Early marathon running metrics from inertial measurement units predict significant pace reduction

Marathon runners occasionally experience significant pace reduction in the latter stages of races, a phenomenon known as "hitting the wall". This study aimed to develop an interpretable model to predict this performance decline using biomechanical variables collected during the early stages of marathons. We analyzed data from 1,437 runners collected during official marathon events held in Japan from August 2022 to May 2025. Biomechanical variables were measured using inertial measurement unit attached to the runners' lower back. "Hitting the wall" was defined as maintaining a pace exceeding 125% of the average pace from 5 to 20 km continuously for more than 5 km after the 25 km point. Conversely, runners were classified as "NOT hitting the wall" if their pace remained less than 110% of the average pace for more than 10 km. Cases not meeting either criterion were excluded from analysis, resulting in 306 positive cases and 359 negative cases. We applied functional principal component analysis to efficiently handle time-series data and developed a functional logistic regression model using data from the first half of marathons to predict the severe pace reduction. Our model achieved 73.9% accuracy, 75.8% recall, and 70.1% precision. Analysis of coefficient functions in the functional logistic regression model revealed that step length, ground contact time, and vertical stiffness were the strongest predictors of subsequent performance decline. The identified biomechanical signatures could inform personalized training strategies aimed at preventing the "hitting the wall" phenomenon during marathon races.