Entropy to the Mean: Winning Streaks Carry a Rising, Measurable Cost: Evidence from Seven Seasons of College Basketball

The hot hand literature asks whether success predicts success. This paper asks the inverse question: conditional on a team continuing to win, does the quality of its performance decay as the streak lengthens? Using 69,022 Division I versus Division I team-game rows across seven college basketball seasons, with point-in-time KenPom opponent adjustment and no future leakage, we estimate the effect of entering win-streak depth on opponent-adjusted margin residual within team-season fixed effects, with standard errors clustered on 2,306 team-seasons. The raw within-team estimate is -0.3207 points per game of depth (SE 0.0280, t = -11.5); an own-construction memoryless null, built at each team’s own rate and passed through the identical pipeline, reproduces a mechanical floor of -0.2238; the claim of this paper is the excess beyond that floor, -0.0969 per game of depth (0 of 200 null replicates as negative; lower-tail p at or below .005). The raw estimate carries a pre-registered threshold shape: flat through depths 1-2, onset near depths 3-5, deepening to roughly -3 points at depths 13 and beyond. The naive cross-team specification is opposite-signed, a rating-lag artifact the within-team design removes. The effect survives fatigue, recent-form, and opponent-preparation controls. A loss-streak placebo is opposite-signed but largely mechanical under its own null. In the decisive horse race, accumulated overperformance collapses to insignificance while duration survives. A pre-registered, hash-locked one-shot replication on the held-out 2021-22 season passes both frozen criteria (coefficient -0.4169, t = -4.6). A validated tennis instrument returns a concordant phase-tier residual in two universes, and an EPL construction replicates enter-depth compression locally. The duration-burden interpretation is [supported]; the causal mechanism is [open]; two pre-registered composition tests remain open and gate the strongest public version of the claim.