Tuesday, July 19, 2011

Saves water… or invests it?

This little placard (about 4" high) was posted near the urinals at Safeco Field.

I hate messages like this, because they are often used to lie with statistics, using math comparisons to hide the real information, usually to make it seem more impressive than it really is.

In this case, though, the placard is outright wrong!

“This urinal flushes with only 16 oz. of water” — okay, that’s clear enough.

“A standard one-gallon urinal” — points for good hyphenation, but deduction for switching from ounces to gallons.  How many ounces in a gallon?  (I had to look it up to be sure, got it wrong at first: 128.)

But the word after the comma, this is where the placard text is wrong.  If it had said “This urinal flushes with only 16 oz. of water, using 88% less water per use than a standard one-gallon urinal”, it would have been correct (albeit overusing “use”).  87.5% of 128 oz. is 112 oz., so saving 88% leaves 16 oz being used:
x - .88x = 16        (where x=ounces used by a one-gallon urinal = 128)
But they had to try to go green and put the word “saving” in there.  That changes the entire meaning.  It is no longer about using less than another urinal does; now it is about saving more than another urinal (saves).  That unwritten word is the key.  It means that we are comparing this urinal and the regular one to some unspecified third option, a presumed baseline.  But what is that baseline?

The EPA refers to an “older, inefficient 1.5 gpf flushing urinal”, and the state of Alabama mentions “older flush type urinals used 2.5 gallons”.  Or going to sit-down toilets, new pressure-assisted flush toilets use 1.4 gallons, and post-1994 ones used 1.6, while ones before then used 3.4 gallons.  Flushometer toilets like those in commercial restrooms also use about 1.6 gallons.  (Interesting side note there: urinals use less water than sit-down toilets, but still more than 2/3 as much, a far higher percentage than I expected.)

If we were just comparing one urinal’s volume to the other, our math formula would be what I listed above.  But with the mystery toilet involved, it is:
128-16 = .88 y        (where y = ounces saved by a regular urinal)
(additional amount saved by special urinal = 88% of amount saved by regular urinal)
Per this formula, for these special urinals to save 88% more than a regular urinal, a regular urinal saves about 128 oz. (one gallon), meaning that the baseline item uses 2 gallons, which doesn’t fit any of the profiles noted.


  1. Your final formula is incorrect, I think.

    128 is the usage of a gallon urinal, and the pint urinal uses 16. So the savings by going to the pint is 112 oz. So far we're in agreement.

    However, 112 is 88% more than some amount. In other words, it's 1y + .88y. So,

    112 = 1.88y

    y = 59.6

    So presumably, a gallon urinal is saving 59.6 oz over it's predecessor, which would flush using precisely 187.6 oz.

    1. According to this reasoning, a 0.75 gallon urinal saves less water than a 1 gallon urinal, since it saves only 0.25 gallons, whereas the 1 gallon urinal saves 0.5 gallons (if the old standard is 1.5 gallons). You have to compare both things to the same old standard! That is what Jim did and arrived correctly to an "old standard" of 2 gallons.

      Hence I agree with Jim that this "save 88% more" sentence makes no sense whatsoever! "How much a one gallon urinal saves ?" Anything as long as the commercial sounds good!

  2. That would be close enough to the “older, inefficient 1.5 gpf flushing urinal” (about 192 oz) that I can accept it. The base point remains, though: “This saves a specific amount more than that saved vs. something that we won't tell you what it was.  We hope that makes this one sound even better.”