Effects of season period, team quality, and playing time on basketball players' game-related statistics

The aim of this study was to identify within-season differences in basketball players' game-related statistics according to team quality and playing time. The sample comprised 5309 records from 198 players in the Spanish professional basketball league (2007-2008). Factor analysis with principal components was applied to the game-related statistics gathered from the official box-scores, which limited the analysis to five factors (free-throws, 2-point field-goals, 3-point field-goals, passes, and errors) and two variables (defensive and offensive rebounds). A two-step cluster analysis classified the teams as stronger (69 ± 8 winning percentage), intermediate (43 ± 5 winning percentage), and weaker teams (32 ± 5 winning percentage); individual players were classified based on playing time as important players (28 ± 4 min) or less important players (16 ± 4 min). Seasonal variation was analysed monthly in eight periods. A mixed linear model was applied to identify the effects of team quality and playing time within the months of the season on the previously identified factors and game-related statistics. No significant effect of season period was observed. A team quality effect was identified, with stronger teams being superior in terms of 2-point field-goals and passes. The weaker teams were the worst at defensive rebounding (stronger teams: 0.17 ± 0.05; intermediate teams: 0.17 ± 0.06; weaker teams: 0.15 ± 0.03; P = 0.001). While playing time was significant in almost all variables, errors were the most important factor when contrasting important and less important players, with fewer errors being made by important players. The trends identified can help coaches and players to create performance profiles according to team quality and playing time. However, these performance profiles appear to be independent of season period.

Modified CADF and CIPS panel unit root statistics with standard chi-squared and normal limiting distributions

In an influential paper Pesaran ('A simple panel unit root test in presence of cross-section dependence', Journal of Applied Econometrics, Vol. 22, pp. 265-312, 2007) proposes two unit root tests for panels with a common factor structure. These are the CADF and CIPS test statistics, which are amongst the most popular test statistics in the literature. One feature of these statistics is that their limiting distributions are highly non-standard, making for relatively complicated implementation. In this paper, we take this feature as our starting point to develop modified CADF and CIPS test statistics that support standard chi-squared and normal inference.