IMPORTANCE American football is the largest participation sport in US high schools and is a leading cause of concussion among adolescents. Little is known about the long-term cognitive and mental health consequences of exposure to football-related head trauma at the high school level.OBJECTIVE To estimate the association of playing high school football with cognitive impairment and depression at 65 years of age. DESIGN, SETTING, AND PARTICIPANTSA representative sample of male high school students who graduated from high school in Wisconsin in 1957 was studied. In this cohort study using data from the Wisconsin Longitudinal Study, football players were matched between March 1 and July 1, 2017, with controls along several baseline covariates such as adolescent IQ, family background, and educational level. For robustness, 3 versions of the control condition were considered: all controls, those who played a noncollision sport, and those who did not play any sport.EXPOSURES Athletic participation in high school football. MAIN OUTCOMES AND MEASURESA composite cognition measure of verbal fluency and memory and attention constructed from results of cognitive assessments administered at 65 years of age. A modified Center for Epidemiological Studies' Depression Scale score was used to measure depression. Secondary outcomes include results of individual cognitive tests, anger, anxiety, hostility, and heavy use of alcohol. RESULTS Among the 3904 men (mean [SD] age, 64.4 [0.8] years at time of primary outcome measurement) in the study, after matching and model-based covariate adjustment, compared with each control condition, there was no statistically significant harmful association of playing football with a reduced composite cognition score (-0.04 reduction in cognition vs all controls; 97.5% CI, -0.14 to 0.05) or an increased modified Center for Epidemiological Studies' Depression Scale depression score (-1.75 reduction vs all controls; 97.5% CI, -3.24 to -0.26). After adjustment for multiple testing, playing football did not have a significant adverse association with any of the secondary outcomes, such as the likelihood of heavy alcohol use at 65 years of age (odds ratio, 0.68; 95% CI, 0.32-1.43). CONCLUSIONS AND RELEVANCECognitive and depression outcomes later in life were found to be similar for high school football players and their nonplaying counterparts from mid-1950s in Wisconsin. The risks of playing football today might be different than in the 1950s, but for current athletes, this study provides information on the risk of playing sports today that have a similar risk of head trauma as high school football played in the 1950s.

We propose a Bayesian procedure for simultaneous variable and covariance selection using continuous spike-and-slab priors in multivariate linear regression models where q possibly correlated responses are regressed onto p predictors. Rather than relying on a stochastic search through the high-dimensional model space, we develop an ECM algorithm similar to the EMVS procedure of Ročková & George (2014) targeting modal estimates of the matrix of regression coefficients and residual precision matrix. Varying the scale of the continuous spike densities facilitates dynamic posterior exploration and allows us to filter out negligible regression coefficients and partial covariances gradually. Our method is seen to substantially outperform regularization competitors on simulated data. We demonstrate our method with a re-examination of data from a recent observational study of the effect of playing high school football on several later-life cognition, psychological, and socio-economic outcomes.

Traditional NBA player evaluation metrics are based on scoring differential or some pace-adjusted linear combination of box score statistics like points, rebounds, assists, etc. These measures treat performances with the outcome of the game still in question (e.g. tie score with five minutes left) in exactly the same way as they treat performances with the outcome virtually decided (e.g. when one team leads by 30 points with one minute left). Because they ignore the context in which players perform, these measures can result in misleading estimates of how players help their teams win. We instead use a win probability framework for evaluating the impact NBA players have on their teams' chances of winning. We propose a Bayesian linear regression model to estimate an individual player's impact, after controlling for the other players on the court. We introduce several posterior summaries to derive rank-orderings of players within their team and across the league. This allows us to identify highly paid players with low impact relative to their teammates, as well as players whose high impact is not captured by existing metrics.

Since the advent of high-resolution pitch tracking data (PITCHf/x), many in the sabermetrics community have attempted to quantify a Major League Baseball catcher's ability to "frame" a pitch (i.e. increase the chance that a pitch is called as a strike). Especially in the last three years, there has been an explosion of interest in the "art of pitch framing" in the popular press as well as signs that teams are considering framing when making roster decisions.We introduce a Bayesian hierarchical model to estimate each umpire's probability of calling a strike, adjusting for pitch participants, pitch location, and contextual information like the count. Using our model, we can estimate each catcher's effect on an umpire's chance of calling a strike. We are then able to translate these estimated effects into average runs saved across a season. We also introduce a new metric, analogous to Jensen, Shirley, and Wyner's Spatially Aggregate Fielding Evaluation metric, which provides a more honest assessment of the impact of framing.