We found that 10 days is not the break even point any longer due to the price increases of the last few years. We just came back from a 15 day trip (it was originally going to be shorter), and for the 1st time we priced out regular tickets as we always have APs. We found that for 10 days, park hopping, expiring tickets, they were cheaper than the DVC AP. We were originally only going for 10 days, and so regular, park hopping tickets were cheaper than APs for 10 days or under.
Once you go over 10 days though, you have no choice but to purchase an AP as the UK 14 day tickets aren't available over here, but on a per day cost, the regular tickets would be cheaper if they were available for days 11 and 12. Once you get into 12+ park days, we found the daily cost with the AP to be cheaper.
We always get 2 trips on our APs, so we have at least 15-20 park days per year, and that makes it very worthwhile for us to have APs.
After reading my post, it now looks confusing, sorry about that! Tiger