Not all player load equations are equivalent: formula choice alters magnitude and interpretation of optical tracking-derived load in elite football

At least eleven distinct player load equations appear under different names across platforms. Despite a common label, these formulae may span different constructs. No study has tested whether formula choice produces meaningfully different values, changes player identification, or alters positional conclusions. This study provides the first systematic empirical comparison of eleven player load equations applied to optical tracking from all 64 matches of the 2022 FIFA World Cup, proposing a three-family taxonomy and validated conversion coefficients. Positional tracking data (PFF Sports; 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 within-match rank-order correlation, conversion modelling, and Bland-Altman analysis. Within-family equations were interchangeable, differing by a fixed scalar. Cross-family differences were substantial: instantaneous magnitude equations were one to two orders of magnitude larger than jerk-based equivalents, and PL_RE diverged in construct, retaining a moderate per-90 association (R2 = 0.700) but with a standard error of 93.85 AU per 90 min, about 19% of the mean, precluding player-level substitution. Jerk-based equations produced near-uniform per-90 values across positions (less than 7% spread) while PL_RE produced 287%. Filtering choice altered absolute values 65 to 85-fold but preserved player ordering. Equation family is the primary determinant of agreement. Practitioners switching families would identify different high-load players and draw different positional conclusions. Conversion coefficients support harmonising historical datasets, and the per-90 values represent the largest tracking-derived load reference dataset in elite international football.