Its a big part of it. Everything about a defense goes into 3rd down D, because what you do on 1st and 2nd dictates your chances on 3rd.
BUT, the Patriots faced a total of 202 3rd down attempts, or about 12-13 a game or 3 a quarter. At 43.1% they allowed 87 conversions, or about 5 1/2 a game of abou
t 1 to 1.5 a quarter.
The #1 3rd down defense was the Cardinals at 31%.
The middle of the league was 37-38%.
If the Pats were totally average in 3rd down stops, they would have allowed 12 fewer all season, or less than 1 a game.
1 extra 3rd down conversion may or may not even lead to points.
The 87 first downs allowed on 3rd represent less than 1/4 of the total 1st downs allowed.
Playing better on 1st and 2nd down is really a much bigger issue. It is very likely that better first and second down defense would cause at least 12 of those 3rd down chances to be from a longer distance with a lesser chance to convert, and the 3rd down D becomes average without improving itself.
Excellent analysis, but one minor quibble regarding the bolded statements.
The Pats defense allowed 370 total 1st downs, including 24 by penalty (two of which were DPI by Sergio Brown that allowed significant opposition scores, BTW). They allowed 95 conversions of 221 total 3rd and 4th down attempts (43%), meaning that they gave up 1st downs on 149 1st and 2nd down plays. So, if the defense plays better on 1st and 2nd downs that would tend to increase the number of 3rd down plays the defense faces.
If, in 2012, they can decrease the number of 1st downs allowed on earlier downs by, say, 1.5 per game, that would increase the number of opposition 3rd/4th down attempts to 245 (about what the Ravens faced). At that point, even if their raw conversion number doesn't improve from 95, their percentage will have improved to about 38%, the league average last season.
Actually, the Pats 3rd+4th down conversions allowed (95) and percentage (.43) weren't all that far off the league averages of 86 and .38 to begin with, though critics have gotten tons of undeserved mileage out of citing that stat.
Where the defense was REALLY GAWDAWFUL was allowing 1st downs on earlier downs - 149 of them, 2nd worst in the league to only Tampa at 158 (GBY was 3rd worst at 147). This was against a league average of 86 first downs allowed on 1st/2nd down. IOW, the defense "forced" 3rd and 4th downs on only 60% of their series vs. a league average of 73%. Atlanta's 3rd/4th down conversions-allowed percentage (.45) was actually worse than the Pats, but they forced 3rd/4th down on 76% of the opposition's series.
So, the key stat for defensive improvement doesn't appear to be 3rd/4th down conversion % or interceptions or even passing 1st down % (the Pats were at 69% vs. a 60% league average) - it's allowing 1st downs on early downs.