The men’s basketball team has already made plenty of history this season.

The Bulldogs have claimed Yale’s first Ivy League title in 39 years. Their 19 overall wins are the most in a decade. They have posted the most league wins, 11, since the ’66-67 team.

The next item on the Bulldogs’ checklist? Yale’s first appearance in the NCAA tournament in 40 years.

The Elis’ (19-9, 11-3 Ivy) quest for a ticket to the Big Dance continues when they oppose Princeton (16-10, 11-3) for the third time this season tonight at 8 p.m. (WYBC-AM 1340, DIRECTV 611) at the Palestra in Philadelphia. The contest is the first of a two-game playoff to decide the recipient of the Ivy League’s automatic berth to the NCAA tournament. The winner will advance to play the University of Pennsylvania (24-6, 11-3) — which received a bye thanks to a 3-1 record against Yale and Princeton — Saturday at 7:30 p.m. at Lafayette College’s Kirby Sports Center.

The two teams split their season series, Yale winning 60-50 in New Haven and Princeton returning the favor, 59-46, in New Jersey.

“Our kids believe they can win,” Yale head coach James Jones said. “Sometimes that is half the battle.”

It has been a battle for Yale to get into its current position. The Bulldogs’ tie for the league championship marks only the ninth occasion when a team other than Penn or Princeton has finished in first place in the league’s 45 seasons, and only the third time since 1968.

Since its inception in 1956, the Ivy League has had six playoff games to determine the recipient of the league’s NCAA bid. Yale has played in a playoff game once before, losing 65-53 to a Bill Bradley-led Princeton team on March 8, 1963. Princeton has been involved in all six of those playoff games, compiling a 3-3 record.

Tonight’s game will be the fourth game in seven days for Princeton — all on the road. The Tigers posted two come-from-behind victories last weekend at Cornell and Columbia before losing 64-48 at the hands of Penn to force the three-way tie.

The Bulldogs, however, are relatively well-rested, having been off since they coasted to victory against Dartmouth Saturday. But Jones does not see an advantage there.

“Their season is on the line just like our season is on the line,” Jones said. “I certainly expect that to bring out the best in our team and to bring out the best in them.”

The last time the two teams played, the Bulldogs did not bring their best offensive performance into the game. Yale shot 34.7 percent in the contest, making a season-low two 3-pointers.

“Any time you play a game and you don’t play well, you have a bad taste in your mouth,” Jones said. “Our guys are happy for the opportunity to go out and improve.”

Defensively, the Bulldogs have succeeded this season in containing the slowdown, motion offense that the Tigers run. The Eli strategy focuses on denying the backdoor cuts Princeton uses to get easy looks at the basket. By forcing the Tigers to shoot more from the perimeter, Yale has held Princeton to 40.2 percent shooting in their two games.

Yale’s outside shooting is key to opening up the interior for the Eli big men, who were ineffective the last go around against Princeton.

“We missed so many open shots it enabled them to use their halfcourt defense to really help inside,” Jones said.

The Bulldogs set a new school record for 3-pointers made in a season with 206, but suffered one of their worst shooting nights at Princeton’s Jadwin Gym Feb. 23.

In Yale’s 72-63 loss to Penn at the Palestra the next night, the Elis poured in 11 3-pointers, their second-highest total this season — a sign that the team is comfortable shooting in the historic Philadelphia arena.

Ivy League rules require all playoff games to be held at a neutral site, with an Ivy League gym preferred. While the Palestra meets those standards, its relative proximity to the Princeton campus likely will give the Tigers the homecourt advantage in crowd support.

“They tell us where to play. There is not much that we can do about it,” Yale center T.J. McHugh ’03 said. “It’s what happens in between the lines that determines who wins.”