The No Score Penalty in Association Football

This paper evaluates a modification of the 3-1-0 league points system in which a team loses c pointswhenever it finishes a match without scoring. The proposed benchmark is c = 0.5. The rule gives a firstgoal value even when the team still loses, but is strategically equivalent to a same-sized first-goal bonusunder appropriate constant translations. The analysis combines algebraic incentive conditions,fixed-score re-scoring of 7,600 English Premier League matches from 2006/07 to 2025/26, an illustrativedynamic game, and descriptive event data. At c = 0.5, re-scoring changes the champion in two of twentyseasons, top-four membership in three, and relegation membership in two; the mean gap betweenseventeenth and eighteenth increases from 3.40 to 3.725 points. In an assumed low-cost scenario, thedynamic model increases the probability that a team trailing 0-2 at minute 80 scores before full time from13.09% to 19.01%, whereas the baseline cost produces no change. A full-season event audit verifies all380 matches and all 9,908 shot xG fields for 2015/16. These historical observations describe existingincentives rather than identify reform effects. The findings establish a conditional mechanism and ameasurable trade-off with ranking stability, not a demonstrated increase in goals or entertainment. Amatched-payoff experiment is proposed to test penalty versus bonus framing separately