Percents Are Tricky

Which saves more fuel?

1. Swapping a 25 mpg car for one that gets 60 mpg
2. Swapping a 10 mpg car for one that gets 20 mpg

[Jeopardy music…]

You know it’s a trap, so the answer must be #2. Here’s why:

If you travel 1,000 miles:

1. A 25mpg car uses 40 gallons. The 60 mpg vehicle uses 16.7 gallons.
2. A 10 mpg car uses 100 gallons. The 20 mpg vehicle uses 50 gallons

Even though you improved the MPG efficiency of car #1 by more than 100%, we save much more fuel by replacing less efficient cars. Go for the low hanging fruit. The illusion suggests we should switch ratings from MPG to GPM or to avoid decimals Gallons Per 1,000 Miles.

Think you got it?

Give “deflategate” a go. The Patriots controversy brought attention to a similar illusion — plays per fumble versus fumbles per play.

If you deal with data analysis you have probably come across the problem of normalizing data by percents and the pitfalls of dividing by small numbers (margins, price returns, etc).

The MPG vs GPM illusion is more clear if you are comfortable with XY plots from 8th grade math recap. Look at the slopes of x/1 versus 1000/x (in this case think of Y=M/G and the recipricol as gallons per mile. I multiplied gallons/mile by a constant 1000 to make the graph scale more legible).