Nice question, but from my newbie point of view the CTR doesn't depend only on the position but the quality of the ad.
Back in the day (I don't have any ads running at the moment) ... my CTR was about the same as long as it was on page one... HOWEVER my conversion rate was higher in the bottom half of page one or the top half of page two. Biggest problem I had was the time I spent manually managing the "sweet spot", where my position, bid, and conversion got me a minimum of a 3:1 pay back.
THAT happens all the time. One day you're at number 1, then 15 minutes later somebody outbids you and you're at number 2, then a lot of people outbid you and you're at number 10 or off the page. Then someone else does something more relevant etc.
Yes, google gives you TONS of statistics, but I focus on maximizing income and profit, not CTR. One of the things I learned early on is that if you have a really high CTR you can get a lot of "Tire Kickers" (people who look but don't buy) and not a lot of customers. With a CTR in the 1% range, in the bottom half of the first page, or the top half of the second page is where I always got my maximum income/profitablity.