# The miles per gallon illusion (Miles per gallon vs. gallons per mile)

Bunnie has an interesting write up about AAAS’s Science publication “The MPG Illusion” he writes…

Here’s an interesting question.

Suppose you had a household with two cars, and each car needs to be driven 10,000 miles per year. One car consumes 34 MPG, and the other car consumes 18 MPG. Since gas is expensive, you want to replace one car. Because of utility constraints, you have two choices:

• Replace the 34 MPG car with a 50 MPG car — a 16 MPG improvement
• Replace the 18 MPG car with a 28 MPG car — a 10 MPG improvement

Which car replacement would save you the most gas?

Normally, I consider myself not bad with quantitative comparisons like this, yet initially I picked the answer of replacing the 34 MPG car with the 50 MPG car based on the superior 16 MPG improvement. Another seemingly more analytical approach also leads to the same conclusion: 50 + 18 MPG giving a 34 MPG household average seems more efficient than 34 + 28 MPG giving a 31 MPG household average.

This very interesting article in Science, “The MPG Illusion” by Richard P. Larrick and Jack B. Soll at the Fuqua School of Business in Duke University (Vol 320, June 20, 2008, p. 1593), points out the mathematically obvious truth that gas used per mile is inversely proportional to miles per gallon, which means that you have a steeper slope at lower MPG ratings, and diminishing returns at higher MPG ratings.

More @ Bunnie’s site. At first glance it seems counterintuitive, but here’s an interesting thought…

Relatively small MPG improvements in the most gas-hungry vehicles pay off greater than larger improvements in already efficient cars (hence, it does make sense to offer tax breaks for modest improvements in SUVs versus tax breaks for hybrids, which typically replacing already gas-efficient sedans).

Ok makers, what do you think? Post up in the comments!

### 35 Responses to The miles per gallon illusion (Miles per gallon vs. gallons per mile)

1. Anonymous on said:

If you are looking at items A and B, and they are changing, and you want to compare those changes to each other, it is often more useful to look at percentage change than to look at the change in the base units. Seems like pretty fundamental analytical stuff, and looking at it as inverting the ratio just clouds the issue, though it makes for a catchier theme. Also reminds me, I can’t understand why most stock tickers favor \$ change instead of % change. Am I missing something?

2. I understand the premise, but shouldn’t they all be aiming for 50 mpg?

3. paipo on said:

stop using MPG, and start using Gallons per 100 miles:

MPG…G/100M…\$/G…\$/100M
34……2,94……\$4,00……\$11,76
18……5,56……\$4,00……\$22,22
50……2,00……\$4,00……\$8,00
28……3,57……\$4,00……\$14,29

It is a lot easier to spot the differences…

4. I thought of it this way…

10 mpg more than 18 mpg is a 55% increase in mpg whereas 16 mpg more than 34 mpg is only a 47% increase in mpg.

Makes sense.

5. What about this since both vehicles travel a known amount determine how much gas they use per year:

10000/34 =294 gal/yr
replace with
10000/50=200 gal/yr
difference 94 gal/yr

for the other vehicle

10000/18 = 556 gal/yr
10000/28 = 357 gal/yr
difference 199 gal/yr

So from this you’d upgrade the less efficient vehicle as it will save you 105 gal/yr

6. Michael on said:

The ford model T was getting 20-25 mpg back in 1908…100 years of progress is getting us 10-18 mpg SUV’s? Wow.

There are cars now boasting an AMAZING 35 mpg when my ’91 camry gets that much in actual driving conditions (versus controlled lab tests).

I can see not focusing on economy if that’s not the selling point at the time, but negative growth in that area is ridiculous!

7. Devin on said:

Isn’t gas use really dependent on your RPM? so
g = C * int(RPM(t),t1,t2)
where C = some constant
int is integral from [t1,t2]
t is time in minutes
g is gas used

I hope they explain why the graph decays exponentially…

8. Ben Johnson on said:

For 10000 miles
50 mpg car will use 200 gallons
34 mpg car will use 294 gallons
28 mpg car will use 357 gallons
18 mpg car will use 556 gallons

Currently
294 + 556 = 850 gallons @\$4/gallon = \$3400

Replace Guzzler
294 + 357 = 651 gallons @4\$/gallon = \$2604

Replace Relatively Efficient
200 + 556 = 756 gallons @\$4/gallon = \$3024

At best you’ll save about \$800 a year. My suggestion don’t replace either car, keep driving them until they die. You will spend more money replacing either car then you’ll save in gas — that is unless the gas price doubles.

9. You should calculate the usage in Litres / km…

Mmmmmmetric

10. Baumann on said:

Trusting the previous poster’s math, you’re saving 199 gallons a year in the best case scenario. (Going from 18 to 28 MPG)

Now, I’m going to assume that you’re not lucky enough to trade straight across, so you also have to factor in the cost of the upgrade. Easiest way to do this? I’ll make yet another assumption that you’re going to spend \$5 a gallon…

So, the difference of ~200 gallons is \$1000.

OR… For every \$1000 you spend upgrading your car, you have to drive it 10,000 miles just to break even.

Going from 34 to 50 is even worse. A savings of 94 gallons per 10,000 miles. (~\$500 per 10,000)

Summary: If you’re trading up to save money then you’re an idiot.

Note: If you’re trying to help the environment, or reduce your dependency on foreign oil, or can think of another reason then I’m with ya. But you’re not going to save money by purchasing a more fuel efficient vehicle.

11. BillyBob on said:

The first poster here hit the nail on the head. This is just a percent problem and his example of the stock market is a good example. If your friend tells you my stock when up \$20 today! You might think wow he must be rich…. But did you ever think that he might only own a few share of Google which is super expensive stuff. Same thing goes for this example and the author makes a terrible example.

Let’s push these case out a little bit more… Let’s pretend car “A” gets 10 MPG and car “B” get 1000 MPG.

You get your choice of a new company upgrade, namely a new car to replace “A” that is now pushing 20MPG or a new car to replace “B” that get’s 1100MPG.

Which one do you choose? If you look at the percent change it’s obvious.

“But Dad, car “B” gets an extra 100MPG!!!!!”

12. Dave Bell on said:

Devin wrote:
I hope they explain why the graph decays exponentially…

It doesn’t – the curve is a hyperbola, and is the normal shape when you plot a reciprocal relationship: MPG is 1/GPM

Dave

13. Sell both cars and use public transportation!

14. Baumann suggests “But you’re not going to save money by purchasing a more fuel efficient vehicle.”

You don’t need to trade up to raise fuel efficiency. For many SUVs, you can trade DOWN and get higher mileage with just as much cargo/people space.
As gas prices continue to rise, the depreciation on these vehicles will accelerate, and the margins for increasing mileage by trading down will be reduced, but the point is, the USA has been ignoring MPG so long that MPG doesn’t correlate to the value of a vehicle, and it will be some time until it does. Better MPG doesn’t mean a more expensive vehicle.

15. some Guy on said:

I’m getting a more fuel eco car (from my truck) cause it’s time for a new car – and now’s a great time to ditch my \$2000 truck and buy fuel eco car. If you’re like one of the retards selling their new truck for eco car then – yes you’re retarded. I’m hoping to go from 15-20mpg to 30-38 mpg and saving most of the utility of my little truck in a cross over suv. We’ll see.
that’s something like a 100% increase in effeciency

16. It is true that a 10mpg increase from 20-30 is not as good as 10-20. However, it is more difficult to improve the fuel economy of a large vehicle than a small vehicle. lets look at the yukon vs the yukon hybrid. Going from 16 mpg to 21 mpg, we get a 24% increase in GALLONS PER MILE. that’s pretty good. Now let’s look at the camry vs the camry hybrid. Going from 23 mpg to 34 mpg is a 32% increase in Gal/Mi. How about that? Who would want a hybrid camry anyway. I drive a camry right now, and I will be buying a prius in about year or two. The return on gas mileage is much better for the extra amount of money you spend. So from a the camry to the prius you get 45 mpg vs 23 mpg. That’s a 50% increase in gal/mi. It would be great if they could boost the yukon by 10 mpg. But it’s not happening right now.

17. Juan C. Mendez on said:

The Science article points out a very well documented fact: people have hard time getting the math right in their heads for non-linear problems.

One case in point: Bunnie, quoted above – very brilliant guy from MIT, very strong math background, has done wonders, nevertheless makes the crass mistake of using plain/weighted average when aggregating a quantity whose denominator is proportional to the aggregation factor.

For MPG average math, you MUST do Harmonic Averages http://en.wikipedia.org/wiki/Harmonic_mean, http://jcandkimmita.info/jc/wp-admin/edit-comments.php — Once you do the math right, or move the problem to a linear space (GPM, lt/100km,…) everything is nice again.

18. volkemon on said:

@Ben Johnson-

Didn’t check the math, but for all the noise here you made a really brief, sensible arguement.

Meh….tric:)

19. the dude on said:

Huh, I’ve never had a car which consumed miles per gallon.

I do have one which consumes gallons per mile. GPM is much simpler than MPG for this sort of question. I’m glad there’s a simple conversion.

20. Saevar on said:

This whole problem stands and falls with the assumption that all cars are driven equal lengths.
Sometimes a household that has two cars, one 18MPG and one 34MGP, uses the more inefficient car less, resulting in a greater benefit when you swap the 34MPG for a 50MPG.

BUT

WHEN they are driven equal lengths, it is without doubt better to replace the more inefficient car. In other words it’s better to have the 34+28 MPG, for fuel efficiency.

21. The Oracle on said:

I can’t belive nobody’s posted this yet, but Metric uses litres per 100km.

The only countries left in the world using imperial are the US and Bhutan. Bhutan doesn’t even have a phone network.

It should be interesting to see what Makers think of Metic.

Also, the better solution to the original question is buy the 50mpg car and keep all 3 vehicles, only driving the 18mpg one when constraints require. But people seem afraid of comprimise, so….

22. Wilhelm on said:

Buy nice bicycles for the whole family.

Pick up a few cheap bikes for your friends to borrow on group-trips.

Purchase a couple bicycle trailers for cargo and/or small children.

Consider also a big red wagon for grocery shopping (if you’re in walking distance).

I’ll bet you can get all this for the cost of that slightly-improved SUV.

Too far from work? Move.

23. As the price of fuel inevitably rises, we see the tired old arguments being pulled out, resistance to change, reasons why there’s no need to swap.

The price of crude oil has doubled over the last 12 months. Every day we see a new high, a new price-per-barrel record being set. That direction is not going to change, although we may not see year-on-year doubling of prices continuing for the moment. Eventually, the price of oil will rise exponentially.

Even the existing price rise has not finished being handed on to consumers.

Poster “Ben Johnson” nails it when he says “You will spend more money replacing either car then you’ll save in gas — that is unless the gas price doubles”

Your gas price *will* double. And then it will double again. And again. It’s already done it, and it will continue doing so.

When I lived in London, I used to commute from one side of the city to the other by motorcycle. When I started doing so, petrol was under 40 pence per litre. It’s now 3 times that – the AA’s reported *average* price for petrol is Â£1.20. Petrol prices in the UK rose by 5.6 pence per litre over the last month.

I now live in France. Prices have gone up nearly 50% over 6 months at my local petrol station. Despite living in a region where pickups and 4x4s make a considerable amount of sense, the majority of 4wds I see these days are parked on the side of the road with a “for sale” sign in the window.

My car gets 60 miles per (US) gallon, and I can barely afford to run it as it stands.

Dependence on oil must go away. Changing your car won’t matter worth a damn if you’re replacing it with another one that eats fuel. All you’re doing is pushing the decision out further. Eventually, you won’t be able to afford to run a petroleum fuelled car *at all*; you will *have* to change your way of life. And ethanol’s not gonna save you. Save it for getting drunk with, cause when there’s no oil left you’re gonna need a drink. And the oil *is* running out. Maybe not today, maybe not next year, but there is a finite supply and we’re using it in exponentially growing quantities. When it’s gone, it’s gone, and it’s gonna be time to move onto something else.

Of all the western states, it’s the US who are going to get hurt by that the most, of course. Your entire way of life revolves around the vehicle, your cities are structured on that basis. You’d have thought that we would have learned in the 1970s, but it seems not.

24. Chris on said:

Yes you get diminishing returns and you MPG goes up

BUT why replace an 18MPG car with a 28MPG??

When you could just as easily replace it with a 35-50MPG just as easily.

The tax breaks are to encourage a culture change, you guys (Americans) love big SUV/pickups etc. so the tax break is there to make you see a saloon car or even a hybrid as a viable car to drive through finical incentives.

25. movetoiceland.com on said:

Replace the 18mpg car with a 50mpg car. Or, even better, replace your 18mpg car with a house closer to work and a bicycle.

26. Chris on said:

It’s a common fallicy that more RPM’s equal more gas being burnt. The major factor is how much air (and gas) you’re dumping in… So you could be burning a LOT of gas flooring it at 1000rpm, or very little gas just holding the engine at 5000rpm. It’s the acceleration that really gets you in the end.

27. Your assumptiom that acceleration is bad is not absolutely correct either. An internal combustion engine actually runs “leaner” when you start to accelerate – that is the petroleum/air ratio weakens, meaning that the engine is consuming LESS gas. Later in the acceleration it reaches the stoichiometric ratio (which varies dependent on engine design but is usually 16:1). It’s when you take your foot OFF the gas that it momentarily burns very rich and you use more fuel. So what you shouldn’t do is decelerate! In reality its the transition from one speed to another constantly (on and off the accelerator and brakes) that causes poor fuel consumption. That’s why living further from work if it’s a highway journey (and you can use cruise control) is better that living close to work but having to do 20 sets of traffic lights. The best answer is keep your car and encourage all US states to install roundabouts, which keep traffic flowing and cost \$0 to operate. That would save waaay more coal and oil…

28. Scott on said:

I agree that a hybrid replacing an already small car is making a smaller difference than a seemingly smaller improvement in an SUV.

But… what if someone replaces an SUV with a smaller car. Or even better and SUV with an electric small car, or hybrid – should they not get the best benefit.

The problem with giving benefit for a particular car is looking at the whole picture.

So even if an SUV saved 50% to go Hybrid, while a Prius type Hybrid also saved 50% then obviously the SUV is saving heaps more fuel and heaps more other emmissions.

But… we want to encourage the people to move away from the SUV altogether, because the Prius (or similar) owner is still producing heaps less overall.

The answer – move to smaller cars. I am sick of hearing the argument that if you have a family you need and SUV. And I am sick of hearing the argument that more power is safer.

29. Bob Snyder on said:

It seems that people always forget about the energy cost of manufacturing the car. If you sell your 15MPG SUV some other person is going to buy it. The vehicle will most likely remain in use until it is worn out. So selling it does nothing to reduce the amount of fuel it will eventually consume. Buying a new car before you need it will cause more energy and more resources to be used sooner than necessary. It takes a lot of energy to mine the iron ore, transport it to the steel mill, manufacture the steel, transport it to the auto plant, form the body panels, etc. If you want to conserve resources, the best solution, in my opinion, is to keep your existing vehicle while driving it and maintaining it in the most fuel-efficient manner. Keep the tires inflated. Avoid jackrabbit starts. Buying a new vehicle may reduce your personal fuel usage, but overall I suspect that it only increases overall resource consumption.

30. mansky on said:

Prius owners, for a few months, got HOV stickers allowing them access to car pool lanes. Curiously backward: priuses are more efficient when entering city traffic, less efficient when traveling highway speeds. Hybrids are a transitional technology, but, perhaps, too little, too late. In any case, rewarding hybrids in HOV lanes is a kind of upside-down logic that focuses on the short-term and has no idea about the long-term.

31. Fredex on said:

I have been doing something similar to the gallon per mile calculation uding dollars per mile.

We buy gas by the gallon but, we use it by the mile. So, cost per mile is a better measure than cost per gallon. What falls out of that is the difference in mileage between different grades of gas can override the cost per gallon difference.

My car loses about three miles per gallon using gas with ethanol. In Wisconsin, the regular and mid grades of gas have 10% ethanol while the more expensive premium does not. Premium gas ends up being a better choice on a \$/mile basis.

As the saying goes, your mileage may vary.

32. Scott on said:

Yes, it is less efficient than itself in the city. So a prius does better MPG (or what ever measurement) in city traffic than freeways.

But… on freeways it is still doing better MPG than almost anything else (apart from some Diesels).

But more importantly it is doing heaps less emmissions, even compared with the Diesel.

A hybrid (and all electric based cars) do better for city driving than country/freeway. Does that mean they are not used. No, you have to ask, worse than what? Only compared to themselves.

33. Some of the common sense suggestions are just not possible in some realities.

“Use Public Transportation” for me public transportation only became “cheaper” at \$3 per US gallon. This was due to the location I worked. Mass transit takes 2 hours each way, where as personal automobile takes 50min.

“Move closer to work” with a modest house here being \$500,000 and one close to work being \$700,000…

“Move closer to work”. I used to commute 30 miles to one major metro area from another. Work moved and now I am 30 miles in a different direction from my original origin. Can I disrupt my kids education and the rest of my family every 2 years?

I’d like to know why hybrids outside CA were petrol and not diesel. Why didn’t Honda merge the GX and HX Civic to give a CNG powered hybrid?

Why is there no LPG option in CA? There is in the UK.

Slight modification in driving habits – I’m from 28mpg to 31mpg in a Pontiac Vibe.

34. OK, so what happens when all the oil is gone? Who cares what your MPG is? Get off of oil. It is not going to happen tomorrow, but it is going to happen. The sooner we are off it the better.

All fossil fuel personal transportation should be heavily taxed! Not based on mpg; across the board, the same tax making them cost prohibitive. Then how many people would be buying Hummers? Also, how many car companies would be pumping out large SUVs with lousy mileage?

35. Stop it.

Why whip out all these stupid charts to make is show how hard it is to use mpg just because you are a euro lover.

If you want to know which vehicle to get, one does not have to get fancy.

* Replace the 34 MPG car with a 50 MPG car — a 16 MPG improvement
* Replace the 18 MPG car with a 28 MPG car — a 10 MPG improvement

This is injecting worthless information. Who cares if it is a 10mpg improvement? Why compare that with a 16 mpg improvement in an UNRELATED car?

replace car A. 50 / 34 = 1.47. a 47% increase.
replace car B. 28 / 18 = 1.55. a 55% increase.

that’s all you need to know. replace car B.

there is no need to calculate how many gallons you would use to drive 10,000 miles..