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. 2017 Jul 25;12(7):e0181781.
doi: 10.1371/journal.pone.0181781. eCollection 2017.

The relationship between movement speed and duration during soccer matches

Kai Roecker  1   2 , Hubert Mahler  1   2 , Christian Heyde  1   2   3 , Mareike Röll  1 , Albert Gollhofer  2
Affiliations

The relationship between movement speed and duration during soccer matches

Kai Roecker et al. PLoS One. .

Abstract

The relationship between the time duration of movement (t(dur)) and related maximum possible power output has been studied and modeled under many conditions. Inspired by the so-called power profiles known for discontinuous endurance sports like cycling, and the critical power concept of Monod and Scherrer, the aim of this study was to evaluate the numerical characteristics of the function between maximum horizontal movement velocity (HSpeed) and t(dur) in soccer. To evaluate this relationship, GPS data from 38 healthy soccer players and 82 game participations (≥30 min active playtime) were used to select maximum HSpeed for 21 distinct t(dur) values (between 0.3 s and 2,700 s) based on moving medians with an incremental t(dur) window-size. As a result, the relationship between HSpeed and Log(t(dur)) appeared reproducibly as a sigmoidal decay function, and could be fitted to a five-parameter equation with upper and lower asymptotes, and an inflection point, power and decrease rate. Thus, the first three parameters described individual characteristics if evaluated using mixed-model analysis. This study shows for the first time the general numerical relationship between t(dur) and HSpeed in soccer games. In contrast to former descriptions that have evaluated speed against power, HSpeed against t(dur) always yields a sigmoidal shape with a new upper asymptote. The evaluated curve fit potentially describes the maximum moving speed of individual players during the game, and allows for concise interpretations of the functional state of team sports athletes.

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Conflict of interest statement

Competing Interests: I have read the journal's policy and the authors of this manuscript have the following competing interests: KR is scientific consultant for Adidas and is owner of a software company (ergonizer.com) for performance diagnostics. HM and MR receive research grants of Adidas. CH is an employee of Adidas. AG is scientific consultant for Adidas. This does not alter our adherence to PLOS ONE policies on sharing data and materials. The commercial affiliation of author KR to ergonizer.com did not play a role in the study.

Figures

Fig 1
Fig 1. HSpeed results overview.
Quantile statistics (boxplots) for the maximal horizontal moving speeds (Hspeed, blue) and HSpeed weighted by acceleration (red) for the 21 calculated time durations (tdur, from Eq 3).
Fig 2
Fig 2. Residuals of the seven evaluated fitting equations.
The differences between the measured and the predicted values against the mean between both are shown. Only the Richards' Logistic 5P equation (Eq. 8, S1 Appendix) does not display a systematic deviation from the measurements. For further descriptions of the applied equations, see the S1 Appendix.
Fig 3
Fig 3. Groups of power-profile curve fittings.
(A) All fitting results. (B) Fitting results grouped by gender (blue: male, red: female). (C) Fitting results grouped by team (red: Team A, green: Team B, blue: Team C). (D) Fitting results of all female participants, grouped by position (red: Central Defenders, green: Central Midfielders, blue: External Midfielder, orange: Full-Backs, cyan: Strikers). (E) Fitting results of all male participants, grouped by position (red: Central Defenders, green: Central Midfielders, blue: External Midfielder, orange: Full-Backs, cyan: Strikers). HSpeed was log-transformed for better clarity in all cases. The close-ups in (D) and (E) show the upper and the lower part of the fittings, respectively.
Fig 4
Fig 4. Independence of the lower against the upper asymptotes.
A linear (Pearson) correlation between parameters c and d from all individual measurements is given (r2 = 0.04).
Fig 5
Fig 5. Graphical description of the fitting parameters.
The five parameters within the favored fitting model for the relationship between HSpeed and tdur (Eq. 8, S1 Appendix). Small open circle symbols (o) are from real results for one participant in one game.
See this image and copyright information in PMC

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