Wednesday, October 8, 2008

The MPG Illusion and the need for GPM

The MPG Illusion

Test your understanding of fuel efficiency with this interactive quiz.

Go here for the original Science article.

This March 2009 post offers a current overview.

The Problem with MPG

What is the problem with MPG? Consider a decision between two cars--a current vehicle and a new vehicle that is more efficient. Which improvement will save the most gas over 10,000 miles?
A) An improvement from 10 to 11 MPG
B) An improvement from 16.5 to 20 MPG
C) An improvement from 33 to 50 MPG

Surprisingly, all save about the same amount of gas over 10,000 miles: About 100 gallons.

The way to calculate the amount of gas used is to divide distance by MPG. A quick check of the numbers above will confirm the following gas usage over 10,000 miles:

10 MPG = 1000 gallons
11 MPG = 900 gallons
16.5 MPG = 600 gallons
20 MPG = 500 gallons
33 MPG = 300 gallons
50 MPG = 200 gallons

We want to emphasize that a higher MPG car is always more efficient than a lower MPG car for a given distance. We are not saying that a car that getst 11 MPG is somehow better than a car that gets 50 MPG -- to the contrary, we encourage all drivers to buy the most efficient vehicle they can. What we are saying is that MPG can be confusing when thinking about the benefits of improving MPG. The bottom line is that equal increases in MPG are not equal in gas savings.

As the examples above shows, small MPG improvements on inefficient cars can save a lot of gas. Of course, most people look at an improvement from 10 to 11, or 16 to 20, and think, why bother? But replacing an inefficient car with a car that is more efficient -- even by just a few miles per gallon -- is valuable in both gas savings and greenhouse gas reductions. Every 100 gallons saved reduces carbon dioxide emissions by 1 ton.

In short, you cannot simply look at an MPG increase from one vehicle to another to know the gas savings. Also, when a family thinks about its average fuel consumption, it cannot simply take an average MPG levels of two vehicles. Given two cars that are driven the same distance, the combination of 18 MPG and 50 MPG uses more gas than the combination of 28 MPG and 30 MPG. Direct comparisons of MPG is what leads to illusions. In each case, you have to convert MPG to know the amount of gas used.* We describe this step next.

The Solution

The solution to this illusion is thinking about gallons of gas used over some meaningful distance. We will use the term GPM (gallons per mile) as a general shorthand for expressing gas consumption over a given distance. We will focus specifically on Gallons Per 10,000 Miles.

We favor 10,000 miles for several reasons. First, 10,000 miles is close to the distance many people drive in a year. Second, it is a round number that is easy to adjust up or down. Third, it overcomes a natural tendency to minimize small gains: What appear to be small gas savings at 100 miles (6 vs. 5 gallons per 100 miles) are more obviously worthwhile when aggregated to a yearly number (600 vs. 500 gallons per 10,000 miles). The value of saving 100 gallons per year is clear. (The effect of scaling on "discriminability" is discussed in a paper that is available by request.)

Of course, because people do drive different distances in a year, final GPM numbers need to be tailored for each person's own circumstance. The tables and calculators below do the GPM math for you.

The Key is Amount of Gas Used

Another way of framing the basic issue is "Which is more useful to know: How far you can drive on a gallon of gas? Or, how much gas you will use while owning a car?" MPG answers the first question. GPM answers the second question.

We suspect that, when buying a car, most people want to know gas consumption. Gas consumption, as measured by GPM, can be directly translated to the cost of driving the car and to the amount of greenhouse gas emissions. MPG cannot.

Tools for GPM Calculations

Follow these links for tools for calculating GPM:

Tools for Calculating GPM from MPG

GPM Calculator Including All 2009 Automobiles

MPG vs. GPM - Which is more Useful?

Does using GPM imply that MPG should be scrapped? No. MPG is useful. Specifically, MPG tells you the range of your car's gas tank. For example, MPG can help you decide whether you can wait two more exits to refill your tank.

Both MPG and GPM have a useful role at different points in owning a car. MPG is useful when you're driving a car. GPM is useful when you're purchasing a car -- it better captures the fuel consumption, and fuel savings, when comparing a current car to a new car, or when comparing two new cars to each other.

Note that both measures serve equally well to tell you what is more efficient: 50 MPG is better than 20 MPG; 200 gallons per 10,000 miles is better than 500 gallons per 10,000 miles. They are not equal, however, in accurately conveying the gas savings from efficiency gains.

The two measures do not provide equal information. We would argue that GPM is better than MPG at helping people see the outcomes of their car decisions:

  • GPM spells out in clear numbers how much gas one is going to use. 1,000 gallons per 10,000 miles is clearly dreadful. 200 gallons per 10,000 is clearly great.
  • One can immediately tell how much a car will cost to fuel over 10,000 miles.

  • One can see the actual magnitude of the gas savings when comparing a more efficient car to a less efficient car. Specifically, one can subtract one car's GPM from another to see the gas savings. MPG cannot be subtracted.

None of these outcomes is apparent with MPG until you do more math.

The Research Findings

Our main research finding is that the majority of people assume that equal increases in MPG are equal in gas savings; a minority thinks that gas savings are equivalent to percentage improvement. Both lines of reasoning lead to erroneous conclusions. In a final study we show that expressing fuel efficiency as GPM (in this case, gallons per 100 miles) leads the majority of people to identify the efficiency improvements that save the most gas. A brief summary of the three studies in Science appears at the Nudge blog. (and reposted here)

The Cause of the Illusion

For those mathematically inclined, the cause of the illusion is simple: MPG creates an illusion because it is a ratio. By necessity, MPG has a curvilinear relationship with its inverse (GPM). Because people do not spontaneously take the reciprocal, they incorrectly map changes in MPG to changes in amount of gas consumed. The formula for calculating GPM in this graph is 10,000 miles divided by MPG. Download a powerpoint copy of this graph here.

Percentage Improvement in MPG is Flawed

Some people expect that, although linear reasoning with MPG is incorrect, percentage increases in MPG captures amount of gas saved over a given distance. Even percentages, however, are prone to illusions with MPG. See this note for three examples of why percentage improvement fails.

For example, it is easy to see in the example given above that improving from 10 to 11 MPG is a 10% improvement; 16.5 to 20 MPG is a 20% improvement; and 33 to 50 MPG is a 50% improvement. Although they all represent different percentage improvements in MPG, they all save 100 gallons of gas over 10,000 miles. Although an improvement from 10 MPG to 13 MPG is only a 30% improvement, it saves more than twice the gas of the 50% improvement from 33 to 50 MPG. The problem with percentage reasoning is that it needs to be applied to a starting level of gas consumed; that amount differs over different levels of MPG. It is captured in GPM.

Imperial vs. Metric

The metric system does not solve the MPG illusion. India uses kilometers and liters but expresses efficiency as kilometers per liter. Because the ratio is distance over volume, it creates a parallel illusion to MPG. See this blog for a nice translation to the Indian context:

Many countries currently use liters per 100 kilometers, which has the right numerator (volume) and denominator (distance) for judging efficiency gains. However, some people living in those countries have questioned how helpful it has been. We think that the base distance should be larger so that differences between efficiency levels are clearer and involve fewer decimal places.

Go here for more thoughts on the metric system.

*Technically speaking, GPM is an intermediate step in calculating the harmonic mean used to measure automaker compliance with CAFE standards. A family also needs to calculate a harmonic mean to understand their total fuel efficiency-the family can't simply weight the MPG of two vehicles by their respective driving distances.

My main webpage at Duke can be found here