FOXBOROUGH, Mass. -- Quick-hit thoughts and notes around the New England Patriots and NFL:

1. The Patriots enter the playoffs with the healthiest roster in Bill Belichick's 17 years as coach, and it isn't even close. Not including players who were physically unable to perform and never made it to the roster (e.g. Sebastian Vollmer), consider that they have placed just four players on injured reserve all year (Michael Williams, Rob Gronkowski, Jonathan Freeny, Greg Scruggs), which smashes the low mark of seven over the last decade. And one of those players, Scruggs, was with the team for just a week when he injured his knee in practice. For a point of comparison, the Patriots placed 15 players on IR last year. Another contrast: The Patriots have had 65 players appear in at least one game this year, while that number was 77 last year. As he's noted multiple times over the course of the season, Belichick has specifically been pleased with first-year strength and conditioning coach Moses Cabrera and some changes he's implemented that have helped reduce soft-tissue injuries.

2. Longtime Patriots cornerback Ty Law (1995-2004) was named one of 15 modern-era finalists for the Pro Football Hall of Fame last week, which is his first time he's been a finalist. The obvious next question: Can he get in? As many as five modern-era finalists will be inducted and this year's field is considered as wide open in recent memory. Looking ahead, several highly regarded first-year eligible candidates will make it tougher for others to break through in 2018. Hall of Fame voter Ron Borges of the Boston Herald will present Law's case, and after his fine work on behalf of Andre Tippett's successful candidacy in 2008, Law has an influential voice in the room in his corner. A few points Borges relayed are that Law has the numbers (his 53 career regular-season interceptions matching Deion Sanders), was the heart of a defense that won three Super Bowls, made big plays in big games, covered top receivers in most games, was a fearless tackler and was still a starting-caliber player at the end of his 15-year career.

3. Three thoughts on the three members of Belichick's inner circle -- offensive coordinator Josh McDaniels, defensive coordinator Matt Patricia and director of player personnel Nick Caserio -- drawing interest from other teams for head coach/general manager openings:

Mike Florio of Pro Football Talk reported on NBC's pregame show Saturday night that Caserio turned down the opportunity to interview with the 49ers. That seems to reflect Caserio's happiness in his current job, and eliminates a scenario that I wondered might entice him to depart: A pairing with McDaniels.

McDaniels interviewed with the Jaguars, Rams and 49ers on Saturday, and I view San Francisco as the best fit for him if he decides to take the plunge. The buzz in media circles has been growing that a McDaniels pairing with Louis Riddick as GM could have legs if McDaniels decides to pursue the job aggressively.

Patricia's interviews with the Rams and Chargers are the second and third of his career, after he talked last year with the Browns. I don't see either as the perfect fit for him at this point.

4a. Did You Know, Part I: Should they win the AFC championship, the Patriots (8) can break a tie with Dallas, Denver and Pittsburgh for most Super Bowl berths in NFL history.

4b. Did You Know, Part II: Robert Kraft (7) can set a NFL record for owners if the Patriots win another AFC championship, breaking a tie with Denver's Pat Bowlen.

4c. Did You Know, Part III: If the Patriots advance to the Super Bowl, Bill Belichick (6) can pass Don Shula for most Super Bowl appearances all-time by a coach.

5. Belichick kept the red challenge flag in his sock for every play this season but one (successfully challenging a fumble and recovery on a Texans kickoff return in Week 3), which was easily the lowest total of any coach in the NFL this season. For a point of comparison, first-year Eagles coach Doug Pederson led the NFL with 11 challenges. The league average was 5.375. I asked Belichick about the low total last week, and if it was reflective of a more conservative approach in 2016, and he said that wasn't the case. Instead, he complimented NFL officiating. “Overall, I haven't really had many issues at all with the officiating, they're in position and they've kept control of the games,” he said. “We've had some emotional games, some tough games, but I think overall they've done a good job of letting the players play, keeping it competitive, not over-officiating the game, just letting the players play. I think that's what we all want.”

6a. Tight end Martellus Bennett is one of the more unique personalities the Patriots have had in their locker room in Bill Belichick's 17 years as coach, and one thing that has stood out is his focus on the business and marketing side of the game. On Thursday, for example, reporters gathered around his locker to see if he would be available to answer questions. He then turned to one media member and said, “Might as well do some free advertising.”

6b. Moments earlier, owner Robert Kraft had walked through the locker room, stopped at Bennett's locker, and perhaps knowing the quickest way to his heart told him about the volume of his children's books that had been purchased for charitable/community causes.

6c. Belichick on how Bennett has fit in this year: “He's done a good job. There are a lot of guys that have good rapport in the locker room. There's a lot of mutual respect in there. Guys are different, but that's OK. They get along, they care for each other, they work with each other, they're good teammates. That's the bottom line.”

7. When do three running backs equal one Ezekiel Elliott? Elliott's rookie season in Dallas has been off-the-charts impressive, so consider this comparison:

Elliott

332 rushes, 1,631 yards, 15 TDs

LeGarrette Blount/James White/Dion Lewis

394 rushes, 1,610 yards, 18 TDs

This is a different way of showing how impressive the Patriots' running game has been this season.

8. I was struck by the respect Patriots defensive coaches and players came away with for first-year Dolphins coach Adam Gase after Sunday's 35-14 victory in the regular-season finale. While it was a lopsided final result, Gase's game-planning and in-game tweaks that included going up-tempo had the Patriots' defense in a vulnerable spot for a few extended stretches. As one player said, it was almost like going up against the Patriots' offense, which is game-plan specific and usually evolving over the course of the game. Gase's presence in the division in the coming years is going to be interesting to watch in terms of how he attacks New England's D.

9. Patriots receiver Julian Edelman (68) needs two receptions to move past Wes Welker for the most postseason receptions in Patriots history. One additional note of context on that stat: Saturday night will be Edelman's 13th career playoff game in New England, while Welker played in nine.

10. While everything sets up well for the healthy Patriots in the AFC playoffs as the No. 1 seed, and I think they should be able to handle either Houston or Miami in next Saturday's division round, an AFC title game at home against either Kansas City or Pittsburgh would be far from a slam dunk. Specifically, Kansas City wins with a similar formula as the Patriots (e.g. 1st in the NFL in turnover differential; excellent special teams), and the experience of coming to Foxborough in last season's playoffs should also benefit them. The more I watch the Chiefs, the more they remind me of some of the early 2000s Patriots in the sense that you have to look closer at them to really appreciate what they're all about.

2016 SNAP COUNTS: Rookie receiver Malcolm Mitchell (offense) and safeties Devin McCourty (defense) headlined the Patriots' regular-season snap-count analysis.