Call it the Keaney Trophy, Mullaney’s Mug or maybe the Rusty Anchor.

How about the Quahog Cup?

With four Division I basketball programs in Rhode Island and virtually all of them playing each other this season, there is a new spin to the term intrastate rivalry. Beginning tonight, when Brown travels to the Ryan Center to face URI, and continuing with games featuring both Bryant University and Providence College over the next few weeks, the state’s colleges will be shooting for bragging rights.

The Governor’s Cup is awarded to the winner of the annual Brown-URI football game, but there is no trophy for the mythical state college basketball champion. Maybe such a prize, along with a growing competitive profile for D-I newcomer Bryant, can develop over time.

The elevation of Bryant to the sport’s highest level has added a new twist to scheduling for the other three long-standing D-I schools. The Bulldogs were quickly accepted by Brown and PC and included on their schedules. Bryant and Brown will begin a home-and-home series Jan. 10 on the East Side. PC is host to Bryant in a guarantee game Dec. 22, when the Friars pay the Bulldogs a sum to come to the Dunkin’ Donuts Center but do not return the game at Smithfield.

As usual, PC will also play Brown and URI as it has for virtually every season over the past 80 years. The one game that will not take place is URI-Bryant. The two schools have talked about a matchup, but URI is resisting because of restrictions on nonleague foes, imposed by the Atlantic 10 Conference. The A-10 urges its schools to not schedule opponents that have weak scores on the Ratings Percentage Index (RPI). Because Bryant is in its first season playing a full D-I schedule, the team does not carry a current RPI.

“We are grateful that right out of the box we have games with two of the other three schools in the state,” said first-year Bryant coach Tim O’Shea. “URI is in a difficult situation because of the A-10 schedule rules.”

O’Shea is playing a killer schedule this season, with games at PC, Boston College, UConn, Iowa, Maryland and Rutgers. He’s actively drawing up next year’s slate and reports that it’ll be much easier. He’ll be hosting Brown and is hoping to play in an exempt tournament hosted by Providence at The Dunk. URI has yet to commit to a game but the two schools have talked. “I have one game to schedule and maybe we can do something with them in the spring when we have an RPI,” O’Shea said.

While there couldn’t be a more perfect kickoff to the college basketball season than a tournament involving PC, URI, Brown and Bryant, don’t hold your breath for that to develop. PC does plan on creating an in-season tourney, and it may be possible to add Bryant and Brown. But PC and URI have a contract for a home-and-home series that guarantees a strong gate and plenty of money for the host school. The two schools, and especially Providence, have expressed no desire to play each other a second time in the same season.

kmcnamar@projo.com