## This story begins...

with a problem. I'd been using Uber and the Metro to get around LA and they just weren't cutting it. I decided it was time to get a car of my own but the market was overwhelming having taken into account the number of manufacturers, models, trims, sizes, and features. The possibilities are endless.

After looking at a random set of cars, I noticed some unifying traits among cars:

- Make
- Type
- Model

*Make* I decided was too broad -- it encompasses all sizes and is not standardized. *Model* was on the other end of the spectrum: far too specialized to be compared to other entities. *Type* is where I saw some meaningful variation to compare against. Although not completely standardized, types of cars (Sedan, Compact, SUV, etc) at least conform to an expected set of parameters. It also seemed like the same set of types could be found across all manufacturers.

## The Goal

I could've just looked at Kelley's Blue Book. But doing that would've just given me the going price for one car of a specific year and mileage. KBB denies one the opportunity to spot trends and patterns that almost always emerge from large, unorganized, but highly correlated datasets. One data point to me is worthless -- true wisdom is in the aggregate. So I began my search.

**I wanted to answer a couple of basic decisions before paying $10,000+ on an automobile.**

- How efficient are cars of different types?
- How durable?
- How fast do they lose value?
- How much fun are they to drive?

## What's my type?

To do this I pulled together a set ~6,000 used cars from zipcodes bordering Culver City (where I live). They range across size, type, and make as well as year of origin. I put together a set of types that seem to cover all the cars the market offers:

- Compact
- Sedan
- SUV
- Sport
^{1} - Luxury
^{1} - Gas-Electric Hybrid
- Pure Electric

#### Fun Factor

Looking at fun-ness seemed like a good place to start. Horsepower is the observable metric here, the car's torque multiplied by its rpms.

Its not too surprising that SUVs have the highest horsepower. The real insight, though, is in the measurements for compact cars and gas hybrids (GEV). Their median horsepower is almost the same despite a large difference in price.

#### Fuel

Fuel economy seemed like a good next step. The amount of torque the engine places on the car's axle is a direct result of the amount of fuel it consumes. I expected there to be some relationship here:

Is there an observable correlation? Below is all types (luxury and sport included)

And here's the 5 we care about:

So there certainly is some correlation^{2}. As fuel economy goes up, mileage tends to down. The inflection point seems to be somewhere in the 28-30 mpg area. Cars that get 30+ miles per gallon have far lower horses than the others.

#### Dollars

Let's move on to price. Here's how the MSRP varies from type to type:

Just to clarify, this is the price for a *brand new* car of a given type. But what about used cars?

Side by side?

Look at that. **There is a huge difference between brand new and used prices for hybrids and electrics**. I suspect this is because there is higher demand for newer technology, so sellers lower the price as an incentive.

This brings up an interesting question: since the price of used cars is much less than new, which should I go for, new or used? We'll return to this question later once we know more about used cars. Their price takes into account many more variables than new cars, so they merit further examination.

## Durability

So far we've gained some insight into price, efficiency, and fun. But a cheap car doesn't matter if it falls apart the second you drive it off the lot. Efficiency can save you money at the pump but what if the car dies prematurely? Let's spend some time looking at durability.

I'm going to define durability as the *existence over time*. We can measure existence as supply of cars of a particular year. Cars that have been around the longest are the most durable.

(Look at that huge spike around 4 years. We'll explain that later on, but make a mental note of it.)

SUVs and sedans win here. But wait, is this really the most complete measure of durability?

Not quite. There's one piece missing, which is something I call *seller confidence*.

#### Price Theory

An assumption I'm making here is that the price of a car reflects the seller's belief that they can sell it for that much. If they're right, the money exchanges hands and if not, the price adjusts to what buyers expect. In this way price is the most accurate gauge of value not because of some inherent worth of the car, but because, ironically enough, the value of an entity is the sum of what others appraise it as.

So the higher the price, the more confidence a seller has. If the aggregate price of a good is higher than average there's a chance there is some value to the good that others of its class don't have.

If we apply this heuristic to cars, an old car with an aggregate price that is higher than average is a car that buyers and sellers see value in despite age. If ever there was a marker of durability, that is it.

So with that in mind, let's look at price of cars as function of age:

Our earlier conclusion seems consistent, SUVs and sedans hug the median for close to 15 years of age^{3}.

Going further, if a car type has high mileage, hugs the median price, *and* is old, there is a good chance it is durable. Let's look at mileage across types:

Point proven again. SUVs and sedans are at the top.

#### A brief aside

But before we zoom in on something more telling, like the *rate* of depreciation, lets zoom in a bit...

Remember that spike in supply around 4 years? It looks like that same spike happens right before 60,000 miles. There are two things that stick out right away:

- 4 years is a common lease period. Dealers probably have an influx of cars that are 4 years old that they try to unload as quickly as possible
**60,000 miles is usually when a car's powertrain warranty expires**

Sellers may have an incentive to sell their car before the warranty expires.

## Depreciation

People work hard for their money. I expect every dollar I spend to be an investment, at least to the extent that it should be worth the same amount now as it will ten years from now. That mentality shouldn't change when you buy a car.

Gauging value goes back to the explanation of price we came up with earlier. If price is an expression of value, how does that value change over time?

The price of all cars decrease with age. It seems to be a fact that all cars depreciate. But... which cars depreciate the least?

#### Miles and Time

Tracking depreciation is tricky because there are two variables at work gnawing away at the value of your car: age and mileage. We already saw that mileage increases over time, but how does mileage relate to price?

As mileage goes up, price goes down. It varies from type to type; notice how SUV prices have a wider steeper decline as mileage goes up.

## Depreciation Rate

Back to the relationship between price, mileage, and age. We can look at each type independently to see how age affects price (included at the bottom to save space)^{5}

But price, mileage, and time when viewed isolated don't give us an accurate picture of how all three of these metrics affect *each other*.

#### PM Ratio

Introducing a new metric: Price to Mileage Ratio. Done correctly, it tells you the relationship between price and mileage over time. Or rather, the rate of price change over time with respect to mileage. Or, depreciation.

First off, check out that huge slope between years 0 and 1^{4}. **That is the value drop in the first year of owning a car**. It is why *there is no reason to buy a brand new car* except to have something brand new.

The PM ratio only has meaning when compared to others across a single dimension (for us, that dimension is type). The higher a car's PM ratio is relatively, the higher its price per mile. Consequently, it follows that cars with higher PM ratios lose value quicker per mile driven.

When time is factored in when we examine the rate of that value loss per mile. Cars whose PM ratio changes at a higher rate can be said to have a higher rate of depreciation. The steeper the curve, the faster the value loss. **Flatter curves win.**

To truly see this in effect, we have to plot the change in PM ratio over time, which is the slope of the line between each year:

Based on the data, Electric cars depreciate the fastest while sedans and compact cars depreciate the slowest. Another interesting insight is that depreciation rates seem to converge at 6 years.

## Conclusion

So let's put it all together. Here are the questions I was trying to answer:

- Efficiency?

**Electric** - Durability?

**Sedan & SUV** - Slowest rate of depreciation?

**Sedan & Compact** - How much fun are they to drive?

**Sedan & SUV**

**Sedans and SUVs are the winner, compact cars are close behind.** The efficiency of electric and hybrid cars is tempting, but their high rate of depreciation and low resale value make me think its not worth investing into.

Check out part 2 where I talk about how specific models compare..

## Footnotes

(As I looked through the data, I realized that Luxury and Sport behaved more like

*traits*as they were sometimes found attached to other types (Luxury Sedan, Sport SUV, etc). So with the exception of a few analyses, I leave those two out) ↩Sports cars take the lion's share of fuel -- just as a point of reference though, that point all the way up near 700 hp is the Lamborghini Gallardo. ↩

Hybrids are a cut above, probably because of their fuel economy or because of the cash incentives the state of California gives to hybrid owners. ↩

It was actually so big I had to crop it out so you could see the other years. ↩

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