Project Descriptions 2014

(Image from Wikimedia Commons.)

Draft Strategies

Dr. Bill Schellhorn

Professional sports leagues conduct drafts in which teams select players to improve their existing rosters.  In many leagues, teams select players in a predetermined order during each round, for example in the National Football League draft.  But other player acquisition scenarios play out more like an auction, for instance the free agency market in Major League Baseball.

The general setup here is that there are m entities (teams) that have agreed to select n objects (players) according to some system (draft).  The aim of each team is to maximize the value of the objects that it acquires.  The challenge is that the following factors may be known or unknown, or may stay fixed or change:

  • the draft strategies employed by the teams; and
  • the valuation of players by the teams.

The overarching theme of this project is to analyze different drafting strategies in various types of drafts.  Our methods will involve:

  • mathematical modeling;
  • computer simulations;
  • game theory; and
  • probability and statistics.

We will use technology in almost every facet of this project.  Therefore all members of this research group must be willing to learn new software and write some computer code.  Previous programming experience is not required, however.

We will start the project by reproducing the results in the articles below with the goal of expanding upon them.

References

  • Fry, Michael J., Andrew W. Lundberg, and Jeffrey W. Ohlmann. “A player selection heuristic for a sports league draft.” Journal of Quantitative Analysis in Sports 3.2 (2007).
  • Chakravarthy, Papa. “Optimizing draft strategies in fantasy football.” Harvard Sports Analysis Collective.

Collective Behavior in Complex Systems

Dr. Aaron Santos

In nature, relatively simple interactions often lead to intricate self-assembled patterns. Snowflakes, ripples in sand, stock price time series graphs, striped nanoparticles, and even life itself can be described as emergent phenomena that arise from simple interactions. “Complex systems” is a new field in which one studies how the mathematical relationships between individual components of a system give rise to that system’s collective behavior.

Computational modeling is one method of predicting the unique patterns that emerge from biological, soft-matter, and other complex systems. We will use simple models in conjunction with statistical methods and simulations to predict what patterns will form when a given set of objects is allowed to interact.  Possible topics include:

  • The assembly of DNA nanostructures [1,2]
  • Forest fires, traffic jams, and other self-organized critical phenomena [3,4]
  • Econophysics (i.e. the physics of economics) [5,6]

References

  1. A T Santos and W Klein 2013 J Phys A: Math Theor 46 415002
  2. A Santos, J A Millan, and S C Glotzer 2012 Nanoscale 4 2640
  3. B.Drossel and F Schwabl 1992 Phys Rev Lett 69 1629
  4. K Nagel and H J Herrmann 1992 Physica A 122 254
  5. A Chakrabortia, I M Tokea, M Patriarcabc, and F Abergela 2011 Quant Financ 11 991
  6. A Chakrabortia, I M Tokea, M Patriarcabc, and F Abergela 2011 Quant Financ 11 1013