Theorem
When Vanderbilt is ranked in the top 25 of the AP and ESPN/USAToday polls, they lose to quality (RPI Top 100) but inferior teams.
Examples of Proof
After beating Lipscomb and St. Mary's to open the season, Vanderbilt found itself included among the top 25 in both polls. The first game upon being ranked, Vandy loses to Cincinnati, an inferior team (according to current kenpom, sagarin, and rpi). Later in the season, upon being ranked, Vandy faced off against Illinois and Western Kentucky. Vandy loses to both teams, fulfilling the requirements of the theorem.
Analysis
Commodore fans should be very thankful that Vanderbilt ended up "just outside" the top 25 this week, as they face an Auburn team more than capable of pulling off the upset (provided they shoot lights out).
Corollary
When Vanderbilt is ranked in the top 25 of the AP and ESPN/USAToday polls, they beat quality but superior (kenpom, sagarin, rpi, ap, espn/usatoday) opponents.
Examples of Proof
None
Analysis
Hopefully should Vanderbilt be victorious against an overmatched Auburn team, the war of attrition that takes place in the polls will vault Vanderbilt into the rankings for the first time since December, just in time for a week of road trips to Knoxville and Lexington to take on two opponents that certainly qualify for examples as proof for the corollary.
Stay tuned.