Hi Alessandro -
How should we get accurate estimates then?
The web total, in our case, isn't even close.
For example: a search for [site:http://www.dell.com/] yields 84,300 results using Live Search. In the API, it yields 220 results.
For other engines, I'm just not seeing this much of a difference. Google, for example, shows 265,000 in the web search and 262,000 in the API. Yahoo! Search shows 81,696 in their web search and 83,461 in their API. While the numbers aren't exactly the same, they are fairly close.
We don't rely on this number for a calculation, but it is an important number for us when doing research.
Thanks.