Question

I have a list of documents each having a relevance score for a search query. I need older documents to have their relevance score dampened, to try to introduce their date in the ranking process. I already tried fiddling with functions such as 1/(1+date_difference), but the reciprocal function is too discriminating for close recent dates.

I was thinking maybe a mathematical function with range (0..1) and domain(0..x) to amplify their score, where the x-axis is the age of a document. It’s best to explain what I further need from the function by an image:

Answer 1

Decaying behavior is often modeled well by an exponentional function (many decaying processes in nature also follow it). You would use 2 positive parameters A and B and get

y(x) = A exp(-B x)

Since you want a y-range [0,1] set A=1. Larger B give slower decays.