Volume 4, Issue 3

New Growth Theory is the science of research, knowledge, and designs. The foundation of New Growth Theory is that technological change, improvement in the instructions for mixing resources, lies at the heart of growth and improvement. Designs are the instructions that turn resources into useful things. The combination of professional baseball history and professional football history teaches us that growth in the National Football League (NFL) springs from better designs such as the Green Bay Packers' power sweep and the San Francisco 49ers' rhythm passing. This paper demonstrates that although football design architectures differ, the outcome of all useful designs is identical: The creation of the same non-rival 2-to-1 edge that the pitcher and catcher (the battery) continuously enjoy over a hitter in baseball. This paper's main conclusions are that, at maximum efficiency, NFL coaching research accounts for more than 25% of the team's efficiency and superior human capital engaged in production (playing) accounts for less than 15% of efficiency. In other words, research and play design contributes more to an NFL team's efficiency than play-making contributes. An NFL growth rate is equal to the productivity of a coaching staff’s research and represents a directional vector. If an NFL team’s growth rate is greater than 100%, it is likely the team is getting better continuously. Such an improving NFL team will generate increasing returns and enjoy an absolute competitive edge over competitors whose research productivity is less than or equal to 100%. Super Bowl results demonstrate that an NFL team that can sustain such growth and avoid turnovers is virtually unbeatable.

The majority of statistical work on college football's Bowl Championship Series (BCS) has involved proposing or categorizing computer ratings of teams. Computer algorithms, a coaches' poll, and a media poll make up the three ratings systems that are currently equally weighted to produce an overall BCS rating, which ultimately determines which schools will compete in lucrative post-season BCS bowls. We focus on investigating the performance of the BCS as implemented for the 2004, 2005, and 2006 seasons to determine whether equal weights are appropriate. Our Bayesian analysis shows that while the posterior mode places more than half the weight on the media poll, the 95% HPD credible interval contains the equally-weighted scheme. We relate our work to the ongoing controversies over the BCS.

This paper begins with a thorough review of previous quantitative literature dedicated to the development of ratings for college and professional football teams, and also considers various methods that have been proposed for predicting the outcomes of future football games. Building on this literature, the paper then presents a straightforward application of linear modeling in the development of a predictive model for the outcomes of college football bowl games, and identifies important team-level predictors of actual bowl outcomes in 2007-2008 using real Football Bowl Subdivision (FBS) data from the recently completed 2004-2006 college football seasons. Given that Bowl Championship Series (BCS) ratings are still being used to determine the teams most eligible to play for a national championship and a playoff system for determining a national champion is not yet a reality, the predictive model is then applied in a novel method for the calculation of ratings for selected teams, based on a round-robin playoff scenario. The paper also considers additional possible applications of the proposed methods, and concludes with current limitations and directions for future work in this area.

Introduction: The Mitchell Report to the Commissioner of Baseball sought to characterize the extent to which the use of performance enhancing drugs (PEDs) proliferated through baseball during the last 15 years. While the Report was not primarily initiated to expose individual players, it nonetheless contained detailed accounts of alleged PED abuse by 89 current and former players including seasons in which the abuse occurred and type of abuse (steroids or human growth hormone (HGH)). Previous analyses have largely focused on the impact of PED abuse on individual players (Barry Bonds and Roger Clemens, for instance). The present study integrates data from the Mitchell Report to make inferences about the overall effects of PED abuse on offensive production.Methods: The Lahman database was queried for all offensive seasons from 1995 to 2007 (minimum 50 PA, no pitchers). Runs created per 27 outs (RC27) was used as an estimate of the offensive production of a player in a season. An adjusted RC27 (ADJRC27) was obtained by accounting for career progression effects to reduce the influence of the expected change in performance over time due to age. Information from the Mitchell Report identified each player season as a PED season or a non-PED season. General linear mixed effects models were constructed that modeled ADJRC27 as a function of PED use (Yes or No). Multiple models were considered to assess the PED effect under various assumptions.Results: The baseline model estimated a mean non-steroid ADJRC27 during the study period of 4.58. The effect of steroid use was an additional 0.58 ADJRC27, an increase in production of 12.6% (p=0.0108). Additional models considered the effect of being a player mentioned in the Mitchell Report, adjustments for baseline performance, and the influential effect of Barry Bonds' performance. The estimated steroid effect ranged from 3.9% to 18.0% among twelve different models. Similar analysis of HGH use showed no evidence of performance improvement.Conclusions: This analysis suggests a significant and substantial performance advantage for players who used steroids during the study period. It is estimated that offensive production increased approximately 12% in steroid users versus non-users. This analysis represents the first attempt to quantify the overall effect of PED abuse on offensive performance in baseball.

Recently it was reported that in the NBA as a whole, two thirds of the home advantage which teams enjoy when playing at home is accumulated in the first quarter. Home advantage can also be determined for individual teams, and there is good reason for doing so. For example, the relation of home advantage to team statistics such as assists, rebounds, and turnovers can be studied team-specifically but not in the league as a whole. Before any such project is undertaken, however, a major technical problem must be addressed. Formally, team-specific home advantage is a difference score between positively correlated variables (games won at home minus games won away), and difference scores are notoriously unreliable. This unreliability, moreover, is not just an empirical generalization. There is a formal basis for it in the theory of mental tests. This study reports that over a four-year period in the NBA the estimated reliability of team-specific home advantage was 0.284, even though the estimated reliabilities of games won at home and games won away were 0.772 and 0.833 respectively. The implications for research on home advantage are discussed.

This paper sets out to estimate univariate time series models on a selected set of offensive baseball measures from 1901 to 2005. The measures include homeruns, bases on balls, runs batted in, doubles, and stolen bases. The paper next estimates the trends in these statistics simultaneously using a vector autoregressive time series model. Along the way, tests of assumptions underlying the time-series models are provided. Univariate time series results suggest that simple lag--1 models fit these offensive statistics quite well. The multivariate results show that a simple lag--1 vector autoregressive model also fits quite well. The results of the vector time series model indicate that most statistics are strongly predicted by their prior values. However, certain temporal dependencies among baseball measures are observed, suggesting the importance of examining covariation in baseball data over time.

In many sport competitions athletes, teams, or countries are evaluated based on several variables. The strong assumptions underlying traditional 'linear weight' scoring systems (that the relative importance, interactions and linearizing transformations of the variables are known) can often not be justified on theoretical grounds, and empirical `validation' of weights, interactions and transformations, is problematic when a `gold standard' is lacking. With µ-scores (u-scores for multivariate data) one can integrate information even if the variables have different scales and unknown interactions or if the events counted are not directly comparable, as long as the variables have an `orientation'. Using baseball as an example, we discuss how measures based on µ-scores can complement the existing measures for `performance' (which may depend on the situation) by providing the first multivariate measures for `ability' (which should be independent of the situation). Recently, µ-scores have been extended to situations where count variables are graded by importance or relevance, such as medals in the Olympics (Wittkowski 2003) or Tour-de-France jerseys (Cherchye and Vermeulen 2006, 2007). Here, we present extensions to `censored' variables (life-time achievements of active athletes), penalties (counting a win more than two ties) and hierarchically structured variables (Nordic, alpine, outdoor, and indoor Olympic events). The methods presented are not restricted to sports. Other applications of the method include medicine (adverse events), finance (risk analysis), social choice theory (voting), and economy (long-term profit).