No abstract

Coaches in basketball often need to know how specific rotation line-ups perform in either offense or defense and choose the most efficient formation, according to their specific needs. In this research, a sample of 1131 ball possession phases of Greek Basket League was utilized, in order to estimate the offensive and defensive performance of each formation. Offensive and defensive ratings for each formation were calculated as a function of points scored or received, respectively, over possessions, where possessions were estimated using a multiple regression model. Furthermore, a Markov chain model was implemented to estimate the probabilities of the associated formation’s performance in the long run. The model could allow us to distinguish between overperforming and underperforming formations and revealed the probabilities over the evolution of the game, for each formation to be in a specific rating category. The results indicated that the most dominant formation, in terms of offense, is Point Guard-Point Guard-Small Forward-Power Forward-Center, while defensively schema Point Guard-Shooting Guard-Small Forward-Center-Center had the highest rating. Such results provide information, which could operate as a supplementary tool for the coach’s decisions, related to which rotation line-up patterns are mostly suitable during a basketball game.

The objective of this study is to contribute to the discussion on the impact of dwelling satisfaction aspects (size, standard, layout, appearance/aesthetics, well-being, cost and area/neighbourhood) and perceived indoor environmental quality (thermal comfort, air quality, satisfaction with daylight and acoustic comfort) on occupants’ overall satisfaction. This article uses data from the Swedish National Survey, BETSI (2007/08). The results are representative of adults living in multi-family and single-family buildings (1597 responses/955 buildings). Linear regression models are developed with overall satisfaction as the dependent variable and independent variables: seven satisfaction aspects, four indoor environmental quality factors and all combined (eleven). An all-model explained 54.7% of the results (best performed). All the retained variables (except satisfaction with daylight) are statistically significant predictors. Satisfaction with well-being (b = 0.286) and satisfaction with dwellings’ standard (b = 0.188) have the greatest effect on overall satisfaction. The model with the IEQ aspects explained only 35.5% of the results. Reliability statistics (Cronbach’s alpha) and confirmatory factor analysis have been implemented in the dataset. The responses can be categorized into two clusters. The two clusters were significantly different across living duration, dwelling type, age category and tenure status.

Semi-Markov processes generalize the Markov chains framework by utilizing abstract sojourn time distributions. They are widely known for offering enhanced accuracy in modeling stochastic phenomena. The aim of this paper is to provide closed analytic forms for three types of probabilities which describe attributes of considerable research interest in semi-Markov modeling: (a) the number of transitions to a state through time (Occupancy), (b) the number of transitions or the amount of time required to observe the first passage to a state (First passage time) and (c) the number of transitions or the amount of time required after a state is entered before the first real transition is made to another state (Duration). The non-homogeneous in time recursive relations of the above probabilities are developed and a description of the corresponding geometric transforms is produced. By applying appropriate properties, the closed analytic forms of the above probabilities are provided. Finally, data from human DNA sequences are used to illustrate the theoretical results of the paper.

In basketball, the offensive movements on both strong and weak sides and tactical behavior play major roles in the effectiveness of a team’s offense. In the literature, studies are mostly focused on offensive actions, such as ball screens on the strong side. In the present paper, for the first time a second-order Markov model is defined to evaluate players’ interactions on the weak side, particularly for exploring the effectiveness of tactical structures and off-ball screens regarding the final outcome. The sample consisted of 1170 possessions of the FIBA Basketball Champions League 2018–2019. The variables of interest were the type of screen on the weak side, the finishing move, and the outcome of the shot. The model incorporates partial non-homogeneity according to the time of the execution (0–24″) and the quarter of playtime, and it is conditioned on the off-ball screen type. Regarding the overall performance, the results indicated that the outcome of each possession was influenced not only by the type of the executed shot, but also by the specific type of screen that took place earlier on the weak side of the offense. Thus, the proposed model could operate as an advisory tool for the coach’s strategic plans.