Wednesday, December 10, 2008

The case for GPM in a nutshell

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. It is useful when judging the range of one's gas tank. But it answers a less important question. GPM answers the question of gas consumption. 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.

People rely on subtraction when comparing MPG, which creates illusions. The improvements from 10 to 11 MPG, 16.5 to 20 MPG, and 33 to 50 MPG all save the same amount of gas over a given distance (e.g., 100 gallons per 10,000 miles). Given the inverse relationship between MPG and GPM, MPG requires division before subtraction (e.g., 1/20 - 1/16.5 or 100/20 - 100/16.5). GPM makes the magnitude of gas savings clear without additional math. GPM allows car buyers to use subtraction to compare the fuel economy of different cars (e.g., 500 vs. 400 gallons per 10,000 miles).

Providing a column of GPM numbers at Consumer Reports and at would make accurate fuel economy comparisons far easier than the current column of MPG numbers. GPM needs to supplement MPG as a measure of fuel economy.

Monday, December 8, 2008

Summary of the MPG Illusion Studies

The MPG Illusion Studies (Originally posted at the Nudge Blog)

Follow this link to access the original Science article and online supplement.

Study 1: In the first study, college students were asked to rank each of the following vehicle changes (old car vs. new car) in terms of total gas saved, assuming that all the vehicles were driven 10,000 miles (shown in a random order):

A) 34 to 50 MPG
B) 18 to 28 MPG
C) 42 to 46 MPG
D) 16 to 20 MPG
E) 20 to 22 MPG

The majority of participants ranked the changes in order of the linear increase in improvement in mpg, (16 mpg for A, 10 mpg for B, etc.) However, in reality, B and D save more gas than A; D and E save more gas than C. Only 1 participant in 77 gave the correct order in terms of gas saved per 10,000 miles: B (198 gallons), D (125 gallons), A (94 gallons), E (38 gallons), C (30 gallons).

The A vs. B comparison is close to a family decision we made (to replace a minivan that got 18 mpg with a small station wagon, or to replace an efficient sedan with a hybrid compact). We were surprised to discover that option B saves twice as much gas as does A. Over 10,000 miles, B saves 198 gallons; A saves 94 gallons.

Study 2: A second study asked college students to price the gas savings from adding more efficient engines to a car that gets 15 mpg and costs $20,000, where the only feature that varies across vehicles was the mpg. Linear reasoning led them to undervalue improvements to 19 and 25 mpg and overvalue improvements to 55 mpg (under a range of discount rate assumptions).

Study 3: A third study showed that the mpg illusion could be broken by expressing efficiency as gallons per 100 miles (GPM). In this study, we asked a cross-section of adults to think about a town’s fleet of vehicles that all drove 10,000 miles per year. Half the vehicles in the fleet got 15 mpg and half got 34 mpg. Participants were asked to choose between 1) replacing the 15 MPG cars with vehicles that get 19 mpg, or 2) replacing the 34 MPG cars with vehicles that get 44 mpg.

Three-quarters preferred the second option when expressed as mpg. However, when gallons per 100 miles (GPM) information was also given, 64 percent correctly preferred the first option (replacing cars that got 6.67 gallons per 100 miles (GPM) with cars that got 5.26 GPM) to the second option (replacing cars that got 2.94 GPM with cars that got 2.27 GPM).

Option 1 (14 to 19 MPG) saves about 1.4 gallons per 100 miles compared to Option 2 (34 to 44 MPG), which saves only .7 for every vehicle replaced. In our scenario, Option 1 saves 14,035 gallons of gas per year; Option 2 saves only 6,684 gallons of gas per year.

Tuesday, December 2, 2008

Monday, December 1, 2008

The MPG Illusion in 2020

GPM shows that replacing the most inefficient cars (those with MPG in the teens) yields larger gas savings than improving already efficient cars. For example, convincing someone to trade in a 14 MPG car for a 20 MPG car reduces as much gas as having two people trade in a 33 MPG car for a 50 MPG car over the same distance.

Does the GPM argument apply only to today's highly inefficient cars? What if all cars in 2020 are "efficient" by 2009 standards (e.g., 50 MPG and above)? Is GPM still useful?

The answer is yes. Imagine that by 2020 cars range in MPG from 50 MPG (the Escalade superhybrid) to 170 MPG (the Prius superhybrid). GPM shows that the policy focus will always need to be on removing the most inefficient vehicles: Replacing a 50 MPG car with a 65 MPG car saves more gas (over a given distance) than replacing a 100 MPG car with a 170 MPG car.

Because of the curvilinear relationship between GPM and MPG, MPG will be potentially misleading even as cars become increasingly efficient. The benefits of thinking in terms of GPM will hold for all future efficiency levels, not just for today's SUVs.

Saturday, October 25, 2008

Tools for Calculating GPM from MPG


For an online GPM calculator that includes conversions for all new 2009 cars, go to this post
This May 29 post has several tables that can help you calculate the gas savings from a Cash for Clunkers trade in.

Original Post

The following table shows how different levels of MPG translate to gallons of gas consumed over 10,000 miles (GPM). The MPG levels are chosen so that they translate to equal improvements in gas saving (100 gallons over 10,000 miles):

10.0 MPG = 1000 GPM (Gallons per 10,000 Miles)
11.0 MPG = 900 GPM
12.5 MPG = 800 GPM
14.0 MPG = 700 GPM
16.5 MPG = 600 GPM
20.0 MPG = 500 GPM
25.0 MPG = 400 GPM
33.0 MPG = 300 GPM
50.0 MPG = 200 GPM

The table makes clear that small MPG improvements on inefficient cars (e.g., 11 to 12.5, 14 to 16.5) save a large amount of gas. Replacing a 14 MPG car with a 25 MPG car saves more gas over a given distance than any possible improvement to a 33 MPG car. Greenhouse gas policy needs to focus on removing the most inefficient cars.

The following table shows how improvements of 5 MPG translate to gas consumption (gallons per 10,000 miles):

10 MPG = 1000 GPM (Gallons per 10,000 Miles)
15 MPG = 666 GPM
20 MPG = 500 GPM
25 MPG = 400 GPM
30 MPG = 333 GPM
35 MPG = 285 GPM
40 MPG = 250 GPM
45 MPG = 222 GPM
50 MPG = 200 GPM

This table makes clear the diminishing marginal returns to higher MPG.

These tables are summarized in this pdf file. Print it and keep it with you to calculate gas consumption when buying a new car.

An online GPM calculator can be found at this post. It also contains calculators for all new 2009 cars.

If you are interested in making GPM calculations for any distance of your choice, these excel files will do the math for you. They open in a new window and can be downloaded and saved to your computer:

GPM calculator for one car

GPM calculator for two cars

The second file (for two cars) is useful for (1) comparing the difference in efficiency between two cars, in which case one would use a single distance for both cars, and for (2) comparing total gas consumption for two cars in the same household, in which case one can let the distances of both cars vary to match expected driving.

If you find graphs helpful, the following picture shows the amount of gas used (on the y-axis) for different levels of MPG (shown as different lines) and for different distances of driving (on the x-axis). Click on the icon below to go to a two-page pdf file (click here for the pdf or here for a powerpoint file). The first page contains MPG values that range from 10 to 50; the second page contains MPG values for (relatively) efficient cars that range from 20 to 50.

Burning one gallon of gas releases about 20 pounds of carbon dioxide (another 20 percent is released in producing gasoline). Every 100 gallons saved reduces carbon dioxide emissions by 1 ton.

Other calculators can be found at these sites (we did not construct these calculators and have not used them extensively): (which is linked to the July 14 post at good republican usa)

Monday, October 13, 2008

"When the time is ripe for certain things, these things appear in different places" (Farkas Bolyai)

Updated May 2009

Others who noticed the problem with MPG or made a case for GPM before June 2008

Clark Williams Derry at Sightline Daily posted here, here, and here.

Eric De Place at Sightline Daily posted here and here, noted by Andrew Sullivan.

Barry Nalebuff and Ian Ayres in Forbes (Why Not?), Dennis Simanaitis at Road and Track here (see halfway down) and here, Automotive News, Boston Herald, Ben Garrido at Reno News & Review, Tony's Climate Blog, Halfbakery, No, Dave, it's just you,

A CarTalk puzzler that illustrates the problem with MPG

Discussion of the MPG Illusion or GPM between June and November 2008

See this collection of links on my Research Highlights webpage.

Discussion of the MPG Illusion or GPM since December 2008

New York Times, Autobloggreen (and here, here, here, and here), New York Times - Greenwire, Green Car Reports here and here, Christian Science Monitor, Good Magazine, Detroit Free Press, Harvard Gazette, Felix Salmon-Reuters, Treehugger, Consumerology, W&M Alumni Magazine, Climate Progress, The Street (AP), Next 100, IEEE Spectrum, Marty Padgett at the Car Connection, Huffington Post, Cognitive Daily, Wattzon, After Gutenberg, BMSeer, Driver Side, Fat Knowledge, National Motorists Association, Hybrid Review here and here, Whipnotic, Science in Society, Metamodern, Master Resource, Lemon Laws, Earth2Tech, Overcoming Bias, EnerBlog, Distributor Cap NY, Will Wilson, Business is Personal, My Black Brick, A Blue View, McKenna VW, Enviroboys, Loyalty Driver,

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