Maths isn't my strong point and I'm at a loss here.
Basically, all I need is a simple formula that will give a weighted rating on a scale of 1 to 5. If there are very few votes, they carry less influence and the rating pressess more towards the average (in this case I want it to be 3, not the average of all other ratings).
I've tried a few different bayesian implementations but these haven't worked out. I believe the graphical representation I am looking for could be shown as:
___
/
___/
Cheers
I'd do this this way
1*num(1) + 2*num(2) + 3*num(3) + 4*num(4) + 5*num(5) + A*3
-----------------------------------------------------------
num(1) + num(2) + num(3) + num(4) + num(5) + A
Where num(i) is number of votes for i.
A is a parameter. I can't tell You exact value of it. It depends on what do You mean by "few votes". In general high value of A means that You need many votes to get average different than 3, low value of A means You need few votes to get different value than 3.
If You consider 5 as "few votes" then You can take A=5.
In this solution I just assume that each product starts with A votes for 3 instead of no votes.
Hope it helps.