Calling all mathematicians

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acjy1985

acjy1985

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acjy1985
I am wondering the fairest way to work out the 'best value for money' car. I am testing cars with strict guidelines which keeps it fair. What would be the best way to calculate the result? Say I've tested 50 cars, my idea was to assign the cars points. 1-50 (1 for the cheapest car). Then assign 1-50 points per track (1 for the fastest car). Then the car with the lowest score after all tracks and cost are taken into account is the winner. I have 5 tracks I've tested on and realised that this probably wouldn't be a fair way to compare the cars as the value would only carry the weight of 1 circuit.
I could always multiply the cost score by 5 to give a range of 5-250 points but can anybody more mathematically gifted than myself come up with a better way to score the cars. Please assume my total of 50 cars just for ease of maths.
 
Nissan GT-R and Tommy Kaira ZZ-S or ZZ-II can't remember (The faster one!)
 
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I am sure a GT-R will top the list, but I am actually after a way to calculate it rather than suggestions of cars.
 
Not points as its not accurate

You could be 1point less but 3-5 seconds

You should do cr. to time round track
 
mjm_98
Not points as its not accurate

You could be 1point less but 3-5 seconds

You should do cr. to time round track
Click to expand...

Firstly, thanks for actually reading what I wrote. Secondly this does seem a fairer way and suggestions like this are the exact reason I came on here for a bit of help. So divide time in seconds by credits and the highest number wins. Or credits divided by time and lowest number wins.
 
What would proberly work is time x credits and lowest is best

If the time was 1:22
It would be best to times it in minutes to keep numbers low and round to nearest second
You would do 22 divided by 60 to give the decimal proportion of the minute add that to 1 an times by cr

If that car costed 20000 it would be 20000 x1.366666666666666667 =27,333.3333 and so on

Also do it completely stock including tyres as that's paid for in car purchase
 
The only way to do it in points would be to do it in a massive league table in a race which still would be less fair
 
I'm currently testing cars with a slightly different purpose (a PP-system based on actual laptimes), but the problem is basically the same.

For my purpose, it is pretty clear that my result will be given in PPs, but you will have to decide what your measure or index for each car should have as a unit.

Things that have to be taken into account in my opinion:
  • Ordering the cars by position is a simple, but not a bad way to do it. The problem with this approach is, that distance from the best time is not taken into account.
  • You could do this by assigning a value of 1 (or 100%) to the car with the best time, and then calculate a percentage the other cars are over that best time. So, if the best car delivers a 1:00 laptime, and the worst will be 1:30, that would be equal to 1 (100%) and 1.5 (150%). This will give a much fairer value for each track as it gets rid of very small differences between cars.
  • You can either sum up the results for each track or make an average - you will arrive with an overall result for all tracks. (both methods are basically giving you the same with lowest value being best)
  • Now you want to set this result in relation to the car's price. This is somewhat tricky, as you will encounter that the lower the laptimes, the higher the price for the same amount of time you will save on laptime. So, the prices of cars rise exponentially with their laptime-capabilities. That means the two are inversely related, so you will have to turn one around to calculate the ratio between laptime and price.

    You will quickly discover that price rises much faster than laptimes get lower, so you will need to determine an exponent for the laptime and the price which would balance the two. That still leaves open the question of what 1% of laptime is worth in credits. This is something that is left to one's own opinion.

My opinion is that there is no objective way of factoring price into the equation. It's probably best, if you try to derive a simple method for indexing the price (the cheapest car being 100% this time, with the most expensive taking a value that is about equal to the slowest cars on the track), and then decide of how much weight you want to give laptimes on the one hand and price on the other.

Example:
Fastest Car: 100% (Laptime), 150% (Price)
Medium fast car: 125% (Laptime), 110% (Price)
Slow car: 150% (Laptime), 100% (Price)

Now you just decide on a weight for each part, and there you go.
 
acjy1985
I could always multiply the cost score by 5 to give a range of 5-250 points but can anybody more mathematically gifted than myself come up with a better way to score the cars. Please assume my total of 50 cars just for ease of maths.
Click to expand...

I think it might work slightly better to just take an average of the points from the tests and add that to the points for the cost.

2nd Cheapest
40th Place Finish
44th Finish
43rd Finish
39th Finish
46th Finish

2+((40+44+43+39+46)/5)=44.4

50 points for being most expensive
1st Place
2nd Place
1st Place
1st Place
1st Place

That would be 51.2 points.

The second cheapest car scores better because it wasn't the second slowest. It isn't nearly as fast as the most expensive, but that isn't the point. The point is, it beat cars that were more expensive.

I assume that is the sort of thing you are looking for.

Cars that I expect to do very well in this will be older Lan Evos and Imprezas. They easily monster cars that cost twice as much. The GT-R will also perform well, since it was built to take on much more expensive mid-engined super cars but doesn't cost near as much.
 
It also dawns on me doing it the average way. A score of 51 means it performs as expected.
 
I'm thinking maybe sod the maths (coming from a GCSE A* achiever) and just make a shortlist:

Dodge Viper ACR - For 300,000cr. maximum, you get a potential perfect drag car, a 260mph rocketship or a homing-missile on tracks with the right setup. And it's just fantastic.

Nissan GT-R '07 - No others, just the cheap-as-chips boggo GT-R which drives like a wasp on steroids. Millimetrically perfect, even on tough corners, and thrashes cars six times the price.

Tommy Kaira ZZ-II - My god is it good value. Less than 100k to buy, yet on tracks it blows McLarens and Mercs and Ferraris into the reeds and smears dog poo all over their overpriced faces.


On the other end of the scale...

Ferrari SP1 - Why you would buy something slower than the 280,000cr. F430 it's based on for 1.5 MILLION cr. is beyond me. Waste of bloody money.

Nissan GT-R Black Mask - Right, it's the same as a normal GT-R, except the front bumper hasn't been painted properly. But it's 3 times the price. Yes the GT-R is as fast or faster than other cars of the same price bracket, so technically is not too bad value, but when you can get the same car and pretty much fully tune it for the same price, why would you buy it?

Alfa Romeo Guilietta TZ2 Carrozzata Da Zagato CN.AR750106 (Catchy name) - Ooh it's fun to drive. But for something only as quick as an M5 or a C63 to be 15,000,000cr. is just ridiculous. It's exclusive I know, but as far as value for money is concerned, it's disgraceful.
 
I think that due to the law of diminishing returns it would be near impossible to rate all cars in this way. It may be possible to do it by using separate classes of cars (by pp for example) but even then the track chosen would drastically affect results i.e. a fast track will make one car look good but a slow one would make the same car look lame.
In any case, with the money available from seasonals this seems unnecessary as no car is unaffordable. I like to try a variety of cars to find ones with the most desirable handling characteristics.
Sorry if this isn't helpful.
 
Lexus IS-F, as it's less then 100k and one of GT's most flexible cars, circuit racing, drags, drifts, epic to look at, RM which is also epic to look at and can also be brilliant around a track and against the Camaro RM and Challenger TC would do a good NASCAR representation.
 
Thanks to everyone who has answered the question. I knew there would be loads of good suggestions. I might have a look and decide on the one that gives the clearest results for the least effort.
 
Alfa Romeo Guilietta TZ2 Carrozzata Da Zagato CN.AR750106 (Catchy name) - Ooh it's fun to drive. But for something only as quick as an M5 or a C63 to be 15,000,000cr. is just ridiculous. It's exclusive I know, but as far as value for money is concerned, it's disgraceful.

Its worth every single penny, stunningly beautiful to drive and view!
 
It's already been mentioned but using a cars earning potential makes a good yardstick on value. For example take a given Seasonal race and find the cheapest car (including all performance enhancing modifications) that can win that race. Yes other cars may do it faster but then you have to decide if the extra seconds saved in lap times are worth the extra credits spent. Still leaves things a bit fuzzy but makes for a simple baseline.

Now my personal pick of best value car was the Daihatsu Mira TR-XX Avanzato. It hasn't seen as much action recently since they removed most of the old Seasonals but it paid for the majority of my 2,000+ (2 accounts) cars plus their modifications. You can buy it for under 10,000 credits. Fully modified with RS tires etc. Adds another 205,000 or so credits. Sounds like a lot until you realize that just about any Seasonals it qualified for and could win, which was a surprisingly large number paid more than that for one race and you had a gold mine. None of the other Kei cars could get close to it in the old Kei car Seasonal race at the custom Eifel track which for most of last year made it either the #1 or #2 fastest way to earn credits on a credit per minute bases. The fact that the car is also fun to drive and can on shorter tight courses challenge much more powerful cars just improves its value.👍👍
 
Average Speed divided by price is a straight-forward way to calculate value for money.
I reckon it would be more suitable if you're only comparing a particular type of car, where the prices are evenly matched.

This is the sort of thing I plan to do eventually.
I personally prefer pointlessly complex coefficient-based ranking point systems like the ones used in sport ranking lists :sly:
 
If ou want to do ur method of 1-50, then you can add up the two values (e.g. 13+39=42) and the car with the lowest added points is the best.

Or, what I would do, would be to do the cost divided by the performance points. The lower the value, the better as 1000/500=2 while 2000/200=10 (if you were wondering why the lower value is better). Generally, higher pp cars are better. This doesn't apply to the Chapparal 2J which would OBLITERATE all other cars near its pp value.

One thing that this doesn't take into account is that more expensive but higher pp cars (e.g. with a value of 50) are better value than those with the same value (e.g. With a value of 50) as they will come more useful in the higher level and harder races.
 
Seeing as I love the statistics and interesting patterns one thing I have been able to deduce from the question I asked, based entirely on the flags of the respondants(so if you have a flag that is not of your own country then shame on you) is that:

37% of UK users can read
25% of US users can read
0% of Philippines users can read
0% of Polish users can read
100% of Austrian users can read
100% of Australian users can read
0% of Irish users can read

How interesting is that?
 
snowgt
...
You can either sum up the results for each track or make an average - you will arrive with an overall result for all tracks. (both methods are basically giving you the same with lowest value being best)
...
You will quickly discover that price rises much faster than laptimes get lower, so you will need to determine an exponent for the laptime and the price which would balance the two.
Click to expand...

I think for any solution theese are the main problems to be solved.

I belive there is a non-linear functional dependency of laptime to price. So what I would do, is to plot your measurings into an diagram with x-axis=time and y-axis=price. With linear regression you might be able to draw a line.
Cars sitting below your line would be the sleepers; cars sitting above would be the lemons.

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Another question is how to sum up the lap-times from various races, because the time-gaps from my observation are quite track-dependant. Longer tracks of course would create larger gaps, offroad-tacks seem to produce a wider variance of lap-times, technical tracks would favour well handling cars, high-speed tracks would favor ... well high speed cars, etc.

So in the very end you might find out that with a lot of effort you gathered no valid information ;)
 
Pagani Zonda R-
Ah-May-Zing car!

Nissan GT-R-
Great driver, never acts up.

And actually...
Honda Civic-
Gets you through most of the beginner races.
 

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