Ideas

The Decision Matrix: Buying a Car

Use a decision matrix to compare criteria and identify the choice that best meets your neds.

By Ted Mitchell
Published January 10, 2007

In the pages of Raise the Hammer, any implied approval of cars might go over as blasphemy; but my primary purpose here is to demonstrate the process of using an engineering decision matrix to address a common problem: how to buy a car that best meets your needs.

Several sources will give you their take on car comparisons, but you can do it yourself using only those criteria which matter to you.

In 2002, Toyota revived the hatchback class with the Matrix. Seeing wildly successful sales numbers, other manufacturers quickly jumped in. These cars are small on the outside, large on the inside, offer reasonable price, safety, fuel economy and practicality.

That is, they provide actual sport and utility, unlike the traditional concept of the euphemistically named SUV. Think Meadowlands, you get the idea.

Maybe one of these is for you, but they are all so similar - how does one make sense of it? Like most people, you could buy on price - or reputation, impulse, colour, shape, or (chuckle) how well your desired self-image fits with those people seen in the commercials.

Decision Matrix

To make an intelligent decision, you should use a decision matrix.

First, compile a list of things relevant to you. For example: power, fuel economy, price, safety, reliability, cargo capacity, and the ability to hold your two teenagers comfortably.

Next, pick specifications that are available and will quantify those qualities.

Set Criteria

The first iteration is to refine the criteria. For example, power by itself doesn't do much if the vehicle is heavy. What you really want is a measure of acceleration.

This is actually tested by performance magazines, but you can't find numbers for all the cars you are interested in. Instead, approximate by dividing horsepower by vehicle weight. You now have Criteria 1: Power to Weight Ratio.

Fuel economy ratings are available from Transport Canada. Your use splits city and highway ratings 50:50. This is Criteria 2: Average Fuel Economy.

How well do the teenagers fit? The best measure is rear legroom, an often compromised dimension. Criteria 3: Rear Legroom.

Cargo capacity is a tough one because companies list many incomparable figures. The only statistic available for all is trunk volume with seats up; Criteria 4: Cargo Capacity. Note, however, that total volume with seats folded does not correlate well with this.

Safety ratings can be found from crash testing. NHTSA has a listing of frontal driver, passenger, side front and rear impacts, as well as rollovers, all out of five stars. All numbers are average them for each vehicle. This gives Criteria 5: Safety Rating.

Reliability data is a bit elusive, especially for such a new segment. Consumer Reports uses a five division system for predicted reliability, and where they have no information, use data for the closest similar model. Voila Criteria 6: Predicted Reliability.

Last but not least, delivery and all-taxes-in Criteria 7: Purchase Price.

Choose Vehicles

Next, choose the vehicles. You should include as many as possible, but let us limit them to a certain rough size, deciding on constraints (features that you must have) of four doors, automatic transmission, ABS, air conditioning, and side airbags.

Pick trim packages that have most features in common.

I have chosen the following five: Honda Fit, Mazda 3 Sport, Nissan Versa, VW Rabbit, and a unibody SUV, the Ford Escape (2WD version). Here are the numbers:

Table 1: Raw Data
Automobile Honda Fit LX Nissan Versa SL CVT VW Rabbit 5 door Mazda 3 Sport GS Ford Escape XLS FWD
hp 109 122 150 156 153
wt (kg) 1143 1261 1423 1338 1479
power/weight 0.095 0.097 0.105 0.117 0.103
l/100k city 7.8 7.9 10.5 9.4 10.4
l/100k hwy 5.6 6.1 7.1 6.9 8.4
avg l/100k 6.7 7 8.8 8.15 9.4
rear legroom (mm) 856 966 896 922 922
cargo up (L) 603 504 400 484 830
cargo down (L) 1186 1427 ? 884 1877
Safety Stars
driver frontal 5 4 4 4 4
pass frontal 5 4 4 4 4
front side 5 5 5 3 5
rear side 3 5 5 3 5
rollover 4 4 4 4 3
average 4.4 4.4 4.4 3.6 4.2
reliability stars 5 3 1 4 3
total price 22350 22460 26492 28265 32567

Note that our prototype, the Toyota Matrix, fails the constraint requirement of ABS and side airbags. Remember that imposing too many constraints is foolish: you will not consider vehicles that otherwise will meet your criteria nicely.

Normalize and Weight the Data

Now, we need to do two more things.

First, normalize the data for ease of comparison. That is, give the highest rank a value of 1 and everything else is divided by that value to give a fraction between zero and 1.

Second, multiply the quantities by a factor which corrects for the relevance of the quantity.

Most of our factors do not need adjustment, but look at legroom: the smallest and largest differ only by 11 percent. If your kids' legs require something in between, this is the difference between very cramped and lots of room.

To make this figure relevant, let's expand by a factor of three. Mathematically, that equals (Value x 3) ? 2.

Also, we need to invert price, as less expensive is the desired outcome. Similarly, we could have adjusted the relative reliability data to have a less severe rating, or simply adjust for this later in the weighting below.

Table 2: Normalized Criteria Rating
Fit LX Versa 5L CVT Rabbit 5 door Mazda 3 GS Escape XLS FWD
power/wt 0.82 0.83 0.90 1.00 0.89
avg fuel economy 1.00 0.96 0.76 0.82 0.71
legroom adjusted 0.66 1.00 0.78 0.86 0.86
cargo cap'y 0.73 0.61 0.48 0.58 1.00
safety rating 1.00 1.00 1.00 0.82 0.95
reliability 1.00 0.60 0.20 0.80 0.60
price (inverted) 1.00 1.00 0.84 0.79 0.69

Finally, weight the relative importance of each criterion. Up to now, the choices have been fairly universal. But this step is entirely your choice. The simplest way is to give equal weight. We will use this:

Table 3: Relative Importance by Criterion
Measure Weight
Power to Weight ratio 10%
Average Fuel Economy 15%
Rear Legroom 10%
Cargo Capacity 15%
Safety Rating 20%
Predicted Reliability 10%
Purchase Price 20%

Now we can multiply each weight by each rating, then add the results to produce a total score and rank.

Table 4: Results
Weight % Fit LX Versa 5L CVT Rabbit 5 door Mazda 3 GS Escape XLS FWD
power/wt 10 8.2 8.3 9.0 10.0 8.9
avg. fuel econ 15 15.0 14.4 11.4 12.3 10.7
legroom 10 6.6 10.0 7.8 8.6 8.6
cargo 15 10.9 9.1 7.2 8.7 15.0
safety 20 20.0 20.0 20.0 16.4 19.1
reliability 10 10.0 6.0 2.0 8.0 6.0
price 20 20.0 19.9 16.9 15.8 13.7
total score 100 90.7 87.7 74.4 79.9 82.0
Rank 1 2 5 4 3

Note that different weightings may produce different rankings. An emphasis on cargo would favour the Ford. Acceleration, the Mazda. Economy, the Honda. Legroom, the Nissan.

There is no weighting which favours the VW. It would take a different set of criteria to get the Rabbit off the ground.

If subjective factors are used such as ride quality and noise, this misses the whole point of using objective, quantifiable criteria.

However, some of these "soft" factors can be significant but are highly prone to marketing suggestion and bias; for example, the good reputation perhaps undeservedly enjoyed by VW in this country.

The next time you need to make an informed, objective decision, have a go at the decision matrix. Or, you can pay the stupid tax.

Ted Mitchell is a Hamilton resident, emergency physician and sometimes agitator who recently completed a BEng at McMaster University. He is fascinated by aspects of our culture that are harmful, but avoid serious public discussion.

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By appalbarry (registered) - website | Posted January 17, 2007 at 20:18:33

I would argue that this matrix really needs to consider a couple of other factors.

The first is the very real question of the overall driveability of a car. There are cars that almost become an extension of the driver, making careful and precise actions easy and reliable.

I compare that to a dreadful little Hyundai that I rented that made it feel as if I was fighting the car every inch of the way.

Yes, driveability is a safety issue.

So, I'll argue, is comfort, especially the seating. If the reason that you are buying a car is because you make long trips, then a good supportive seat makes you more alert and more focused on your driving.

If your back aches after twenty minutes, or you can never get the heat and cooling where you needed it, or if the dimmer switch is in some odd place that's never quite where your hand is, well you're going to have problems driving safely.

Ride quality and noise are not "subjective." They are quite measurable, and both reflect safety and comfort considerations that should not be ignored.

Finally, it has been my experience that cars with a red paint job are MUCH better than all others.

Barry

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By appalbarry (registered) - website | Posted January 18, 2007 at 08:57:01

I would argue that this matrix really needs to consider a couple of other factors.

The first is the very real question of the overall driveability of a car. There are cars that almost become an extension of the driver, making careful and precise actions easy and reliable.

I compare that to a dreadful little Hyundai that I rented that made it feel as if I was fighting the car every inch of the way.

Yes, driveability is a safety issue.

So, I'll argue, is comfort, especially the seating. If the reason that you are buying a car is because you make long trips, then a good supportive seat makes you more alert and more focused on your driving.

If your back aches after twenty minutes, or you can never get the heat and cooling where you needed it, or if the dimmer switch is in some odd place that's never quite where your hand is, well you're going to have problems driving safely.

Ride quality and noise are not "subjective." They are quite measurable, and both reflect safety and comfort considerations that should not be ignored.

Finally, it has been my experience that cars with a red paint job are MUCH better than all others.

Barry

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By yrraB (anonymous) | Posted January 18, 2007 at 11:20:04

Barry, the point isn't that this is the set of criteria you're supposed to follow, but that you're supposed to decide what criteria are important to you and then make your own matrix based on those criteria.

Your matrix would include criteria like "responsiveness", "seat comfort", "usability of controls", "noise", and so on, weighted based on the relative importance of each criterion. That's the right matrix for you, and it will help you choose a car that best fits your wants.

Someone else with different wants will compile a different set of criteria for *their* matrix. The commonality is the method used to pick and evaluate the criteria that matter to each person, not the criteria themselves.

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By bslorence (anonymous) | Posted June 03, 2007 at 01:42:21

Where did you get the "rear legroom" numbers? In my matrix, rear legroom would weigh much more than 10%. But so far all I have to go on is photos on eBay of the rear seats. Did you have to call dealers or is there a web site that can help me out?

Thanks, Ben

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By Hugh (anonymous) | Posted March 28, 2008 at 23:33:02

Having just bought a Fit without using a decision matrix, or even a "decision tree," I am realizing the error of my qualitative ways. I resolve, starting Saturday, to create a decision matrix to help decide how to optimize breakfast (oatmeal or back bacon and eggs?), then again to optimize the right glide wax for my my morning skate ski(cera-F powder overlay or straight high flouro?). Whoops, it's Saturday night and I have neither eaten nor skiied. Gosh Darn-it:)

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