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Rob Gronkowski working hard behind the scenes at stadium

Rob Gronkowski has been at the team facilities at least four days a week rehabbing. Richard Cashin/Icon Sportswire

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

1. Things are quiet around Gillette Stadium as many Patriots players have returned to their year-round homes until the start of the offseason program in April, but a few have stayed in the area and are working out regularly at the team's facility. Most notable on the list is tight end Rob Gronkowski, whose recovery from back surgery continues to progress. Gronkowski has been at the stadium at least four days a week, joining a few other teammates who are also rehabbing, such as running back Dion Lewis (hamstring injury in Super Bowl). While Gronkowski often generates headlines for his off-field endeavors -- such as a recent trip to Barcelona -- often overlooked is his work ethic and commitment in the weight room and conditioning-wise. Few work harder than him.

2. One of the surprising stories to the start of free agency was the lower-than-expected market for tight end Martellus Bennett, who agreed to a three-year, $21 million contract with the Green Bay Packers. That had some asking, "Why wouldn't the Patriots have done that?" It was my sense that New England -- which had unsuccessfully attempted to extend Bennett's deal last offseason for around $7 million in 2017 -- were moving on from Bennett regardless for a younger option. I don't believe the sides ever discussed contract terms before New England traded for tight end Dwayne Allen (three years, $17.5 million remaining on his contract).

3a. Cornerback Malcolm Butler and the Patriots have a difference of opinion on his value when it comes to a potential contract extension. It isn't the first time a player and team have seen things differently, and it won't be the last. That's business. But the point that Butler's agent Derek Simpson was making last week when he said the Patriots haven't talked to Butler about a contract extension since last year was that it's unfair for anyone to paint Butler as someone who keeps asking for more money when there haven't been talks. What Butler has done is kept his mouth shut, busted his butt, played at a high level and put the team first while vastly outperforming a contract that paid him $510,000 in 2015 and $600,000 in 2016. Those are the types of players to reward and in that sense it would be a major disappointment if the team trades without exhausting every possibility to retain him.

3b. More compelling to me with the Butler-Patriots situation is if the team truly views him as a bonafide No. 1 corner. The Patriots obviously see the taller, longer Gilmore (6-1, 190) that way based on the generous contract they gave him, but my sense is they view Butler a cut below -- somewhere between Logan Ryan (reported average of $10 million per season in Tennessee) and Gilmore ($13 million per season). So if both sides are committed to remaining in New England, and focus on striking a compromise, that's the sweet spot to hit. Butler is scheduled to earn $3.91 million this season as a restricted free agent. Add on three years and $34.5 million to the end of the 2017 year ($11.5 million per season on extension), with some of that money paid out in an up-front signing bonus to give Butler more immediate security, and maybe that gets it done. Then you have Gilmore and Butler paired together for at least the next four seasons, which is more appealing than, say, dealing Butler to the Saints in exchange for a first-round pick (No. 32 overall).

4. The Patriots continue to invest in their facilities in hopes of providing the team the best chance to win. Not long after a major Gillette Stadium office renovation that created new offices for the video department, among other things, one of this year's projects is expanding the team's lower practice field so there will be an area behind one of the end zones where players can work out without being on the actual field. It might not sound like a big deal, but the workout area behind the upper practice fields -- which includes a hill that players run for conditioning purposes -- was credited by some for the team's stamina and endurance in Super Bowl LI. Every little thing counts.

5. Linebacker Dont'a Hightower turns 27 today, and perhaps there's a nice present waiting for him in the form of a lucrative contract extension. That would be worth the wait for him, as his status remains unresolved entering the fourth day of free agency. Retaining Hightower and Butler would add two more exclamation points to the Patriots' aggressive offseason.

6. NBA commissioner Adam Silver attended the MIT Sloan Analytics Conference earlier last week and was part of a two-person "Silver asks Silver" panel with Nate Silver of ESPN's FiveThirtyEight. When asked about how the NFL seems to have more family-run franchises that have been passed down from generation to generation, he shared his personal admiration for the Patriots and Kraft family. After listening to a panel at the conference that included Jonathan Kraft, Silver called him, "as progressive and forward-thinking as any owner in the NBA" before adding, "I also sat next to his dad, Robert Kraft, and same thing for him. That family, their approach to sports, is as innovative as any owners I know in any sports."

7. Safety Jordan Richards, the Patriots' 2015 second-round draft choice out of Stanford, told me last week that he is changing up his offseason approach by spending the entire offseason in Foxborough. Last year, he had returned home to California for parts of the offseason. Richards (5-11, 210) played 239 defensive snaps as a rookie, but only 18 this past season in part because of a knee injury (the first time he's experienced an injury in football). Richards is the next man up if something happened to starter Patrick Chung.

8a. After a flurry of moves to open free agency, but with some key business they hope to still handle with Hightower (27th birthday today) and others, the Patriots have $36.1 million in salary cap space, according to Miguel Benzan of Patscap.com. That number doesn't include the four-year agreement with former Ravens defensive lineman Lawrence Guy on Saturday, but even after that, there will be plenty of room to strike a deal with Hightower and even Butler.

8b. If ever there was a reminder about the importance of understanding economics, player value and the salary cap when covering pro football, it's this week. So it's timely to highlight how Jason Fitzgerald of OverTheCap.com and Vijay Natarajan have co-authored a NFL salary cap book "Crunching Numbers." The book gets into the collective bargaining agreement, contract negotiations and the salary cap, and has been a big help for a beat reporter trying to gain a better understanding of this complex side of the business.

9. With the Saints confirming terms of the trade that sends receiver Brandin Cooks and a fourth-round pick (118) to the Patriots in exchange for first-round (32) and third-round (103) picks, there is one trickle-down effect of the trade: The NFL takes 118 away from the Patriots as part of Deflategate penalties that call for the team to surrender its highest fourth-round pick. Previously, the Patriots had picks 132 and 137, and had 132 stripped. That left them with 137, which went to Indianapolis in the deal for Dwayne Allen. So after the trade for Cooks, the Patriots now lose 118 and have 132 reinstated. They have seven total picks.

10a. Did You Know, Part I: Gilmore is one of five players to record at least three interceptions in each of the last three seasons, joining Brent Grimes, Reggie Nelson, Aqib Talib, and Kurt Coleman.

10b. Did You Know, Part II: Gilmore's $40 million in bonuses and guarantees ties for fourth most by a cornerback in the NFL, behind only Washington's Josh Norman ($50 million), Arizona's Patrick Peterson ($48 million) and Cleveland's Joe Haden ($45.1 million) while tying Seattle's Richard Sherman.