Light entertainment: how to compare apples and oranges
Light entertainment: taxing our mental capacity

An achievable target. And how?

The Wall Street Journal tells us that GM car buyers may react to the "volatility" of gas prices by demanding higher miles-per-gallon from their vehicles. They commissioned an analysis which finds that new GM cars sold today on average have an MPG of only about 21, and suggested that 30 would be a "challenging but achievable target". (Article here).

There are many problems with the analysis, such as no specification of when such a target should be met, and whose target this is, nor any comment on the potential impact on car sales (since higher-priced vehicles tend to have lower MPG) or the existence of government subsidies for larger (lower-MPG) vehicles. Complete silence too on reducing pollution or lowering our dependence on gasoline.

In any case, let's focus on the chart that comes with the article. First, take a look at the caption:


Then, the chart itself:


Readers is presented with this puzzle: how could a minor shuffling in the mix of cars lower the average MPG to 30 when today, the least gas-guzzling vehicle class (subcompact) only averages 30.6 MPG, barely above the target?

Oops, the chart portrays (less than) half of the solution. Tucked into the caption, the analyst tells us that she has assumed an across-the-board increase of 25% in MPG for every class of vehicle. Think this information is important? Perhaps so. A 25% improvement is about 5 MPG, bringing the average MPG (at the current mix of sales) to 26.5, so the shift in mix of vehicles accounts for about 3.5 MPG of the targeted improvement.

While the chart designer very sensibly ordered the vehicle classes from highest to lowest MPG, it is baffling why the row of MPG data is not labelled directly but given a dark background so as to justify adding a third item to the legend.

The use of stacked columns to represent data at two points in time is confusing. This type of data is much better presented in a Bumps-style chart (left chart below):


The chart on the right shows an across-the-board increase in MPG and gives a sense of how the different vehicle classes stack up along this dimension. (I should've put a marker on the current average of about 21 and the targeted average of 30 but didn't.)

There is a data error in the current sales data as the proportions add up to about 115% rather than 100%. (The last three categories alone add up to about 50%.)


This analysis has the flavor of the Facebook valuation projection I discussed on the sister blog a while ago. Both require several assumptions to all come true in order to be realized. Not only must the MPG for every vehicle grow by 25% but a large proportion of new-car buyers must also choose to purchase higher-MPG vehicles. From the chart above, one sees that the proportion buying subcompacts must increase 7-fold from about 2% to 14% while the proportion buying large vans must drop from 15% to 3%, cut by four-fifths!

According to the analyst, this is an "achievable" target.  



Feed You can follow this conversation by subscribing to the comment feed for this post.


So actually I don't see how they compute the "needed" sales! For example why do we need more 19.6MPG (almost double) luxury sports cars. I can see maybe that the reduction large truck might only be compensated by buying more small trucks. Nevertheless I'm puzzled.

For me the bump chart doesn't work very well I don't understand whether the colors have any meaning (efficient/inefficient, differentiation?). Nor do I manage to connect the lines with the car groups (esp. the large group of cars in the lower third).


How do you draw these charts? Excel or some other software?


Charting aside, MPG is a backwards metric for measuring fuel efficiency, especially when you're averaging across a fleet. Gallons per mile (or per 100 miles, which get the units easier) is a more appropriate measure. Improvements to "Average" MPG overstate the actual efficiency gains.

Let's imagine the simple case: two cars, each drives 1000 miles.

Let's start with MPG since that's familiar. one car is 20 MPG, one car is 33.3 MPG. Average MPG = 26.7. Let's improve MPG by 25% in both cars. Now we have 25 and 41.6 MPG, for an average of 33.3 MPG.

25 better fuel economy, right? But if you look at the gallons used you get a different picture. You started using 50 gallons for the one car and 30 gallons for the other to drive 1000 miles, for a total of 80. In the new case, you'll use 40 and 24 gallons for a total of 64. So your efficiency really only rises 20% for your "25% MPG improvement." This difference gets worse as the efficiency difference between the cars is larger.

Short story is that the gas guzzlers use most of the gas, so improving a 15 mpg (er, .07 GPM) car by 10% is far more important than improving a 40 mpg (er, .005 GPM) car by 20% or even 30%.

It's a case of measurement (MPG) affecting decisions in a counterproductive way.


Seems as if the government is making us cut our purchasing of these vehicles just by the inflated gas costs. It's got to happen some way and I just assume they are making it seem like our own decision.


I realized my example wasn't extreme enough.

Two-car example again: one with 20 mpg and one with 33.3 mpg. I can more than quadruple the average mpg from 26.7 to 110 by increasing the second car's mpg to 200mpg. But my gallons to drive 1000 miles have dropped only from the original 80 to 50+5 = 55 gallons, which is a savings of only 40% or so. You see some of this if you target average GPM instead of MPG.

Mathematically, there are a lot of solutions to the "get to 30mpg average fuel economy" but they don't all result in the same fuel savings. We should target the ones that do, not the ones that don't (get the prius up to 100mpg!).

Chris Pudney

I had a quick go at combining the MPG and Sales targets into a single scatter plot. It was done in an Open Office SpreadSheet so I wasn't able to add arrows to the lines. I can share the data if there's any interest.


Floatofmath: yes, their proposed shift in mix of vehicles is certainly not the only solution that can bring the MPG to the target level. There is an infinite number of possible solutions. The color scheme for the bumps chart: dark blue (increase in proportion needed); light blue (decrease in proportion needed); gray (no change in proportion).

Rohit: most of my charts are "scratch book" charts which has upset a certain contingent of readers. For me, getting the concept right is much harder than finding the right software to make a nice chart. Bumps chart can be made using the line chart function in Excel, making the data fall on the axis ticks rather than between, adding a secondary axis, and a few other cosmetic changes.

Chris: good idea to test out.


On Gary's comment about MPG vs gallons-per-mile, the actual way CAFE standards are calculated uses the harmonic mean to accomplish this more relevant measure of efficiency. Citation:


@Gabe - thank you for that piece of information; I am glad the EPA (who makes the rules I assume?) thought this through. Did the WSJ article use the appropriate methodology? I can't tell at a glance.

Junior Perrera

It seems like people would most likely buy cars that can carry the whole family, even if it's less fuel-efficient. In order to balance the target sales, car companies should be willing to boost the marketing of small vehicles since these have high MPG rate.

Used Cars Minneapolis

From my understanding, it seems like the CAFE standards apply to the entire fleet and not individual cars. Car companies can still sell SUV's and trucks if they offset them with EV's and hybrids.

The comments to this entry are closed.