The Patriots improved in many categories, especially on offense — where you wouldn’t think they’d need much improvement. But new offensive coordinator Josh McDaniels obviously had his eyes on a few areas to increase production, and he succeeded almost universally over the course of a long season.

According to Stats LLC, the Patriots led the league in, among other offensive categories:

■   Offensive points scored, 499. They were No. 3 in 2011 with 485.

■   Three-and-out drives, 12.4 percent (league average was 22.4). They were fifth in 2011 at 15.6 percent.

■   Third- and fourth-and-1 conversions, 79.4 percent (league average was 63.1). Improvement from 68.6, tied for eighth.

■   First downs, 444 (league average was 318). That’s up from 399, second.

■   Plays of 10 or more yards, 261 (league average was 211). They were third at 252 in 2011.

■   Red zone touchdown efficiency, 70 percent (league average was 49 percent). They were second at 65.3 percent in 2011.

One of the areas where the Patriots improved dramatically was in third-down conversions, a very important category.

Not only did they go from fifth in the league at 45.9 percent to first at 48.7 percent, they were better across the board relative to the rest of the league in every category: third-and-1 (12th to first), third-and-10-plus (18th to first), third-and-short (fifth to third), third-and-medium (seventh to first), and third-and-long (15th to fifth).

And the explosiveness of the rushing attack showed a dramatic uptick as the Patriots went from tied for 25th with 39 rushes of 10 or more yards to tied for eighth with 60. They also had 11 rushes of 20 or more yards (tied for 15th), more than double the five they had in 2011 (31st).

Where will the Patriots look to improve heading into the 2013 season?

On offense, they will look to become more explosive in the passing game. Despite the improvement in the rushing attack, the Patriots slipped from seventh in the league with 77 plays of 20 or more yards in 2011 to 10th with 68.

Much of that slippage can be attributed to a dip in yards after the catch. They went from leading the league with 51.5 percent of their passing yards coming after the catch to 48.6 percent, though that still led the league. The Patriots set a record under Bill Belichick in 2011 with an average of 6.7 yards after the catch. They declined to 5.9 this season, their lowest number since 2009.

The Patriots had 50 rushes for negative yards, which was tied for 24th. In 2011, they tied for second with only 28. BenJarvus Green-Ellis might not have been explosive, but he had an uncanny ability to fall forward.

The percentage of kickoff returns of 20 or more yards was 52.6, which ranked 30th in the league and lagged well behind the league average of 66.3. The Patriots ranked 22d (65.2 percent) in 2011. Injured running back Jeff Demps would have helped there.

Defensively, the Patriots still have a lot of work to do in regards to big pass plays. They were dead last for the second straight season with 74 pass plays of 20 yards or more allowed (79 in 2011). They got only marginally better down the stretch, as they were tied for 28th with 36 allowed in the final eight games (31st with 44 in 2011).

The Patriots also must work on their first-down defense. They were last in the league, at 48.8 percent, in allowing first-down rushes to go for 4 or more yards (30th at 48 percent in 2011). And they were 31st in allowing all first downs to go for 4 or more yards 51.7 percent of the time (also 31st at 53.3 percent in 2011).

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Here’s a further trip through numbers, from our own tabulations, Stats LLC, and ProFootballFocus.com

■   227: Total plays of 10 or more yards allowed, ranked 28th in the league. The Patriots allowed 253 such plays in 2011 and ranked 32d.

■   261: Total plays of 10 or more yards by the Patriots offense, which led the league (252 and third in 2011).

■   79: Total plays of 20 or more yards allowed (31st). League average was 60. They allowed 89 (32d) in 2011.

■   44: Rushes allowed of 10 or more yards, 10th in the league. They allowed 51 and were 17th in 2011.

■   57: Completions of 20 or more yards for the Patriots, which ranked seventh. They led the league with 72 in 2011.