Composition of the current Patriot roster (with apologies in advance for any errors or omissions):
43 have never been with any other team:
- 28 players drafted by the Patriots
- 15 signed as a rookie udfa
31 have been with another NFL organization:
- 19 free agents that were previously with another team
- 2 restricted free agents
- 1 signed off another team's practice squad
- 7 acquired via a trade
- 2 waiver claims
Originally drafted by the Patriots:
12 - QB Tom Brady, 2000, 6.199, Michigan
90 - DT Malcom Brown, 2015, 1.32, Texas
61 - OT Marcus Cannon, 2011, 5.138, TCU
49 - LS Joe Cardona, 2015, 5.166, Navy
43 - ST Nate Ebner, 2012, 6.197, Ohio State
71 - OT Cameron Fleming, 2014, 4.140, Stanford
98 - DE Trey Flowers, 2015, 4.101, Arkansas
3 - K Stephen Gostkowski, 2006, 4.118, Memphis
87 - TE Rob Gronkowski, 2010, 2.42, Arizona
30 - S Duron Harmon, 2013, 3.91, Rutgers
75 - OL Ted Karras, 2016, 6.221, Illinois
69 - G Shaq Mason, 2015, 4.131, Georgia Tech
32 - S Devin McCourty, 2010, 1.27, Rutgers
37 - S Jordan Richards, 2015, 2.64, Stanford
52 - LB Elandon Roberts, 2016, 6.214, Houston
18 - ST Matthew Slater, 2008, 5.153, UCLA
77 - OT Nate Solder, 2011, 1.17, Colorado
62 - G Joe Thuney, 2016, 3.78, North Carolina State
28 - RB James White, 2014, 4.130, Wisconsin
91 - DL Deatrich Wise, 2017, 4.131, Arkansas
11 - WR Julian Edelman, 2009, 7.232, Kent State [IR]
54 - LB Dont'a Hightower, 2012, 1.25, Alabama [IR]
41 - CB Cyrus Jones, 2016, 2.60, Alabama [IR]
19 - WR Malcolm Mitchell, 2016, 4.112, Georgia [IR]
95 - DE Derek Rivers, 2017, 3.83, Youngstown St [IR]
99 - DT Vincent Valentine, 2016, 3.96, Nebraska [IR]
63 - OT Tony Garcia, 2017, 3.85, Troy [NFI]
92 - DE Geneo Grissom, 2015, 3.97, Oklahoma [PS]
Signed as undrafted rookie free agent (never been with another team):
6 - P Ryan Allen, 2013, Louisiana Tech
60 - C David Andrews, 2015, Georgia
38 - RB Brandon Bolden, 2012, Ole Miss
70 - DT Adam Butler, 2017, Vanderbilt
21 - CB Malcolm Butler, 2014, West Alabama
74 - OL Cole Croston, 2017, Iowa
47 - TE Jacob Hollister, 2017, Wyoming
31 - CB Jonathan Jones, 2016, Auburn
36 - ST Brandon King, 2015, Auburn
51 - DE Keionta Davis, 2017, Tenn-Chattanooga [NFI]
76 - OL Andrew Jelks, 2017, Vanderbilt [NFI]
48 - LB Harvey Langi, 2017, Brigham Young [NFI]
81 - WR Cody Hollister, 2017, Arkansas [PS]
26 - S David Jones, 2017, Richmond [PS]
39 - S Damarius Travis, 2017, Minnesota [PS]
Signed as unrestricted free agent, previously with another team:
80 - WR Danny Amendola, 2013 via Rams (orig w/Dallas; also w/Philly)
97 - DT Alan Branch, 2014 via Bills (orig drafted by Arizona; also w/Seattle)
34 - RB Rex Burkhead, 2017 via Bengals (drafted by Cincy in 2013)
23 - S Patrick Chung, 2014 via Eagles (NEP 2009 draft pick, 2.34)
46 - FB James Develin, 2012 via Bengals (UDFA, 2010)
24 - CB Stephon Gilmore, 2017 via Bills (Buf 2010 draft pick, 1.10)
93 - DE Lawrence Guy, 2017 via Ravens (GB 2011 7th round draft pick, also with Indy and San Diego)
45 - LB David Harris, 2017 via Jets (NYJ 2007 draft pick, 2.47)
2 - QB Brian Hoyer, 2017 via 49ers (Pats UDFA, 2009; also w/Steelers, Cardinals, Browns, Texans and Bears)
94 - DE Ricky Jean-Francois, 2017 via GB (drafted by SF; also w/Indy, Wash)
33 - RB Dion Lewis, 2015 via Eagles (5th round 2011 draft pick; also w/Browns, Colts)
51 - LB Trevor Reilly, 2017 via Dolphins (2014 7th round pick by Jets)
58 - LB Shea McClellin, 2016 via Bears (2012 1st round pick by Chicago) [IR]
64 - C James Ferentz, 2017 via Broncos (udfa w/Texans) [PS]
27 - CB Ryan Lewis, 2017 via Cardinals (2017 udfa w/Arizona) [PS]
84 - WR Riley McCarron, 2017 via Texans (2017 udfa w/Houston) [PS]
?? - WR Bernard Reedy, 2017 via Bucs (2014 udfa w/Atlanta) [PS]
44 - TE Will Tye, 2017 via Jets (2015 udfa w/Giants) [PS]
22 - CB Jomal Wiltz, 2017 via Eagles (2017 udfa w/Philly) [PS]
Signed as a restricted free agent:
35 - RB Mike Gillislee, 2017 via Bills (drafted by Miami, also w/Arizona)
15 - WR Chris Hogan, 2016 via Bills (orig UDFA w/SF; also w/NYG, Miami)
Signed off another team's practice squad:
55 - DE Eric Lee, 2017 via Bills (2016 UDFA w/Texans)
Acquired via trade:
83 - TE Dwayne Allen, 2017, from Colts
29 - CB Johnson Bademosi, 2017 from Lions (orig UDFA w/Browns)
14 - WR Brandin Cooks, 2017 from Saints (NO 2014 draft pick, 1.14)
13 - WR Phillip Dorsett, 2017, from Colts (Indy 2015 draft pick, 1.29)
59 - LB Marquis Flowers, 2017, from Bengals (Cin 2014 draft pick 6.212)
25 - S Eric Rowe, 2016 from Eagles (Phil 2015 draft pick 2.47)
53 - LB Kyle Van Noy, 2016 from Lions (Det 2014 draft pick 2.40)
Claimed off waivers:
88 - TE Martellus Bennett, 2017 from Packers (drafted by Dallas; also w/Giants, Bears, Patriots)
68 - OT LaAdrian Waddle, 2015 from Lions (Det UDFA, 2013)
Note: some players such as Brandon King and Cameron Fleming were released and re-signed, but were included in their original status since they were never with another organization. Same goes for a player who became a free agent after his contract expired but re-signed with the Patriots. Players such as Chung and Bennett are placed in the categories depending on how they were most recently acquired, rather than how they were originally signed before departing to another team.
The Patriots have 31 player that have played on a cumulative 63 different NFL teams.
It stands to reason that better teams (like the Patriots) would presumably have a lower than average number (63) on their own roster, and higher than average number (99) of their former players on other team's rosters. The reason is simple: it is more difficult to make the roster of a good team and easier to make the roster of a bad team.