Using weightings for dissimilar values

Jammerz

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Sep 25, 2017
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I'm trying to calculate the relative ranking of a number of sellers using the following values:

- Total Product Sales
- Total Items Sold
- Total Product Visits

I want to be able to assign a weighting to each number to reflect how important I think each value is, but since the values aren't similar, how do I adjust for that?

For example, say I decide that the relative weighting should be something like this:

- Total Product Sales (5)
- Total Items Sold (3)
- Total Product Visits (1)

and the corresponding values are:

$10,000
15
450

I'm not sure how to make this work so that I can compare one seller to another. Please note that this is not a homework problem, but a situation in my business that I would like to get right.

Thanks for any pointers!
 
I'm trying to calculate the relative ranking of a number of sellers using the following values:

- Total Product Sales
- Total Items Sold
- Total Product Visits

I want to be able to assign a weighting to each number to reflect how important I think each value is, but since the values aren't similar, how do I adjust for that?

For example, say I decide that the relative weighting should be something like this:

- Total Product Sales (5)
- Total Items Sold (3)
- Total Product Visits (1)

and the corresponding values are:

$10,000
15
450

I'm not sure how to make this work so that I can compare one seller to another. Please note that this is not a homework problem, but a situation in my business that I would like to get right.

Thanks for any pointers!

First, let me say that the particular weighting you have would not be my choice at all unless sales value is always going to dominate and you are just trying to find the minor differences between employees.

Generally if you have a set of values which are more important that others, the formula used is a weighted sum. This can be used with or without a normalizing factor N but to sort of be consistent normalizing factors are generally used so if all weights are the same you just get the 'usual average'. In your case you would multiply each quantity by its weight and divide the sum by N [=5+3+1 in your case]
 
I'm trying to calculate the relative ranking of a number of sellers using the following values:

- Total Product Sales
- Total Items Sold
- Total Product Visits

I want to be able to assign a weighting to each number to reflect how important I think each value is, but since the values aren't similar, how do I adjust for that?

For example, say I decide that the relative weighting should be something like this:

- Total Product Sales (5)
- Total Items Sold (3)
- Total Product Visits (1)

and the corresponding values are:

$10,000
15
450

I'm not sure how to make this work so that I can compare one seller to another. Please note that this is not a homework problem, but a situation in my business that I would like to get right.

Thanks for any pointers!
Why bother with weightings so lopsided.

Person 1: Sales 10,000, Items sold 3, Visits 1

Score = 50,000 + 45 + 450 = 50,495.

Person 2: 10,000, Items sold 6, and Visits 2.

Score = 50,000 + 90 + 900 = 50,990 < 51,000.

In other words, doubling items sold and visits has less than a 2% effect on the score. If what you are trying to do is encourage visits made or items sold, this weighting scheme will not do it.

We can help with math, but we cannot help until you figure out what is important to you.
 
Why bother with weightings so lopsided.

Well, you will notice the subject of my question. These are dissimilar values, and I need to know how to go about accurately weighting such values.

I'm not trying to "encourage" anything. I am trying to create a ranked list of performance, where sales amount is roughly double the importance of the number of items sold, while the product visits are of much less importance. These are rough weights, which I will adjust after monitoring some results.

FYI, the final value will be used to affect the relevance of search results, so that sellers with better performance will have their items returned higher in the search. SOme other factors will be introduced, but I need to understand the correct approach first.

Hope that explains what I'm looking for a bit better.
 
You MUST scale to reasonably consistent values and THEN assign the weights. There are any number of encodings. You must find one you believe to be suitable. It will likely take a few tries as you encounter situations not anticipated.

One thing you might do is contemplate a reasonable maximum amount that might be achieved. Divide each result be the theoretical maximum and then apply your weightings.

Also, you may wish to consider "Independence". Number of Items and Total Value of Items are not independent. You may not be weighting like you think you're weighting if your values partially measure the same thing.
 
Well, you will notice the subject of my question. These are dissimilar values, and I need to know how to go about accurately weighting such values.

I'm not trying to "encourage" anything. I am trying to create a ranked list of performance, where sales amount is roughly double the importance of the number of items sold, while the product visits are of much less importance. These are rough weights, which I will adjust after monitoring some results.

FYI, the final value will be used to affect the relevance of search results, so that sellers with better performance will have their items returned higher in the search. SOme other factors will be introduced, but I need to understand the correct approach first.

Hope that explains what I'm looking for a bit better.
We need to find a common vocabulary here.

In your example with $10,000, 15 items, and 450 as the raw data, you want to end up with scores of 5, 3, and 1 respectively. Is that correct?

The obvious way to set up a scoring system to achieve that result from those raw data is to divide them by weights of 2000, 5, and 500 respectively and then round to the nearest whole number.
 
Well, you will notice the subject of my question. These are dissimilar values, and I need to know how to go about accurately weighting such values.

I'm not trying to "encourage" anything. I am trying to create a ranked list of performance, where sales amount is roughly double the importance of the number of items sold, while the product visits are of much less importance. These are rough weights, which I will adjust after monitoring some results.

FYI, the final value will be used to affect the relevance of search results, so that sellers with better performance will have their items returned higher in the search. SOme other factors will be introduced, but I need to understand the correct approach first.

Hope that explains what I'm looking for a bit better.

(1) In order to compare these numbers you should 'compare apples to apples'. So, after tkhunny, normalize your data first to let us say 'percentages'. Let S be total sales in the rating period, I the total number of items, and V the total number of visits. Using your 'numbers of importance'
your individual weights would then be wS=5/(N*S) for sales, wI=3/(N*I) for items sold, and wV=1/(N*V) for the number of visits where
N = 5/S + 3/N + 1/V

The 'rating' of your example seller would then be
R = wS * 10000 + wI*15 + wV*450

If a typical R is 'small', you might consider multiplying by some 'large number' and truncating to an integer.

(2) Although the categories you have may be important, I suggest there are others just as important [I know you said you might change the category list]. To get an idea of what categories to use you might ask the sellers and customers.
 
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