Unveiling the nonlinear dynamics of player performance in China’s super league as a function of age

To explore the dynamics in physical and technical performance of professional football players and changes across age groups. Match statistics were collected from 1900 games across ten seasons (2012–2021) in the Chinese Super League. Generalized additive models visualized age-related trends in 12 key performance indicators including technical and physical variables. Revealed nonlinear trajectories characterized by rapid early declines, stable peak periods and accelerated late decreases. Physical indicators decreased progressively from the early 20 s before stabilizing briefly then declining further after 30. Conversely, technical metrics gradually improved into the late 20 s and early 30 s prior to decreasing again. This study provides novel evidence that football performance changes nonlinearly across age. Targeted training and development strategies should be tailored to the specific needs of different career stages.

and unbalanced matches, firstly we ruled out the matches where there emerged red card(s) during the course of the match, leaving 1990 matches selected.The unit of analysis was individual player match observations.The final sample consisted of 32,348 observations.And in order to provide a clearer representation of the sample, we conducted a statistical analysis of the number of players in different age groups, as shown in Table 1.

Data collection
Physical and technical performance data were provided by the Amisco tracking system (Amisco, Nice, France).The validity and reliability of this system have been verified for quantifying player metrics 13 .Raw data were extracted and imported into a customized database.Only outfield players participating in over 50% of league matches were included, consistent with previous studies 14 .Players' match data were normalized to account for substitutions and game duration using the formula: Standardization provided more consistent match profiles 15 .Based on literature precedents [16][17][18] , six technical indicators and six physical indicators representing key elements of football performance were selected for analysis as defined in Table 2.

Statistical analysis
Data were analyzed using RStudio (Version 4.0.2) with R software (Version 4.3.0.).Generalized additive models (GAMs) were constructed using the package gamm4 to flexibly model nonlinear patterns in the performance variables across age.GAMs avoid imposing predefined functional forms and estimate smooth regression curves from the data 11 .To account for individual differences and correlations between repeated measures data across ages for the same player, players were included as a random effect in the models.Physical and technical indicators   Notably, a discernible trend of diminishing performance is evident in sprint (R 2 = 0.515; P < 0.001) and high speed running (R 2 = 0.699; P < 0.001) indicators as age advances, with the rate of decline exhibiting notable variability across different age cohorts.This decline, however, presents intriguing nuances: between the ages of 23 and 28, the rate of decline notably decelerates, and in the case of high speed running, an intriguing stabilizing trend emerges.Nevertheless, both indicators experience rapid declines prior to the age of 23 and beyond the age of 30.Similarly, TD (R 2 = 0.875; P < 0.001), medium speed running (R 2 = 0.779; P < 0.001), and low speed running (R 2 = 0.857; P < 0.001) display coherent age-related patterns.These indicators also exhibit an accelerated decrease before the age of 23, followed by a gradual attenuation in the rate of decline after this age threshold.Notably, medium speed running is a noteworthy exception, revealing a slight increase after the age of 35.
The performance indicators pass (R 2 = 0.471; P < 0.001) and challenge accuracy (R 2 = 0.172; P < 0.001) both exhibit an upward trajectory prior to the age of 25.Notably, Challenge accuracy displays a gradual increase, while pass demonstrates a more pronounced improvement.Following the age of 25, challenge accuracy demonstrates a consistent linear growth, while Pass maintains a steady performance from ages 23-28, subsequently experiencing progressive enhancement until a rapid decline becomes evident around the age of 35.Moreover, pass accuracy (R 2 = 0.262; P < 0.001) and ball retention (R 2 = 0.219; P < 0.001) both exhibit an ascending pattern before the age of 30.Pass accuracy undergoes a rapid surge, whereas ball retention displays linear growth.Beyond the age of 30, ball retention gradually decreases, while pass accuracy displays distinct trends across various age groups.

Discussion
This study analyzed age-related changes in the match performance of professional football players competing in the CSL across ten seasons.Generalized additive models revealed nonlinear trajectories characterized by more rapid declines in the early career and later veteran stages interspersed with periods of stabilization around the peak ages.Physical capacities are crucial determinants of football performance, underpinning actions like repeated sprinting, jumping and changes of direction 19 .However, physical capabilities eventually decline due to age-related changes in muscle morphology and physiology 20 .Consistent with prior research 8 , our results exhibited decreasing total distances covered as players progressed through their 20 s.High-speed activities showed pronounced drops early in careers, aligning with studies demonstrating running-based attributes peak around 22-23 years 21,22 .Interesting, from ~ 23 to 28 years high-speed running stabilized suggesting players adapted training to maintain athleticism 23 .Thereafter, sharp downward shifts likely indicated deteriorating physiological capacities that could not be attenuated 20 .
Conversely, most technical indicators improved into the late 20 s and early 30 s. Gradual refinement of passing, challenges and ball control over this period highlights the ongoing development of tactical skills and decision-making 18 .Cognitive abilities enable older players to offset physical losses by applying experience and pattern recognition 24 .Thereafter, downward turns probably reflected declining physical capacities constraining technical execution 8 .However, passing accuracy and challenge success continued improving suggesting players retained remnants of developed technique 3 .
Overall, these findings provide novel insights into football performance dynamics over careers.The nonlinear changes align with lifespan development models describing phases of growth, maintenance and decline 4,5 .
Targeted training interventions should be tailored to athletes' specific career stages 10 .For instance, developing physical capacities is crucial initially before shifting emphasis to technical and tactical refinement during peak ages.Thereafter maintaining fitness while applying cognitive experience becomes paramount.
Strategic player recruitment and team development policies could also leverage understanding of age-related performance trajectories 25 .Blending youthful athleticism with veterans' tactical expertise within squads may maximize overall capabilities 26 .Furthermore, substituting players demonstrating accelerated declines for fresh legs late in games could enhance team performance 27 .Consideration of both current ability levels and projected progression rates can inform team selections and contracts.

Conclusion
In conclusion, this study revealed age-related changes in professional football match performance followed nonlinear trajectories characterized by more precipitous declines in early and later career stages compared to during peak ages where stabilization occurred.Physical capacities decreased progressively from the early 20 s before briefly stabilizing then falling sharply again after 30 years.Conversely, technical indicators improved into the late 20 s and early 30 s before subsequent decreases.These results provide novel evidence that football performance evolves nonlinearly across the lifespan.Targeted development strategies tailored to athletes' specific career stages should be designed leveraging these insights.Furthermore, understanding nonlinear performance changes provides an opportunity to strategically optimize player recruitment, team development and in-game decisions.

Practical applications
The findings from this study highlight several practical implications for player development and team management in professional football.
Customizing adaptive physical conditioning for different stages of a professional career is crucial.Early career: emphasize maximizing sprinting and endurance.Peak: focus on skill development while ensuring physical health.Later career: maintain physical abilities.Recruitment should anticipate career progression rates, not just current skills.Optimizing overall team strength involves integrating promising young players with tactically experienced veterans.Substituting fresh players for fatigued ones late in games can offer a tactical advantage.Similarly, reducing playing time for aging athletes can enhance performance.
Overall, an integrated approach leveraging understanding of nonlinear performance changes across age can inform strategies enhancing player development, team balance and in-game management.Findings highlight the ongoing refinement of physical power, technical execution and tactical expertise required throughout careers in the dynamic, multifaceted sport of football.

Limitations
This study has certain limitations.Modeling physical and technical indicators separately is not conducive to showing the mutual effects of technology and physical fitness on players in games.Only CSL matches were assessed and findings require verification across diverse leagues and levels of play.Finally, variations between player positions were not addressed.Future studies should examine larger samples over multiple seasons and leagues.Exploring differences between player positions would provide further insights.
Physical performance-related parameters: operational definition (TD) Total distance (km): distance covered in a match by all the players of a team (LSR) Low-speed-running (m): distance covered at a speed of 7.1→14.3km/h in a match (MSR) Middle-speed-running (m): distance covered at a speed of 14.3→19.7 km/h in a match (HSR) High-speed-running (m): distance covered at a speed of 19.7→25.1 km/h in a match Sprint (m): distance covered at a speed over 25.1→ + km/h in a match (NS) Number of sprints (n): number of sprints covered at the speed over 25.1→ + km/h in a match Technical Performance-Related Parameters: Operational Definition Pass (n): an intentional played ball from one player to another Pass accuracy (%): successful passes as a proportion of total passes (NC) Number of challenge(n): actions when two players are competing for ball possession, which is not in the control of any player, i.e., both players have approximately a 50% chance of gaining control of the ball; includes ground and air challenges Challenge accuracy (%): successful challenges as a proportion of the total challenges Ball retention (%): ball retention is defined as being when your team keeps possession of the ball following your pass, which can be complete or incomplete (FP)First time Pass of individual possession (%): The percentage of immediate passes made by a player after gaining possession out of the total times the player gained possession

Figures 1 and 2
Figures 1 and 2 illustrate distinct performance indicators, namely number challenge (R 2 = 0.398; P < 0.001) and number sprint (R 2 = 0.526; P < 0.001), both of which exhibit a consistent decline as individuals progress in age.Notably, a discernible trend of diminishing performance is evident in sprint (R 2 = 0.515; P < 0.001) and high speed running (R 2 = 0.699; P < 0.001) indicators as age advances, with the rate of decline exhibiting notable variability across different age cohorts.This decline, however, presents intriguing nuances: between the ages of 23 and 28, the rate of decline notably decelerates, and in the case of high speed running, an intriguing stabilizing trend emerges.Nevertheless, both indicators experience rapid declines prior to the age of 23 and beyond the age of 30.Similarly, TD (R 2 = 0.875; P < 0.001), medium speed running (R 2 = 0.779; P < 0.001), and low speed running (R 2 = 0.857; P < 0.001) display coherent age-related patterns.These indicators also exhibit an accelerated decrease before the age of 23, followed by a gradual attenuation in the rate of decline after this age threshold.Notably, medium speed running is a noteworthy exception, revealing a slight increase after the age of 35.The performance indicators pass (R 2 = 0.471; P < 0.001) and challenge accuracy (R 2 = 0.172; P < 0.001) both exhibit an upward trajectory prior to the age of 25.Notably, Challenge accuracy displays a gradual increase, while pass demonstrates a more pronounced improvement.Following the age of 25, challenge accuracy demonstrates a consistent linear growth, while Pass maintains a steady performance from ages 23-28, subsequently experiencing progressive enhancement until a rapid decline becomes evident around the age of 35.Moreover, pass accuracy (R 2 = 0.262; P < 0.001) and ball retention (R 2 = 0.219; P < 0.001) both exhibit an ascending pattern before the age of 30.Pass accuracy undergoes a rapid surge, whereas ball retention displays linear growth.Beyond the age of 30, ball retention gradually decreases, while pass accuracy displays distinct trends across various age groups.

Figure 1 .
Figure 1.Generalized additive model plots for age-related changes in physical performance metrics.Solid lines indicate smoothers surrounded by 95% confidence intervals depicted by dashed lines.

Figure 2 .
Figure 2. Generalized additive model plots for age-related changes in technical performance metrics.Solid lines indicate smoothers surrounded by 95% confidence intervals depicted by dashed lines.

Table 1 .
The sample size for different seasons and age groups, as well as the total sample size for 10 seasons and different age groups.

Table 2 .
Operational definition of technical and physical performance-related parameters.
Specifically, it tends to stabilize between the ages of 30 and 35 before resuming a gradual rise.Lastly, the indicator FP (R 2 = 0.305; P < 0.001) demonstrates rapid escalation with age until the age of 23, after which the growth trend diminishes and approaches stability between ages 23 and 28.Following the age of 30, FP once again embarks on a progressive upward trend.