In Or Out?

TigerBlog had a teacher named Mr. Eovino for a probability and statistics class back in high school.

TB was a junior, and he took the class that was probably two-thirds seniors. Back when TB was in high school, the kids a year older than he was were an academic powerhouse of a group, and taking an upper-level advanced math class with them was as challenging as anything TB ever did in high school.

TB remembers Mr. Iovino as a great teacher, one who managed to combine being funny and approachable with having extraordinarily high standards in his class. When TB thinks back to his days in high school, Mr. Iovino is one of the very few teachers - along with maybe four others - who stand out to him as having all of those qualities and who, as a result, really pushed TB to do his best.

He also had a great sense of humor, something he demonstrated during the school talent show one year, when he put white powder in his black beard, dressed in flowing robes and danced around the stage as a group of kids turned the Kinks' song "Lola" into "Ayatollah."

One day in class, he interrupted himself and started flailing away futilely, swatting at an unseen annoyance in front of his face. Eventually, the flailing got to be quite energized and somewhat violent - until he stopped abruptly and said to the class: "There's no bug here."

Probability and statistics was a difficult subject, and it was often confusing for TB to remember all the starting points and formulas and such.

Still, he's pretty sure that if there are six events with two possible outcomes for each event, then the total number of outcomes is two to the sixth power, or 64.

That means there are 64 possible outcomes of the remaining six Ivy League men's lacrosse regular-season games, and those 64 outcomes will take the race for the four Ivy League tournament spots in almost as many different directions.

Right now, this is how it looks:

Cornell 4-0 (Brown, Princeton remaining)
Penn 3-2 (Dartmouth remaining)
Yale 3-2 (Harvard remaining)
Princeton 2-2 (Harvard, Cornell remaining)
Harvard 1-3 (Princeton, Yale remaining)
Brown 1-3 (Cornell, Dartmouth remaining)
Dartmouth 1-3 (Penn, Brown remaining)

As of now, Cornell is in the tournament and none of the teams have been mathematically eliminated or have clinched a spot. Also, Princeton could still host the tournament, mathematically at least.

In its most simplistic form, a Cornell win over Brown and a Princeton win over Harvard Saturday gives Cornell the outright title and home field in the tournament and puts Penn, Yale and Princeton in the field, locking Princeton into the fourth seed.

But ...

There could be some wild stuff if the right outcomes happen, including:

* Princeton could NOT be in the tournament at 3-3 but make the field at 2-4
* there could be a five-way tie for second at 3-3 ... should this happen, Princeton would be out
* Harvard could have its fate decided by who wins Dartmouth-Brown, two teams Harvard has already played
* there could be multiple combinations of teams that could finish in a four-way tie at 3-3
* there could be a four-way tie at 2-4 for the last spot between the same four teams, but they could get there in two different ways, and whichever way they got there would determine who got the fourth spot
* there could be a three-way tie for the last spot that would have to be broken by a random draw

Cornell, obviously, is in, and Yale and Penn would be in simply by winning their last remaining game.

Princeton, likewise, is in a win-and-you're-in situation.

Is anyone else?

Brown definitely isn't, since a 3-3 Brown team could still finish behind Cornell, Yale, Penn and Princeton or even with Princeton in a two-way tie for fourth, but the Tigers defeated Brown.

Dartmouth isn't definitely in, since it could win out to 3-3 and find itself tied with Princeton and Penn for the last two spots. Each would be 1-1 against the other, so the next tiebreaker would be how each team did against the teams from the top of the standings down.

In this case, should Princeton get to 3-3 with a loss to Harvard and win over Cornell and, assuming a Yale win over Harvard, then Princeton would be third, leaving Penn and Dartmouth fourth and giving Dartmouth the spot with its head-to-head win over Penn.

But if Princeton lost to Cornell and beat Harvard, then Penn would be third because it would have beaten Yale. That would leave Princeton and Dartmouth, and Princeton's win over Dartmouth would knock out the Green.

As for Harvard, TB may be overlooking something, but he can't see any way that Harvard isn't in with a win over Princeton and Yale. But it's really, really complicated in some of those scenarios, so hey, he may be wrong.

The last Saturday of the 2010 Ivy League lacrosse season was the wildest day in Ivy League men's lacrosse history. There were three games involving six teams, all of whom still had a shot of getting in the tournament.

All three games were one-goal games, and one went into OT. When the dust cleared, there were four teams tied at 4-2, the first four-way title in league history in men's lacrosse.

This year? Hey, it could be just as nuts.