Tell me how much your opponent team runs and I will tell you how much you should run: A predictive model applied to Spanish high-level football

INTRODUCTION

Effective playing time in football refers to the actual amount of time the ball is in play during a match, excluding stoppages for events such as fouls, injuries, substitutions, and other breaks in play. It represents the duration in which the game is actively progressing. More than a decade ago, it was proposed that effective playing time strongly conditions the physical response of professional football players in competition. Usually, the effective playing time accounts for a little over 50% of the total match time. Regarding external load, close to 70% of the running performance is accumulated in this period of play, being able to reach more than 95% when it comes to high-speed running [1]. In domestic league matches, only in effective game time can teams score or concede a goal. Above all, at this moment of the game, players are especially active. This does not prevent teams from making strategic use of breaks, trying to reduce stoppages when losing or lengthening them when the score is favourable [2].

Huge amounts of research have been carried out thanks to computerized tracking systems, applying the five properties under the concept of “the five Vs” [3]. One of these concepts is volume, that is, the magnitude of the data. Nowadays, due to the size of datasets in team sports, studies can be developed that span multiple leagues [4], categories [5, 6] or seasons [7]. The studies that gather thousands of individual and collective performances in their analyses address explanatory proposals based on the inclusion in the models of situational variables (e.g., match location, match outcome, level of the opponent, type of competition, etc.). Overall, nowadays, physical response is being better understood [8].

With respect to match location (e.g., home or away), the results are incomplete [9, 10], and probably influenced by other contextual variables (e.g., match outcome), which could explain the disparity of results [9]. Regarding match outcome, researchers reported that football players perform significantly less high intensity activity when winning than when losing or drawing [1, 10]. However, the category of the league in which the teams participate (e.g., the second division compared to the Spanish first division of soccer) could increase the connection between physical response and success in the competition at the end of the season [6]. The results of one recent study [8] that studied the differences between both phases of play (attack and defence) show that the distance covered by teams when they have the ball is shorter than when they do not (relativizing the physical response to each minute of ball possession or non-possession). Finally, the results of the academic literature emphasize the importance of taking into account the opponent’s level (e.g., high, medium, and low) during the assessment of the physical response of football performance [11, 12], briefly concluding that the higher the opponent’s level, the higher will be the physical demands required. However, it is unknown whether the physical performance of the opponent affects the physical response of the other team.

Despite the constant use of descriptive and explicative analytical techniques in match analysis, there are still few available studies that have developed predictive models of sports performance [13]. These types of studies have the common purpose to determine the most effective ways of playing and using multidimensional qualitative data instead of unidimensional frequency data. The ability to describe football match play has improved [14]. Previously, a study proposed the implementation of predictive models of the physical response of running in professional football [10]. The authors attempted to predict the distance players would cover when the match status changed or the team played home/away against strong/weak opposition. It seems that in the dynamics of a match, the team performance is a combination of knowing what to do, wanting to do it, and what the opponent allows one to do. Furthermore, all this is conditioned by the independent and interactive effects of fixed (e.g., match location, type of championship) and changing (e.g., match status, substitutions, injuries) situational variables.

The aim of this study was to predict the total distance covered by a football team and the total distance covered above 21 km/h from different situational variables of the competition. The predictive variables involved in this study were: the match location (home or away), the final match outcome (lost, drawn or won), the level of the team and opponent team, the effective playing time (in min), the possession of the ball (in min), and the distance accumulated by the rivals in both total distance and at > 21 km/h. The starting hypothesis is that, especially, the physical performance of rival teams conditions the physical performance of the team and vice versa, in addition to other contextual variables. The results of the present study may allow football practitioners to predict the physical response in competition depending on possible scenarios in order to prepare players/teams during the training process.

MATERIALS AND METHODS

RESULTS

Table 2 shows the descriptive analysis (mean and standard deviation, median and interquartile interval, or absolute and relative frequencies) and inferential analysis (confidence intervals for a mean, median, or proportion) of the variables used to build the multiple linear regression model.

To predict TotDisTea or TotDis21Tea a total of 254 linear models (127 models for each outcome) were estimated from all the possible regression procedures. An attempt was also made to build a model for predicting TotDis21Tea, but it was ultimately not built because both the maximum model and the 126 derived sub-models had little predictive power (R²_adj < .38).

Table 3 presents only 17 models (10 multiple and 7 single) of the 127 models estimated in total to predict TotDisTea, ordered from lowest to highest Mallow’s C_p. Specifically, the model with the lowest C_p (9.47) and highest R²_adj (.8237) was the model containing six predictor variables out of the initial seven and excluding MatOut. The second model with the lowest C_p (13.00) and highest R²_adj (.8236) was the maximum model with seven predictor variables, which had a prediction loss of 0.01% with respect to the first model in the table. The rest of the models in the table had a prediction loss between 0.04 and 0.24% with respect to the first model. Thus, the model with all predictor variables except MatOut was selected as the best model to predict the TotDisTea for the following reasons: (a) model with two parameters less than the maximum model; (b) model with lower C_p and higher R²_adj; and (c) only model with a C_p value lower than its number of parameters (C_p < p+1), which indicated that the selected model had a lower error variability than the maximum model.

In relation to the reliability of the selected model, R²_mean = .8229 was obtained from cross-validation. This result indicated that the true predictive capacity of the model when executed with external samples was around 82%.

Regarding the diagnostics of the selected model, 13 observations with studentized residuals > |3|, with leverage values > 2×(p+1)/n, with DFITs > |√((4×(p+1))⁄n)|, or with covariance ratios outside the interval 1±3×(p+1) were found. However, these outliers or influential observations were not removed from the sample because they were correctly recorded and because they were part of the reality of the game. The data did not present collinearity because the variance inflation factor was less than three in all the predictor variables. The normality assumption was met because all the internally studentized residuals were on the diagonal of the normal P-P plot; and the assumptions of linearity and homogeneity of variances were met because the externally studentized residuals did not present any defined pattern and were randomly distributed in the scatter plots.

The F-test of global significance revealed that the set of parameters of the selected model explained a significant part of the variability of the TotDisTea, F_(10,2935) = 1376.84, p < .001; and the F-tests of individual significance revealed that each predictor variable included in the model had a statistically significant contribution (p < .005) to the multiple linear regression equation (see Table 4). The b coefficients and their confidence intervals indicated that playing at home (relative to playing away), playing against a Champions League team (compared to playing against a relegation team), for each minute of increase in effective playing time, and for each kilometre of increase of the total distance covered by the opponent, the mean total distance, in kilometres, covered by the team increased significantly; in contrast, being a Champions League team (compared to being a relegation team) and for each minute of increased ball possession, the mean total distance covered by the team decreased significantly. For their part, the beta coefficients indicated that predictors TotDisOpp, EffPlaTim, and BalPos had a greater contribution to the TotDisTea outcome than the predictors OppLev, TeaLev, and MatLoc.

From the b coefficients in Table 4, the following equation was defined to predict the mean total distance covered by the team in kilometres:

In Table 5, the previous equation was applied and the mean TotDisTea was predicted for different values of the predictor variables selected with practical criteria. This equation can be applied to other different values as long as they belong to the range of values observed in the sample used to estimate the model (i.e., TeaLev and OppLev between relegation and Champions League, EffPlaTim between 36.8 and 68.2 min, BalPos between 12.4 and 49.4 min, and TotDisOpp between 52.5 and 98.0 km). For example, to predict the mean total distance covered by a Champions League team that possesses the ball 41 min in a match with an effective playing time of 65 min and plays away from home against a team that is staying up, that covers a total distance of 55 km, the equation is applied as follows:

Without the TotDisOpp predictor variable, the equation was the following, but this model had R²_adj = .6429 and a prediction loss of 18.08%:

DISCUSSION

The main aim of this study was to estimate two predictive linear regression models using the TotDisTea and TotDist21Tea by combining eight predictor variables. A total of 127 models were estimated from the all-possible regressions procedure for each outcome variable. The model with all predictor variables except MatOut was selected as the best model to predict the TotDisTea (R²_adj = .82). The predictors TotDisOpp, EffPlaTim, and BalPos had a greater contribution to the TotDisTea outcome than the predictors OppLev, TeaLev, and MatLoc. The model to predict TotDis21Tea was not built because both the maximum model and the 126 derived sub-models had little predictive power (R²_adj < .38). With the results, it could be concluded that theoretically, the interaction of teams in the football matches has also been verified in the conditional dimension, with a close relationship between the physical responses of both teams. From a practical point of view, practitioners could have the possibility to estimate physical performances of teams in matches when it has not been possible to obtain that outcome (e.g., TotDisOpp).

Football is a sport of interaction and, therefore, the performance of a team is dependent on the performance of the opponent [20]. Multidimensional proposals to characterize playing styles are increasing [21]. The unique way teams play means that the distribution of roles among players is specific, so individual dimensions (e.g., emotional, cognitive, affective, behavioural, social, and conditional) will be unequally demanded. For this reason, the same positions in different teams carry with them different conditional responses, that is, adjusted to the way the team competes [22], greater movement of the ball or models that enhance the exploration of a more direct game. A revealing aspect of this study was the effect of TotDisOpp on TotDisTea when the rest of the model’s predictors were held constant; the interpretation is as follows: for each km run by the opponent team, there is an expected increase in mean TotDisTea of 0.71 km, 95% CI [0.69, 0.74]. This would affect both positively (the need to run more) and negatively (forced to run less) whether the conditional profile of the opponent faced is higher or lower than the reference team. When the predictive model has been applied eliminating the variable TotDisOpp (equation 2) the model had R²_adj = .64, and a level of prediction loss of 18.1% with respect to equation 1 (with TotDisOpp), which carries a great weight within the predictive model. For this reason, when one wants to assess the physical performance of a team, as can be deduced from this study, keeping in mind the physical performance of the opponent is essential.

The second predictive variable that most influenced the prediction of TotDisTea was EffPlaTim. More than a decade ago it was reported that in the effective playing time (EPT), the player accumulates the largest amount of physical demand, this percentage increasing as the running speed increases, and it can be close to 100% in the case of high-speed running [1]. On the other hand, nowadays, in professional football leagues, since the implementation of the Video Assistant Referee (VAR), there have been some changes, especially in total (TPT) and effective (EPT) playing time [23]. Although there was no significant effect in the technicaltactical dimension (e.g., passes, dribbles, crosses, shots, goals, corners, fouls, width, length, height, distance from the goalkeeper to their defence), physical performances in Spanish LaLiga teams had a slight decrease in the total distance covered (108.9 vs. 107.9 vs. 106.9 km) when VAR intervened (VAR0, VAR1 and VAR2, respectively). Probably, it is due to the decrease in EPT between VAR0 and VAR1 (52.5 vs. 51.5 min, respectively) and a slight increase in TPT in VAR2 compared to VAR1 and VAR0 (99.1 vs. 96.0 vs. 95.1 min, respectively).

Ball possession is one of the most studied variables in elite football, above all, in the attempt to associate it with success [5]. From the interpretation of the results, as shown in Table 4, the BalPos variable is the third of the variables in predictive importance of TotDisTea. For each minute of ball possession, a decrease in mean TotDisTea of -0.27 km, 95% CI [-0.29, -0.25] is expected. Usually, successful teams are those that have greater possession [5] and less accumulated distance [24, 25]; nevertheless, the methodology used in this type of research does not tell us whether the offensive phase is more or less physically demanding compared to the defensive phase. A recent study [8] tried to relate the effective time of the game (distinguishing the phases of possession and non-possession of the ball) with the locomotor response, from an intensity variable, meters per minute covered by the team. Two of the main conclusions of the study were that teams ran more per minute when players did not have the ball than when they did, and the distance accumulated per minute by the teams in ball possession does not correlate with the distance accumulated in the non-possession phase and vice versa [8]. Then, the physical response assessment needs information about the accumulated time of possession.

To assess the level of the teams, result indicators are usually used, such as the number of goals [5] or accumulated points [26], or the classification at the end of the championship [24], among others. In a previous study, carried out in the same Spanish league [5], some significant differences were observed (with a trivial effect size) in the physical performance of the teams in the upper half of the table compared to the last in the standings. Similarly, in the current study, the Europa League teams also had a greater physical response (increase of almost half a kilometre) with respect to the reference value taken from the relegation teams. By contrast, the groups of teams staying up and in the Champions League showed negative values with respect to the reference value; it can be interpreted that physical response was not a dimension that characterized them. It seems that each team tries to take advantage of its strengths (e.g., running or passing more than the opponent does) as their style of play. However, regarding the particularity of each match, the quality of the opponent shows a linear trend like that described in the literature [1, 10]; the greater the quality of the opponent (determined by their standing in the league) the greater is the locomotor activity demanded from the reference team. From the models proposed in the present study, unlike what was observed in a previous study [27] where the time of possession of the ball was not taken into account, it can be predicted that the teams having to face teams that are in the Champions League will increase the TotDisTea between 0.4 and 1.1 km. In any case, caution must be exercised when interpreting the results because the small differences in the final standings depend not so much on the team’s usual way of playing [21], but rather on the effectiveness of the team in shots on target [28]. Furthermore, exploring this study in other divisions (e.g., the Spanish second division of soccer) could be of interest [6].

The influence of match location on the physical response of players and teams is not new [1, 10]. The home teams usually covered a greater distance than away teams. A recent study found [8] that match location affected the distance covered at > 21 km/h but not the total distance accumulated per minute by the teams, running greater distance in matches played at home. In line with this, in the prediction model of our study, to play at home meant between 0.1 and 0.5 more km for teams. Several years ago, a review of the evidence for the hypothesized reasons for a home advantage was made [29]; crowd support, referee bias, psychological factors, travelling of away teams, familiarity with local conditions, territoriality and specific playing tactics were suggested as other possible influences. In any case, home teams seem to be forced to get a good result when they play at home.

MatOut was not included in the final predictive model. Nevertheless, it is known that match status has a big influence on the adopted strategy of the teams during a match, which accounts for the fact that players do not always use their maximal physical capacity for an entire match [2]. Changes in the match status create special needs within the team, being particularly affected the different positions in a playing system [30]. In line with this, Lago et al. observed that for every minute losing, players covered an extra metre of sprinting (> 19.1 km/h). However, while the team’s overall physical performance might not be greatly affected by changes in the match status, it could alter the distribution of locomotor demands among teammates. Losing status could increase the total distance and the distance covered at 14–21, 21–24 and > 24 km/h by defenders, while attacking players could increase the distances accumulated in these ranges of velocity during winning status [30]. The difference between the studies could be explained by two reasons: methodologically, the fact that the physical performance evaluated in the present study is limited exclusively to effective playing time; and conceptually, because although the outcome of the match has been classified as win, draw or loss, it is known that during matches there may have been changes in the match outcome, being able to have a different temporal distribution (% of time winning, losing and drawing).

One of the methodological limitations of the present study was to determine the minimum sample size required to conduct a multiple linear regression analysis; the general rule-of-thumb of N ≥ 50 + 8 × p was applied [31, 32], where p is the number of parameters of the maximum model. In our case, if the maximum model had 13 parameters, then this model had to be built with at least 50 + 8 × 13 = 154 observations. The reason for applying this rule was that no previous football studies were found that built a model to predict the total distance covered by teams. However, considering the results obtained in the present study (R²_adj = .82; M and SD of TotDisTea = 78.3 and 6.3 km, respectively) and the four-step procedure proposed by Riley et al. [33, 34], future football studies will be able to more adequately calculate the minimum sample size required to build a linear regression model to predict the total distance covered by a team. A second limitation of the study concerns the levels set for some situational variables. Probably, distributing the match outcome according to minutes winning, losing or drawing could improve the degree of prediction of the model. In addition, the level of the team and its rivals, which has been established considering the ranking at the end of the season, does not take into account the variability of the position occupied by the teams on each match day of the championship. The third limitation is related to the idiosyncrasy of the players and teams in the way of task solving, that is, playing a football game. It would be interesting to know the weight carried by physical demand in each team performance, then apply this type of predictive model to each team in LaLiga.

CONCLUSIONS

Our results highlight a number of variables that could explain physical workload in football players, and combinations of these variables could be used to develop a model for predicting (from a probabilistic viewpoint) the physical activity profile in competition. The main conclusions of the present study focus on the importance of the opponents in the physical performance when a team tries to resolve the task of playing a match. Apart from the opponent, effective playing and possession times are placed in a secondary position. Finally, with less importance, match location and match-up quality must be considered when planning to predict the total distance that will be covered by the team. The findings of this study suggest again [8] that an effective assessment of football performance at a behavioural level needs to incorporate both the different contextual variables (and their interactions) where the match has developed, and the particular strategic variables that the teams have proposed in the match according to the needs at each moment of the match.