I didn't bother adding up percentages of successful '3rd and x' plays from those stats because once I posted all those third down plays it became apparent that a '3rd and x' percentage without including the score and time remaining was a meaningless stat. What I did see is that the Pats appear to be very much better at stopping 3rd down plays at crucial times than with a decent size lead. It looks to me that many of the 3rd down conversions - whether it be 3rd and short or 3rd and long - are coming in the 4th quarter with a lead of over 7 (or 14) points when the Pats are looking to prevent a quick score by the opponent.
Another thing I saw was that it looks like many of the opponents 3rd down conversions are coming in the first quarter. That would tell me that the Pats are making adjustments on the fly and tightening up while the game is still in question.
Bottom line is that I think the 3rd down rankings are deceiving. First, the conversions appear to have improved dramatically in recent games. Second when you consider the context - for example, 4th quarter and up by more than 14 - the 'problem' with third down defense is not nearly as dramatic as the overall NFL rankings would make it appear to be.
Back to the OP's question, I don't really see the Pats defense being worse on third and long than on third and short. I think it's more a case of us as fans paying more (negative) attention to giving up a 3rd and long than we do to giving up a 3rd and short, and conversely we also pay more (positive) attention to making a stop on 3rd and short than we do on 3rd and long.
I appreciate your in depth analysis, but I don't pay attention to stats much, mine are general impressions based on watching the same defensive approach (I assume) over the years.
I read the NY times article saying how we rely on the run and hardly ever pass and wonder if I really am seeing what's going on, but that's another story.
Posters keep saying we let teams pass all over the field and play soft and that's partly true. The intent IMO, is not to let the other team march up the field unimpeded, it's to make the other team complete a lot of passes, analyze their patterns, then become aggressive, without exposing ourselves to the long pass.
My point is, with a veteran group, players can cover for each other and take the occasional gamble. We've never played tight coverage and gambled on the long ball because of pressure, though some teams do.
It's the same defense, but we're not going to gamble until we're basically sound, so we'll give up more yards and TDs on long drives than people would like.
We're playing a special teamer as a starting CB for crissake. We're 6-1 and still haven't got Butler straightened out or Wheatley worked in, so it's hardly a secondary you want to gamble with.