The Patriots were below average on third down in 2013. 17th in the league, in fact. This was a sharp fall for the team who has finished 1st in 2012. In fact, it was the first time in the past decade that the team didn't finish in the top 10 (yes, they finished 6th in the league with Matt Cassel at the helm)- they finished 17th back in 2003. The only other season they didn't finish in the top 10 was Bill Belichick's inaugural year in 2000 (24th).
Every other season, the Patriots finished in the top 10.
Plenty of the struggles are linked to injuries and poor offensive play, but I'd like to direct the focus to the offensive line. It's a position group that I've always tagged as the most important on the team; if they play well, the Patriots can beat anyone. Play poorly, and you get 2013.
Mark Daniels of the Providence Journal pointed out that 50% of the sacks on Tom Brady came on 3rd down. While the connection between 3rd down conversion rates and successful offenses is slightly dubious, the link between protecting the quarterback and having a successful passing offense and converting 3rd downs is strong.
So when Tom Brady gets sacked on 3rd down, it's the most negative non-turnover play than can occur.
And when 51.4% of sacks on Brady over the past two seasons have occured on third down, that's a point of concern with regards to offensive playcalling and protection. Especially when that 51.4% is the worst in the league out of two year starters.
In fact, only Joe Flacco can lay claim to a worse situation; the Average Joe has had 50% or more of his sacks over the past three seasons come on third down. Brady at least dipped to 48.6% in 2011.
You should note that these high rates have not had a tremendous effect on the Patriots conversion rates. When the Patriots finished 1st in conversion rate in 2012, 50% of Brady's sacks came on third down, ranking 5th worst in the league out of quarterbacks with 20 or more sacks.
On the other hand, sacks were more frequent against the Patriots across the board, with Brady seeing a 50% increase in the rate he was sacked in 2013 (4.2% up to 6.4%). That, more than anything, likely impacted the Patriots success rate in converting third downs by putting the offense in less desireable situations.
The offensive line needs to keep Brady clean whenever he's in the pocket, but there was no stat that showed it more than how often he hit the ground on third down. Brady needs help and, in turn, he will get the offense back on track.