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Article

Association Between Substitutions and Match Running Performance Under Five-Substitution Rule: Evidence from the 2022 FIFA World Cup

International College of Football, Tongji University, Shanghai 200092, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(17), 9540; https://doi.org/10.3390/app15179540
Submission received: 9 July 2025 / Revised: 18 August 2025 / Accepted: 27 August 2025 / Published: 29 August 2025
(This article belongs to the Special Issue Sports Performance: Data Measurement, Analysis and Improvement)

Abstract

This study investigated associations between substitutions and match running performance (MRP) under the new five-substitution rule, utilising running data from the 2022 FIFA World Cup involving all 32 participating men’s national teams, comprising elite professional football players at the highest international competitive level. A paired sample t-test compared running performance among entire match players (EMP), replaced players (RP), and substitute players (SP) per team per match. A linear mixed model (LMM) was used to analyse the association between substitutions and MRP while also considering match-related factors associated with MRP as covariates and controlling for team variations. The main finding was that substitute players exhibit superior running performance compared to RP and EMP. Running metrics related to match outcomes indicate that more substitutions are associated with increases in total running distance and the number of sprints. This study highlights the importance of substitutions on team running performance under the new rules in modern elite football. Coaches can optimise their substitution strategies and physical training according to the new rules to meet the high-intensity demands of the game.

1. Introduction

The external load in football has been extensively studied over the past two decades, with particular focus on the distance covered across different intensity zones [1,2]. Match running performance (MRP), especially sprinting and high-intensity running, has consistently been linked to match success [3,4], as these explosive efforts often decide key moments in elite competition [5,6].
Therefore, many studies have investigated associations between match-related factors and match running performance (MRP) to enhance team competitiveness and optimise team performance in matches. Studies on the World Cup reveal that teams using a 4-2-3-1 formation cover greater distances [7], with wingers and forwards typically exhibiting higher speeds and more frequent high-intensity runs [8]. In the Women’s World Cup, team offensive styles are significantly associated with MRP [9]. Plakias et al. [10] confirmed that fast counterattacks and high pressing strategies can notably increase team running distance. Additionally, data from the UEFA Champions League show that away players run more [11], while teams with higher possession see an 8.7% increase in high-intensity running distance but a 9.5% decrease in acceleration frequency [12]. A review study by Trewin et al. [13] summarised that factors such as team and opponent quality, match outcomes, temperature, humidity, altitude, and congested scheduling are all associated with MRP.
In recent years, technological advances [14] (e.g., the introduction of VAR) and continued changes to the rules of the game have been potentially associated with the MRP. In particular, rule adjustments may be associated with MRP patterns and team strategies. In response to the COVID-19 pandemic, FIFA temporarily permitted five substitutions per match in 2020, increasing the number of substitutions allowed from three to five. In June 2022, FIFA officially incorporated this regulation into the standard rules [15]. Concurrently, the International Football Association Board (IFAB) initiated trials of concussion substitution protocols in 2021, which became official in 2024.
The new rules have increased the number of substitutions allowed during the game [15], which means more substitute players have the opportunity to participate. In the match, substitute players play a crucial role in enhancing physical and technical performance in scoring, passing, and defence [16]. A review study concluded that substitute players (SP), especially offensive players, significantly increased their running intensity in the last 15 min of the game. Compared to the entire match participants (EMP), the distance covered at high-intensity running increased by 25%, and the sprinting distance increased by 63%. Substitutes exceed replaced players (RP) by 10% in high-intensity running distance [17]. The study by Dijkhuis et al. [18] on real-time monitoring reinforces the finding that substitute players exhibit superior performance in the later stages of the game, demonstrating greater high-intensity running distances and enhanced sprinting abilities. Therefore, substitute players enhance the physical intensity of the game by increasing their running, becoming a key tactical means for coaches to adjust fatigue and change the course of the match [19]. Previous studies have mainly focused on individual differences between starting and substitute players [16,20], and most relevant research has been conducted in the context of a three-substitution limit. In such cases, the majority of teams tend to use all their available substitutes. Therefore, there are few studies that explore whether the number of substitutions systematically affects team-level running intensity. With the introduction of the five-substitution rule, different teams have shown varying choices regarding the number of substitutions [15,21]. This allows us to further explore the relationship between the number of substitutions and the running performance of teams during the match.
As previously mentioned, the performance of team running during matches is influenced by a combination of various factors. Therefore, this study plans to investigate whether increasing the number of substitutions leads to an enhancement in team running intensity after controlling for known background and tactical factors. Although additional substitutions may seem to boost physical output, this relationship is not straightforward. Teams might use extra substitutions to slow down the game pace, solidify a lead, or adjust their formation [17]. Thus, the specific impact of substitutions on running at different speed zones per minute still requires further empirical research.
This study focuses on two specific research questions: (i) under the five-substitution rule, are there significant differences in running metrics among entire match players (EMP), replaced players (RP), and substitute players (SP) across different speed zones? (ii) Under the control of known confounding factors, increasing the number of substitutions may improve which running metrics at the team level? Are these metrics associated with match outcomes?
By analysing data from top-level international tournaments, this study aims to provide empirically-based insights into the relationship between substitutions and running under modern rules and to offer practical guidance for coaches to optimise substitution strategies, aiming to achieve an effective balance between tactical needs and physical performance goals.

2. Materials and Methods

2.1. Sample

This study used match data from the 2022 FIFA World Cup, which implemented revised regulations permitting five substitutions per team (including concussion substitutions). As FIFA’s premier international competition, the World Cup provides highly representative data for elite football performance. Our analysis included all 32 participating nations.
Total substitutions encompassed all player changes, including concussion substitutions. MRP and other related match metrics were obtained from FIFA’s official post-match reports (available online: https://www.fifatrainingcentre.com/en/fwc2022/post-match-summaries/post-match-summary-reports.php, accessed on 4 April 2025). FIFA collected the data using the TRACAB Gen5 multi-camera optical tracking system (ChyronHego), with data captured at 25 Hz by high-definition cameras. The effectiveness and accuracy of this system have been validated in previous studies [22,23]. These datasets have been used in recent research to investigate the MRP of substitute players and the relationship between offensive and MRP during matches [9,24]. Given the public accessibility of these datasets, ethical approval was not required for this study.

2.2. Procedure

This study used quantitative methods to analyse and compare differences in MRP among EMP (n = 827), RP (n = 580), and SP (n = 564). To reduce the interference of outliers in the performance per minute of the game and avoid the impact of tactical substitutions on the progress of the game, this study, referring to the research methods of previous scholars Sydney et al. and Wei et al., excluded data from players who played less than 5 min [19,24].
Subsequently, we conducted a linear mixed model (LMM) analysis that included covariates related to MRP to explore the relationship between the number of substitutions and team MRP. Given that the 2022 World Cup has strict rules on stoppage time, requiring the additional time to make up for the rule-specified time lost, it is considered to study using the duration of stoppage time as a covariate for the length of game interruptions [25]. The Qatar World Cup did not take into account factors such as the environment, schedule, and match location due to the format of the World Cup tournament. Our analysis included 125 match samples of teams and excluded matches where red cards occurred within 90 min to ensure standard 11 vs. 11 matches. See Table 1 for specific variables and definitions.
MRP was evaluated through relative running metrics for players. Relative variables indicate the intensity of the player during the entire play, used to measure the relative values of physical exertion and athletic output per minute.

2.3. Statistical Analysis

Descriptive statistics were evaluated using Kolmogorov–Smirnov tests for normality [26]. We used a paired sample t-test to analyse differences in running performance among EMP, RP, and SP for each team in every match [27].
Cohen’s d was used to evaluate the effect size (ES): trivial (d  ≤  0.2), small (0.2 < d  ≤  0.6), moderate (0.6< d  ≤  1.2), large (1.2< d  ≤  2.0), very large (d  >  2) [28]. A linear mixed model (LMM) [11] was used to examine both:
Y i j = β 0 + β 1 X 1 + κ = 1 ρ γ κ C κ + u j +   i j
Y i j is the MRP metric for observation i in team j , X 1 is the number of substitutions (fixed effects), C κ is the covariate (fixed effects), u j is the random intercept for team j ( u j ~N (0, σ u 2 )), and i j is the residual error ( i j ~N (0, σ 2 ).
This study developed eight models to assess associations between fixed effects (independent variables and covariates) and random effects (team ID) and dependent variables. Categorical variables (match stage, match outcome, and formation) were dummy-coded. Continuous variables (stoppage time, team quality, opponent quality, possession %, counterattack %, high press %) remained scale variables. Random effects accounted for between-team performance variability.
Analyses used IBM SPSS 29.0, and data visualisation employed GraphPad Prism 9.5. Statistical significance was set at p < 0.05.

3. Results

Paired sample t-tests showed significant differences across EMP, RP, and SP for seven running metrics (TD, LID, MID, HID, SD, number of_HIR, number of sprints, all p < 0.05). Specifically, SP was significantly higher than both RP and EMP (all p < 0.05, d = 0.08–2.13). RP was significantly higher than EMP (all p < 0.05, d = 0.84–2.4). Additionally, EMP’s WJD was significantly higher than RP’s (p = 0.002, d = 0.28). See Figure 1 for a detailed description.
The LMM analysis results show that the substitutions have a positive association with total distance and five running metrics. Specifically, each additional substitution increases TD by 2.36 m per minute (p < 0.001), LID by 1.54 m per minute (p < 0.001), MID by 0.36 m per minute (p = 0.032), HID by 0.22 m per minute (p = 0.019), the number of HIR by 0.04 times per minute (p = 0.002), and the number of sprints by 0.02 times per minute (p = 0.004).
The match outcome is related to TD, WJD, SD, and the number of sprints, where TD and the number of sprints are also associated with the number of substitutions. During the game, the winning team’s TD and number of sprints were significantly higher than those of the losing team (p = 0.02–0.03).
For other MRP-related factors, stoppage time has a negative association with TD, WJD, LID, MID, the number of HIR, and the number of sprints (all p < 0.05). Stage is associated with WJD, LID, and SD. In the first group stage, WJD and LID were significantly lower than in the final match (p = 0.013–0.041), while SD was higher than in the final match at all stages (p = 0.003–0.05). High press has a negative association with WJD (p < 0.001) and positive associations with MID, SD, number of HIR, and number of sprints (all p < 0.05). Counterattack has a positive association with MID, HID, SD, and the number of HIR (all p = 0.009–0.029). Team quality shows a very slight negative association with the number of sprints (β = −0.0001, p = 0.008). Possession has a positive association with WJD (p = 0.046). No significant associations were found between formation and MRP metrics (all p > 0.05).
The associations between substitutions, other match-related factors and MRP are presented in Table 2 and Table 3.

4. Discussion

This study investigates the differences in running performance of players under different substitution conditions. The association between substitutions and MRP was analysed while controlling for team differences and incorporating relevant MRP variables. The main findings were that (i) substitute players exhibit better running performance compared to replaced and entire match players; (ii) more substitution actions were associated with increased total distance and low-, mid-, and high-intensity running and sprints; and (iii) substitutions were associated with key running performance indicators that influenced match outcomes.
These findings align with Sydney et al. [19] and Pan et al. [16], demonstrating that substitute players perform better during high-speed running. This has also been verified in different leagues. In the Premier League, substitutes, especially attacking players, cover significantly longer high-intensity running distances [29]. In the Bundesliga, substitutes surpass both the RP and the EMP in total distance covered and sprinting frequency [30]. Research related to the World Cup shows that substitutes make more high-intensity runs than starting players, but it does not compare them to replaced players [24]. Additionally, the study by López-Valenciano et al. [31] indicates that matches using the five-substitution rule significantly enhance the team’s sprinting ability compared to the three-substitution rule. From a physiological perspective, studies by Mohr et al. [32] and McLellan et al. [33] have shown that during prolonged high-intensity intermittent running, players consume large amounts of glycogen and experience a decline in neural conduction efficiency. This makes starting players prone to fatigue towards the end of the game, resulting in a reduction in the frequency of high-intensity running, a decline in sprinting ability, and a decrease in muscle strength. In contrast, substitute players, due to their lesser playing time, can maintain better muscle glycogen reserves and neural mobilization capacity. Sydney et al. [19] also found that substitute players can maintain higher levels of physical fitness in the later stages of the match. They can ‘enter the game and increase the pace’ or ‘replace players who are tired or underperforming’, thus meeting the physical demands of the matches. Therefore, the introduction of the five-substitution rule provides teams with more substitution options, effectively reducing player fatigue while ensuring that the entire team can consistently maintain high-intensity running performance [17,34].
Our LMM analysis results not only revealed the association between the number of substitutions and team running performance but also further confirmed that in the 2022 FIFA World Cup matches, the TD and the number of sprints by a team were positively correlated with their probability of winning. Multiple previous studies have also shown that high-speed running and sprinting have a significantly greater impact on match outcomes compared to low-speed running [4,35,36,37]. The winning or drawing team covers 16% more sprint distance than the losing team and performs 2.6% to 15% more sprints [38,39]. Additionally, research by Wei et al. [15] found that with more substitution options, the number of goals scored by substitute players tends to increase. Thus, it can be inferred that an increasing number of sprints during critical moments, as an alternative strategy, can effectively promote competitive success. However, our current research has only confirmed that increasing the number of substitutions can increase the team’s running intensity, but there is still no conclusive evidence that this action improves their win rate. Future studies need to delve deeper to further verify this and prove the inference.
Additionally, our research also found that high press and counterattack result in more high-intensity running and sprinting, while teams with higher possession rates tend to have more low-intensity running. These results align with previous research findings. To gain a competitive edge, teams may adopt high-pressing tactics. However, research by Low et al. [40] found that such aggressive defensive strategies lead to a more dispersed team formation, necessitating coverage of greater high-intensity distances, which imposes higher physical demands on players. A study by Abebe et al. [41] also indicates that high-press games elicit stronger physiological and physical responses from players. Counterattacks are considered one of the most effective scoring methods in football [42]. A study by González-Rodenas et al. [43] found that counterattacking tactics can more effectively create goal-scoring opportunities. Furthermore, González-Ródenas et al. [44] demonstrated that during the second half of the match, there are more opportunities for offensive advancement through counterattacks. Research by Plakias et al. [10] revealed that teams focused on ball possession have lower average sprint values compared to those employing a counterattacking style. Therefore, from a tactical perspective, substitutes may be deployed during high pressing or fast counterattacks, their short bursts of sprints directly increasing the number of high-intensity efforts [24,29,45]. Having more substitution options not only maintains the pace of the game and boosts its speed and intensity but also provides greater flexibility for tactical adjustments and better execution [17].
However, a study on women’s football differs from our findings. Research by Kobal et al. [46] found that there was no significant correlation between increased substitutions and running performance. This discrepancy may be due to the limitations of using single-club team samples, differences in league and cup schedules, and variations in physiological demands based on gender and skill level. Data from the World Cup, representing the highest level of international competition, suggests that the intensive cup schedules may particularly benefit from more substitutions due to rapid fatigue accumulation, high base intensity requirements, and short recovery times. Thus, more substitutions can help sustain this explosive running [15]. Nevertheless, the specific effects in league settings require further investigation [20].
Among the factors related to MRP that were included, our research had a new finding: the longer the stoppage time, the fewer occurrences of moderate and low-speed running, as well as high-intensity running and sprinting per minute. FIFA’s revised method of calculating stoppage time takes into account substitutions, injury assessments, disciplinary actions, permitted medical pauses such as hydration and cooling breaks, VAR delays, and other interruptions to play. The time lost due to interruptions will be precisely compensated through added stoppage time [25]. So, longer stoppage time may result from more frequent interruptions during the game. Lin et al. [47] believe that during game interruptions, players tend to stand or walk, leading to an increase in total game time while the distance covered remains unchanged, thereby reducing the relative running distance. Zhao et al. [48] point out that frequent interruptions in football games slow down the pace of the game, affecting its fluidity. Therefore, we speculate that interruptions weaken players’ offensive organisation efficiency, causing them to need more time to re-adjust and organise their offence, which makes it difficult for the team to quickly switch to a fast-forward mode. Consequently, interruptions during the match have a negative impact on players’ running performance [47].
This study significantly contributes to our understanding of substitutions and their impact on physical performance in elite football. Our findings validate the potential of substitute players to enhance a team’s high-intensity running during matches. Furthermore, they indicate that increasing substitutions is not solely for improving running intensity but also involves tactical intentions such as counterattacks and high pressing in various match situations. This study, validated under the new five-substitution rule, highlights the crucial role of substitutions in optimising match physical output. These findings are important for coaches, sports scientists, and athletes, offering insights into the strategic use of substitute players in modern football. In the context of modern football rules, through data-driven analysis, we demonstrate how substitutions can enhance match performance and suggest that tactical strategies should consider substitutes’ specific abilities. Adopting substitution strategies at appropriate times is also crucial for adapting to and addressing complex match situations and environmental factors. Coaches can use these insights to refine substitution strategies, adjust tactics, and optimise player fitness, ultimately improving team performance and gaining a competitive advantage in high-level competitions [24,49].
This study mainly focuses on the running data of starting players, substitutes, and players who were substituted off, as well as the average running data of players for each team. This still has some limitations. Our analysis failed to capture the real-time intensity of team running before and after substitutions, as well as the dynamic changes during the game and the differences in spatiotemporal characteristics among players with different roles. Future research integrates individual tracking data to reveal the real-time effects of substitution strategies and combines position-specific analyses to quantify intensity demands. These refinements would enable more precise training prescriptions and in-game management strategies.

5. Conclusions

This study analysed data from the 2022 World Cup and found that substitutions were significantly associated with player running performance. More substitutions were associated with increased total running distance and number of sprints, which are closely related to match outcomes, and substitute players play a key role in maintaining match intensity. These findings provide an important basis for coaching teams to optimise substitution strategies and physical training under new rules.

Author Contributions

Conceptualisation, J.W.; data curation, Y.Z.; writing—original draft preparation, Y.Z.; writing—review and editing, J.W.; visualisation, Y.Z.; supervision, J.W. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Restrictions apply to the availability of these data, which were obtained under licence from FIFA’s Training Centre (https://www.fifatrainingcentre.com/en/ (accessed on 29 August 2025)) and require platform authentication for access. The processed dataset supporting the conclusions of this article will be made available by the authors on request.

Acknowledgments

During the preparation of this manuscript, the authors used the ChatGPT-4o model for the purposes of improving the language. The authors have reviewed and edited the output and take full responsibility for the content of this publication.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
MRPMatch running performance
EMPEntire match players
RPReplaced players
SPSubstitute players
TDRelative total distance
WJDRelative walking and jogging distance
LIDRelative low-intensity running distance
MIDRelative mid-intensity running distance
HIDRelative high-intensity running distance
SDRelative sprint distance
Number of HIRRelative number of high-intensity runs
Number of sprintsRelative number of sprints
LMMLinear mixed model

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Figure 1. The differences in running metrics among entire match players, replaced players, and substitute players.
Figure 1. The differences in running metrics among entire match players, replaced players, and substitute players.
Applsci 15 09540 g001
Table 1. The variables used when performing the eight linear mixed-model analyses.
Table 1. The variables used when performing the eight linear mixed-model analyses.
TypeVariablesAbbreviationDefinitionUnit
Independent variablesSubstitutionsTotal in-match number of substitutions (including concussion substitutions)-
Dependent variablesRelative total
distance
TDTotal distance covered per minutem
Relative walking and jogging
distance
WJDSpeed range: 0–7 km·h−1 Distance covered per minutem
Relative low-intensity running distanceLIDSpeed range: 7–15 km·h−1 Distance covered per minutem
Relative mid-intensity running distanceMIDSpeed range: 15–20 km · h−1 Distance covered per minutem
Relative high-intensity running distanceHIDSpeed range: 20–25 km · h−1 Distance covered per minutem
Relative sprint distanceSDSpeed range: ≥25 km · h−1 Distance covered per minutem
Relative number of high-intensity runsNumber of HIRTimes of high-intensity running per minute-
Relative number of sprintsNumber of sprintsTimes of sprints running per minute [24]-
CovariatesMatch stages1 = group stages 1; 2 = group stages 2;
3 = group stages 3; 4 = round of 16;
5 = quarter-finals; 6 = semi-finals;
7 = final/3rd place
-
Team qualityElo-based ratings: https://eloratings.net/2022 (accessed on 26 April 2025)-
Opponent quality-
Match outcome1 = win; 0 = draw; −1 = loss-
Stoppage timeThe seven main types of match interruptions covered are player substitutions, injury treatment, time wasting, disciplinary penalties, medical time-outs (hydration/cooling), VAR review delays, and other obvious delays in resuming play [25].min
PossessionPossession control shows the percentage of time each team is in possession of the ball [10].%
Formation1 = 5-3-2; 2 = 5-4-1; 3 = 4-3-3; 4 = 4-4-2; 5 = 4-5-1; 6 = 3-4-3; 7 = 3-5-2-
CounterattackFollowing a loss of possession of the ball, the out-of-possession team immediately aims to regain the ball through aggressive pressure on the opponent [10].%
High pressThe defensive team engages the opposition high up the pitch and attempts to aggressively apply defensive pressure against the attacking team [10].%
Table 2. Associations between independent variables, covariates, and running metrics (Model 1–4).
Table 2. Associations between independent variables, covariates, and running metrics (Model 1–4).
CoefficientsSEdft Valuep95% CI
lowerupper
Model 1 (TD)
(Intercept)111.05512.351788.918.99<0.00186.51135.60
Substitutions2.3640.502093.794.71<0.0011.373.36
[Results = −1]−2.7541.195487.75−2.300.024−5.13−0.38
[Results = 0]−0.1291.128184.55−0.120.909−2.372.11
[Results = 1]
Stoppage time−0.7810.1217100.78−6.42<0.001−1.02−0.54
OthersNS
Model 2 (WJD)
(Intercept)35.2543.450286.3310.22<0.00128.4042.11
[stage = 1]−1.6590.653081.54−2.540.013−2.96−0.36
[stage = 2]−1.3920.664181.90−2.100.039−2.71−0.07
[stage = 3]−0.8990.660881.36−1.360.178−2.210.42
[stage = 4]−0.6230.683081.58−0.910.364−1.980.74
[stage = 5]0.8470.747380.381.130.26−0.642.33
[stage = 6]−0.8770.818477.20−1.070.287−2.510.75
[stage = 7]
[Results = −1]−0.9190.325986.86−2.820.006−1.57−0.27
[Results = 0]0.1640.307183.140.530.595−0.450.77
[Results = 1]
Stoppage time−0.0710.033498.98−2.120.037−0.140.00
Possession %0.0340.0170102.022.020.0460.000.07
High Press−0.2200.046698.54−4.73<0.001−0.31−0.13
OthersNS
Model 3 (LID)
(Intercept)49.2208.266585.355.95<0.00132.7865.65
Substitutions1.5430.327190.474.72<0.0010.892.19
[stage = 1]3.2121.546681.332.080.0410.136.29
[stage = 2]1.5661.573181.651.000.322−1.564.70
[stage = 3]2.9261.565281.101.870.065−0.196.04
[stage = 4]0.6521.617781.330.400.688−2.573.87
[stage = 5]1.9221.769880.231.090.281−1.605.44
[stage = 6]0.5841.937077.310.300.764−3.274.44
[stage = 7]
Stoppage Time−0.5480.078699.53−6.97<0.001−0.70−0.39
OthersNS
Model 4 (MID)
(Intercept)18.5674.180185.354.44<0.00110.2626.88
Substitutions0.3570.164390.532.180.0320.030.68
Stoppage Time−0.1250.039997.96−3.130.002−0.20−0.05
Counterattack0.3780.170893.772.210.030.040.72
High Press0.2240.055797.974.02<0.0010.110.33
OthersNS
SE: standard error; df: degrees of freedom; CI: confidence interval; −: reference groups were set for categorical variables; NS: independent variables and covariates not significant in model. TD: Total running distance; WJD: walking and jogging distance; LID: low-intensity running distance; MID: mid-intensity running distance.
Table 3. Associations between independent variables, covariates, and running metrics. (Model 5–8).
Table 3. Associations between independent variables, covariates, and running metrics. (Model 5–8).
CoefficientsSEdft Valuep95% CI
lowerupper
Model 5 (HID)
(Intercept)6.8522.170592.183.160.0022.5411.16
Substitutions0.2220.092898.442.390.0190.040.41
High Press0.1290.0310101.824.16<0.0010.070.19
OthersNS
Model 6 (SD)
(Intercept)1.3311.0488103.001.270.207−0.753.41
[stage = 1]0.6130.2325103.002.640.010.151.07
[stage = 2]0.7270.2359103.003.080.0030.261.20
[stage = 3]0.5060.2349103.002.160.0330.040.97
[stage = 4]0.4800.2427103.001.980.050.000.96
[stage = 5]0.6180.2678103.002.310.0230.091.15
[stage = 6]0.7280.2997103.002.430.0170.131.32
[stage = 7]
[Results = −1]−0.2430.1149103.00−2.120.037−0.47−0.02
[Results = 0]0.0400.1086103.000.370.714−0.180.26
[Results = 1]
Counterattack0.1270.0481103.002.650.0090.030.22
High Press0.0350.0155103.002.280.0250.000.07
OthersNS
Model 7 (number of HIR)
(Intercept)1.54610.292886.485.28<0.0010.962.13
Substitutions0.03750.011691.293.220.0020.010.06
Stoppage Time−0.01340.002898.74−4.75<0.001−0.02−0.01
Counterattack0.03030.012194.472.510.0140.010.05
High Press0.01490.003998.483.78<0.0010.010.02
OthersNS
Model 8 (number of sprints)
(Intercept)0.57550.130393.634.42<0.0010.320.83
Substitutions0.01690.0057102.862.950.0040.010.03
[Results = −1]−0.03130.014091.93−2.240.027−0.060.00
[Results = 0]−0.00670.013293.22−0.510.611−0.030.02
[Results = 1]
Stoppage Time−0.00330.001395.26−2.490.014−0.010.00
Team quality−0.00010.000038.00−2.790.0080.000.00
High Press0.00740.0019102.903.89<0.0010.000.01
OthersNS
SE: standard error; df: degrees of freedom; CI: confidence interval; −: reference groups were set for categorical variables; NS: independent variables and covariates not significant in model. HID: high-intensity running distance; SD: sprint distance; number of HIR: number of high-intensity runs.
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Wang, J.; Zhai, Y. Association Between Substitutions and Match Running Performance Under Five-Substitution Rule: Evidence from the 2022 FIFA World Cup. Appl. Sci. 2025, 15, 9540. https://doi.org/10.3390/app15179540

AMA Style

Wang J, Zhai Y. Association Between Substitutions and Match Running Performance Under Five-Substitution Rule: Evidence from the 2022 FIFA World Cup. Applied Sciences. 2025; 15(17):9540. https://doi.org/10.3390/app15179540

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Wang, Jibing, and Yujia Zhai. 2025. "Association Between Substitutions and Match Running Performance Under Five-Substitution Rule: Evidence from the 2022 FIFA World Cup" Applied Sciences 15, no. 17: 9540. https://doi.org/10.3390/app15179540

APA Style

Wang, J., & Zhai, Y. (2025). Association Between Substitutions and Match Running Performance Under Five-Substitution Rule: Evidence from the 2022 FIFA World Cup. Applied Sciences, 15(17), 9540. https://doi.org/10.3390/app15179540

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