Not all player load equations are equivalent: Formula choice alters load magnitude and interpretation in elite football.

Abstract

Background: At least eleven distinct player load equations appear in the literature under different names across platforms. Despite sharing a common label, these formulae span fundamentally different mathematical constructs. No study has tested whether formula choice produces meaningfully different values, changes player identification, or alters positional conclusions. Purpose: This study provides the first empirical comparison of eleven player load equations applied to optical tracking data from all 64 matches of the 2022 FIFA World Cup, proposing a three-family taxonomy and validated conversion coefficients. Methods: Positional tracking data (PFF Sports; 29.97 Hz; 1,986 player-match observations) were processed under four conditions (raw, Kalman-smoothed, Butterworth 2 and 4 Hz). Eleven equations spanning three families (instantaneous magnitude, jerk-based, energy-weighted) were compared using Bland-Altman analysis and conversion modelling. Results: Within-family equations were interchangeable, differing only by a fixed scalar. Cross-family differences were substantial: instantaneous magnitude equations were 2 to 25 times larger than jerk-based equivalents, and PL_RE was structurally distinct enough that individual-level conversion is not feasible (R² = 0.290). Jerk-based equations produced near-uniform per-90 values across positions (less than 7% spread) while PL_RE produced 287%. Signal processing changed absolute values but not player ordering. Conclusions: Equation family is the primary determinant of agreement. Practitioners switching between families would identify different players as high-load and draw different positional conclusions. Conversion coefficients support harmonisation of historical datasets and the per-90 values represent the largest optical tracking PlayerLoadTM reference dataset in elite international football.