For my own personal calculations, I need a way to combine ratings of businesses into one weighted rating. I want my weighted rating to take into account how many people gave the rating as well as multiple ratings of said business.
Here is the data I wish to use as input:
- $G_A$ - Google Rating: A number rating from 1 to 5
- $G_B$ - Google Reviewers: Number of Google users who gave a rating
- $F_A$ - Facebook Rating: A number rating from 1 to 5
- $F_B$ - Facebook Reviewers: Number of Facebook users who gave a rating
I have come up with the following for a weighted rating formula:
$$\frac{(G_AG_B) + (F_AF_B)}{G_B + F_B}$$
The resulting numbers look good (my goal was to have them be between 1 and 5 like the original ratings), but I want to make sure - is my equation getting a fair weighted rating?
Taking the question a little further, I want to know if it would be feasible to take into account the following variable and, if so, how to go about adding it to the equation:
- $L$ - Facebook Likes: Number of likes a business has on Facebook