# The mpg confusion

What reduces emissions more?

A. Someone swapping their old SUV (which gets 12 miles per gallon) for a hybrid version (18 mpg) or

B. someone upgrading their 25 mpg compact to a new 46 mpg Prius?

(ignore for a minute manufacturing issues or driving habits and assume the miles driven are the same).

The surprising answer (for those who don’t work it out) is A. It’s easy enough to see why this is the case. If the driving distance is 100 miles, then for case A the saving in fuel used (and hence emissions) is 100/12-100/18 = 2.8 gallons, while for B, you have 100/25-100/46 = 1.8 gallons. The confusion arises because people like to think linearly about numbers, not inversely, and so tend to assume that a similar change in mpg has a similar impact on fuel usage. This is not however the case – improvements in efficiency at the low end of the scale are much more useful at reducing emissions. This is actually a very general point – when trying to raise efficiency it is always sensible to start with the least efficient processes.

This confusion got some attention a couple of months ago after a piece that was published in Science by Larrick and Soll. They tested peoples instinctive reactions to changes in mpg numbers and found that people very often got it wrong, leading to less than optimal decisions. They also tested a different way of giving fuel usage information (the number of gallons used per mile), and since this is linear in emissions, people made the correct judgment much more often (it’s worth noting that the standard in most of Europe is already litres per 100 km). Rewritten in those terms, the choices above become:

A. Someone swapping their old SUV (which takes 8.3 gallons to go 100 miles) for a hybrid version (5.6 gallons/100 miles) or

B. someone upgrading their 4 gallons/100 miles compact to a new 2.2 gallons/100 mile Prius?

Much easier, right? The authors of the Science piece are trying hard to get US manufacturers and the EPA to switch over from mpg to this new standard (though they prefer gallons/10,000 miles). It all seems eminently sensible to us.