Monday, September 16, 2013

Weighting Attractiveness Ratings

For those of you who haven't seen on my Facebook, I'm conducting a survey of the attractiveness of starting NFL quarterbacks (survey here!). As I was thinking about the analysis of the survey, I came across the idea of having different weights for each rating. The naive value for each rating is its own numerical value (1=1, 2=2, etc), but I believe that this doesn't accurately capture what each rating represents. I've made my own value system which which I'll apply to the data along with the default values, and I can't wait to see what changes, if any, it will make to the data. Of course, I'm probably overthinking things, but whatever. This was fun to think about.

Ratings and their Corresponding Values
Attractiveness Rating
1
2
3
4
 5 
 6 
 7
8
9
10
Value
-7
-5
-3
-2
 0 
2
 3 
 5 
 6 
9



Explanation/Rationale

1) Shifted down - I've shifted all the values down so that any negative value indicates someone who is "unattractive" and any positive ranking indicates someone who is "attractive".

2) Rating 5 is the center - When we say "Rate someone on a scale from 1-10", I believe that most people subconsciously make 5 the center, neutral value, without realizing that the center between 1 and 10 is actually 5.5.

3) Ratings 4 and 6 are +/-2 away from 0 - While 5 is neutral, ratings 4 and 6 are indicate someone who is definitively attractive or unattractive.

4) "Buckets" - When rating attractiveness, I believe that ratings of 3 and 4 (kinda ugly), 6 and 7 (kinda attractive), and 8 and 9 (very attractive) are very close and almost interchangeable. As a result, each of these buckets differ in rating only by 1. However, the difference between each "bucket" is greater, warranting a difference of 2 between each bucket.

5) The unattainable 10 - Rarely is a perfect rating of 10 ever given to someone's attractiveness. Ten is in a class of its own, yielding the difference of 3 between 9 and 10.

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