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Old 7th June 2010, 17:45   #271
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Originally Posted by Dr.AD View Post

A very interesting suggestion and thanks for it. Yes, it does satisfy the intuitive constraint for the best and the worst case. However, I could see two potential issues:

1. What about the in-between cars? Currently, the formula is simple: normalized score = (x-xmin)/(xmax-xmin); Note that the final difference in normalized scores is linearly proportional to the actual values of "x". In other words, the distribution of normalized scores is the same as of original values. How do you get the geometric series for all in-between values? And also, won't this change the type of distribution? If so, it will introduce errors similar to those of using pure ranking positions as used by Smartcat in the first place. Note that the distribution of ranks (1 through 26) is an uniform distribution whereas the distribution of actual values under any category is not uniform (it could be normal, or something else also).

2. With scale of 0 to 1, the nice property is that multiplication of any numbers (for any number of categories) between 0 to 1 is also a result between 0 to 1. I somehow like this property. This will be lost if some cars are given points such as 2 or 1.5. But this may be a relatively minor point.

By the way, my apologies if I have misunderstood your suggestion and the above points are not true. Please clarify if that is the case. Anyway, thanks a lot for suggestion.

Actually I have thought of a method to take care of this. I will work on this tonight (hopefully will get some time) and will post new results here late tonight. That method has some advantages and some drawbacks, and we will see what happens to the results. May be another revision will be required to take care of the drawbacks

Thanks,
-AD
You have understood my system and perfectly pointed out the possible drawbacks.

I interpret the range of lower base to higher base as follows:
Bottom is "0" and Top is "1": The topmost is infinitely better than bottom.
(I doubt that we are saying this)
Bottom is "0.01" and Top is "1": The topmost is 100x better than bottom.
(This number also seems slightly over the top)
Bottom is "0.1" and Top is "1": The topmost is 10x better than bottom.
(I believe, we are starting to make some sense here)

What I am suggesting is to decide this ratio. Then we can peg the geometric mean (only between the top and bottom) at 1. The other (24 in this case) parameter values are proportionally distributed in the range. This also neatly divides the cars into bottom-half and top-half based (1 is the division point).

Anyway, this is just a suggestion. I trust that you will come up with some good suggestion. All the best for your new methodology.

Regards,
Prasad.

[PS: This is my first post as a BHPian. I need not wait for moderator approval ]

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Old 7th June 2010, 20:16   #272
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Originally Posted by smartcat View Post
I have data on top speed of each car. Does that help?

I guess at 130 kmph, a car that has been built for a top speed of 200 km/hr will be more stable, comfortable & confidence inspiring than a car that has been built for a top speed of 160 km/hr.
Relatively, yes I do agree with what you are saying, but from the cars in consideration I guess only Manza/CS are the only ones with the top speed of 180 or something. I believe all others have a top speed of atleast 200. What I meant to say was, let us for examples sake consider 2 cars 1) An Optra 2) ANHC. Now since the top speeds of both these cars is atleast 200, which one is better at riding at a speed of 130km/hr? Which steering has more feedback, which car feels more planted on road, which car manages tthe twisties well

This info cannot be gotten first hand in all the cars but then we do have the TBHP database right
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Old 7th June 2010, 22:15   #273
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Default Addressing the problem of zero

OK, so lot of you mentioned that giving a score of zero to a car is not right. So here is a modified method that takes care of this.

However, before we proceed further, I would like to mention that this is purely an academic exercise. I am myself not convinced of any real utility of this. I believe that the earlier table I presented (where some cars got final score of zero) is still the right one. As I explained, cars with zero score simply mean that they were last in at least one of the categories, and as a result, they also stand last in the final rankings. I will trust those results more than the results presented in this post.

This method has a few drawbacks (just as any other method would have), and I will explain those later. Also, this method has unearthed one more issue with my proposed compounding method, and I will also comment on that towards the end.

This method, in principle, is the same as the one presented yesterday, but with one difference. The normalization scale is changed. Earlier, the normalization was done using the best and the worst numbers in a given category. Thus, the best car got a score of 1.0 in that category, and the worst car got a score of 0.0 (and this became a bit of unacceptable issue to some of us).

New normalization scale: Instead of using the best and the worst scores out of the cars under consideration, let us use some other pre-defined notions of the best possible ("dream score") and the worst tolerable ("nightmare") score for that category. For example, one could say that for performance measured in 0-100 km/h times, the dream score is 8.0 seconds, whereas the nightmare score is 20.0 scores.

Now, if we normalized our cars on this scale, the best car will not score 1 (unless it actually achieves the dream score of 8.0 seconds; but then I am sure it will cost way more than 12L as we are in a BMW territory here), but something less than 1. Similarly, the worst car will not score 0 (unless it actually '"achieves" the nightmare score of 20.0 seconds), but something more than 0 but lesser than 1.0

Thus, the range of normalized scores is still between 0 to 1 (which means we maintain all desired properties of this scale), we get rid of the zeros, and also we did not cook up any artificial corrections such as arbitrarily changing 0 into 0.01.

Advantages:
1. Intuitive: We can understand what the best score in any category could be and also understand the worst possible score. We can also use our preferences into deciding on these numbers, and recalculate our own ratings.
2. As mentioned above, the numbers are still within 0 to 1 scale.
3. The method is statistically fair: Just as we eliminated zeros from the lower end of the spectrum, we also eliminated 1's from the higher end, so that the adjustment is not biased towards any one end.
4. The distribution is not changed. This means that if the actual scores have normal or lognormal distribution, the normalized scores will have the same distribution.

Disadvantages:

1. The method requires "extraneous parameters" (dream score and nightmare score). Previous normalization using the highest and lowest scores in the data was free from this defect, and effectively derived these parameters from the data itself. I believe that any method that derives the required parameters from the data itself is superior to one that requires supplement of extra parameters.
2. The scores get influenced by the choice of these extra parameters. So now we have introduced some unwanted subjectivity in the method.
3. While it was easy to decide on these parameters for straightforward categories such as times for 0-100, it is difficult to decide the values for these parameters in categories where a lot of sub-categories are combined. An example of this is the "practicality" category, where many sub-categories such as turning radius, boot space, legroom etc. are combined.

Changes in the implementation:

Considering the above mentioned drawbacks, I had to make a few changes in the implementation, as listed below. These changes also make it impossible to compare the results presented here with the earlier results. Therefore, these results should be treated as outcome of an independent academic exercise, and should not be compared with the previous results.

1. Sub-categories under performance and drivability are split-up and used as separate categories.
2. Safety features and braking distance are split-up into two separate categories.

Choosing values of dream scores and nightmare scores:


For total features, I have used dream score as the maximum score if a car had all features (I counted 50 features being considered in the sheet). Nightmare score is of course, 0. Same for safety features (I counted 6 as maximum number of airbags. One could use 2 here as well). The trickiest part of choosing these numbers for "practicality". Here, I used some arbitrary numbers looking at the range of current numbers. This is the unwanted subjective part, and you could rightly argue that my numbers don't make sense to you.

The data used (again, same as that collected by Smartcat), along with the dream scores and nightmare scores is given below for reference.

Sedans Under Rs. 12 Lacs - A Quantitative Ranking-dataforrevisedscores.jpg

Results:

The table below gives the normalized scores using this new scale, the compounded scores per unit OTR, and the new rankings.

Sedans Under Rs. 12 Lacs - A Quantitative Ranking-revisedscores.jpg

Observations:

Since I believe this is now becoming an academic exercise, I will not read too much into these results. These will also change depending on the dream scores and nightmare scores used. Nonetheless, Fiat Linea is finally at the top. I was joking to myself that I should invent some method that puts Linea at the top, and inadvertently, I seem to have managed that.

Bigger issues unearthed:


As I mentioned earlier, this exercise, although academic in nature, helped me identify one critical flaw in my method. This is always a good use of such academic exercises, that they help you see something you missed earlier.

Noise in the data or lesser relevant data, and lack of weighing the categories: As the number of categories increase, as is the case here, the compounding by multiplication becomes overly sensitive (and unstable) to some smaller, less relevant categories, which could be treated as noise. Thus, this method is extremely sensitive to noise and unstable. For example, if we were to use all categories under "practicality" as separate categories, then we will realize that a bad score on turning radius will pull the net score down as badly as a bad score of engine performance will. In reality, we know that engine performance is a much more critical parameter than turning radius. Also, using weighs to categories will not help because the final score is a multiplication and not addition.

Thus, if we use many smaller, lesser relevant parameters that essentially add more noise to the data, the method will become less reliable.


Solution:

As I had mentioned in my first post (post # 48) on this thread, the ideal way to compound the scores is to use some sort of "area methods". For example, one could represent the scores for each car as a polygon where each axis of the polygon corresponds to each category. The area methods combine the best properties of multiplication methods and addition methods, and will give more fair results. They are also free of the drawbacks mentioned above. Unfortunately, we will keep moving further and further away from the KISS principle. Anyway, as and when I get enough time to work on this, I will surely work on the area methods and let us see what happens then.

Thanks,
-AD
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Old 8th June 2010, 02:39   #274
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Awesome. After a while, we will all go mad with figures. Now when I think of a car, I also think of the corresponding co-related 0.012xyz

I seriously think you invented the perfect dream and nightmare scores just to get Linea on top

In my case of looking for a car, my usage indicates that I should go for a petrol car (<1000/mo expected, roughly 10k/yr, no long distance driving).

City is the best overall petrol, but I spend close to 2L more than the nearest petrols (fiesta, sx4, linea) - with half the features as some (SX4, Linea) - is it worth it?

The diesel justified by its top 5 ranking in most cases - Linea D is cheaper than City by about 50k (could be more based on current fiat freebies), so should I go for the diesel instead?

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Old 8th June 2010, 10:49   #275
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PNREDKAR - I really liked your simple idea given to Dr. AD

Dr. AD - Awe Inspiring are the words for your latest analysis.

Yep Linea is on top - possibly correctly, but possibly Manza slipped too much - There there as seen too much subjectiveness about the dream and nightmare scores.

Bigger / biggest Flaw - The weightage given to each parameter is equal as of now, but each individual is unique some drive hard and perfromance and stability is important to them, some sit in the back seat and features and ride are most important, weightage given to price, safety and rest of the stuff is almost equal - cannot be so in real life.
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Old 8th June 2010, 11:35   #276
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PNREDKAR - I really liked your simple idea given to Dr. AD
Thanks. Being an electrical engineer, amplification and attenuation comes naturally to me .
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Old 8th June 2010, 12:02   #277
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Originally Posted by echo77 View Post
I seriously think you invented the perfect dream and nightmare scores just to get Linea on top
Well, it will seem so. But please believe me, I did not play with these numbers. I chose some set of numbers that made sense to me, and just tried it out, and listed whatever results I got. It just so happened that Linea came on top, and even I was surprised.

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Originally Posted by ACM View Post
PNREDKAR - I really liked your simple idea given to Dr. AD
Yes, the idea is really good. Prasad, after you explained it better the next time, I liked it better.

But here is a thought: essentially we can achieve similar results by choosing dream score as (say) 10% over the highest score, and choosing the nightmare score as (say) 10% worst than the lowest score. That way, the scale is automatically changed from 0.1 to 0.9, without using any extra parameters. This will achieve the same "attenuation" that you are talking about (if I understood it right). So basically both our methods are similar in spirit, and just appear to be different.

Quote:
Originally Posted by ACM View Post

Yep Linea is on top - possibly correctly, but possibly Manza slipped too much - There there as seen too much subjectiveness about the dream and nightmare scores.

Bigger / biggest Flaw - The weightage given to each parameter is equal as of now, but each individual is unique some drive hard and perfromance and stability is important to them, some sit in the back seat and features and ride are most important, weightage given to price, safety and rest of the stuff is almost equal - cannot be so in real life.
I accept both these flaws and I have already pointed them out. However, here are some further thoughts:

1. The dream scores and nightmare scores can be chosen as 10% (or something) similar outside (both plus and minus) the actual data range, as I mentioned above. This will solve the first problem.

2. Yes, this (weightage) is the bigger issue, but you can think that choosing the dream scores and nightmare scores is a way of deciding weightages. You can decide these scores depending on what you think are relevant weights. For example, if I don't care for 0-100 kmph performance, then I can select a very high dream score (such as 3.0 seconds). None of the cars will even come close to this, and they will end up getting very small scores (all of them) in this category. On the other hand, if I think "features" is more important, I can use low (easily achievable) dream score, and all the cars will score relatively better here. Thus, indirectly, we have given more weightage to features and less weightage to performance.

When we use weightages, all we are doing is changing the scale linearly. The dream and nightmare score do the same, and also method suggested by Pnredkar does the same. So I believe all of us are talking about the same, and we can have methods for doing this.


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Originally Posted by pnredkar View Post
Thanks. Being an electrical engineer, amplification and attenuation comes naturally to me .
Cool. From this, it seems like we may have other topics of common interest that we can talk about (but not in this thread)
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Old 8th June 2010, 14:43   #278
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Originally Posted by echo77 View Post
In my case of looking for a car, my usage indicates that I should go for a petrol car (<1000/mo expected, roughly 10k/yr, no long distance driving).

City is the best overall petrol, but I spend close to 2L more than the nearest petrols (fiesta, sx4, linea) - with half the features as some (SX4, Linea) - is it worth it?
I am in the same position, except that I do some long distance driving (on average, one ~1000 km road trip in about 3-4 months). Given that City is so much more expensive and has less features, I am also stuck with this set of Fiesta, SX4 and Linea. Not much choice here

Quote:

The diesel justified by its top 5 ranking in most cases - Linea D is cheaper than City by about 50k (could be more based on current fiat freebies), so should I go for the diesel instead?
By the way, I would not go by these ratings when buying a car. Lot of test driving and experiencing the feel of driving each car is my preferred way of choosing the car. The feel of driving a diesel is very different than that of driving a petrol. One should also consider these subjective factors instead of buying diesel just because it ranks little higher here and still fits in the budget. Of course, a lot of such analysis has to be done as a part of our "background research", but ultimately, the test drives should be the litmus tests for car buying decisions.

What do you think?

Thanks,
-AD
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Old 8th June 2010, 14:54   #279
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I have TD'd both Linea p & d and City. I was quite happy with all at first glance. I think I need to redo them a couple of times more.
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Old 8th June 2010, 15:45   #280
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Smartcat, Echo77 and Dr AD, you guys are doing a brilliant job. This is absolutely a very educative and knowledgable thread. This has definitely helped me in identifying which car to buy.

Keep the thread rolling.

On a lighter note, I feel like nicknaming you all as "Gods of Ranking". hehe.
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Old 8th June 2010, 20:19   #281
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Thanks, nekfar! Welcome to the board. Can you tell us which car you have selected, and what part(s) exactly helped you to take the decision?

Btw, can someone tell me which of all the cars in the rankings have rear a/c vents?
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Old 8th June 2010, 20:34   #282
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^ Linea E+ has it for sure (both Petrol and Diesel).

@ Dr AD. Post numbers 271 and 272 went over my head .
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Old 10th June 2010, 15:10   #283
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This may have been posted in this thread, but how will the dezire with the new k-series engine rank if at all we consider that also here? Will it be about the same as the diesel or higher? Any reasons not to have that in the list?
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Old 10th June 2010, 15:14   #284
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I don't have the engine performance data on the DZire with K-series engine yet.
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Old 30th June 2010, 21:47   #285
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must- read -before -you - buy a car!

is it posible to another another ranking factor : Re-sale value say after 4 yrs and or 50000 kms
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