With free agency set to start Tuesday at 4 p.m., we decided to take a look back at the 20 finest free agent moments of the Bill Belichick era in New England. The rules for inclusion are fairly standard -- a player had to be signed as a free agent by the franchise from when Belichick took control in 2000 until the present day. In putting together who was ranked where, we included contract, value and overall impact on the franchise, both on and off the field.

After careful consideration, three things about this group really stand out. One, several of the players acquired (particularly in the early stages of Belichick’s tenure in New England) weren’t necessarily statistical standouts, but instead helped transform the culture among the team thanks in some part because they were with Belichick in previous stops. Two, there are more defensive guys on the list than offense -- 13, if you count special teamer Larry Izzo as a linebacker. And three, there are only five skill position players on our list. It’s evident that most of the transcendent offensive players the Patriots have acquired since 2000 (including Randy Moss, Wes Welker, Corey Dillon, Rob Gronkowski and Aaron Hernandez) have been either picked up via the draft or in trade.

(Oh, and we’ll have the worst free agent signings coming Tuesday.)

With that, here’s our list.

20. Keith Traylor (acquired in 2004) -- The veteran defensive lineman only spent one season in New England, but his work with then-rookie Vince Wilfork did a lot when it came to preparing Wilfork for the rigors of succeeding in the trenches at the NFL level. Played with the Patriots in 2004.

19. Damon Huard (2001) -- One of the most notable of Tom Brady’s backups, he distinguished himself for two reasons. One, he looked more like Matthew Perry than any other quarterback in the league. And two, his work as the scout team quarterback in the week leading up to the 2003 AFC title game against the Colts (Huard spent the whole week serving as Peyton Manning’s stand-in during practice) was good enough to get him a postgame shout-out from Belichick and a game ball for his efforts. Played with the Patriots from 2001-2003.

18. Larry Izzo (2001) -- A gonzo linebacker who made his bones as a special teamer, Izzo was absolutely invaluable when it came to making over the special teams unit. While he wasn’t an every-down player, he made his mark in several other areas, and was a locker room favorite. Played with the Patriots from 2001-08.

17. Christian Fauria (2002) -- The tight end position wasn’t always a perennial Pro Bowl spot for the Patriots, and this journeyman was able to bring some consistency and veteran leadership to the position after arriving in 2002. In four seasons with the Patriots, he caught 45 passes, including 13 touchdowns, and was a steady and reliable presence at a position that didn’t have a whole lot of either at the time. Played with the Patriots from 2002-05.

16. Bryan Cox (2001) -- Another one-year guy, Cox was another transformative presence in the locker room. Many consider his September 2001 hit on Colts wide receiver Jerome Pathon -- in Tom Brady’s first NFL start -- as the moment when things started to turn for the Patriots that season. An eminently quotable presence in the New England locker room, his season ended early because of a leg injury, but his influence was felt throughout the year. Played for the Patriots in 2001.

15. Mark Anderson (2011) -- Similar to Andre Carter, Anderson spent just one season with the Patriots, but he distinguished himself as a good situational pass-rusher who provided a boost on the outside for the New England defense. Saw an uptick in his playing time after Carter went down for the season early, and finished the year with 10 sacks, which was good enough to earn a big deal last offseason from the Bills. Played with the Patriots in 2011.

14. Anthony Pleasant (2001) -- This veteran defensive lineman had little left in the tank when he arrived in New England, but he was another transformative force in the Patriots locker room, serving as a veteran presence for young defensive linemen like Richard Seymour in the early days of the New England dynasty. Another Belichick guy -- he followed him from the Browns to the Jets before coming to New England -- he had six sacks in 2001. Played with the Patriots from 2001-03.

13. Leigh Bodden (2009) -- The only guy who could earn a spot on both the best and worst free agent signing lists. In his first season in New England, he ripped it up, coming out of nowhere to post five picks and having one of the better single seasons for a defensive back in recent franchise history. He then signed a four-year, $22 million deal with the Patriots the following offseason, and never managed to bounce back from injury -- he played just five games after signing the deal, (he went on season-ending IR at the start of the 2010 campaign) and was eventually released in October 2011. Played with the Patriots from 2009-11.

12. Rosevelt Colvin (2003) -- You knew Belichick liked him in 2002 when he brought his name up unsolicited on several occasions in the week leading up to a game against the Bears that season. So in the offseason, it was no surprise that the Patriots went out and spent (relatively) heavily on acquiring the likeable Colvin, who was a very good pass-rushing presence when healthy. In all, he had 26.5 sacks in 65 regular-season games with New England. Played with the Patriots from 2003-08.

11. Alge Crumpler (2010) -- He didn’t set the world on fire statistically in his only season in New England (6 catches, 52 yards, 2 touchdowns), but he was an important locker room presence who helped then-rookies Rob Gronkowski and Aaron Hernandez with the bumps that go along with life in the NFL. Played with the Patriots in 2010.

10. Antowain Smith (2001) -- The running back was considered a bit of a project after a few successful years with the Bills, but he was a perfect fit in New England for most of three seasons, helping power the running game from 2001 through 2003. Not an elite back, he managed to do a pretty consistent job moving the chains and keeping drives alive -- in two of his three seasons, he rushed for at least 980 yards. Played for the Patriots from 2001-03.

9. Roman Phifer (2001) -- Another former Belichick guy who was imported to help get the new guys up to speed with the coach, Phifer was a talented physical presence who also brought a cerebral approach to the game. The inside linebacker was one of the best linebackers in the league when it came to pass coverage -- in part, it was his work in the 2003 playoffs against Indy’s pass-catchers that helped spur former Colts exec Bill Polian to institute rule changes that would help receivers get more leeway when it comes to hand-checking. Played with the Patriots from 2001-04.

8. Danny Woodhead (2010) -- The running back was a rare in-season free agent pickup -- he was cast off by the Jets that September -- and would go on to become a key cog in the New England offense. He signed a new deal that November, and would help ease the post-Kevin Faulk era when it came to looking for a pass-catcher out of the backfield. (This past season, he became the first New England running back since Faulk to post at least 40 catches and 40 carries in a season.) Played with the Patriots from 2009-present (currently a free agent).

7. David Patten (2001) -- One of the singularly nicest men in the game, Patten was a pro football journeyman (which included a stint in the Arena League) before he hooked on with New England prior to the 2001 season. Patten, who signed with the Patriots for next to nothing, ended up having an extraordinary four-year career with New England, catching 165 passes for 2,513 yards and 16 touchdowns. (In 2001, he became just the sixth player in NFL history to run for a touchdown, catch a touchdown pass and throw for a touchdown in the same game in a win over the Colts.) Played with the Patriots from 2001-04. He signed with New England again in 2010 but retired days into training camp.

6. Andre Carter (2011) -- The veteran defensive end spent just one season in New England but established himself as a clubhouse leader and very good situational pass-rusher. He had 10 sacks in 2011 and played a key role on the defensive side of the ball before going down with a season-ending calf injury in December. Played with the Patriots in 2011.

5. Brian Waters (2011) -- Waters was the consummate pro in his one season with the Patriots, stepping into the right guard spot a week before the season began and playing more than 90 percent of the snaps at the position over the course of the year. It may have ended weirdly for him with New England this past year, but for that stretch, he was a terrific presence up front. Played with the Patriots in 2011.

4. Rob Ninkovich (2009) -- A part-time long snapper who had trouble catching on with the Saints and Dolphins early in his career, Ninkovich signed with the Patriots in the summer of 2009 and has become an indispensable part of the New England defense -- in 2011, only two players in the NFL had at least six sacks and two picks: Ninkovich and Baltimore’s Terrell Suggs. Played with the Patriots from 2009-present.

3. Junior Seau (2006) -- The veteran linebacker ended up coming out of retirement for what would be portions of four seasons with New England. He actually became a pretty important part of the defense in 2006 and 2007 -- he finished the 2007 season with 3.5 picks -- and left an indelible imprint on the franchise with his leadership skills and intensity. Played with the Patriots from 2006-09.

2. Mike Vrabel (2001) -- The linebacker was wasting away on the bench in Pittsburgh -- he was considering quitting the game and going to law school -- before he was signed by the Patriots in the spring of 2001. Instead of becoming a lawyer, he turned into one of the most important parts of the New England dynasty. The outside linebacker played eight seasons with the Patriots and came away with 48 sacks and three Super Bowl rings. Played with the Patriots from 2001-08.

1. Rodney Harrison (2003) -- Simply put, it’s hard to overstate the impact that Harrison had on the franchise during a key stretch. Signed in the spring of 2003 -- after a visit to New England that included a stop at Ground Round, of all places -- he was able to keep things together when it looked like it was about to come bursting apart in the wake of the decision to release Lawyer Milloy that September. His leadership, attitude and feistiness were vital to the success of the franchise, and he remains one of the best defenders in recent franchise history. Played with the Patriots from 2003-08.