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[calder]

Ok, I'm an idiot. Especially with math.

Let's say we have a formula to create a score for a vendor's proposal. It's straightforward junior high math (and was part of the wording of the original RFP) and basically it takes the score generated by the evaluators and eventually divides it by the cost of their proposal.

Easy peasy, but now I have a couple of numbers ranging from 2ish to maybe a bit higher. I don't know what all the scores are so I can't guess how high the final numbers will go. The first few seem to all be under 5.

My problem, because I's a idjit with da numberfication, is how do I take all the final scores and present them as a score out of 10? I'm a little thrown off by the fact that I won't know the final numbers for a while, so I don't know what range the scores will be. What's the easiest way to take several numbers ranging from 2 to, say, 5 and present them as a final out of 10? Can I not do it until the final numbers come in? I don't want ordinals or anything like just rankings, I want to be able to say Vendor A scored 7.45/10, Vendor B has 8.9/10, etc. and have it make sense.

Bah I'm not sure I'm presenting, or even imagining, my question right.

 

[Orion]

What is the highest possible score?

 

[JoshuaJSlone]

Orion hit the important part... and you already mentioned that you don't know how high they can go. It's pretty impossible to get a score from 10 (or from anything) if you don't know the max. Unless you're willing to have some 12/10 later on.


But to answer the partial question of re-scoring a continuum of 2-to-5 as 0-to-10, you'd... well, if S is the original score, then the out-of-10 score would be (S-3)*10/3.

 

[calder]

Ahh thanks. Asking the question helped me realize we can't answer it yet, but at least now I don't think it's there but I just can't see it. In fact, I'm starting to think some of the 'final' numbers will be under 0. I don't think I can tell him how to find the final /10 score until we know for sure how big or small the scores will be. If the dumb 'on-site' scores get added and eventually we have numbers like 4500 divided by 15 million dollars, then I think they'll have to call legal and change the stupid formula.

Either way, this shit is about 9 levels above me. Thanks for the clarification guys!

 

[Dilbert]

Here's a formula...maybe this will help. Let:

H = highest raw score in the group
L = lowest raw score in the group
x = the score you are currently considering
x_normalized = the score you are currently considering, adjusted to be on a scale of 0 to 10

x_normalized = 10(x - L)/(H - L)

Let's look at an example. You have five vendors which have earned the following scores:

Vendor A = -2 (lowest raw score)
Vendor B = 5
Vendor C = 13 (highest raw score)
Vendor D = 0
Vendor E = 7.5

Looking at the data, we can tell a couple of things intuitively:

1) Vendor A should end up with a score of 0, since they have the lowest score in the group.
2) Vendor C should end up with a 10, since they have the highest score in the group.
3) The range (difference between the highest and lowest scores) is 15 points. This means that 1.5 points of raw score is equal to 1 point on the 0-to-10 scale -- or, considered differently, 1 point of raw score is worth 2/3 of a point on the 0-to-10 scale.

So, apply the formula and see if the results make sense with our intuition:

Vendor A = 10(-2 -(-2))/(13 -(-2)) = (10 * 0)/15 = 0
Vendor B = 10(5 -(-2))/(13 -(-2)) = (10 * 7)/15 = 4.67
Vendor C = 10(13 -(-2))/(13 -(-2)) = (10 * 15)/15 = 10
Vendor D = 10(0 -(-2))/(13 -(-2)) = (10 * 2)/15 = 1.33
Vendor E = 10(7.5 -(-2))/(13 -(-2)) = (10 * 9.5)/15 = 6.33

Sure enough...it turned out exactly as we expected!

Side note: The equation can be represented in words a little more clearly. The term 10/(H - L) is usually called the "scale factor," since it converts between the range scale (one point of "raw score") and the desired scale (0 to 10, in this case). The term (x - L) adjusts a particular raw score so that it is expressed with respect to the LOWEST score, rather than to zero.

Hope this helps...

 

[calder]

Whoa thanks jinx that's perfect!

I think I have all the final numbers now, and one of them is under zero. When I get back to work tomorrow I'll check it out.

Thanks again to everyone, if the CIO asks tomorrow how I worked it out I'll be sure to credit you guys. Kinda.