Moot Court Analysis

Yes, I did the math. But before I get into that, the disclaimers: This place really likes secrets, so I'm looking at a black box--it is conceivable the officers do a better job matching teams than it seems. Also, my numbers are a result of the competition and do not address any conceptual flaws there may or may not be--like arbitrary and rigid cutoffs that only serve administrative convenience.

There were 66 teams competing in this quarter's moot court competition. 16 of them made the break (24%) after four rounds. Here's the breakdown we expect to see after each round:

Round 1
1-0: 50% of teams
0-1: 50%

Round 2
2-0: 25%
1-1: 50%
0-2: 25%

Round 3
3-0: 12.5%
2-1: 37.5%
1-2: 37.5%
0-3: 12.5%

Round 4
4-0: 6.25%
3-1: 25%
2-2: 37.5%
1-3: 25%
0-4: 6.25%

This is Pascal's Triangle with a few complications in practice. First, the first two rounds are independent, so the curve may vary slightly due to chance. Second, it is possible to split ballots, so these groupings are not so well-defined. However, given the size of this competition, we would still expect five 3-1 teams not to make the break, so we can be reasonably certain no 2-2 team will make it.

The odds that the 16th best team (in an absolute sense) faces a better team in the first round is 15/65. If they do, the odds they face another better team in the second round is 14/64. There is slightly more than a 1 in 20 chance the 16th best team is actually excluded due to bad luck. There is also the possibility that they face a better team in rounds 3 or 4 after only losing one of the first two.

If you extend the reasoning to higher teams, the odds become even more remote very quickly. If you aggregate the odds to find how likely there was a problem *somewhere*, the first-order approximation is 28%. There are independence problems, but they are second order and to some extent work against the odds of unlucky matches in rounds 3 and 4. The ultimate conclusion is that on a list of a few more than one hundred upper quarter barristers, we expect about two of them don't "deserve" to be there. Those improperly excluded can make it in through inter-school moot court competition teams or as one of the top 10 speakers, so unless they give up, we expect deserving students to make it one way or another.

The competition is held every fall and spring quarter. It is a requirement for Legal Analysis, Research, and Communication (LARC). Summer starters end up delaying their third of three quarters of LARC until the spring when they take it with the fall starters, and some upper quarter students participate outside of the class. Of the 66 teams in this competition, 14 are non-LARC teams. We would expect 3 or 4 to make the break. 1 did. The best speakers in the upper quarters would have been selected already, in theory, which might explain this. As outliers, we ignore them for the analysis of the remaining 15 places.

There are 35 third quarter teams. If selected randomly, we would expect 10 or 11 of them to make the break. 11 of them did.
There are 16 fourth quarter teams. We would expect 4 or 5 to make the break. 4 did. There is no statistically significant difference between the two populations.

There are 18 male LARC teams. We would expect 5 or 6 of them to make the break. 6 of them did.
There are 19 mixed gender LARC teams. We would expect 5 or 6 to make the break. 6 did.
There are 14 female LARC teams. We would expect 4 or 5 to make the break. 3 did. This is still within the variation reasonably allowable by chance, and even if it weren't, you don't know whether this is correlation or causation. But to the extent you do have a choice between equally skilled male and female classmates to be your partner, it may not hurt to chose the male.

Other than frustrating the students who don't want to argue, and lose any chance of making the break after losing the first two rounds, but have to argue the last two anyway without knowing the score, it seems to work.

[Update to show record matching is better than random selection:

Situation 1:
You are the 16th best team in absolute terms.
There are four rounds.
Each round is randomly matched, without substitution.
There are 66 teams.

Therefore you have four chances in which to encounter 2 of the 15 teams better than you. The odds the first two going against you is about 1 in 20. With more chances, the odds are far greater.

Situation 2:
You are the 16th best team in absolute terms.
There are four rounds.
Each round is matched by record, randomly within tied groupings.
There are 66 teams.

Your odds of losing the first round is 15 out of 65 (or 3 out of 13). It would take a freak statistical anomaly, but at most, only 7 teams better than you could also have lost. In that event, your odds of losing the second round is at most 7 out of 32. So there is about 1 in 20 chance of losing both of the first two, but only if the universe really hates you.

In a universe that acts a little more like the odds would suggest, you're far more certain to get deserving teams making the break if you match records than do four random matchings. When you factor in later rounds the discrepancies between the two methods is more pronounced]