Volume 3, Issue 2

Division 1-A college football adopted overtime rules in 1996. There have been 328 overtime games since, and only four times have coaches opted to go on offense first upon winning the coin toss. Thus, there is an accepted belief that starting on defense first is advantageous, as validated by surveying college coaches. This study examines past game data to analyze whether there is truly an advantage to being on defense first. Results show some support for this idea, but that there may also be situations where not following the defense first strategy is worthwhile. Implications to coaches are discussed.

Rating -- and subsequently ranking -- college football teams requires making sense of sometimes conflicting pair-wise comparisons. Classical statistical techniques fall into one of two classes: win/loss models, which focus on binary outcomes, and point-scoring models, which consider the distribution of component scores. Annis and Craig (2005) illustrate deficiencies of both, and propose a hybrid method that considers both sources of data. Their method, while providing satisfactory results in many circumstances, can be difficult to implement numerically. This paper presents a refinement of their hybrid rating algorithm which preserves their original intent but simplifies greatly its implementation. Like its predecessor, the new model enjoys robustness to model misspecification, while offering substantial simplification.

This article describes a new strategy for objectively quantifying the performance exhibited by each and every team as derived from that year’s games. When applied to the last sixteen seasons of division I-A college football, one can readily observe a strong correlation between the final rankings computed using this new strategy and the combined average ranking of the weekly polls administered by the Associated Press (AP) and USA Today (since 1991, and by the United Press International – UPI – before then). The nearly identical ordering of the top teams in these two rankings after all the post season bowl games have concluded, and the similarity of these rankings before the bowl games were played the past eight seasons, i.e. the "BCS years", are submitted here as evidence for the validity of this strategy.

Major League Baseball's geographic line-up essentially was constant between 1903 and 1953, when the Boston Braves moved to Milwaukee and the new publicly financed stadium built on their behalf. Other MLB teams moved prior to the 1954, 1955, 1958, 1961, 1968, 1970, 1972, and 2005 seasons. In addition to team relocation, MLB has added new teams several times since 1950. The first expansion occurred in 1961, in response to the threat of a proposed third league, with the addition of the Los Angeles Angels and a new incarnation of the Washington Senators. Subsequent MLB expansion occurred in 1962, 1969, 1977, 1993 and 1998. What had been sixteen-team league in 1960 grew to thirty franchises by 2006, an increase of 87.5%. While there has been relatively little academic study of the effects of team relocation, "conventional wisdom" holds that MLB league expansion leads to distribution of the available baseball talent across more teams, and that the thinning of talent has a greater negative effect on quality of pitching than on hitting. Furthermore, it is widely believed that competitive balance is reduced for at least the first year following expansion. This paper analyzes the effects of MLB expansion and team relocation between 1950 and 2004 on trends in game attendance, within-season competitive balance, and the balance between offense and defense. This is done by testing a series of time-series "shock" models on a comprehensive statistical data set assembled from The Baseball Archive and number of other sources. The models consider the effects of relocation and expansion shocks of differing relative magnitudes, while controlling for changes in MLB’s population coverage, the effects of new stadia, and the consequences of labor strife. Taking these controls into account, team relocation was found to have a depressing effect on the trend of increasing average MLB attendance per home date during 1950-2004, but not on competitive balance, or on the balance between offense and defense. League expansion was found to have no net effect on trends in average MLB home date attendance, or the balance between offense and defense. However, expansion was found to depress growth in home date attendance for incumbent (i.e., non-expansion) teams, to reduce competitive balance, and to set back the trend of increasing of average team fielding percentage. The reduction in competitive balance in expansion years was found to hold across all teams, as well as among incumbent teams only.

Sports leagues conduct new player entry drafts in which franchises select, in a pre-determined order, players to complement their existing rosters. We model the decision-making process of a single sports franchise during a player selection draft. The basic premise of our model is that a team selects a particular player based on a combination of the player's estimated value, the value of the other players currently available, and the team's need at each position. We first conceptualize a sports league draft using a stochastic dynamic program. However, this formulation is not directly solvable for practical-sized problems due to the overwhelming computational complexity. Therefore, we introduce additional assumptions and restrictions that result in a tractable deterministic dynamic program. We implement the model within a spreadsheet-based decision support system that allows the user to compute solutions under a variety of conditions. To benchmark our approach, we perform computational comparisons against several competing draft strategies in a series of simulated fantasy football drafts for the 2005 season. With perfect information regarding opposing teams' selections, our drafting strategy dominates these competing strategies. With imperfect information, there are draft instances in which our method is not guaranteed to dominate an alternate strategy; however, our drafting strategy outperforms the competing strategies on average and is more robust on the instances tested. Furthermore, we demonstrate that the decision-maker can incorporate information regarding the drafting behavior of opposing teams to improve the performance of our method.