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.
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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.
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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.
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Read the full article here