1. Introduction
The application of new technologies has resulted in the evolution of performance analysis providing appropriate means to track, capture and analyse movement characteristics of soccer players [
1]. Many performance variables are routinely captured during match-play/training, helping determine player activity and assess individual player performance profiles to design personalised and novel training approaches [
2,
3,
4]. Match-analysis observations have extensively reported that soccer players typically cover 9–14 km during a game with high-intensity running between 5 and 15%, and running speeds are used as the main parameter for the classification of soccer activity [
5,
6,
7]. Moreover, focusing on running speeds, which comprise of continual changes in speed and direction, is not deemed appropriate for soccer [
8,
9], and it has therefore been suggested that using “critical” metabolic power (MP) derived from a variable-speed activity is more suitable [
10,
11]. Thus, attributing a specific metabolic demand related to acceleration and deceleration actions, such as expanding on the description of gameplay with an energetic approach, appears most useful for this purpose [
12,
13,
14].
However, the metabolic demand imposed by soccer match-play and training estimates is calculated from energy cost paradigms derived from laboratory models of constant-speed linear running that do not reflect the totality of soccer-related actions [
13]. To effectively measure the energy cost of constant-speed linear-running (C
r) in soccer
, several factors influence the accuracy of energy cost (C) determination [
15]. First, the original algorithms were based on running on a compact terrain (e.g., a treadmill; [
16,
17]). Second, running on a grass surface and also the appropriateness of the footwear has been shown to elevate C
r by ~30% and impact kinematics, respectively, when compared to running on a dense terrain [
18]. Third, fitness levels have been shown to influence C
r as running economy can easily be improved through training [
19,
20], with research on professional soccer players showing a higher C
r by 14% from pre-season compared to in-season [
21].
Osgnach et al. [
13] based their MP equation on the research conducted by Minetti et al. [
17] and added the Pinnington and Dawson [
18] correction, which consists of a multiplication term of 1.29 (KT = 1.29) to reflect the difference between running on a treadmill and grass. However, the incorporation of this multiplication term may impact the accurate determination of the C of soccer-specific activities as the KT was developed in recreational runners, which may not represent a suitable kinematic model of running in elite soccer [
18]. Therefore, the multiplication coefficient needs to be revisited to ensure a better and more accurate representation of the metabolic constant expressed in elite soccer players on soccer-specific activities [
22]. As aforementioned, Osgnach et al.’s [
13] investigation does not fully reflect the accurate C
r imposed by running on grass and did not use elite athletes, therefore potentially underestimating MP.
More recently, Buchheit and Simpson [
23] discussed the efficacy of the MP approach considering the difference between the direct measurement of metabolic power (
) and the indirect approach proposed by Osgnach et al. [
13]. It was observed that several limitations contribute to the underestimation of metabolic power through the global positioning systems (P
GPS) relating to the GPS sampling frequency about the mathematical model data [
24] and the soccer simulation protocol used for the MP calculation [
25]. In addition, soccer-specific work–rest: ratios [
26] and movements-activities [
27] (e.g., sprint, running, jogging, walking, etc.) need to be incorporated. Therefore, additional research is needed to clarify di Prampero’s approach to professional soccer players. Therefore, the aims of this study were: (1) to determine the energy cost of running on grass (C
r) in ecological conditions on elite soccer players and (2) to validate an updated MP with a new equation using a soccer-specific exercise protocol.
4. Discussion
The first aim of the present study was to determine the C
r of elite professional soccer players in ecological conditions, which was found to be 4.66 J·kg
−1·m
−1. Previous findings have observed that O
2 consumption measured during constant-speed linear-running amounts to 73% of maximum O
2 consumption, thus confirming the aerobic nature of the metabolic demand due to the set C
r assessment speed used in this study. Pinnington and Dawson [
18] and Rodio et al. [
37] have reported values of 4.64 and 5.70 J·kg
−1·m
−1 when running on natural grass in a group of recreational runners and sedentary males, respectively. In amateur soccer players, Sassi et al. [
38] reported a C
r value of 4.20 J·kg
−1·m
−1, which is slightly lower than the value determined in the current study. More recently, Stevens et al. [
22] determined C
r be approximately 4.6 J·kg
−1·m
−1 at a running speed of 10 km·h
−1 on artificial turf in a group of non-elite soccer players. Present data differs from previous findings with differences in C
r estimates potentially due to variations in the population (elite vs. non-elite), playing surface (artificial vs. non-UEFA grass) and use of footwear, which affect running kinematics and energy cost [
39]. It is also important to note that the C
r presented herein reflects elite players in a non-fatigued state. It remains to be determined whether the C
r changes as a function of fatigue-related changes in metabolic, biomechanical and neuromuscular efficiency fluctuations during match-play and training.
Having established a new C
r in elite professional soccer players of 4.66 J·kg
−1·m
−1, a further aim was to incorporate this finding into and validate a new MP algorithm that includes a specific C term. This was established on elite soccer players, on an elite UEFA grass playing surface, with soccer-appropriate footwear to best replicate factors deemed important in the determination of movement economy in this population. This was facilitated through the use of the new constant term of C
r and regression prediction equation for the assessment of the C, by using the average MP on a soccer-specific test through direct and indirect measurements of O
2 consumption using di Prampero’s et al. [
16] approach while modifying Minetti’s et al. [
17] equation of energy cost. The validation takes into account locomotor kinematic data for the P
GPSn calculation, which is as soccer-specific as possible. The method has developed progressively through the work of di Prampero et al. [
16] and Osgnach et al. [
13], together with the calculation of the C [
17]. These approaches cannot be applied to other sports, but only for soccer which has a “predominately horizontal” mode, where running on flat terrain represents the largest portion of the energetic performance model.
Stevens et al. [
22] described that it is currently not clear to what extent it is possible to compare MP and C between varying running activities. Therefore, the validation of the different running activities is the main goal of this research. There are some criticisms and limitations present within the current research studies available in the literature because of previous protocols proposed and utilised. Present findings established that shuttle running using low speeds only, thus negating maximal actions, negatively affects the P
GPS. Current P
GPS observations are lower than the values found in other studies [
22,
25] due to the decreased error using 10 Hz sampling frequencies, thus preventing a drastic decrease. Further, that type of running is not ideal or specific for amateur soccer players. The proposed speeds have an influence on cost when establishing values of P
GPS (due to the absence of sub-maximal bouts) and are very much in direct relation with
, therefore amplifying the difference between the indirect measure and gold standard [
22].
Highton et al. [
26] observed that during a rugby-specific protocol incorporating contacts (collisions) and extensive passive rest (standing recovery), these measures were directly responsible for the underestimation of the EEE from the GPS data. The lack of agreement between direct and estimated values was deemed to be a result of the inability of GPS to detect EE associated with non-locomotor exertion. Brown et al. [
27] previously examined the validity of a GPS tracking system to estimate EE during exercise and field-sport locomotor movements in healthy adults, but differences in population sample make comparisons related to C observations with our study difficult. In addition, a GPS system that interpolates (via accelerometers) 5 Hz data is deemed insufficient for the speed variations present in the “modern” soccer game and is therefore not comparable to our results [
10]. Finally, the incorporation of extensive recoveries in their exercises, which are then used for the calculation of EEE, result in an increase in the differences between
and P
GPS, underestimating the latter. In addition, the failure to collect [La
−]b measurements is a further limitation.
Buchheit et al. [
25] used a test incorporating a ball within their assessment protocol, which increases the specificity related to soccer. However, they did so without considering the proportion of time a player is in possession of the ball during a game, making this a key factor causing P
GPS underestimation. Findings show that soccer players are in possession of the ball for less than 1% of the total playing time and less than 2% of the total distance they travel during a match [
40,
41]. The C of running with the ball is higher than without the ball, meaning that the
will rise during the technical parts and other activities with the ball [
25,
42]. The P
GPS will always be underestimated when incorporating an assessment protocol focusing on technical aspects with the ball since the kinematic data assessed is closely related to the exercise performed. Therefore, a lack of high-speed, acceleration and deceleration movement patterns adversely affects P
GPS estimation. Potentially, the decelerations will be further emphasised (e.g., stop and kick, ball control during a slalom, passing and reception with a rebound wall, etc.) which from a metabolic point of view (P
GPS) has a low C. Additional limits are present such as the use of a 4 Hz GPS sampling frequency, the intensity percentage of the
which was found to be up to 64% despite the “low” mechanical demands and the absence of high-speed (>14.4 km·h
−1) movement patterns as previously observed in detail by Osgnach et al. [
43].
Considering all of the research which has been conducted, it is important to consider the previous limitations observed in order to create/develop a test that can validate P
GPS in soccer and be compared to
. It has been found that three fundamental macro-aspects are required to ensure that the energy estimation method proposed by di Prampero et al. [
16] and Osgnach et al. [
13] best represents the soccer game and these are classified as follows:
- (i)
using a GPS system with a minimum sampling frequency of 10 Hz and a mathematical reduction (or smoothing, e.g., moving mean) of the speed data at 5 Hz to reduce noise in GPS elevation data. This has been found to be a methodologically verifiable value as established in a study performed by Gaudino et al. [
44], through performing calculations on contact and flight times in players on natural grass;
- (ii)
using an appropriate method to calculate the MP in an intermittent sub-maximal exercise, including the anaerobic amount [
30,
45];
- (iii)
using an appropriate experimental design by ensuring the work protocol includes an adequate population (elite soccer players), a specific terrain (natural grass) and appropriate footwear (soccer shoes) for calculating a specific C. Further, the performance model, such as the work: rest ratio and different locomotor activities (e.g., sprinting, walking, jogging, high-speed running, CoD, etc.), must be suitable to the activity as the duration of pauses/recoveries plays a decisive role on the metabolic response in soccer.
With regard to creating a test, other precautions related to the relationship between total high speed (TS) and total high-power (TP), which has been found to be between 55% and 32% in favor of TP [
46,
47], and the dimension changes as we move from SSGs’ (small-sided games) scenarios to the whole field (105 × 68 m), must also be considered. Therefore, choosing a soccer-specific circuit with an average MP greater than the 11–12 W·kg
−1 game intensity [
48] is necessary to respect the methodological criterion of the power–time relationship on intermittent exercises [
49]. Furthermore, the high-intensity actions (>20 W·kg
−1) are found to be around 4.7 actions per min (
Table 6), a value that is higher than previous findings where only 2 intense actions per min have been described in studies that only considered speed thresholds [
50,
51]. In addition, O’Donoghue [
50] shows that the most frequent recoveries are <30 s, and about 57% of those are <20 s. It is important to note that resting periods are never cumulative (pause of 30s consecutive) but fractioned in the game and must therefore also be incorporated in this way. Further, Bradley et al. [
52] showed that recovery time, defined as the time that elapsed between high-intensity running actions, is about 52 ± 18 s. For this reason, in our soccer-specific intermittent exercise protocol, a maximal action (triangle) is repeated every single lap (1 min). If you compare this to work conducted by Buchheit et al. [
25], where the passive recovery of 30 s was entirely spent at the end of the work minute, our proposed model of the circuit respects the intermittent nature of soccer by dividing the ~25 s of total recovery into shorter breaks (<10 s).
According to Buchheit and Simpson [
23], Malone et al. [
53] and Varley et al. [
54], acceleration is measured from GPS data mostly derived from the doppler-shift velocity. The time interval over which acceleration is calculated can significantly alter the data with a wider interval resulting in a smoothing effect on the data. Typically, acceleration is calculated over 0.2 or 0.3 s when using 10 Hz GPS, although the most appropriate interval will depend on the brand and the model of the device [
53,
55]. In the present soccer-specific intermittent exercise protocol, it was preferred to export raw data from commercial software and process it independently. The method used to calculate the high accelerations, using the kinematic data of official Serie A matches (Savoia et al. unpublished data) as a reference database, is based on the equation by Sonderegger et al. [
56] and modified accordingly:
where a
max is expressed in m·s
−2 and the
vinit in km·h
−1 (
Table 6).
The conceptual basis of the new MP approach to soccer, as initially described by Osgnach et al. [
13], was predicated upon a formula that was based on a population non-specific to soccer. The data reported in this study was assessed through C
r of running on grass using a new version of the “C equation” (modified equation [
17]). It was then applied to a soccer-specific high-intensity protocol for the first time relative to that observed in the original equation. The principal finding of this study directly determined the physiological demands simultaneously with GPS derived modeling of the MP. This indicates that in an elite soccer population, the GPS metabolic power paradigm provides similar point estimates of determining work rate during the soccer simulation protocol/activities undertaken. Specifically, data shows that where there are periods of repeated accelerations and decelerations, CoD when superimposed upon an aerobic background MP estimates were approximately similar between the direct (
) and indirect approaches (P
GPSn and P
GPSo;
Figure 6). Comparisons between both equations demonstrate that both effectively estimate MP with the P
GPSn having a marginal advantage over the P
GPSo. The former has a marginally lower fixed bias and similar proportional bias suggesting that as MP increases, the error remains relatively constant, i.e., no heteroscedasticity suggesting it works across the range of running activities and speeds incorporated into the protocol. The widths of the prediction intervals are also similar. In order to improve the prediction interval precision, a larger validation in a similar elite population would be needed. Interestingly, MP during the first phase of the soccer-specific protocol was higher, possibly due to the higher metabolic demand associated with the acceleration phase of running. It has previously been determined that a very low metabolic demand is associated with phases of deceleration during nonlinear runs and that acceleration or re-acceleration phases display an increased metabolic requirement [
57].
Further, we show that using a high-frequency GPS system sampling at 10 Hz, movement patterns are subject to rapid CoDs and that the C paradigm still provides a representative metabolic formula that is optimised to elite soccer match-play and training. The accuracy of the GPS estimates is based upon higher sampling frequency and accuracy for both acceleration and deceleration phases of soccer-specific movement. Present data are also indicative of the essentially aerobic nature of soccer-specific movement patterns. The protocol as applied in this study elicited a physiological strain approximating just over 70% of
and 90% of HR
max, which is in line with that reported during match-play [
41,
58]. Such observations provide support for the soccer-specific model utilised in the present study to compare directly and indirectly measured MP and reflect its specificity in relation to soccer match-play.
Applying a model that evaluates matches and incorporates training variables through biomechanical and energy intuition is easy to apply when the kinematic data are available. Through the study of and PGPS, it has been possible to widen the vision of the external training load by rationally integrating the information derived from speed alone with those related to its variations over time. explains only 24% of PGPS (r = 0.49), thus suggesting that players with a higher maximal O2 consumption consequently have a higher MP. However, such an assumption would lead to an assessment error, given that there are subjects capable of expressing a PGPS of ~15.7 W·kg−1 with a maximal O2 consumption of 70 mL·kg−1·min−1 and 57 mL·kg−1·min−1, which equates to a 23% reduction/difference in aerobic power. Therefore, a high does not necessarily imply a high PGPS, which represents the external load: the effect on the speed data calculated through the movements tracked by the GPS.
Ultimately there are three issues that need to be methodologically expanded:
- (i)
the extra energy, reasoning on the use of 100 Hz tri-axial accelerometers together with the correct mathematical filters. Buchheit and Simpson [
23] addressed this discourse by arguing that accelerometers are practical assessment methods to quantify stride variables when used indoors (i.e., no GPS signal is required), therefore allowing the use of these for intermittent team-sports (e.g., basketball, handball, etc.). All of this could improve the assessment of eventual muscle strength deficits in players, leading to progress in the field of injury recovery [
23,
59]. Further, Osgnach et al. (unpublished data) are currently focusing on a study related to “Muscle Power” (GPEXE ©, Exelio Srl, Udine, Italy), with the aim of considering the greater muscular load of the braking activities (decelerations) compared to those observed during accelerations. Findings could reduce the underestimation of P
GPS compared to
by considering and evaluating the addition of a small energy surplus deriving directly from neuromuscular fatigue. Technologies such as surface electromyography in correlation with current estimates of MP could be decisive for developing new C equations (with more attention to, e.g., decelerations, CoD, etc.) according to Buchheit et al. [
59] and Hader et al. [
57]. The main reason why it was chosen not to implement the update to the concept of equivalent slope [
60], in addition to the changes proposed by di Prampero and Osgnach [
61] on the inclusion of a lower energy cost for the walking phases (C
w), is dictated by the fact that the original equation [
17], with small adjustments as presented in
Figure 2, is already able to estimate the EE of an intermittent exercise albeit within a confidence interval range [
62].
- (ii)
The performance model in the choice of tests that we want to validate together with the calculations on the energetics of muscular exercise. In support of this, Brown et al. [
27] mentioned that using other criterion procedures that can measure both anaerobic and aerobic EE directly can help with the assessment of validating the approach, a concept found to positively work in this study. Further incorporations could have been made to help improve the current study: (1) the insertion of the ball in the soccer-specific circuit for a maximum of 5 to 10s per lap (e.g., sprinting with the ball or 5s of ball control and passing or shooting, etc.); (2) the inclusion of some walking/slow running phases given the active nature of the recovery (5–10 W·kg
−1) in soccer; (3) an increase of the sample studied in order to statistically understand the relation of the P
GPS when compared to the
measurement; (4) the addition of a camera at the start to record the time during the maximum triangle performed at each lap, in order to obtain a series of times to assess the min-by-min performance decrement [
63,
64]. This “new” test could be an alternative to the various repeated sprint ability tests previously used in the literature [
65,
66,
67], as it alternates the maximal bouts with runs and recoveries of various kinds, thus better simulating the intermittent scenario of the game. These concepts are closely linked to the decisive role of the C, which was shown to be ~38% higher than C
r on the grass at a constant speed (6.41 J·kg
−1·m
−1 > 4.66 J·kg
−1·m
−1,
Table 2 and
Table 4) in our soccer-specific intermittent exercise protocol. Therefore, it is essential that the training plan is soccer-specific and focuses on the economy of movements throughout the gameplay (training drill), in order to not obtain a greater efficiency of the running technique (i.e., athletics), as this would lead to an improvement of the C
r. Observations by Buglione and di Prampero [
21] found C
r to get worse during a competitive soccer season, highlighting the need for tests and training to be sport-specific, respecting the biomechanics related to running in soccer.
- (iii)
The application of the “MP” approach to video match- and time-motion analysis using the same equations and algorithms as used by the GPS software for training load analysis represents the future of soccer. This would enable coaches and practitioners the possibility of assessing the metabolic performance of each player during every match and help with the study of trends related to the loads incurred during training and gameplay. The uniformity and homologation of the algorithms would really represent a “turning point” to compare training methodologies/philosophies (i.e., traditional, integrated, structured, tactical periodization, etc.) and similarities and/or differences between championships and competitions (with respect to the presence or absence of cup tournaments). Its usefulness could further extend on the choice of purchasing the appropriate player(s) during the transfer window by helping to update databases which are useful for soccer scouting and match analysis (such as, Wyscout, InStat, Stats Perform, Transfermarkt, etc.). Further, combining the technical-tactical information, the physical performance and the history of injuries provides a better understanding of the players’ official performance parameters and the current training loads carried out at their club through the use of “integrated soccer language” [
68].
However, despite some of the current limitations, as well as the sample, the information provided can help better describe the activity currently present in the game of soccer and its concept related to intensity by providing a “new” opening to the scenario of analysis and observation. Player practice on the field imposes the application of these models to the daily activity of analysis of training sessions, both with and without the ball. In the last few years, most games have almost total coverage of video tracking systems in the stadiums and have the possibility of applying high-frequency GPS to the players during their weekly microcycles. The comparison and the periodization of training have become a great interest among the professionals working within this sector. A modern-day data scientist who wants to get closer and closer to fully understanding the game cannot merely untie the purely physical data (response) from the technical-tactical aspect (cause) during match-play. Considering soccer is a situational sport, its performance is mainly influenced by the need for strategical and tactical developments in the field, which could also impose moments of pause/rest between repeated high-intensity actions.
In the future, it would be desirable to use larger data sets through machine learning and data-mining systems so that the spectrum of player-specific analysis can be further expanded. This will help with the association of not only the “static information” to the physical data, such as player position, the system of play, result, percentage of ball possession, etc. but also the “dynamic information”, such as the flow of tactical attitudes tagged through video match-analysis. Further research will provide information that helps with the understanding and the explanation of the observed physical data in accordance with specific moments/actions during a game. Ultimately, it could help managers/coaches choose a “winning” strategy.