I'm not sure how they did it, but the Patriots coaching staff put together the worst possible mix of their starting defensive players. Apart from nose tackle Vince Wilfork, the Patriots decided to play a full unit of 4-3 players and insert them into a 3-4 front.
No one has any idea why and it's unlikely Bill Belichick will disclose the reason at a later date.
Let's start with the basic fact of the 3-4: either the defensive line or the linebackers will have to two-gap.
That's just how the defense functions if either of the linebackers drop into coverage. There are six gaps with the basic five man offensive line, seven gaps if there's a tight end (in between each player and then to the outside of the last person on the line). With three defensive linemen and four linebackers, either all seven will have to commit to maintain a single-gap assignment, or someone in the front seven will have to two gap.
Vince Wilfork can two gap, even if he didn't play his best. He plays the nose and he covers both A gaps (to either side of the center). Chandler Jones and Joe Vellano, on the other hand, cannot two gap.
Jones is 265 pounds and asking him to hold his ground against an offensive tackle and guard (assuming a two-gapping principle) is just asinine. In fact, it makes running the ball even easier for the Dolphins because the tackle and guard can seal Jones out of the play, while the Guard can break off into the second level to take on a linebacker; it's an easy five yards.
Let's also ignore that the Patriots are taking their most dangerous pass rusher and asking him to have multiple-gap responsibility.
Vellano is 300 pounds, but he's the new edition of Kyle Love at 6'1. He doesn't have the length to maintain multiple gaps and he was overwhelmed even in single protection.
With both Jones and Vellano unable to guard multiple gaps, it allowed the Dolphins to run at will, which they did.
But let's say that the Patriots didn't ask the defensive linemen to cover multiple gaps. Let's assume the defensive line was operating under single-gap ideas, and that it was the linebackers responsibility to cover two gaps. They have the speed, so they should be able to, right?
The issue comes with their strength. There's no Brandon Spikes on the roster, the only linebacker capable of standing up an offensive lineman. Even if Jamie Collins or Jerod Mayo were able to get in the right position to stop the running back, they were met head-on with an offensive lineman, who had no trouble sealing them out of the play.
By assigning the linebackers multiple gaps, they have to approach the rushing lanes from an angle, instead of directly, allowing blockers to seal the pathway.
There's no question that the best solution for this defense is to go back to the 4-3 front. The coaches fielded a defensive line too small to sustain a 3-4 front. They have linebackers too weak to stand-up offensive linemen.
Jones and Vellano were put in terrible situations and their production showed. They were the least effective players on defense, and that is not their fault; the blame lies with the coaches.
When the Patriots face the Vikings and Adrian Peterson, they cannot afford to give the same running lanes that they gave Knowshon Moreno and the Dolphins. They need to field a defensive line of Chandler Jones, Vince Wilfork, Sealver Siliga, and Rob Ninkovich. They need to operate the way the roster intended.