Brain isn't working - math problem: how to optimize two opposing variables?

[fuzzybabybunny]

Say that I'm comparing different cars of the same model and I'm comparing them based on two variables - the selling price and the mileage.

Generally as the selling price goes up the mileage goes down, but not necessarily. Sometimes you'll see a 100k car being sold for $5000 while a 120k car is being sold for $5100, for example.

Is there a way to take in a list of all the different cars and quantitatively compare them to select a car with an optimal value based on the price and mileage?

This feels straightforward but it might not be. Brain's not working too well at the moment.

 

[dave_the_nerd]

Picture a scatter plot, where each point is a car. One axis is mileage, the other is cost.

The car that is closest to the origin (lowest cost and lowest mileage) should be the "best" one. (Ideally, you'd get a brand new never-driven car for free, right?) So you just use the formula for distance between two points. (Good old Pythagoras.)

 

[fuzzybabybunny]

Picture a scatter plot, where each point is a car. One axis is mileage, the other is cost.

The car that is closest to the origin (lowest cost and lowest mileage) should be the "best" one. (Ideally, you'd get a brand new never-driven car for free, right?) So you just use the formula for distance between two points. (Good old Pythagoras.)

I don't think this works.

So the distance of the point to the origin (zero cost and zero mileage) would be:

distance to origin of a point at (x, y) = sqrt(x^2 + y^2)

distance to origin of the car = sqrt(mileage^2 + cost^2)

So if we have two cars:

Car 1:
$5,000
100,000 miles
Distance to Origin: 100,124

Car 2:
$100,000
100 miles
Distance to Origin: 100,000

So the car that's $100,000 but driven 100 miles is the better value?

 

[sdifox]

Just do dollar per mile

 

[fuzzybabybunny]

Just do dollar per mile

That also doesn't work.

Car 1:
$5,000
100,000 miles
$0.05/mile

Car 2:
$100,000
100 miles
$1000/mile

Ok, since Car 2 is clearly not a good value just based on common sense, it appears we should minimize $/mile, right?

Car 3:
$5,000
500,000 miles
$0.01/mile

$0.01/mile (Car 3) is smaller than $0.05/mile (Car 1), but Car 3 is clearly a worse value than Car 1.

 

[sdifox]

That also doesn't work.

Car 1:
$5,000
100,000 miles
$0.05/mile

Car 2:
$100,000
100 miles
$1000/mile

Ok, since Car 2 is clearly not a good value just based on common sense, it appears we should minimize $/mile, right?

Car 3:
$5,000
500,000 miles
$0.01/mile

$0.01/mile (Car 3) is smaller than $0.05/mile (Car 1), but Car 3 is clearly a worse value than Car 1.

You wanted to derive value based on dollar and mileage, you have only two variables. Unless you add a third one, like a value curve of some sort, you are not going to get what you want.

 

[fuzzybabybunny]

You wanted to derive value based on dollar and mileage, you have only two variables. Unless you add a third one, like a value curve of some sort, you are not going to get what you want.

You can definitely get value based on just two variables.

Take ribeye steak for example.

Store one:
$5/lb

Store two:
$3/lb

Store two is the better value.

So it's not solely because there are only two variables.

 

[sdifox]

You can definitely get value based on just two variables.

Take ribeye steak for example.

Store one:
$5/lb

Store two:
$3/lb

Store two is the better value.

So it's not solely because there are only two variables.

... I gave you dollar per mile and you didn't like that. How is that different than dollar per lb? You decided it wasn't good, not me.

Bottom line is whatever factor you want to use to evaluate something, it has to be part of the evaluation.

 

[Charmonium]

Why do you care about mileage? Most likely because you feel that is going to reflect the expected life of the vehicle. But it doesn't work that way. A relatively new but high mileage car has probably been driven mainly highway miles which means that the wear on the engine is minimal since from what I understand, most wear happens at start up when the cylinder walls are dry. So what you really care about is how many starts has the engine been through.

However mileage might be a better indicator of how much longer other components might last - things like transmission, brakes, hydraulic systems, etc.

What I've noticed is that in terms of blue book prices, you get only a nominal bump for a car that has very low mileage. For instance I have a 2008 Civic Si than only has 25k miles on it. Sure, I will probably get a better price for it than one with 100-150k miles but no one is going to pay double the blue book price. At least I rather doubt it.

But that's probably because people have a strong preference for appearance rather than sustainability so they place a much higher premium on age than on mileage. Whether or not that's smart however is subject to debate.

 

[Charmonium]

dupe

 

[shortylickens]

what are the make and model of each car?
cuz I think if we're honest with ourselves, Japanese machinery is much better than American machinery.

wait.......


they're the same......


Fuck it. Just buy the color you like. it wont matter.

 

[lxskllr]

You can get closer by weighting the variables. The first 30k miles don't matter. You still have a brand new car at that point. The higher you get, the more the miles matter. You can math your way out of just about anything, but it doesn't mean it's smart to do so, especially for a single purchase. Math works better if you need a 1,000 car fleet. *on average*, if you do it right you'll come out ahead. Some cars will die in a week, others will run forever. The preponderance will give a valuable lifespan.

Unless this just an academic exercise to amuse you, it's better to use common sense, and keep your eyes open for a deal, especially if you don't need a car *now*.

 

[snoopy7548]

You can definitely get value based on just two variables.

Take ribeye steak for example.

Store one:
$5/lb

Store two:
$3/lb

Store two is the better value.

So it's not solely because there are only two variables.

But this is just one variable, not two. You need to give the "mileage" of the ribeye. $5/lb is a worse deal than $3/lb when you're only comparing prices, but the condition of the meat is just as if not more important. It should be more like...

Store one:
$5/lb
Freshly butchered

Store two:
$3/lb
Sitting in shrink wrap for four days

 

[radhak]

Picture a scatter plot, where each point is a car. One axis is mileage, the other is cost.

The car that is closest to the origin (lowest cost and lowest mileage) should be the "best" one. (Ideally, you'd get a brand new never-driven car for free, right?) So you just use the formula for distance between two points. (Good old Pythagoras.)

This is the right tool, but wrong interpretation.

Car Price and Car Mileage are inversely proportional, so the line of best fit for their scatter plot will have a negative slope, from top left to bottom right.

Here's one graph: (from http://bytes.schibsted.com/price-car-data/)

While it shows different makes and does not have actual price value in $, the theory holds: When new, a car has zero mileage, and has maximum price. When old, those numbers flip.

You should plot all available price/mileage numbers similarly to see your own best fit line.

There is no single point on this graph that you can pick for the 'best' generically; it's all how you need it: you'd just slide along the line to a point where the price of the car is low enough for your budget, but the mileage is not too high for your tastes, and that becomes your optimal point.

 

[dave_the_nerd]

I don't think this works.

So the distance of the point to the origin (zero cost and zero mileage) would be:

distance to origin of a point at (x, y) = sqrt(x^2 + y^2)

distance to origin of the car = sqrt(mileage^2 + cost^2)

So if we have two cars:

Car 1:
$5,000
100,000 miles
Distance to Origin: 100,124

Car 2:
$100,000
100 miles
Distance to Origin: 100,000

So the car that's $100,000 but driven 100 miles is the better value?

Ah, yes, good point - you have to standardize the units so they are comparable. (What number of miles is equivalent to what number of dollars.) I think KBB has a formula/ratio for that.

So if ~13k miles is equivalent to $900 in depreciation, then a "4" on one axis is 52k miles and on the other axis it's $3600.

 

[IronWing]

You can get closer by weighting the variables. The first 30k miles don't matter. You still have a brand new car at that point. The higher you get, the more the miles matter. You can math your way out of just about anything, but it doesn't mean it's smart to do so, especially for a single purchase. Math works better if you need a 1,000 car fleet. *on average*, if you do it right you'll come out ahead. Some cars will die in a week, others will run forever. The preponderance will give a valuable lifespan.

Unless this just an academic exercise to amuse you, it's better to use common sense, and keep your eyes open for a deal, especially if you don't need a car *now*.

Yep, OP you have to weight the variables based on what is important to you. In my world, cup holders get rated higher than manual vs automatic and maintenance records rate as highly as the odometer reading.

 

[lxskllr]

I've already put more thought into this than I should, but I think converting mileage to years would give the closest approximation. Pretty much every car that isn't a lemon will give 200k miles. Under that, you got ripped off, over that, you're on bonus time. Figure how many miles you drive in a year, and factor in price. That'll give you how much per year it costs to have the car. Modifiers are gas mileage, features, and comfort. Gas mileage is the most objective.