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

1. Veteran tight end Dwayne Allen, whom the Patriots acquired from the Colts in a trade on March 9, has a well-earned reputation as a consummate pro on and off the field. He was the Colts' Ed Block Courage Award winner in 2014 and their Walter Payton Man of the Year in 2015.

It is obviously something he takes pride in, which is why he was hard on himself for what was a difficult entry into the Patriots' program.

"Spring was horrible," he told ESPN.com last week. "It's one of those things where you have an offseason where you're training, you're doing well, you're thinking that you've trained and prepared enough, and then you come into OTAs and it's like, 'Oh my goodness, I have not trained enough.'

"But thankfully, I was able to stick around and do some more training and get into a little better shape. Any time you're learning something new, a new offense, you're not performing at top speed, things seem a little off to you. That's exactly what it was for me."

Allen's willingness to stick around after the team's spring practices -- a time when most players return to their year-round homes -- provided him a foundation for training camp. While acknowledging that he still has a long way to go, he smiled when asked if he feels he's where he needs to be.

"I'll say I'm a little bit better than horrible," he remarked.

It shows on the field. The 6-foot-3, 265-pound Allen, who is expected to fill the critical No. 2 role alongside Rob Gronkowski, is running better than he was in the spring and seems more comfortable with the offense. He didn't play in the preseason opener this past Thursday, a game in which coach Bill Belichick held out most of the team's top players.

One thing that has stood out to the 27-year-old Allen during his five months with the Patriots is the focus on conditioning. Asked how eye-opening that has been to him, he said "very."

"I don't think you are ever in optimum conditioning," he relayed. "That's why we hit the hill. That's why we do other things to make sure that we are conditioning our legs, our minds, our lungs -- daily.

"It's just uncommon."

2. One indication that Patriots top draft pick Derek Rivers (third round, 83rd overall) has made a favorable first impression on the club is that he has been given one of the front-row parking spots reserved for those who are offseason award winners. Rivers, a defensive end from Youngstown State, was widely viewed across the NFL as a prospect with top-end intangibles. In the preseason opener, he played 36 of 57 snaps and rotated at end after Deatrich Wise and Adam Butler, which was a first glimpse of his current standing on the depth chart topped by Trey Flowers (who didn't play).

3. Belichick held 40 players out of the preseason opener (some weren't cleared to play/managing injuries, while the vast majority were coach's decisions), which was easily the highest total of any NFL team through Friday's preseason games. The Steelers, with 24, were next on the list while the Buccaneers (7) had the fewest players held out. Of the 20 teams that played preseason games this past week through Friday, the average number of players who didn't play per team was 11.2 (this note was updated late Sunday).

4. Belichick can be a task-master with his players, but that doesn't mean he doesn't lighten the mood at times. That's what happened last Tuesday in Patriots-Jaguars joint practices when Belichick dropped to the ground to take 10 push-ups with his third-unit offense.

Veteran Jaguars defensive lineman Calais Campbell saluted Belichick as he was doing the push-ups, and later explained how the moment unfolded.

"He offered to do one more rep for push-ups: The winner doesn't have to do them, the loser has to do push-ups. So we were like, 'Coaches too? Or just players?' He said, ‘I got the whistle. I'm not doing any push-ups!'

"But when they lost, he hopped down there and did those push-ups. Very impressed. It's a team thing; everyone who is involved has to do push-ups. I thought that was pretty cool that he got down and paid his debt with his team."

Campbell, now in his 10th NFL season, said being around Belichick and the Patriots last week for three joint practices reaffirmed what he had heard from others around the league.

"I've had the pleasure of playing with guys that played underneath him before, and everyone always says the same thing: He's real tough when understanding what you're supposed to do, your responsibilities, understanding your opponent, but it's a fun place to play. Coming out here and experiencing this, you can tell the guys like playing for him and he has a program that breeds winning."

In turn, Campbell believes the experience of being around the Patriots and seeing "their style, the way they prepare, the way they lock in and focus, the small details of what it takes to prepare to win" will benefit the Jaguars, a team with a new regime under executive vice president of football operations Tom Coughlin and head coach Doug Marrone.

5. We know how strongly Tom Brady feels about Alex Guerrero, his business partner and friend. What we learned last weekend was that Pro Football Hall of Famer LaDainian Tomlinson feels the same way. In his induction speech, Tomlinson thanked Guerrero, who sat in the crowd in the row behind Chargers owner Dean Spanos. Tomlinson had said that he played 11 years and never underwent one surgery, due in part to the team of therapists (led by Guerrero) that worked for him.

6. There are 25 days until the NFL opener between the Patriots and Chiefs, and as part of their numbers-based theme, ESPN Stats & Information passes along the following nugget: Brady has won 25 career playoff games, five more than any other player in the Super Bowl era. Former Patriots and current Colts kicker Adam Vinatieri is next on the list (20).

7. Key things to know about the Chiefs from their preseason opener: The starting defense didn't allow a first down in two drives against the 49ers; quarterback Alex Smith hit wide receiver Tyreek Hill on a 32-yard pass down the right sideline on the first offensive play from scrimmage; Smith led an eight-play, 75-yard touchdown drive to open the game and then was pulled with the rest of the starters; kicker Cairo Santos has a groin injury, which led the team to sign rookie Sam Ficken, but coach Andy Reid told reporters he thinks Santos will be ready for the regular season.

8. Tough preseason draw for Patriots season-ticket holders, with Games 1 and 4 hosted at Gillette Stadium. That means the first time the home fans will see Brady and most of the team's top players will be the Sept. 7 season opener against the Chiefs. No chance Belichick plays Brady and Co., in the preseason finale against the Giants on Aug. 31 because it's so close to the opener. Not that anyone's really complaining; when the team brings home the Lombardi Trophy in two of the past three years, it's hard to argue with the approach.

9. From the thinking-out-loud department: One roster-management area that I wonder Belichick might ultimately second-guess himself on is not starting second-year receiver Malcolm Mitchell on the physically unable to perform list in training camp. Mitchell didn't practice all spring as the club took a cautious approach, in part because of his history of knee troubles going back to college. That has continued into the start of training camp, with Mitchell once again being brought along slowly and only really taking part in individual-type drills to his point. Given that background, it's not a stretch to say Mitchell could have qualified for PUP status, which could have provided some potential early-season roster flexibility. It could have made it easier to initially keep another promising young receiver such as Devin Lucien or Austin Carr.

10. The Patriots are scheduled to visit the Jaguars in the 2018 season -- they play the AFC South and NFC North -- which could mean it's time to get their passports ready. The Jaguars have annually played one home game per season in London since 2013. The Patriots haven't been to London since trips in 2009 and 2012, victories over the Tampa Bay Buccaneers and Los Angeles Rams, and have a strong fan base there.