This week’s bracket projection carries with it a preemptive history lesson — just in case a couple unusual (but not impossible) scenarios unfold. Both involve teams likely to require an at-large berth in this year’s NCAA tournament.

Let’s start with Penn (5-4), which owns a top-five RPI despite a record the Quakers just nudged back over .500 on Saturday thanks to a victory over Harvard. Mike Murphy’s team could very easily miss the Ivy League tournament (it would lose head-to-head tiebreakers to Brown, Princeton and Yale) even with a triumph at Dartmouth to close conference play Saturday.

But here’s the thing: If the Quakers win out against Dartmouth, Saint Joseph’s and Albany, they’re almost certainly going to be in the NCAA tournament. There’s a decent chance they could land a home game, too.

This would not be unprecedented. Army missed the 2004 Patriot League tournament and still landed an at-large berth. More recently, Virginia (2014 and 2015) and North Carolina (2014) both landed NCAA invitations despite missing the ACC tournament. The Cavaliers, in fact, landed home games in both seasons (as a No. 8 seed in 2014 and a No. 7 seed in 2015).

So Penn wouldn’t be the first team to secure an at-large bid even while missing its conference tournament. It wouldn’t even be the first team in the last 10 years to do it.

There’s also a potential solution to travel-related cost containment sitting in front of the committee should it end up needing three flights simply because of the composition of the field. For the moment, that could be a combination of Jacksonville and Utah winning their respective conferences and Ohio State either claiming the Big Ten tournament or securing an at-large.

While tinkering with this week’s bracket projection, it was tempting to solve some of the issues by giving Duke a short bus trip to … Virginia. That wasn’t the outcome (you’ll have to read to the end to learn how it was sorted out), but it wouldn’t be unprecedented for a league without an automatic berth to have two of its teams paired together in the first round of the NCAA tournament.

The last time it happened was 2011, when Maryland and North Carolina (rivals at the time in what was a four-team ACC) met in the first round after the committee required flights to get opponents to both Denver and Notre Dame. Since the start of the 16-team tournament era, there was also a Georgetown-Rutgers first round game in 2003 when both teams were in the ECAC.

Is it a likely outcome? Not necessarily. But don’t think of it as an impossibility, either.

AUTOMATIC QUALIFIERS

Maryland (11-0) Big Ten

RPI	SOS	T5	T10	T20	25+L
1	12	2-0	4-0	5-0	—

Princeton (9-2) Ivy League

RPI	SOS	T5	T10	T20	25+L
2	4	3-1	4-2	5-2	—

Georgetown (10-1) Big East

RPI	SOS	T5	T10	T20	25+L
3	16	1-1	1-1	5-1	—

Boston University (9-3) Patriot League

RPI	SOS	T5	T10	T20	25+L
9-3	14	23	0-1	0-2	0-3	—

Saint Joseph's (10-2) NEC

RPI	SOS	T5	T10	T20	25+L
16	47	0-0	0-0	0-0	Delaware (29), at Drexel (36)

Utah (7-3) ASUN 

RPI	SOS	T5	T10	T20	25+L
7-3	19	50	0-1	0-1	0-2	at UMBC (51)

Jacksonville (12-2) SoCon

RPI	SOS	T5	T10	T20	25+L
21	33	0-0	0-0	3-1	—

Towson (5-7) CAA

RPI	SOS	T5	T10	T20	25+L
27	13	0-1	0-1	0-5	at Delaware (29)

St. Bonaventure (8-3) MAAC

RPI	SOS	T5	T10	T20	25+L
40	71	0-0	0-0	0-2	at Siena (61)

Vermont (7-6) America East

RPI	SOS	T5	T10	T20	25+L
50	32	0-0	0-1	0-3	at Dartmouth (34), at Providence (47)

Maryland’s four top-10 victories (Princeton, Virginia, Rutgers, Ohio State) have come by an average of 7.75 goals. The Terrapins could probably take a loss and still be pegged as the No. 1 overall seed at the moment. ... Princeton didn’t have an easy time against Dartmouth, but it survived on a weekend other Ivies (Cornell and Yale) took serious drubbings. …

Georgetown has up to five games remaining, and it’s possible only one of them (a Big East final, likely against Denver or Villanova) will be against a top-20 team. The Hoyas host 5-6 Loyola (RPI: 24) on Tuesday in their final nonconference game. ... Despite losing a pair of mainstays to injury, Boston University impressed in its victory at Loyola. With Lehigh’s loss at Colgate, the Terriers lead the Patriot League by a game with two weekends to go.

Saint Joseph’s can clinch the top seed in the Northeast tournament with a victory over Sacred Heart on Saturday. … Utah can do the same in the Atlantic Sun if it wins at Bellarmine on Saturday. …

Jacksonville outscored VMI and Hampton by a combined 51-9 and slipped in the RPI, an utterly predictable development. The Southern Conference regular-season champions, the Dolphins play host to Mercer on Saturday before a 12-day layoff. … Towson gets the nod this week in the Colonial because of a superior RPI to both Drexel and Fairfield. All three teams are 2-1 in the league. …

St. Bonaventure squandered a 9-1 lead in its 14-11 loss to Siena, but it can still clinch the Metro Atlantic’s top seed with victories over Quinnipiac and Canisius to close the regular season. … Vermont is the last unbeaten team left in America East play. The Catamounts can clinch the top seed and conference tournament hosting rights with a defeat of Binghamton on Saturday.

AT-LARGE (14 TEAMS/8 SLOTS)

	W-L	RPI	SOS	T5	T10	T20	NOTABLE LOSSES (25+)
Penn	5-4	4	1	0-2	1-4	3-4	—
Rutgers	11-2	5	19	0-2	1-2	2-2	—
Yale	7-3	6	5	2-0	2-2	4-2	at Penn State (31)
Virginia	9-3	7	10	0-1	0-1	3-3	—
Cornell	10-2	8	14	0-1	2-1	3-2	—
Brown	7-4	9	15	1-1	2-1	2-3	—
Ohio State	8-4	10	3	0-2	0-3	3-4	—
North Carolina	8-4	11	2	0-0	1-3	3-4	—
Duke	10-5	12	8	0-1	1-1	4-2	at Syracuse (30)
Denver	7-5	13	8	0-1	1-2	2-4	—
Harvard	7-3	15	21	0-1	1-3	2-3	—
Notre Dame	5-4	17	20	0-2	0-4	1-4	—
Richmond	7-4	18	24	0-1	1-1	1-3	—
Army	10-2	20	29	0-1	1-1	1-1	Lehigh (26)

Seven of Penn’s nine games this season have come against top-20 RPI teams. The other two were against Villanova (No. 23) and Penn State (No. 31). The Quakers remain about as good at scheduling in a way that helps their RPI as anyone in Division I. … It’s looking more and more like Rutgers will land a home game in the NCAA tournament, its first since 2003. A victory over Penn State to close the regular season might be enough to get the job done; tossing in a Big Ten semifinal victory almost certainly will lock that up. …

Losing to Brown, even in lopsided fashion, doesn’t hurt Yale that much. It still has its defeats of Penn and Princeton to keep it in solid shape for a first-round home game. … Is Virginia guaranteed a postseason home game? It’s not such a silly question. The Cavaliers don’t have a top-10 win (and thus will be rooting for North Carolina the next two weekends), and they won’t get any RPI help from Syracuse (No. 30) and Lafayette (No. 57) to close out their regular-season slate. …

Cornell didn’t play well Saturday against Army, but it still has a case for a first-round home game thanks to defeats of Yale and Ohio State. … Brown has jumped from 19th to 17th to ninth in the RPI over the last two weeks thanks to defeats of Penn and Yale. A victory at Cornell would further solidify the fast-rising Bears’ profile. …

Ohio State played Maryland as well as anyone has, at least for three quarters, but that doesn’t do the Buckeyes any good in the hard math of the RPI. Still, those victories over North Carolina, Notre Dame and Harvard are distinguishing factors. … North Carolina’s early victory over Brown looks more and more valuable. But the Tar Heels are going to need to beat Notre Dame and/or Duke to earn their way into the tournament. …

Duke landed its signature victory Thursday against Virginia, and its head-to-head defeats of Denver and North Carolina are useful in making an at-large case, too. … Denver dropped two places in the RPI just by taking the field against St. John’s (2-10, No. 55 in the RPI). …

Harvard’s best victory (Brown) keeps looking better, but the Crimson can ill-afford to lose out after dropping games to Cornell and Penn. Harvard finishes at home against Princeton and at Yale. … Notre Dame has a victory over Duke and little else going for it. Its three-game closing stretch (North Carolina, at Syracuse, Duke) begins Thursday night. …

Richmond couldn’t have been thrilled to see Virginia lose at Duke. The Spiders’ best (and maybe only) path to the postseason remains via the Southern Conference’s automatic berth. … Army’s numbers just don’t hold up compared to the rest of the at-large field, and there probably isn’t a way to change that even if the Black Knights beat Navy, Boston University and a Patriot League semifinal opponent and then drop a conference title game.

BRACKET

A few notes worth remembering:

• The NCAA will return to eight campus-site games in the first round this season. First-round conference matchups will be avoided, which can lead to some movement for the unseeded teams.

• With the return of the Ivy League from last year’s hiatus and the addition of the Atlantic Sun, there are 10 conferences eligible for automatic berths. That means there will be two play-in games, featuring the four lowest-ranked automatic qualifying teams. The rankings will be determined by the committee and not specifically by the RPI.

• Limiting air travel remains a priority for the NCAA, so this won’t necessarily be a 1-through-16 bracket. Historically, the NCAA tries to bracket the field so only two teams must travel more than 400 miles for a first-round game, though it isn’t a completely inflexible rule.

• Quarterfinal hosts are funneled into their home sites. Whichever quadrant of the bracket Ohio State lands in will play a second-weekend game in Columbus.

• This exercise is an attempt to project what the NCAA committee would do based on its history and on this season’s results to date. It is not an attempt to predict future results or suggest what the committee should do.

Hempstead, N.Y., quarterfinal    

(1) BIG TEN/Maryland vs. COLONIAL/Towson-METRO ATLANTIC/St. Bonaventure
(8) Penn vs. Duke

Columbus, Ohio, quarterfinal

(5) Rutgers vs. Brown
(4) Yale vs. PATRIOT/Boston University

Hempstead, N.Y., quarterfinal

(3) BIG EAST/Georgetown vs. ATLANTIC SUN/Utah
(6) Cornell vs. SOUTHERN/Jacksonville

Columbus, Ohio, quarterfinal      

(7) Virginia vs. Ohio State
(2) IVY/Princeton vs. NORTHEAST/Saint Joseph’s-AMERICA EAST/Vermont

Last three in: Brown, Duke, Ohio State
First three out: North Carolina, Denver, Harvard

Moving in: Brown, Duke, Vermont
Moving out: Binghamton, Denver, Harvard

Conference call: Ivy (5), Big Ten (3), ACC (2)