You have to be pretty unlucky to play on the New England Patriots in the Bill Belichick era and miss making a Super Bowl appearance.

In a brief brainstorm, the best players who played on the Patriots from 2000 to 2018 to have not made a Super Bowl were cornerback Aqib Talib (2012-2013) and defensive tackle Akiem Hicks (2015). Wide receiver Terry Glenn, left tackle Bruce Armstrong and linebacker Chris Slade also played on the 2000 Patriots but all were gone before Super Bowl XXXVI.

So, it was pretty easy to put together an All-Belichick Era Super Bowl roster, compiling the best players from 2000 to 2018. The list includes 10 current Patriots (in italics)

Here’s what it looks like:

QB Tom Brady (XXXVI, XXXVIII, XXXIX, XLII, XLVI, XLIX, LI, LII)

RB Corey Dillon (XXXIX)

Third-down back James White (LI, LII)

WR Randy Moss (XLII)

WR Julian Edelman (XLVI, XLIX, LI, LII)

WR Wes Welker (XLII, XLVI)

TE Rob Gronkowski (XLVI, XLIX, LI, LII)

LT Matt Light (XXXVI, XXXVIII, XXXIX, XLII, XLVI)

LG Logan Mankins (XLII, XLVI)

C Dan Koppen (XXXVIII, XXXIX, XLII, XLVI)

RG Shaq Mason (LI, LII)

RT Sebastian Vollmer (XLVI, XLIX)

DE Trey Flowers (LI, LII)

DE Willie McGinest (XXXVI, XXXVIII, XXXIX)

DT Richard Seymour (XXXVI, XXXVIII, XXXIX, XLII)

DT Vince Wilfork (XXXIX, XLII, XLVI, XLIX)

LB Mike Vrabel (XXXVI, XXXVIII, XXXIX, XLII)

LB Tedy Bruschi (XXXVI, XXXVIII, XXXIX, XLII)

LB Dont’a Hightower (XLIX, LI, LII)

CB Ty Law (XXXVI, XXXVIII, XXXIX)

CB Stephon Gilmore (LII)

FS Devin McCourty (XLVI, XLIX, LI, LII)

SS Rodney Harrison (XXXVIII, XXXIX, XLII)

Nickel Asante Samuel (XXXVIII, XXXIX, XLII)

K Adam Vinatieri (XXXVI, XXXVIII, XXXIX)

P Ryan Allen (XLIX, LI, LII)

LS Lonie Paxton (XXXVI, XXXVIII, XXXIX, XLII)

If we were to take out players who never actually won a Super Bowl, then Deion Branch and Troy Brown would replace Moss and Welker, Joe Thuney would replace Mankins and Darrelle Revis would replace Gilmore.

It was difficult to leave out Kevin Faulk, Nate Solder, David Andrews, Stephen Neal, Marcus Cannon, Chandler Jones, Rob Ninkovich, Jerod Mayo, Patrick Chung and Lawyer Milloy, but we opted to go with White, Light, Koppen, Mason, Vollmer, Flowers, Hightower and Harrison instead.

We used a 4-3 to put together the defense, but it works in a 3-4 instead. Just move Seymour to defensive end and McGinest to outside linebacker. Voila.

It’s amazing that Allen has over 10,000 more punting yards than the next most prolific Belichick-era punter, Ken Walter. Allen also leads all Patriots punters with 45.3 yards per punt. Notice I said punter because someone else leads the Patriots in all-time yards per punt, and you’ll never guess who it is*.

For someone who loves punters and punting, Belichick sure went through a lot of them until settling on Allen.

*OK, fine. It’s Matt Cassel — 57 yards per punt. Look it up.