Bradley-Terry Rankings: Introduction to Logistic Regression

In a recent post, we identified the Colley Matrix methodology for ranking NBA teams. The methodology provided insight but abused the originating statistical construct in an effort to enforce a correlated, solvable, set of equations to identify a “probability” of winning. Unfortunately, we witnessed that not only were those statistical assumptions violated, but the resulting…

Statistics of Colley’s Ranking Methodology

In 2002, Wes Colley (Princeton) developed a methodology that became a part of College Football BCS rankings lore: The Colley Method. In his original paper, Colley claims that his method is “bias free” for estimating the ranking of a team given a particular schedule. The resulting values for each team is identified as a ranking…

Breaking Down Player Efficiency Rating

Warning: Lots of Math Ahead… With the introduction of Player Efficiency Rating (PER), John Hollinger constructed a methodology for comparing the relative accomplishments of players across leagues, as well as across years. While being commonly viewed as complex and unidentifiable, the idea is relatively simple: produce a value for each player such that it captures their personal…

Markov Simulation: NBA Playoffs

With the NBA Playoffs set to get underway, we take a quick look at the probabilities for each team becoming the NBA Champions. Common consensus would place any combination of the five strongest teams: Golden State – Houston – San Antonio versus Cleveland – Boston. But the question is how likely? To answer that, we…