# Domain scoring based on ranking

I am a computer science student working on a small information retrieval project. I have a dictionary with a domain as a key and it's ranking as value.

Based on that ranking, I need to score every domains. I was thinking to do 1/ranking but the disparity is too high. For example the first domain will have a score of 1 (1/1) and the domain ranked 10th will have a score of 0.1 which does not make sense for this.

I have 1000 domains in total and the last one should be close to 0.10 and the first one close to 1

## 1 Answer

You are essentially asking how Google calculates the score of the domains. The correspondence of the score with ranking is different for every search. Sometimes it is closer to x(i) = alpha*x(i-1) (exponential weights). Sometimes it could be linear x(i) = (n-i)*2/((n+1)*n). I've seen some papers that just use the number of the ranking for regression (linear), but this was not about internet domains, but some other topic.

I will try to answer the question about your weights and you weighting system:

You are using 1/1, 1/2, 1/3 ... 1/100 ... 1/1000

Instead you could use 1/1, 1/1.01, 1/1.02, 1/1.03 ... 1/2 ... 1/10

So your weights are $$weights = \frac{1}{1+ranking*0.01*\frac{9}{9.99}}$$ where ranking starts with 0 and ends with 999