Reasonable Theory or Bad Math?

I had a little “discussion” with a friend of mine earlier tonight on our way home from a local SEO meetup. We were discussing the scalability of a product’s sales relative to how much of the search market share a site or sites can get for a given term. I’ll use “buy red widgets” as an example.

Let’s say that according to competetive intelligence, (something like Hitwise) there are x searches (PPC & organic combined) for “buy red widgets” and Site A gets y visitors off of those who searched for “buy red widgets.” As the owner of Site A, you know that you really get 1.5y visitors off of that search term and a reasonable assumption would be that there are really 1.5x overall searches for “buy red widgets.”

Thinking about the user’s intent when searching for “buy red widgets,” let’s assume the following (obvously there are probably more intentions, but keeping it simple here…) :

a% will buy if the price is less than $50
b% will buy if there is free shipping
c% will buy if they can get it shipped to them by the day after tomorrow
d% will buy if they think they can trust the site that they land on
e% are just price shopping and will not buy right now

Whether we have 1,000 searches or 100,000 searches for “buy red widgets,” these percentages will remain pretty constant long-term.

Now, let’s say that the owner of Site A knows that m% of visitors (whether it’s PPC or organic search) from “buy red widgets” actually purchase a red widget given that he has the pricing and shipping policies that he does, which gets users to buy based on their intent. The owner of Site A decides to turn Site B (which he also owns and is an authority site on widgets) into a store that also sells red widgets. The owner expects that, given the authority, age, research, etc. of Site B, it can get 200% more traffic than Site A for “buy red widgets” and Site B will have the same pricing and shipping policies (for the sake of having a constant in the setups).

Here’s where the argument discussion comes into this. What I see happening is that the following equation can be applied to determine sales associated with searches for “buy red widgets” to Site B no matter how many searches there are or what percentage of the market a site has because, as noted above, in the grand scheme of things, searcher/buyer intent does not change just because there are more or less searches :

2(1.5x)m = # of estimated sales

My friend was trying to convince me that the more searches there are for “buy red widgets,” the lower the conversion rate becomes. IMO, there’s no way that the conversion rate would drop or be lower on Site B just because it gets more traffic. One thing he was assuming was that the total number of red widgets that would be sold relative to the number of searches was a constant figure. The reason that doesn’t make sense is that searches and intent of the searchers doesn’t change just because the volume of searches or visitors increases. If more visitors end up on a site that fits their intent, more people will buy. If fewer searchers find sites that fit their intent, fewer people will buy.

Maybe I’m off base…thoughts?