From discrete classification to continuous space: compositional analysis reveals training intensity distribution migration across competition cycles in competitive swimmers

Introduction Training intensity distribution (TID) is usually summarized by discrete types (pyramidal, PYR; polarized, POL; threshold, THR; low-intensity, LOW). The three zone proportions form a composition, but discrete labels do not capture changes in relative zone allocation within compositional space. We described weekly heart-rate zone compositions as points in a continuous compositional space and examined their migration across preparation cycles. Methods Heart rate was recorded in 25 competitive swimmers over four competition-preparation cycles (P1–P4), giving 1,202 athlete-weeks (84.4% of potential weeks). Time in three zones defined by fixed percentages of estimated maximum heart rate was expressed in isometric log-ratio coordinates (1,173 weeks, after excluding weeks with time in the lowest zone only). Cycles were compared at the athlete level, with one centroid per athlete per cycle, by paired sign-flip permutation tests with Bonferroni correction. Results PYR was the most frequent type in every cycle (80.3–85.7% of weeks). The cohort centroid of P3 lay toward higher Z2 and Z3 than that of P1 (Aitchison distance 0.717, standardized effect 0.82, p = 0.0002) and that of P2 (0.495, 0.60, p = 0.0019); no other comparison was significant. Both differences remained significant under all alternative zero treatments, zone definitions and interpolation limits; with a minimum number of recorded sessions per week, the P2–P3 difference was not significant at the strictest minimum. The size of the migration depended on how weeks without Z3 time were treated. Among PYR weeks alone, the P1–P3 migration was in the same direction in 22 of 25 athletes, but the evidence was weaker. Conclusion The recorded heart-rate zone composition migrated between preparation cycles while the most frequent discrete type stayed the same. Compositional coordinates give the position and displacement of a week or cycle and can complement discrete TID types in longitudinal monitoring; their relation to training prescription, adaptation and performance remains to be examined.