Key indicator for winning soccer matches: net efficiency

Abstract

Background

Current soccer match analysis focuses predominantly on team tactics and technical aspects, such as offensive and defensive strategies and their transitions. However, match efficiency has received limited attention, making it difficult to explain scenarios where a team dominates possession but fails to secure victory.

Methods

This study introduced the concept of soccer match efficiency and proposed computational formulas for offensive efficiency (OE), defensive efficiency (DE), and net efficiency (NE). Using data from the Chinese Super League (CSL) between 2014 and 2019, we analyzed NE as a metric for evaluating the balance between a team’s offensive and defensive performance.

Results

Net efficiency effectively reflected the balance between offensive and defensive performance and elucidated the phenomenon of “dominating possession but failing to score.” In the CSL: (1) an NE ≥ 0.2 corresponded to an 80.62% win probability; (2) an NE between 0.1 and < 0.2, 64.38%; (3) an NE between 0 and 0.1, 46.07%; (4) an NE of 0, 0%; (5) an NE between − 0.1 and 0, 24.69%; (6) an NE between − 0.2 and − 0.1, 11.25%; and (7) an NE ≤ -0.2, 5.38%.

Conclusion

(1) Net efficiency showed a clear positive association with match outcomes, with higher NE values corresponding to higher winning rates. (2) Net efficiency provided a quantitative measure of offensive-defensive balance and offered a clearer explanation for why teams may dominate possession yet lose.

Introduction

In football, it was common to see a team dominate possession yet fail to win, a phenomenon often termed “dominating possession but failing to score.” This paradox, documented in prior sports analytics research [1, 2], highlighted a limitation of possession-based performance metrics. For instance, in the 2022 World Cup semi-final, Croatia had 61% possession but lost 0–3 to Argentina. In club football, Barcelona had 73% possession in a 2020/21 La Liga match but lost 0–1 to Getafe.

To better understand why possession dominance did not guarantee victory, this study introduced the concept of match efficiency, shifting the focus from specific tactics and techniques to a broader analysis of key performance indicators.

Therefore, the aim of this study was to introduce the concept of net efficiency (NE) in soccer, quantify its association with match outcomes, and examine its utility in explaining the offensive-defensive balance using data from the Chinese Super League (CSL).

Match efficiency could be categorized into two main types. The first type measured the effectiveness of match actions completed within a unit of time. Professional basketball leagues, such as the NBA, had long employed such efficiency metrics. For example, points scored per 100 possessions to evaluate team performance [3–6]. These metrics provided a conceptual precedent for introducing similar efficiency concepts into soccer.

The second type used a specific model, such as Data Envelopment Analysis (DEA), to compute efficiency scores. DEA had been applied to assess the technical efficiency of football teams based on match derived inputs and outputs. For instance, Espitia-Escuer and García-Cebrián used DEA to evaluate Spanish First Division teams (1998–2001) and found that high DEA efficiency scores did not always correspond to top league finishes [7]. Beyond overall efficiency, DEA had also been used to separate offensive and defensive efficiency. Boscá et al. applied DEA to Italian and Spanish football and found that improving defensive efficiency was more critical for success in Italy, whereas enhancing offensive efficiency was key in Spain [8]. Villa and Lozano further developed a Multiple Modes of Functioning DEA model to determine the optimal time allocation between defensive and offensive play [9].

Previous football research had extensively examined isolated technical actions, such as passing accuracy [10], shooting efficiency [11], and defensive interventions [12], as predictors of match outcomes. However, these studies often treated each action independently, without integrating them into a unified measure of how efficiently a team converted possession into scoring opportunities or prevented opponents from doing so. Consequently, a conceptual gap remained in understanding how the balance between offensive and defensive efficiency collectively determined match results.

Unlike previous studies that had focused on isolated technical actions such as passing behavior [2], this study shifted the analytical focus toward overall match efficiency and offensive - defensive balance as determinants of winning.

Methods

The dataset used in this study consists of match data from the Chinese Super League between the 2014 and 2019 seasons. A portion of this dataset has been previously analyzed to investigate the contextual influencing factors of passing behavior [2]. In contrast, the present study focuses on developing and validating a novel efficiency-based indicator to explain match outcomes, representing a distinct analytical perspective and research objective. This research received approval from the relevant institutional ethics committee. Furthermore, formal permission for data usage was obtained from CHAMPION Sports Information Technology Company.

This study employed a retrospective observational design based on historical match data from the CSL. Due to its exploratory nature in defining and validating a novel efficiency metric from this existing dataset, a formal pre-registration of the analysis plan was not undertaken. However, the core analytical framework, which defined OE, DE, and NE and examined their relationship with match outcomes, was determined during the study design phase.

Samples

This study analyzed data from the Chinese Super League spanning the 2014 to 2019 seasons. The sample consisted of 16 teams that participated in the league for at least three seasons during this period, encompassing a total of 1,014 matches, which correspond to 2,028 team-match observations. Teams were classified into four performance tiers — high-level (average rank 1–4), upper-middle (rank 5–8), lower-middle (rank 9–12), and low-level (rank 13–16) — based on their average league standings across the six-season time frame.

Definition and calculation formula for offensive efficiency

Aligned with the fundamental concept of efficiency — work completed per unit of time — and accounting for the characteristic low-scoring nature of soccer, this study defines offensive efficiency (OE) as the rate at which a team generates shots on target per minute of its possession. Formally, it is calculated as the ratio of the number of shots on target to the total possession time in a match, as expressed in Formula (1):

1

In this formula, “Number of shots on target” refers to the count of shots directed within the goal frame. “Ball possession time” denotes the team’s total ball possession time, measured in minutes. A higher OE value indicates a greater capacity to create scoring opportunities efficiently during possession.

Notably, this study defined offensive efficiency as the rate of generating shots on target per minute of possession rather than the rate of generating expected goals (xG) per minute of possession. The primary reason was that shots on target represented a simple and definitive binary event, whereas xG values may vary due to differences in underlying algorithms, leading to model-dependent discrepancies. We acknowledged that shots on target capture only one dimension of offensive output, namely shot quantity, and do not incorporate shot quality, which may affect offensive effectiveness.

Definition and calculation formula for defensive efficiency

This study defined defensive efficiency (DE) as the rate at which a team conceded shots on target per minute of the opponent’s possession. It was calculated as the ratio of the number of shots on target a team allowed to the total possession time of the opponent in a match, as specified in Formula (2):

2

In this formula, “Number of shots on target against” refers to the count of shots on target faced by the team. “Ball possession time for the opponent” denotes the total duration, in minutes, for which the opposing team possesses the ball. A lower DE value indicates a stronger defensive performance, as it reflects a greater ability to limit the opponent’s chances relative to their time in possession.

Definition and calculation formula for net efficiency

This study defined net efficiency (NE) as the difference between a team’s offensive efficiency and its defensive efficiency, as shown in Formula (3):

3

Given that a higher OE value indicates stronger offensive performance and a lower DE value indicates stronger defensive performance, the NE metric yields the following interpretive characteristics:

1. NE > 0: A positive NE indicates superior combined efficiency. A higher positive value reflects stronger performance in offense, defense, or both.

2. NE ≈ 0: An NE value approximating zero indicates that offensive efficiency (OE) and defensive efficiency (DE) are numerically similar. However, since OE is a positive indicator (higher values reflect stronger offensive performance), whereas DE is a negative indicator (lower values reflect stronger defensive performance), a near-zero NE may result from different underlying configurations: (a) both OE and DE are low (weak offense but strong defense), or (b) both are high (strong offense but weak defense). Therefore, NE ≈ 0 does not reflect balanced performance but rather an imbalance between offensive and defensive efficiencies.

3. NE < 0: A negative NE signifies weaker overall efficiency. A lower (more negative) value indicates poorer performance in offense, defense, or both, highlighting deficiencies in one or both phases of play.

Analysis of factors affecting net efficiency

This study utilized a Generalized Linear Mixed Model (GLMM) to examine the factors influencing net efficiency. The assignment of effects as either fixed or random followed established statistical principles [13]: (1) An effect was treated as a fixed effect if the levels of the explanatory variable were finite and of specific interest to the study’s hypotheses. (2) An effect was treated as a random effect if the levels of the explanatory variable could be considered a random sample from a larger population (infinite or large number of levels). In accordance with these principles, season was included as a random effect to account for variability across the six sampled years, while all other explanatory variables were treated as fixed effects in the model. Team identity was not included as a random effect because the analysis focused on match-level predictors (venue, result, and technical indicators) that varied within teams across matches, and team-specific performance heterogeneity was captured through multiple technical indicators that directly reflected team characteristics. In addition, supplementary tests including team identity as a random effect showed that its variance component was negligible (approaching zero), indicating minimal between-team variability after accounting for the fixed effects. Therefore, team identity was not retained as a random effect in the final model.

Dependent variable

The dependent variable in the model is net efficiency.

Fixed effects

The model incorporated two categorical variables as fixed effects: match venue (home/away) and match result. Furthermore, recognizing that net efficiency synthesizes both offensive and defensive performance, the model included a comprehensive set of 15 in-match technical indicators that theoretically influence these components. These continuous and count variables were: possession rate, total passes, pass success rate, offensive dominance rate, free kicks, free kicks in the opponent’s half, corner kicks, key passes, offsides, fouls suffered, tackles, interceptions, blocked passes, clearances, and yellow cards.

Random effects

To account for non-independence and unexplained variability across the longitudinal dataset, season (spanning the six seasons from 2014 to 2019) was included as a random intercept effect in the model.

The model was estimated under the assumption that the dependent variable, net efficiency (NE), follows a normal distribution. An identity link function and a variance components structure for the random effects covariance were specified. The model’s goodness-of-fit, as indicated by the Akaike Information Criterion (AIC), was − 3479.958. The structure of the GLMM for factors affecting net efficiency is formally expressed by Eq. (4):

4

In formula (4), Y_NE is the dependent variable, which is net efficiency; β₀ represents the intercept; β₁ to β₁₇ are the fixed-effect coefficients for their respective predictor variables: match venue, match result, possession rate, total passes, pass success rate, offensive dominance rate, free kicks, free kicks in the opponent’s half, corner kicks, key passes, offsides, fouls suffered, tackles, interceptions, blocked passes, clearances, and yellow cards; T_ij represents the random intercept effect; ε_ij is the residual error term.

Measurement variables and statistical analysis

The key performance indicators (KPIs) used in this study—shots on target, possession time, key passes, offensive dominance rate, tackles, interceptions, etc.—are standard, widely adopted metrics in professional soccer performance analysis. Their construct validity for representing offensive threat, defensive pressure, and overall team performance is well-established in the sports analytics literature [14].

The match data were provided by CHAMPION Sports Information Technology Company, a leading sports data provider in China. The company employs trained, certified data analysts who record events using a standardized, real-time coding system. The reliability of such professional data collection systems, characterized by high inter-rater agreement and consistency, has been documented in prior studies utilizing data from similar providers (e.g., OPTA, STATS) [15]. Furthermore, the dataset from this provider has been used in previously published, peer-reviewed research on the CSL [2], supporting its acceptance in the scientific community.

For factors (e.g., team level) found to have a significant overall effect, post hoc pairwise comparisons between groups were conducted using Mann-Whitney U tests. To control for Type I error inflation due to multiple comparisons, the Bonferroni correction was applied. Accordingly, adjusted significance levels of P < 0.008 were used to determine statistical significance.

Results

Analysis of offensive efficiency, defensive efficiency, and net efficiency in the CSL

Table 1 presents the statistical analysis of offensive, defensive, and net efficiency across different performance tiers in the CSL over six seasons. The mean offensive efficiency for high-level, upper-middle-level, lower-middle-level, and low-level teams was 0.201, 0.171, 0.168, and 0.152, respectively. A one-way ANOVA revealed that these group differences were statistically significant (F = 23.063, P < 0.001, η² = 0.033).The effect size (η² = 0.033) indicates a small but statistically detectable difference. Post hoc comparisons indicated that the offensive efficiency of high-level teams was significantly higher than that of the upper-middle, lower-middle, and low-level teams (all P < 0.008). Furthermore, upper-middle-level teams demonstrated significantly higher offensive efficiency than low-level teams ( P < 0.008). No significant difference was found between upper-middle-level and lower-middle-level teams.

Table 1.

Statistical analysis of match efficiency in the CSL

	High-level teams (A) (N = 600)	Upper-middle-level teams (B) (N = 552)	Lower-middle-level teams (C) (N = 502)	Low-level teams (D) (N = 374)	F	P	η2
Offensive efficiency	0.201 ± 0.098BCD	0.171 ± 0.093AD	0.168 ± 0.096A	0.152 ± 0.094AB	23.063	< 0.001	0.033
Defensive efficiency	0.164 ± 0.092BD	0.187 ± 0.101AC	0.169 ± 0.094BD	0.187 ± 0.102AC	8.370	< 0.001	0.012
Net efficiency	0.037 ± 0.135BCD	-0.016 ± 0.133A	-0.002 ± 0.126AD	-0.035 ± 0.136AC	27.294	< 0.001	0.039

Superscript letters indicate statistically significant differences between group means based on post-hoc comparisons. The letters A, B, C, and D denote significance at the P < 0.008 level when compared to the high-level, upper-middle-level, lower-middle-level, and low-level groups, respectively

Mean defensive efficiency differed significantly across the four performance tiers, with values of 0.164 for high-level, 0.187 for upper-middle-level, 0.169 for lower-middle-level, and 0.187 for low-level teams (F = 8.370, P < 0.01, η² = 0.012). Post hoc tests revealed that both high-level and lower-middle-level teams exhibited significantly higher defensive efficiency (i.e., lower DE values) than upper-middle-level and low-level teams (all P < 0.008). No significant difference was found between high-level and lower-middle-level teams.

This pattern can be interpreted through the components of defensive efficiency. Lower-middle-level teams conceded an average of 4.51 shots on target per match—higher than the high-level teams’ average (3.91) but lower than that of upper-middle-level (4.66) and low-level teams (5.10). Concurrently, opponents’ average possession time against lower-middle-level teams was 26.954 min, which was lower than against low-level teams (27.506 min) but higher than against upper-middle-level (25.250 min) and high-level teams (24.089 min). Together, these figures illustrate that lower-middle-level teams allowed longer opponent possession but restricted shooting opportunities more effectively, resulting in relatively higher defensive efficiency.

Finally, a significant overall difference was observed in mean net efficiency across groups: 0.037 for high-level, -0.016 for upper-middle-level, -0.002 for lower-middle-level, and − 0.035 for low-level teams (F = 27.294, P < 0.001, η² = 0.039). High-level teams demonstrated significantly higher net efficiency than all other groups (all P < 0.008). Both high-level and lower-middle-level teams had significantly higher net efficiency than low-level teams (both P < 0.008). No significant difference was detected between upper-middle-level and lower-middle-level teams.

Relationship between net efficiency and match results in the CSL

Table 2 presents the association between net efficiency (NE) intervals and match outcome percentages. When a team’s NE is negative (NE < 0), reflecting lower combined efficiency, the observed winning percentage is markedly low (below 25%), while the observed losing percentage is high (46%). The observed winning percentage increases progressively with higher NE values, indicating stronger overall efficiency. Specifically, when NE exceeds 0.2, teams achieve an observed winning percentage of approximately 80% and an observed losing percentage of only 5.43%. In the unique case where NE equals zero, both the observed winning and losing percentages are precisely 0% within the sampled data.

Table 2.

The relationship between net efficiency and observed winning and losing percentages in the CSL

Net efficiency range (NE)	Wins	Draws	Losses	Total matches*	Observed winning percentage (%)	Observed losing percentage (%)
NE ≥ 0.2	104	18	7	129	80.62	5.43
0.1 ≤ NE < 0.2	206	78	36	320	64.38	11.25
0 < NE < 0.1	258	165	137	560	46.07	24.46
NE = 0	0	6	0	6	0.00	0.00
-0.1 < NE < 0	139	165	259	563	24.69	46.00
-0.2 < NE ≤ -0.1	36	78	206	320	11.25	64.38
NE ≤ -0.2	7	18	105	130	5.38	80.77

The analysis was confined to 16 teams that participated in at least three seasons within the study period. Consequently, because matches involving other teams were excluded, the numbers of games within each net efficiency interval do not sum to the total match count of the league. The NE = 0 category contains only 6 observations; the 0% win and loss rates should be interpreted with caution given this small sample size.

Analysis of factors influencing net efficiency

Table 3 reports the fixed effects results from the GLMM on factors influencing net efficiency (NE) in the CSL. The analysis confirmed a significant home advantage effect (t = 6.278, P < 0.001), with NE being on average 0.023 units higher in home games than in away games. Match outcome was also a significant determinant of NE. Using matches won by two or more goals as the reference, the estimated NE was 0.081, 0.120, 0.160, and 0.243 units lower for matches won by one goal, drawn, lost by one goal, and lost by two or more goals, respectively (all P < 0.001).

Table 3.

Fixed effects analysis of factors influencing net efficiency in the CSL

	Estimate(β)	SE	t	P	95%CI
Intercept	0.318	0.037	8.656	< 0.001	0.246, 0.390
Home	0.023	0.004	6.278	< 0.001	0.016, 0.030
Away	0#
Loss by 2 Goals or More	-0.243	0.006	-39.473	< 0.001	-0.255, -0.231
Loss by 1 Goal	-0.160	0.006	-27.370	< 0.001	-0.172, -0.149
Draw	-0.120	0.005	-22.480	< 0.001	-0.131, -0.110
Win by 1 Goal	-0.081	0.006	-14.391	< 0.001	-0.092, -0.070
Win by 2 Goals or More	0#
Possession rate	-1.218	0.071	-17.233	< 0.001	-1.357, -1.079
Total pass	< 0.001	< 0.001	1.053	0.293	< -0.001, < 0.001
Pass success rate	0.037	0.044	0.836	0.403	-0.050, 0.123
Offensive dominance rate	0.510	0.040	12.611	< 0.001	0.431, 0.589
Free kick	-0.001	0.001	-0.908	0.364	-0.002, 0.001
Freekick in the opponent's half	< 0.001	0.001	0.095	0.924	-0.002, 0.002
Corner kick	0.002	0.001	3.167	0.002	0.001, 0.004
Key pass	0.006	0.001	11.309	< 0.001	0.005, 0.007
Offside	0.003	0.001	2.768	0.006	0.001, 0.005
Foul suffered	0.002	0.001	2.590	0.010	0.001, 0.004
Tackle	0.001	< 0.001	2.528	0.012	< 0.001, 0.002
Interception	< 0.001	< 0.001	2.376	0.018	< 0.001, 0.001
Block pass	< 0.001	< 0.001	0.044	0.965	-0.001, 0.001
Clearance	< -0.001	< 0.001	-0.984	0.325	-0.001, < 0.001
Yellow card	-0.002	0.001	-1.215	0.224	-0.004, 0.001

# indicates a redundant parameter and has therefore been set to zero

Among the continuous variables, offensive dominance rate [β = 0.510 (0.431, 0.589), t = 12.611, P < 0.001], corner kicks [β = 0.002 (0.001, 0.004), t = 3.167, P < 0.01], key passes [β = 0.006 (0.005, 0.007), t = 11.309, P < 0.001], offsides [β = 0.003 (0.001, 0.005), t = 2.768, P < 0.01], fouls suffered [β = 0.002 (0.001, 0.004), t = 2.590, P < 0.01], tackles [β = 0.001 (< 0.001, 0.002), t = 2.528, P < 0.05], and interceptions [β < 0.001 (< 0.001, 0.001), t = 2.376, P < 0.05] have a positive impact on match net efficiency. Possession rate [β = -1.218 (-1.357, -1.079), t = -17.233, P < 0.001] has a negative impact on match net efficiency.

However, variables such as total passes [β < 0.001 (<-0.001, < 0.001), t = 1.053, P > 0.05], pass success rate [β = 0.037 (-0.050, 0.123), t = 0.836, P > 0.05], free kicks [β = -0.001 (-0.002, 0.001), t = -0.908, P > 0.05], free kicks in the opponent's half [β < 0.001 (-0.002, 0.002), t = 0.095, P > 0.05], blocked passes [β < 0.001 (-0.001, 0.001), t = 0.044, P > 0.05], clearances [β < -0.001 (-0.001, < 0.001), t = -0.984, P > 0.05], and yellow cards [β = -0.002 (-0.004, 0.001), t = -1.215, P > 0.05] do not have a significant impact on match net efficiency.

In the random effects analysis of factors influencing team net efficiency, the estimate for the season [β < 0.001 (< 0.001, < 0.001), z = 1.551, P > 0.05] was not statistically significant, indicating that the season had no substantial impact on team net efficiency (Table 4).

Table 4.

Random effects analysis of factors influencing net efficiency in the CSL

	Estimate（β）	SE	z	P	95% CI
Intercept	< 0.001	< 0.001	0.673	0.501	< 0.001, 0.001
Season	< 0.001	< 0.001	1.551	0.121	< 0.001, < 0.001

Discussion

Distinguishing between capability and efficiency in offense and defense

A team’s offensive and defensive capability is conventionally assessed through a combination of relatively stable, long-term factors. These include player market value, historical performance, and seasonal results, or are inferred from aggregate match statistics such as goals scored/conceded, total shots, shots on target, and possession rates. A team with high offensive capability is typically characterized by elite forwards, high player valuations, effective dribbling, prolific scoring, and sustained possession [16–18]. Similarly, strong defensive capability is associated with skilled defenders, coordinated team defending, low goals conceded, and a high frequency of successful tackles and interventions [19]. As these assessments are multidimensional and composite, it is challenging to define capability precisely with a single metric.

Traditional in-match statistics can be misleading indicators of capability. For instance, the number of goals scored does not solely reflect offensive strength, as a team can dominate key metrics yet fail to win. A salient example is the Germany vs. Japan match in the 2022 FIFA World Cup Group E: Germany dominated possession (74% vs. 26%), total shots (26 vs. 12), and shots on target (9 vs. 4), but lost 1–2. This demonstrates that assumptions like “higher possession or more shots indicate superior capability"require nuanced, multi-dimensional analysis beyond simple tallying.

To establish a more objective measure of in-game performance, this study introduced offensive efficiency (OE, shots on target per minute of possession) and defensive efficiency (DE, shots conceded per minute of opponent possession). A clear distinction was drawn between efficiency conversion of possession into chances within a match and capability a team’s underlying potential based on player quality and historical performance. The negligible correlation between OE and DE (r = 0.031, P > 0.05) supported this distinction. This framework might help explain why teams could win despite being outperformed in conventional metrics: match outcomes might depend more on efficiency in key moments than on aggregate possession or shots.

Evaluating the offensive and defensive Strengths of CSL Clubs

While NE provides a valuable metric for assessing the balance between offensive and defensive performance based on actual match data, its interpretation requires caution in the presence of extreme values. A high NE can occasionally result from an extreme imbalance between exceptionally high OE and poor DE, rather than indicating strength in both phases. For instance, a team with an OE of 0.35 and a DE of 0.20 would yield an NE of 0.15, profiling it as offensively strong but defensively weak, not strong in both. It is important to note that such extreme outlier cases were rare in our CSL sample, occurring in only 24 out of 2,028 team-match observations (1.18%).

Figure 1 presents the offensive efficiency, defensive efficiency, and net efficiency for the 16 CSL teams across the 2014–2019 seasons. Based on this analysis, teams were categorized into distinct profiles:

• Strong in both offense and defense: Guangzhou Hengda, Shandong Luneng, Shanghai Shanggang, Beijing Guoan, Henan Jianye, and Jiangsu Suning.

• Strong offense but weak defense: Shanghai Shenhua.

• Strong defense but weak offense: Tianjin Taida and Changchun Yatai.

• Weak in both offense and defense: Tianjin Quanjian, Hangzhou Lvcheng, Chongqing Lifan, Liaoning Hongyun, Hebei Huaxia, Dalian Aerbin, and Guangzhou Fuli.

Fig. 1.

Analysis of Offensive, Defensive and Net Efficiency for the 16 Teams in the CSL (2014-2019 Seasons). Note: 1) Using the median offensive efficiency of 0.169 and the median defensive efficiency of 0.173, the graph is divided into four quadrants. Teams in the "strong in both offense and defense" quadrant have a net efficiency ≥ 0.010; teams in the "strong offense but weak defense" or "weak offense but strong defense" quadrants have a net efficiency between -0.010 and 0.010 (excluding the endpoints); teams in the "weak in both offense and defense" quadrant have a net efficiency ≤ -0.010. 2) In the graph, golden bubbles represent positive values, with larger diameters indicating higher net efficiency. White bubbles represent negative values, with larger diameters indicating lower (more negative) net efficiency. 3) Team codes in the graph:1: Guangzhou Hengda 2: Shandong Luneng 3: Shanghai Shanggang 4: Beijing Guoan 5: Henan Jianye 6: Jiangsu Suning 7: Shanghai Shenhua 8: Tianjin Taida 9: Changchun Yatai 10: Tianjin Quanjian 11: Hebei Huaxia 12: Chongqing Lifan 13: Dalian Aerbin 14: Hangzhou Lvcheng 15: Liaoning Hongyun 16: Guangzhou Fuli

Differential analysis of generalized linear mixed models

This study employed a Generalized Linear Mixed Model (GLMM) to analyze factors influencing net efficiency, a method well-suited for our longitudinal dataset comprising repeated observations of teams across six seasons [13]. The GLMM framework accounts for the non-independence of observations (e.g., multiple matches from the same team) and unexplained variability across clusters (e.g., different seasons) through the inclusion of random effects, yielding more robust and reliable parameter estimates than traditional regression models.

Our GLMM analysis revealed insightful relationships between in-match actions and net efficiency. The negative association between possession and net efficiency suggests that in the CSL, high possession without effective penetration lowers efficiency. Offensive dominance rate and key passes, which are metrics of purposeful attack, support this view and indicate that optimizing possession quality rather than its duration enhances efficiency.

It is important to distinguish the objective of our GLMM analysis from that of Data Envelopment Analysis (DEA), another prevalent method in sports efficiency research. DEA is primarily a benchmarking tool designed to evaluate the relative efficiency of decision-making units (e.g., clubs) by comparing their multiple inputs and outputs, often from a season-long or managerial perspective [9]. In contrast, the GLMM applied here is an inferential statistical model. Its purpose is not to rank units, but to identify, quantify, and test the statistical significance of specific in-match technical indicators and contextual factors (the fixed effects) that are associated with variations in the net efficiency metric. This approach allows us to move beyond evaluation towards understanding the mechanistic drivers of efficiency within a match.

Limitations

The findings of this study and the established relationship between NE values and win probability should be interpreted within the context of its specific data source. A primary limitation is the exclusive reliance on match data from the Chinese Super League (CSL). Football styles, competitive intensity, and tactical paradigms vary significantly across different leagues and cultural contexts (e.g., the high-pressing style prevalent in some European leagues versus a more possession-based approach in others). Consequently, the quantitative thresholds of NE associated with win probabilities (e.g., NE ≥ 0.2 corresponding to an 80.62% win rate) identified here may not be directly generalizable to other leagues. The external validity of our model requires further testing with datasets from diverse competitions and levels of play. Future research should aim to incorporate multi-league data to investigate whether the NE-win probability relationship remains consistent or varies according to the specific competitive ecosystem, which would enhance the metric’s utility as a universal performance analysis tool.

Secondly, the study was not pre-registered. Future confirmatory studies building upon the net efficiency metric presented here would benefit from a pre-registered analytical plan to enhance reproducibility.

Conclusion

This study deconstructed match efficiency into offensive efficiency, defensive efficiency, and net efficiency, establishing their conceptual definitions and calculation methods. Using a generalized linear mixed model, it investigated the determinants of offensive efficiency, defensive efficiency, and net efficiency in the Chinese Super League and examined variations across teams of different performance levels. The primary findings are as follows: (1) Net efficiency showed a clear positive association with match outcomes, with higher NE values corresponding to higher winning rates. (2) Net efficiency provides a quantitative measure of offensive-defensive balance and offers a clearer explanation for why teams may dominate possession yet lose. This metric may offer a useful perspective for assessing team performance and informing tactical decision-making. However, these findings are based on data from a single league, and further research across different competitions is needed to assess their generalizability.

Abbreviations

CSL

Chinese Super League

OE

Offensive efficiency

DE

Defensive efficiency

NE

Net efficiency

NBA

National Basketball Association

DEA

Data envelopment analysis

GLMM

Generalized linear mixed model

AIC

Akaike information criterion

BIC

Bayesian information criterion

Authors’ contributions

Conceptualization, YZ, XX and HZ; methodology (model), YZ, XX and HZ; formal analysis, YZ and XX; data processing, YZ; writing—original draft preparation, YZ and XX; writing—review and editing, HZ; project administration, HZ; funding acquisition, HZ. All authors have reviewed and agreed to the published version of the manuscript.

Funding

This work was supported by the Key Research and Development Program of Zhejiang [No. 2024C03259] and the Fundamental Research Funds for the Central Universities [grant number S20230138].

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

The study was approved by the ethics committee of College of Education of Zhejiang University, and we obtained permission for the use of the CHAMPION Sports Information Technology Company.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.