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Friday, June 20, 2008

You Don’t Understand Fuel Economy; Blame MPG

posted by on June 20 at 16:25 PM

Assuming you drive the same miles per year, which change will save more gas in a given year:

* Switching from a Dodge Ram at 13 MPG to a Toyota Tundra at 15 MPG

* Switching from a Honda Fit at 32 MPG to a Toyota Prius at 44 MPG.

(Mileage figures are from Consumer Reports.)

Have your answer? Ok, next question.

Assuming you drive the same miles per year, which change will save more gas in a given year:

* Switching from a Dodge Ram that needs 770 gallons per 10,000 miles, to a Toyota Tundra that needs 667 gallons per 10,000 miles

* Switching from a Honda Fit that needs 313 gallons per 10,000 miles, to a Toyota Prius that needs 238 gallons per 10,000 miles.

Did your answer change?

As a measure of fuel economy, miles-per-gallon is incredibly unintuitive. One must consider both the change and the starting point when deciding the significance of an increase in MPG. Nasty.

How nasty? Richard P. Larrick and Jack B. Soll collected data to discover just how confused people become when considering changes in miles-per-gallon. Their work was just published in the Journal Science.

The most telling passage from the study:

The study was presented in an online survey to 171 participants who were drawn from a national subject pool. Participants ranged in age from 18 to 75, with a median age of 35. All participants were given the following scenario (5): “A town maintains a fleet of vehicles for town employee use. It has two types of vehicles. Type A gets 15 miles per gallon. Type B gets 34 miles per gallon. The town has 100 Type A vehicles and 100 Type B vehicles. Each car in the fleet is driven 10,000 miles per year.” They were then asked to choose a plan for replacing the original vehicles with corresponding hybrid models if the “overriding goal is to reduce gas consumption of the fleet and thereby reduce harmful environmental consequences.”

One group of 78 participants was randomly assigned to a policy choice framed in terms of MPG. They were asked to choose between two options: (option 1) replace the 100 vehicles that get 15 MPG with vehicles that get 19 MPG and (option 2) replace the 100 vehicles that get 34 MPG with vehicles that get 44 MPG. Note that town fuel efficiency is improved more in option 1 (by 14,035 gallons) than in option 2 (by 6,684 gallons). As expected, the majority (75%) of participants in the MPG condition chose option 2, which offers a large gain in MPG but less fuel savings [95% confidence interval (CI) = 65 to 85%].

Participants in the GPM condition (n = 93) were given the same instructions as those in the MPG condition. In addition, they were told that the town “translates miles per gallon into how many gallons are used per 100 miles. Type A vehicles use 6.67 gallons per 100 miles. Type B vehicles use 2.94 gallons per 100 miles.” They read the same choice options as used in the MPG condition, including the MPG information, but with an additional stem that translated outcomes into GPM for the hybrid vehicles [(option 1) replace the 100 vehicles that get 6.67 gallons per 100 miles with vehicles that get 5.26 GPM and (option 2) replace the 100 vehicles that get 2.94 gallons per 100 miles with vehicles that get 2.27 GPM]. As expected, the majority of participants (64%) in the GPM frame chose option 1, which offers a small gain in MPG but more fuel savings (CI = 54 to 74%). Overall, the percentage choosing the more fuel-efficient option increased from 25% in the MPG frame to 64% in the GPM frame (P < 0.01).

When talking about fuel efficiency in terms of gallons per mile, people were nearly three-times as likely to make the rational choice as compared to the same numbers in miles-per-gallon. Remember this when making your next car purchase.

Updated for the graphically minded, like me:

RSS icon Comments


For more, including a handy graph, Eric de Place at Sightline wrote about this a while back...

Posted by cdc | June 20, 2008 4:34 PM

Or you could just take the bus, bike, or walk more often and have an even greater impact.

Posted by Will in Seattle | June 20, 2008 4:38 PM

Let me get this straight; people don't understand that quantity of change isn't the same as the percentage of change?

this is why people need financial advisers I suppose.

Posted by Bellevue Ave | June 20, 2008 4:41 PM

Incidentally, up here in Canada, fuel economy is measured in L/100km. It took me a little bit to get used to that -- and that lower is better -- but it's waaay more intuitive to think about.

If I drive 100km in this hybrid thingie, I use 4 L of gas; if I drive 100km in this dumbass SUV land barge, I use 20 L of gas.

It makes more complicated stuff (like what the study looked at) a lot simpler, too.

Posted by Cow | June 20, 2008 4:44 PM

you can also show a linear relationship which makes it faster to digest.

Posted by Bellevue Ave | June 20, 2008 4:49 PM

I was all over this seeming paradox right here in the comments several months back. I remember Will didn't get it then, either.

Posted by Fnarf | June 20, 2008 5:08 PM

Here's an idea: don't possess a car.

You'll save HEAPS of money.
You'll be in better shape because you'll walk more.
You'll drive a fancy new rent-a-car like a Yarus from time to time. You'll never break down and will be fully insured.
You'll help protect the environment by driving less.
And, finally you'll promote public transit by using it more especially, in cities.

Posted by lark | June 20, 2008 5:20 PM

Oh, go drink a liter of premium, Fnarf.

Posted by Will in Seattle | June 20, 2008 5:31 PM

If someone owned both the the Ram and the Fit, they would simply drive the Fit more and not buy anything at all. It's always dangerous to as people to start imaging choices that they would never in fact make. If they were capable of that, so many people wouldn't have failed the math WASL.
Abstractly speaking though, the switch from 13-15mpg would come with a margin of error that could easily make the switch of negligible value for you, whereas you would be sure to save fuel switching from the Fit to the Prius.

Posted by kinaidos | June 20, 2008 5:33 PM

Yes, we're innumerate. For one person with one car the innumeracy shouldn't matter so much as replacing that single vehicle with a vehicle with higher MPG or lower GPM is almost a no-brainer. For the individual responsible for making a decision on a fleet of vehicles, well, one would hope she'd do the math.

Good post, though. This fits in with the million-and-one economics/econometrics studies showing just how irrational we are.

Q: Why did you stop the graph at MPG=100? I was wondering when the curve crosses the x-axis.

Posted by umvue | June 20, 2008 5:40 PM

Some of the comments here are amusing: arguing that getting rid of your car excuses being bad at math is like arguing that leaving a non-sequitur comment involves pretending to actually read a blog post.

Posted by Cow | June 20, 2008 5:55 PM


Not exactly. The error applies to both MPG and gallons per 10,000 miles.

Gallons per mile (or 10k mile) is what we really care about--how much gas will it take to drive what you drive.

Provided the variance is similar across all the vehicles, the larger difference in GPM between the pickups makes that choice the more meaningful one.

The way I interpret this is, pick the lightest kind of vehicle that will do what you need to do. Focus more on small differences in MPG, when the average MPG between the choices is low.

umvue ---

Damn asymptotes!

Posted by Jonathan Golob | June 20, 2008 5:56 PM

asmyptotes are a graphs best friend

Posted by Bellevue Ave | June 20, 2008 6:18 PM

Or as Bellevue pointed out: focus on percentage change. This has consequences for national policy, too. For instance, it means that CAFE is calculated wrong if the goal is to enforce fuel economy. They should make the automakers calculate the average GPM, not the average MPG.

Posted by F | June 20, 2008 6:20 PM

I feel like it's important to point out that even a small increase in fuel efficiency is better than no change in fuel efficiency at all.

I know you have to factor in the fossil fuel cost of constructing the new vehicle but in most cases I'd assume it would more than balance out over the life of the car.

Posted by Dawgson | June 20, 2008 6:33 PM

Asymptotes PRETEND to be a graph's best friends, but they never quite get there.

Posted by Fnarf | June 20, 2008 6:42 PM

Am I missing something? Do people really have a hard time understanding that if you use less fucking gas to go the same distance, that it's better? Really?

Am I an asshole, or are people just retarded?

Posted by Mike in MO | June 20, 2008 6:51 PM


Well, Mike, it does sound like you missed the point too. A lot of people do.

Posted by elenchos | June 20, 2008 7:23 PM

Asymptopia! Yes, it's a pretend friend and you never seem to get there, but you will (almost surely).

Statistic: Third day in a row SLOG has been ruined by topics and/or comments with content mathematical and/or statistical.

Posted by umvue | June 20, 2008 7:48 PM

umvue, you know in your heart statistics is the most awesome thing ever.

Posted by Bellevue Ave | June 20, 2008 7:58 PM

Statistics is life. In fact, life only exists to produce better, more interesting statistics.

Posted by Fnarf | June 20, 2008 9:17 PM


Posted by jejajaj | June 20, 2008 10:23 PM

Yeah, statistics is pretty gosh-darned awesome. Yeah, statistics is life. But, more often, statistics is death. I'm working on a clinical trial of a particular intervention for traumatic injury leading to TBI (traumatic brain injury) or hypovolemic shock. It's Friday night. A great night for increasing enrollment. Imagine the gallows humor. So, drink up, drive fast, shoot somebody. I want data.

Posted by umvue | June 20, 2008 10:26 PM

does balls out drunkenness count?

Posted by Bellevue Ave | June 20, 2008 10:41 PM

@17: No, you're right. I'm not entirely sure why this is interesting either.

People might over/under estimate the value of a more fuel efficient vehicle but it's still true that using less gas is better.

Posted by Dawgson | June 20, 2008 11:37 PM

The problem, Dawgson, is that absent high gas prices the only people who give a shit about fuel economy are the kind of people who already drive pretty efficient cars, and moving from an efficient gas sedan to a Prius doesn't actually use much less fuel. The big gains in fuel consumption are at the other end of the spectrum -- convincing people to get out of their 11-MPG F-350s and whatnot. Even if they only move into a 20 MPG truck instead, they're reducing the amount of fuel used in America by much more than the enviros moving to Priuses.

And that is counter-intuitive.

Posted by Fnarf | June 20, 2008 11:57 PM

I think this is being misinterpreted. The point here shouldn't be about how to describe fuel efficiency. The point is that we have some really inefficient vehicles that should not be on the roads. (unless I'm misunderstanding the point)

I like the graph, but I think it should be used to say all vehicles should get no less than 40 MPG, but more than 40 MPG is not that essential. That is, unless there aren't other factors (perhaps how long the car lasts?) that should be included in determining its environmental impact efficiency.

Does MPG or Gal/10k miles change of a cars lifetime?

Posted by Phil | June 21, 2008 11:27 AM

I always fit the graph with the most tight-fitting equations, and then buy it a pair of spike heels.


Posted by Will in Seattle | June 21, 2008 11:30 AM

Just imagine you're looking for a job and the listings are in hours to a dollar (hrs/$).

Posted by daniel | June 21, 2008 1:49 PM

@17 & @15

What Fnarf said. And furthermore, as F pointed out: this is not just about the public kind of not understanding when a 10 MPG gain is worth it. The federal CAFE regulations are mired in this terrible error.

The average now is 27.5 MPG for a company's whole fleet. Add a car that gets 10 MPG less than that, and another car that gets 10 MPG over, and it's a wash. Your fleet average MPG has remained constant and you pay no penalty. But each added car that only gets 17.5 MPG is consuming an extra 271 gallons of gas per 10k miles. While the car that is getting 37.5 MPG is only saving 96 gallons per 10k miles. You're consuming 175 gallons more per 10k miles even though your average is not any worse.

This defective formula goes a long way to explaining why American cars suck so much and haven't gotten much better.

Posted by elenchos | June 21, 2008 2:38 PM

Elenchos, suck so much how? I can say "amen" on a host of issues (quality, styling, fun to drive, and all sorts of intangibles) but when it comes to mpg, the impression I get is that:

huge advances have been made in engine efficiency over the past 25 years, and the vast majority of the progress has been plowed back into a horsepower war. People are driving around with oodles of power that they just aren't using. (I know, I'm out there going faster than them with 110 hp.)

And the Euros have been just as bad on this as Detroit.


Detroit lovey the big bumbling SUV's, because they were so profitable to build. And their customers acted like the gas-sucking beasts weren't a financial problem.

As of, oh, a few months ago, those customers are now wailing about how it's a big financial problem for them, and while it's true, I also think it was true before all of the price spikes. It was a bad personal financial decision in the past, too.

Speaking of rational economic actors, federal regs forced the automakers to put the EPA city/hwy stats on the window sticker, many moons ago. How'd that work out? Har har har...

All of this academic splitting of hairs about people's innumeracy may be futile, if people don't even look at the numbers in the first place. I know of people out there who think their Ford Explorer gets good fuel economy because they only have to fill it up "every two weeks."

Posted by CP | June 22, 2008 11:21 AM

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