When does a two-for-one yield a second possession? A Bayesian logistic analysis of NBA end-of-quarter timing

Abstract

This study examined how possession-start time and first-shot delay were associated with the probability of obtaining a second possession before quarter end. The play-by-play data were pooled across 10 NBA regular seasons (2016–17 to 2025–26). Among 44,036 possessions beginning with 30–45 s remaining, 14,436 (32.78%) had no detected field-goal attempt and could not contribute first-shot-delay information; the primary timing analysis included 28,075 possessions. A Bayesian logistic regression model was estimated with possession-start time, first-shot delay, a quadratic delay term, their interaction, and contextual controls for score margin, home status, quarter, and possession origin. Analyses showed that second-possession rates were highest when teams gained possession earlier in the window and acted quickly. For instance, the probability of the second possession is 0.928 (95% high density interval: 0.920–0.935) when the first possession is 34 s with a shot delayed by 6 s. This reduces to 0.80 (95% high density interval: 0.78–0.82) for the possession at 34 s but with a 12-s delay. Posterior estimates confirmed that possessions beginning with more time remaining generally had higher second-possession probabilities. The timing relationship was nonlinear and interactive, indicating that the effect of delay depended on when the possession began. One limitation is that the analysis relies on play-by-play rather than player-tracking data, so it does not directly observe shot quality and play design. These findings suggest that successful two-for-one execution is governed by a conditional timing structure rather than one universal rule and provide probability-based approach for evaluating end-of-quarter offensive decisions.