By Jeph Duarte | Pounding The Rock (PtR), 2026-08-09 19:00:00
我最近看到了这条动态。
NBA上赛季修改了规则，不再将最后一秒的超远投篮计为球员投篮不中，这极大地改变了他们的行为。
德克萨斯理工大学两位教授詹姆斯·W·肯珀 (James W. Kemper) 和诺亚·利普塔克 (Noah Liptack) 发表的一篇新研究论文发现，上赛季球员在面对这种机会时，出手比例高达94%，而在此前的十年里，这一比例仅为58%。
论文指出，在规则修改之前，最不愿意出手这类投篮的群体“集中在高效率射手和处于合同年的球员中”。 pic.twitter.com/63X248sJq6
— 迈克·沃库诺夫 (Mike Vorkunov) July 23, 2026
“NBA上赛季修改了规则，不再将最后一秒的超远投篮计为球员投篮不中，这极大地改变了他们的行为。
德克萨斯理工大学两位教授詹姆斯·W·肯珀和诺亚·利普塔克发表的一篇新研究论文发现，上赛季球员在面对这种机会时，出手比例高达94%，而在此前的十年里，这一比例仅为58%。
论文指出，在规则修改之前，最不愿意出手这类投篮的群体‘集中在高效率射手和处于合同年的球员中’。”
虽然不惩罚球员在最后一秒的投篮会带来出手次数的增加并不令人意外，但这一变化的幅度（从58%升至94%）确实相当惊人。话虽如此，这36%的增幅是跨越了十年的时间，而在那十年的早期，三分球出手还没有现在这么普遍。
作为一名数学老师，我也觉得其中的研究方法和公式非常有趣。
逐回合数据。 我们使用了2015-16赛季至2025-26赛季NBA和WNBA的ESPN逐回合数据（ESPN，2026），这些数据是通过sportsdataverse的hoopR（NBA）和wehoop（WNBA）数据包获取的（Gilani，2021；Gilani & Hutchinson，2021）。1 对于每一次球权，这些记录报告了涉及的球员、事件类型、比赛时钟、单节、即时比分以及投篮坐标。结合这些数据，我们可以重构每位进攻球员在每节最后几秒的选择，并恢复模型的统计状态变量——具体而言，即剩余时间 t、投篮距离 d 以及分差 m。
他们的结论不仅对篮球运动，而且对整个风险决策行为都提供了一个全面的视角：
“通过取消对节末投篮的个人数据惩罚，我们观察到球员的行为立即与球队的集体成功达成了近乎一致的契合。这些发现超越了篮球本身，为组织经济学提供了一个更广泛的警示：不合理的绩效评估必然会滋生策略性的规避行为。如果设计得当，消除扭曲的指标惩罚可以作为一个非常有效的杠杆，使个人激励与组织的总体目标保持一致。”
您可以在此处阅读完整的报告。
由生成式 AI 翻译，译文内容可能不准确或不完整，以原文为准。
查看原文：Open Thread: NBA’s rule change on buzzer beaters yields increase in attempts
Open Thread: NBA’s rule change on buzzer beaters yields increase in attempts
I saw this post recently.
NBA’s rule change last season to not count last second heaves as missed FGs for players had a big effect on their behavior.
A new research paper by 2 Texas Tech professors, James W. Kemper & Noah Liptack, found players took that shot 94% of the time last season after taking it 58% in the decade prior.
The paper said the most reluctance to shoot, before the rule change, was “concentrated among efficient shooters and players in contract years.” pic.twitter.com/63X248sJq6
— Mike Vorkunov (@MikeVorkunov) July 23, 2026
“NBA’s rule change last season to not count last second heaves as missed FGs for players had a big effect on their behavior.
A new research paper by 2 Texas Tech professors, James W. Kemper & Noah Liptack, found players took that shot 94% of the time last season after taking it 58% in the decade prior.
The paper said the most reluctance to shoot, before the rule change, was ‘concentrated among efficient shooters and players in contract years.’”
While it should come as no surprise that not penalizing players for last second shots led to an increase of attempts, the amount of change (58% to 94%) is quite drastic. That said, the 36% rise was over a decade, when three-point attempts were less common.
As a math teacher, I found the methodology and formulas interesting as well.
Play-by-play. We use ESPN play-by-play data (ESPN, 2026) for the NBA and WNBA
covering the 2015–16 through 2025–26 seasons, obtained via the sportsdataverse hoopR
(NBA) and wehoop (WNBA) packages (Gilani, 2021; Gilani & Hutchinson, 2021).1 For
every possession, these records report the players involved, the event type, the game clock,
the period, the running score, and shot coordinates. Together, they let us reconstruct what
each offensive player chose to do in the final seconds of a quarter and recover the model’s
statistical state variables—specifically, the time remaining t, the shot distance d, and the
score margin m.
Their conclusion offers a comprehensive overview of not just basketball, but risk-taking as a whole:
“By removing the individual statistical penalty for end-of-quarter shots, we observed an immediate, near-universal alignment of player behavior with collective team success. These findings transcend basketball, offering a broader cautionary tale for organizational economics: poorly calibrated performance evaluations inevitably breed strategic subversion. When designed correctly, eliminating distorted metric penalties serves as a highly effective lever to align individual incentives with overarching organizational goals.”
You can review the report in its entirety HERE.
By Jeph Duarte, via Pounding The Rock