How can Penn qualify for Ivy League Tournament? It's complicated

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Penn men's basketball has two games left in the regular season. With a strong showing this weekend, the Quakers could make the inaugural four-team Ivy League Tournament, although it's not completely under their control. Penn is currently tied for fourth with Columbia at 5-7 in conference, two games behind Yale and two games ahead of Brown, Cornell and Dartmouth. Each team has two games left with Penn hosting Dartmouth and Harvard this weekend while Columbia travels to Brown and Yale.

Here's what needs to happen for the Quakers to make the tournament with each scenario this weekend.

Scenario A: If Penn loses to both Dartmouth and Harvard, the Quakers would need:
A. Columbia to lose both games
B. Dartmouth to lose to Princeton (a likely event as Princeton is undefeated in conference play)
C. Cornell to beat both Brown and Yale

Scenario B: If Penn beats Dartmouth and loses to Harvard, the Quakers would need:
A. Columbia to lose both games

Scenario C: If Penn loses to Dartmouth and beats Harvard, the Quakers would need:

Option 1
A. Columbia loses both games

Option 2
A. Columbia beats Brown but loses to Yale

Option 3
1. Columbia beats Yale but loses to Brown
2. Cornell beats Brown and is ahead of or tied with Dartmouth in the Ivy standings

Scenario D: If Penn beats both Dartmouth and Harvard, the Quakers are still not automatically in. Here's what they would still need:

Option 1
1. Columbia loses to Brown

Option 2
2. Columbia loses to Yale

Option 3
1. Columbia wins both games but ...
2. Yale loses both its games

Option 4
1. Columbia wins both games but ...
2. Yale beats Cornell
3. Cornell beats Brown

If Option 3 takes place, then a Cornell win over Brown would give Penn the No. 3 seed while a Brown win over Cornell would give Columbia the No. 3 seed and Penn the No. 4 seed.

Explaining the tiebreakers
OK, you're confused as to how last place Cornell vs. last place Brown factors into a tiebreak between Columbia and Penn, right? Very fair. Here's how the Ivy Tournament tiebreakers actually work.

The first tiebreaker is head-to-head. In the case of a two-team tie, that's simple. Penn played Columbia twice and each team won on its home court.

In the case in which both Penn and Columbia lose its final two games, there is an opportunity for a three-way tie for the No. 4 seed if Cornell, Brown or Dartmouth win its respective final two games. Cornell plays Brown, so only one of those two can actually do so. In a three-way tie with Penn, Columbia and Cornell, Penn has two wins over Cornell while Columbia split with the Big Red, so Penn is 3-1 vs. the two teams and would get the tournament bid. The opposite is true for Brown, hence how it factors into that first option.

If Dartmouth wins its final two games and Penn loses its final two, then Dartmouth would have defeated Penn twice and would eliminate Penn from any three- or- four-way tie in Scenario A.

The second tiebreaker
This, believe it or not, gets more complicated. Really, really complicated. The second tiebreaker reads as follows:

If a tie still exists, the tie will be broken by comparing each team’s record against the highest seed outside of the tie and continuing through the full league standings (if there is a group of tied teams, use each team's record against the group rather than the individual teams) if necessary. 

This is relevant in any Penn-Columbia two-way tie. The highest seed in the Ivy standings is Princeton, but the Tigers don't factor in because they haven't lost to anyone in conference, having beaten the Quakers and Lions twice.

The next seed is Harvard. Penn lost its first matchup with the Crimson while Columbia split its two meetings. If Penn ends up tied with Columbia but hasn't picked up a win against Harvard (Scenario B), then the Red and Blue are eliminated from tournament contention. 

The third seed right now is Yale. Penn split its matchups with the Elis while Columbia lost its first game vs. Yale. Therefore, if Penn beats Harvard this weekend -- thus neutralizing Columbia's tiebreaker advantage -- and ends up tied with Columbia, the Yale tiebreaker is key. If Columbia hasn't beaten Yale (Scenario C, Option 2), Penn gets the tiebreak and thus the tournament bid. 

If Columbia and Penn are tied and the teams have picked up wins over Harvard and Yale, respectively, we move on to the next tiebreak unless both schools have won each of its games AND Yale loses both of its contests. Then, it would be a three-way tie for third through fifth place. The head-to-head tiebreaker would be even at 2-2 each, but Penn and Columbia would each have a win over Harvard while Yale wouldn't have wins over Princeton or Harvard, so Yale would be eliminated. (Scenario D, Option 3)

But that takes us to what if Columbia and Penn are even through the first three seeds of the second tiebreak. Then you go to the three current last-place teams. Penn swept Cornell, split with Brown and lost its first meeting with Dartmouth. Columbia split with Cornell and Dartmouth while winning its first game against Brown. That colors the rest of this and why that Cornell-Brown is relevant.

If Penn beats Dartmouth this weekend and the Quakers/Lions are tied and this far down the tiebreak, then both teams would have the same results vs. Dartmouth and the only thing that would matter is which team has a better spot in the standings: Cornell or Brown. That will be decided by the two schools facing on Saturday night.

If Penn loses to Dartmouth this weekend and the Quakers/Lions are tied and this far down the tiebreak, the Big Green can ruin the Quakers by being ahead of both Brown and Cornell. This would only happen if Dartmouth beat Princeton, so it is highly unlikely. This is relevant in Scenario A and Scenario C, Option 3.

Third and fourth tiebreak
The third tiebreak, which I'm 99.999 percent sure can't come into play this weekend, is based on which team leads in the weighted average of a series of metrics. For what it's worth, Penn leads in these tiebreaks and would win it.

The fourth tiebreak is a coin toss. Tails never fails? 

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