This study aimed to quantify the break shot characteristics and identify their significance in predicting the game outcomes in 9-ball tournaments. The break shot of 275 frames (241 men’s, 34 women’s) of professional tournaments were analyzed from two aspects: 1) cue ball position, represented by the distance between the cue ball and the table center, and 2) ball distribution, indicated by the standard deviation of Voronoi cell areas determined from all remaining balls on the table. Spearman correlation and binary logistic regression were utilized to identify associations and to predict the frame outcomes, respectively. Results showed that the more balls falling into the pockets during the break, the more clustered the remaining balls (rs = 0.232, p < 0.001). The closer the cue ball ending towards the table center, the more balls potted in the visit immediately after the break (rs = -0.144, p = 0.027). Neither cue ball position nor ball distribution could predict table clearance or winning of a frame. In conclusion, pocketing more balls during the break is associated with more clustered balls remaining on the table. Parking the cue ball near the table center after the break can facilitate potting more balls immediately after.

中文翻译：

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一个好的破门能决定 9 球的比赛结果吗？

本研究旨在量化突破击球的特征并确定它们在预测 9 球锦标赛比赛结果中的重要性。从两方面分析了职业比赛275帧（男子241帧，女子34帧）的破发球：1）母球位置，用母球与台球台中心的距离表示；2）球分布，用从桌子上所有剩余的球确定的 Voronoi 单元格区域的标准偏差。Spearman 相关性和二元逻辑回归分别用于识别关联和预测框架结果。结果表明，在休息期间落入口袋的球越多，剩余的球越聚集（rs = 0.232，p < 0.001）。母球越靠近桌子中心，休息后立即访问中的球越多（rs = -0.144，p = 0.027）。母球位置和球分布都不能预测桌面间隙或赢得一局。总之，在休息期间将更多球放入袋中与留在桌子上的更多聚集球有关。中场休息后将母球停在桌面中心附近，可以方便随后立即装入更多球。