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Ranking of Football Teams

Ranking of Football Teams. Casey Sader. Topics. Basis is Google PageRank . Perron-Frobenius Theorem. Example of problem. Started with college football, went to NFL My failure. Same as Google PageRank. Created a small, 5 site internet.

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Ranking of Football Teams

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  1. Ranking of Football Teams Casey Sader

  2. Topics Basis is Google PageRank. Perron-Frobenius Theorem. Example of problem. Started with college football, went to NFL My failure

  3. Same as Google PageRank Created a small, 5 site internet. One site didn’t go to any others. If that is the case, the value for that row is 1/n where n is the number of columns in the matrix. Can be applied to rankings of anything

  4. The Perron-Frobenius Theorem If A has nonnegative entries, then there exists nonnegative solution of Ar=λr. •If A is irreducible, then r is strictly positive and unique, and λ is simple and maximal. •r can be calculated using the power method: r=lim (A^n)(r^0)/|(A^n)(r^0)| n→∞ *exactly from The Mathematics of Ranking Schemes powerpoint by J.P. Keener

  5. Example of football teams You have team 1, team 2, team 3, team 4. Teams are on columns and rows. Name of losing team on rows, winning team on columns. Put difference in score in correct spot in entry of matrix Find total of the row and divide each entry by total. Find eigenvalues for the matrix and order from largest to smallest to decide best team

  6. College Football to NFL I started out wanting to compare college football teams and rank them to compare to BCS and other ranking systems. Became difficult because I wanted to do top 10 teams, but the problem is almost all hadn’t played each other. Switched to NFL, mainly AFC West/NFC East

  7. My Failure It took me a long time to figure out how it worked. I thought I entered values correctly but eigenvalues wouldn’t come. Why did Perron-Frobenniusnot work?-

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