Advocate staff photo by CATHERINE THRELKELD -- LSU center fielder Jake Fraley (23) celebrates a three-run homer with teammates Chris Sciambra, Christian Ibarra and Kade Scivicque during a game against Texas Southern on Feb. 23.

Sean McMullen, LSU’s designated hitter, is playing for that imaginary trophy Tuesday against Louisiana-Lafayette.

You know, the trophy awarded to the Louisiana team that goes through the season undefeated against other in-state squads.

The fact that it doesn’t exist means little. To a few, at least, it’s very real.

“The biggest part, it’s a Louisiana team and we all kind of have our own rivalries,” said McMullen, from Metarie. “You want to win in-state, kind of get that trophy that doesn’t really exist.”

LSU’s game Tuesday night against the Ragin’ Cajuns isn’t just a clash between two Louisiana teams — it’s a top-25 duel.

LSU (7-0) surged up the baseball rankings Monday, even landing in the No. 1 spot in one poll. The Tigers are in the top 10 in three others.

UL-Lafayette (7-1) is as high as No. 10 in the major polls.

The meeting between the two teams — set for 6:30 p.m. Tuesday at Alex Box Stadium — is somewhat historic.

It is believed to be the first time in nearly six years that LSU has played an in-state team ranked in the top 25, with the last coming against UNO in 2008.

When’s the last time two Louisiana teams met while both were ranked in the top 10?

The answer might be more than a decade ago.

“It’s going to be,” said centerfielder Andrew Stevenson, “a little more hyped up.”

The connections are everywhere.

UL-Lafayette was the No. 2 seed in the NCAA Baton Rouge Regional last year and lost to LSU 5-1 in the tournament’s finale.

UL-Lafayette starting pitcher Carson Baranik pitched for LSU as a freshman in 2012 before transferring, and Cajuns’ starting outfielder Evan Powell is a former LSU signee.

Stevenson is from Youngsville, La., just outside of Lafayette, and was recruited hard by the Cajuns.

For LSU, this brewing rivalry isn’t as important as this fact: UL-Lafayette provides the Tigers with their toughest challenge yet two weeks into the 2014 season.

You want a measuring stick?

This is it.

“There’s no question ULL will be the best team we’ve faced at this point in the season,” coach Paul Mainieri said.

The Cajuns have won seven straight after a season-opening loss and they’re high-flying offense is soaring of late.

They’ve scored at least eight runs in four games and most recently swept a three-game series at Southern Miss.

UL-Lafayette will start Greg Milhorn, an uknown junior college transfer from Arkansas who started — and won — Game 2 this season.

He pitched a shutout in that opener and then closed out the series sweep of Southern Miss, pitching a scoreless 11?3 innings.

UL-Lafayette returns eight starters from a team that led the nation in home runs, was second in slugging and sixth in batting average.

“They have an aggressive approach,” McMullen said.

“I’m telling you, they’ve got some men they’re going to send up to the plate,” Mainieri said. “You better make some good pitches against these guys if you want to be successful because if you miss, it could be three runs with one swing of the bat.”

LSU pitcher Cody Glenn has the task of shutting down one of the nation’s most explosive lineups. He’ll start his second game on the mound.

Who will start around him is unclear.

Mainieri has shuffled freshmen into the group recently. He declined to reveal his lineup Monday during interviews.

During Monday’s practice, LSU’s infield and outfield personnel showed tweaks, but it’s uncertain if that group will start Tuesday’s game — one Mainieri knows is more than just about Louisiana vs. Louisiana.

This one has the trappings of an SEC duel, a one-game affair between the nation’s bests.

Said Mainieri: “Should be a packed house.”