Date of Toilet Paper Apocalypse Now Known

Introduction

Fig. 1. Charmin toilet paper roll in 2015

Have you noticed how rolls of toilet paper fit into their holders more loosely than they did in the past?  Take a look the next time you are doing your Charmin paperwork, and you will see the first signs of the impending Toilet Paper Apocalypse.

Methods and data

Like the proverbial frog in boiling water, the first signs of the Toilet Paper Apocalypse were not obvious.  I first became aware that it was coming in 2009, when I happened to buy two 8-packs of Charmin Giant rolls and noticed that one of them was noticeably shorter than the other:

Fig. 2. Roll size change observed in 2009.

Careful examination of the quantity details showed that the width of each roll had been decreased from the standard width of 11.4 cm to 10.8 cm.  Although this decrease of 0.6 cm wasn't that apparent when comparing single rolls, it was pretty obvious when the rolls were stacked four high.  When I noticed this, I had a sinking feeling that I was seeing the beginning of a nefarious plot being carried out by faceless bureaucrats at Procter and Gamble.  But without additional data, it was hard to know whether this 5% decrease in the size of rolls was a fluke or part of a pattern.

Fast-forward to 2015 and another trip to the store.  This time it was a purchase of two 6-packs of Charmin Mega rolls:

Fig. 3.a. Charmin roll size change in 2015.

Close examination of the details tells the story:

Fig. 3.b. Charmin roll size change in 2015 (detail).

Sometime between 2009 and 2015, P&G decreased the width of their rolls again, from 10.8 to 9.9 cm, another 8% decrease in the size per sheet.  Now in 2015 the number of sheets per Mega roll was reduced from 330 to 308, a further 7% decline in the amount of toilet paper per roll and a corresponding increase in P&G's profits (since the price of the product has stayed the same with the size decreases).  

What first seemed an idle conspiracy theory is now a known fact.  Being an analysis nerd, I had to search for additional data from the years between 2009 and 2015.  Google did not disappoint.  I was able to find this 2013 post from the Consumerist, which documented another decline in roll width, from 10.8 cm to 10.0 cm (a  7% decrease in sheet size):

Fig. 4. Charmin roll size change in 2013.  Image from http://consumerist.com/2013/10/31/charmin-deploys-toilet-paper-sheet-shrink-ray-slims-rolls-down/

Analysis

Unfortunately, not all of the changes involved rolls of the same size.  I also did not have exact dates for each change.  However, by estimating the dates and doing some size conversions, I was able to assemble the following data:

Fig. 5. Data showing relationship between year and roll size.

 I conducted a regression analysis on the data and the trend was clear:

Fig. 6. Regression analysis predicting the relationship between year and roll size.

The regression had P=0.0203, so there is no question about the significance of the relationship.  Note also that the regression line has an R² value of 0.96, which means we can safely extrapolate into the future to predict the course of events leading up to the apocalypse.  Rearranging the regression line and solving for the year when the toilet paper surface area goes to zero gives a year value of 2046.  So we can now confidently predict the date when the apocalypse will come to pass.

Discussion

This analysis has three important implications. 

1. Charmin toilet paper will disappear on or about the year 2046.  For those of us who are devoted Charmin users, that means shortages, hoarding, and chaos in the grocery stores during the 2040's.  Remember the horror that was Y2K?  We have that to look forward to all over again.

2. Since each Charmin roll size decrease was accomplished without a corresponding decrease in price, the profits for Procter and Gamble will increase as an inverse function of the area of paper per roll.  A little elementary math will prove that a linear decrease in the roll area to zero results in Procter and Gamble's profits increasing to infinity in the year 2046.  The implications are clear: by taking advantage of their customer's addiction to their product, P&G intends to dominate the world economy by mid-century. 

3. As the amount of toilet paper per roll decreases, other effects will begin to appear.  For example, if we assume a constant number of sheets per roll and a length per sheet of 10.1 cm, we can project based on the regression line from Fig. 6 that the width of sheets will reach 2.0 cm in approximately 2040 (Fig. 7).

Fig. 7. Simulated Charmin roll size in 2040.

When the sheet size reaches that shown in Fig. 7, it becomes questionable as to whether the toilet paper can actually perform its intended function. In that case, we can expect cascades of related effects caused by the increase in transmission of fecal-borne pathogens, such as pandemics of cholera, hepatitus A, and typhoid fever.  It is possible that the human population may collapse due to these pandemics several years before the actual disappearance of toilet paper altogether.

Conclusions

This paper should be considered a clarion call for action.  The most likely solution to the problem is probably some form of government regulation of roll and sheet size.  However, given the widespread gridlock in facing lesser issues, such as climate change and refugee crises, it is likely that inaction by governments on this issue will continue.  In that case, we should expect widespread hoarding, followed by rationing as 2046 approaches.

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Steve Baskauf is a Senior Lecturer in the Biological Sciences Department at Vanderbilt University, where he introduces students to elementary statistical analysis in the context of the biology curriculum.