allocate half of those packages to clips, which sell for about $2.15 per thousand, and the other half to twist-ties, which cost about 80 cents per thousand, we’re talking about a $10.6 billion market,
(they've since modified it)


If you're quick you might already notice the problem there. 

7.2 billion units were sold.   7.2 billion is 7,200,000,000.   

The clips or ties cost at most $2.15 per  1000 units.   Therefore you can buy 1000 clips for $2.15.   We could also say they cost roughly 0.2¢ each.

You would need 1000 x 7,200,000 units  to cover the market.   You can buy that many clips for $2.15 x 7,200,000.  or $15,480,000.    Thats $15.5 million.    Worst case.

The market for clips or ties should be closer to $10-15 million.    They are off by a factor of 1000.

Remember I said the quick folks might have already spotted the problem?   Look at the bold/underline parts.   7.2 billion ... $2.15 per thousand ... $10.6 billion.
If you just look at the units there billion ... per thousand ... billion you can see their mistake.
They're basically taking billions / thousand and getting billions.   But the "per thousand" is a division operation and dividing billions / thousand gives us millions.

They instead approximated the price somewhere between the $2.15 amount for clips and 80¢ for twist ties so they're guessing average cost of $1.47.  

Lets look at it another way for a second quick common sense fact check.   The entire bakery industry has $30 billion in annual revenues.    I think its pretty clear that 1/3 of the bakery revenues don't go to pay for those little plastic clips, so clearly the $10 B figure is in the wrong ballpark.

I'm a little surprised that Businessweek would publish an article with a headline based on a math error.    I'm also surprised NPR would pick up the story without questioning it.   Does it not seem obvious that $10 billion is far too large of a number for something trivial like bread bag clips?   Maybe its not so obvious given how numbers like billion and trillion are thrown around daily yet are really hard to grasp the magnitude of them.

I'm sure most journalists can do math well enough and we all make occasional mistakes.   However it is alarming that a major publication like Businessweek would let a fairly big math error like this get through their editorial process and end up a article title.   Its also concerning that other journalists like those at NPR would perpetuate the error without catching it.

In the end this one was caught by commenters and fixed on the Businessweek article. 

Bottom Line:  We need to watch and question the numbers you see reported by the media.


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