There is a website that is at the number one position for my target keywords almost every time I search those keywords. It has been this way for at least a year. That keyword is searched 300-400 thousand times per month, and yet alexa ranking has the site not showing in the top 100 000. This makes no sense to me. Shouldn't that site be getting higher traffic than that?
Alexa rank and Google traffic are totally unrelated. You may have millions of visitors on your site, but its not necessary that all those visitors have alexa toolbar installed.
I see your point but utilizing the law of large numbers, when you're talking in millions of visits the percentage of people with the Alexa toolbar should be pretty close to the general population. On the basis of a 40% click rate on a #1 ranking, that's 150,000 visits per month (and that's discounting visits that will come from other keywords) - how does that many number of visits relate to an Alexa ranking?