Stroke-level performance fluctuation analysis in elite table tennis

Abstract

Background

Table tennis is characterized by high intensity and short rallies, where the stability of technical and tactical execution is crucial to performance. Existing research on performance fluctuations has primarily focused on psychological or score-based metrics, neglecting the technical execution of strokes. To address this gap, this study introduces a novel metric: Stroke Performance Fluctuation (SPF).

Method

The dataset consists of 100 elite matches (50 male and 50 female matches) between 2021 and 2025, analyzing 2,163 rallies and 29,406 strokes. SPF is quantified as the deviation between Rally Winning Probability (RWP) and Expected Rally Winning Probability (ERWP). SPF values were also compared across gender, competitive level and games.

Results

(1) Male players exhibited significantly higher fluctuations than female players, particularly in Block, Flick, Push, Touch Short, Topspin, and Twist; (2) Top 20 players are more consistent than others in serving, receiving, and offensive techniques; (3) Performance in Touch Short against Pendulum and Topspin against Topspin exhibited a significant decline in the later stages of the match.

Conclusions

The SPF indicator provides a novel and effective measure of stroke behavior stability in elite table tennis. By quantifying fluctuations in technical and tactical performance, the SPF indicator reveals gender- and competition-level differences in stroke stability. In addition, we used performance deviation to describe how consistency changes across games within a match. This framework not only advances performance analysis beyond score-based or psychology-based measures but also offers practical applications for coaches, enabling targeted training and tactical interventions to reduce stroke instability and enhance competitive resilience.

Introduction

Table tennis can be viewed as a dynamic and interactive process [1], where both players take turns stroking the ball until one side wins the rally [2]. Each stroke directly affects the final outcome of the rally; therefore, technique (pattern of single strokes) and tactics (pattern of consecutive strokes) are considered to be the key factors in winning the match. Therefore, exploring how to help players achieve better technical and tactical performances in matches has long been the focus of much table tennis related research [3].

The most representative of the technical and tactical assessment of a player is the “three-phase evaluation method” [4]. This method segments a rally into three distinct phases—serve, receive and stalemate—to isolate and evaluate performance in specific tactical scenarios. Due to its diagnostic clarity, it is easy to understand and widely used by coaches and players in China. Based on this, numerous researchers have developed more advanced iterative methods to enhance the accuracy of the assessment. Examples include the Improved Three-stage Method [5], the Double Three-stage Method [6], and the Dynamic Three-stage Method [7]. In addition, some researchers have conducted studies to optimize the analytical metrics. For example, the inclusion of the concept of the shot number [8] and a visual analysis of the tactical benefits [9]. To gain a deeper understanding of the impact of tactics on game performance, a number of analytical models have been introduced into the field to analyze tactics in different dimensions. For example, artificial neural network models [10, 11], data mining models [12, 13], and Markov chain models [14]. These methods significantly improve our understanding of technical and tactical patterns and the probability of winning from a global or aggregate perspective.

However, a player’s performance during a match is seldom stable and is subject to dynamic fluctuations over the course of a match. Therefore, research on performance dynamics has sought to capture the nonlinear fluctuations inherent in competition. These methods have relied heavily on score-based metrics to analyze players’ psychological states or “match momentum”. For example, cubic spline interpolation functions have been used to model score fluctuations and relate these fluctuations to players’ mental states at different stages of the game [15]. Similarly, double moving average (DMA) models have been developed to quantify match momentum and to categorize match phases into periods of advantage, stalemate, and disadvantage based on scoring trends [16, 17]. These macro-models provide valuable tools for identifying key turning points and assessing instantaneous match strength based on win–loss sequences.

Despite these advances in detecting match dynamics, a critical research gap remains in assessing technical and tactical stability. While existing models of fluctuations are able to recognize fluctuations in player states (based on scoring), they fail to capture the stability of the technical execution itself. For example, in DMA-based approaches, smoothed fluctuations may originate from certain technical and tactical changes, but cannot distinguish between these sources due to the fact that they are modeled only for rally outcomes. As a result, current metrics are unable to distinguish whether a player’s performance decline is due to overall fatigue or instability in the particular stroke technique itself. There is a lack of metrics that can quantify stroke-level stability in specific tactical contexts independent of match outcomes.

Addressing this research gap, this study developed a context-based Markov chain model and stroke performance fluctuation (SPF) index to explore stroke performance fluctuations in elite table tennis matches. This study advances traditional score-based evaluation metrics by quantitatively linking rally winning probability with stroke execution stability. In practice, the SPF metric serves as a granular diagnostic tool to help coaches pinpoint technical vulnerabilities that are often overlooked in outcome-oriented analytical summaries.

Based on this framework, we formulate the following three hypotheses: (a) previous research suggests that male players prefer more aggressive, high-risk offensive techniques, whereas female players prefer stable techniques [18, 19]. Given that high-risk behaviors are inherently accompanied by higher execution variability, we hypothesize that male players have higher volatility in stroke performance than their female counterparts; (b) the level of motor skill is dependent on the repeatability and consistency of the motor skill. As higher-level players usually have better skill control and resistance to interference than lower-level players [20]. Therefore, we hypothesize that the top 20 players are more consistent (lower SPF values) in their stroke performance than the others; (c) as the match progresses, the accumulation of physical fatigue and psychological stress affects the players’ execution performance [21]. Therefore, we hypothesize that stroke performance will exhibit a decline relative to expectation in the later stages of a match compared to the early stages.

Methods

This study was designed as an observational retrospective cross-sectional analysis focusing on fluctuations in technical and tactical performance in elite table tennis matches. The study utilized match data from 2021 to 2025, covering the Olympic Games, World Cup, World Championships, and WTT Series. The study design took into account factors such as player gender, competitive level, and game within a match, and employed statistical methods to compare fluctuations in stroke performance under different conditions.

Samples

This study analyzed a total of 100 matches held between 2021 and 2025, including competitions from the Olympic Games, World Cup, World Championships, and WTT series. The sample comprised 50 men’s matches and 50 women’s matches, after excluding 147 rallies that included accidental strokes or abnormal situations. A total of 2,163 rallies and 29,406 strokes were counted. The sample size depended on the availability of match videos that met the inclusion and exclusion criteria. All match videos were obtained from public broadcasts (official TV or online platforms). The use of this public data for research purposes complies with relevant data usage regulations. As the study involved the observation of public behavior without intervention, formal ethical review was waived.

Inclusion and exclusion criteria

Figure 1 shows the process of inclusion and exclusion criteria for the samples required for this study. Specifically, all competitors in the study are players who use a shake-hand grip and an offensive style. The shake-hand grip and offensive players were selected because, among the top 100 players in the latest world rankings, 93% of female players and 99% of male players employ a shake-hand grip and offensive style (https://www.ittf.com/rankings/). This ensures that the sample reflects the mainstream tactical patterns of the highest competitive level. Given this widespread adoption, focusing on offensive players ensures that the study captures the predominant playing style in modern elite table tennis. In addition, all matches were between players ranked in the top 20 and other players (based on the ITTF live world rankings at the time of the match) in order to make meaningful comparisons of stroke performance stability between different competitive levels. Matches involving non-offensive styles or videos with insufficient quality were excluded. Finally, rallies containing accidental or abnormal situations were also removed.

Fig. 1.

Study flowchart showing selection and exclusion process. Note: The process resulted in a final dataset of 100 matches (50 male and 50 female matches),comprising 2,163 rallies and 29,406 strokes. A total of 147 rallies containing accidental or abnormalsituations were excluded

All match videos were sourced from official television broadcasts or public online platforms. Furthermore, this study does not involve the collection or analysis of sociodemographic, anthropometric, or body composition variables, as the focus is solely on the technical and tactical indicators collected from match videos.

Observation indicators and data collection

In this study, the variables were the stroke techniques in table tennis, and the technical observational metrics were based on the studies (Table 1) by Molodzoff [22] and refined by Zhou and Zhang [9]. The objectivity of the observation indicators was confirmed by two independently trained observers using Cohen’s kappa statistic [23], with Cohen’s kappa value > 0.8 ().

Table 1.

Observation indices and definitions in table tennis matches

Stroke Technique	Definitions
Pendulum	It’s a type of serve (the first stroke of each rally)
Reverse	It’s a type of serve (the first stroke of each rally)
Topspin	an attacking stroke that imparts a topspin effect on the ball
Flick	an attacking stroke performed when the ball bounces close to the net
Twist	an attacking stroke performed with a backhand flick/flip when the ball bounces close to the net
Smash	an attacking stroke characterized by a linear trajectory and no spin of the ball
Push	a controlling stroke that puts the ball to the bottom line of the table
Touch Short	a controlling stroke that puts the ball close to the net
Block	a defensive stroke performed in response to an attacking stroke in a passive fashion
Lob	a defensive stroke performed when the player is far from the table, consisting of lifting the ball to a considerable height

¹ In the subsequent text and figures, the term "Touch Short" is abbreviated as "Short" for brevity

Model structure and calculation

In this study, the fluctuation value of stroke technique behavior was calculated in three steps: (1) calculating the RWP for each stroke technique behavior in each state; (2) determining the ERWP for each stroke technique behavior in each state based on the rally winning probability; and (3) calculating RWP-ERWP to obtain SPF for each stroke technique behavior.

Each rally in a table tennis match is modeled as a context-based Markov chain process, represented as a tuple < R, S, A, P, T, V, W >. Where R = {r₁,r₂,…,r_i} denotes all the rallies in the match and each rally consists of an ordered set of several of strokes, S = {s₁,s₂,…,s_j} is the state space representing all the stroke techniques behavior, P = {p_0, p₁} denotes the two players in the match, A = {Win/Lose} is denoted as the two absorbing states, which are the final outcome of the rally, is the transfer matrix of the current stroke player p_i which includes all stroke technical states and absorbed states (Win/Lose), is the context-based state vector representing the normalized frequency of occurrence of each stroke technique state up to (including the k-th)stroke in the r_i, is the winning probability of the k-th stroke in the rally (Fig. 2).

Fig. 2.

Simulate the state transition of stroke behavior between two players in a rally using Markov chains

For the k-th stroke of the r_i during the simulation, the state vector is used as the initial state, and the iterations are performed according to the corresponding transfer matrix used by the current executor p_i (applied alternately based on the turn-taking structure), as shown in the formula:

1

Starting from the k_i state and iterating until convergence, the rally winning rate (probability of absorbing as a Win) for that stroke is finally obtained by the formula:

2

Specifically, RWP represents the rally winning probability from the perspective of the player executing the k-th stroke. The RWP of the current stroke is obtained based on the context of the kth stroke in the r_i, after which the ERWP is further computed for different states of stroke technique behavior, which can be represented as:

3

Here, a_j denotes a specific stroke technique behavior transition from state s_j to perform a certain behavior b_j (a_j = s_j → b_j), denotes the total number of stroke technique behavior transitions, and denotes the stroke technique used on the k-th stroke in r_i. Specific stroke patterns are represented as “state → behavior.” In this notation, “State” refers to the technical type of the incoming ball (the opponent’s stroke technique from the previous stroke), while “Action” denotes the technical type of the current player’s response. This will be described as “Action against State” in subsequent results sections. For example, “Pendulum → Short” is described as Short against Pendulum, indicating the current player uses a Short to respond to the opponent’s Pendulum serve.

Subsequently, stroke performance fluctuation (SPF) was calculated for each stroke to measure the magnitude of deviation in that stroke during the rally compared to the expected performance. It is defined as the absolute difference between the contextual winning probability and the expected winning probability, as represented by the formula:

4

The state vector constructed by using the frequency distribution of 1-k strokes in the rally as the context contains not only the probabilistic information of the current stroke technique behavior but also the structural context of the historical stroke behavior in the rally, which enables the model to more realistically simulate the performance of different stroke technique behaviors in different states. In addition, the SPF can be used to find the deviation of stroke technique behavior from the expected performance of a player in different states and to analyze the stability of the player in the match.

To make the computation process clearer and easier to understand, we provide a simple example of a hypothetical rally. Suppose a rally r_i consists of five strokes: (1) The server uses a Pendulum serve (Init → Pendulum); (2) The receiver returns with a Short against the Pendulum (Pendulum → Short); (3) The server attacks with Topspin (Short → Topspin); (4) The receiver responds with a Block (Topspin → Block), and (5) the server finishes the rally with a winning Topspin (Block → Topspin), ending in the absorbing state “Win”.

Focusing on the third stroke (Short → Topspin), we first construct a context vector . This vector represents the normalized frequency distribution of stroke techniques executed in the current rally sequence (from the first to the third stroke). We then use it as the initial state and iteratively propagate it through the corresponding player-specific transition matrix until the probability mass is fully absorbed into the “Win” or “Lose” states. The resulting cumulative probability of the “Win” state is the rally win probability (RWP) for this specific stroke context (assumed as RWP = 0.62). Next, we retrieve the expected rally winning probability (ERWP) for “Short → Topspin” behavior from the historical dataset (Assuming the global average win rate for this behavior is 0.55). The stroke performance fluctuation (SPF) is calculated as the absolute deviation between the contextual RWP and ERWP:

5

In this study, a higher SPF value indicates a larger deviation from expected stroke performance, meaning lower stroke stability, whereas a lower SPF value indicates a more consistent stroke performance with expected stroke performance.

In addition, analyzing performance at specific games within a match requires understanding not only the magnitude of stroke performance fluctuation but also its direction—that is, whether performance exceeds or falls short of expectations at a given game. Therefore, for the game-wise analysis we calculated performance deviation, defined as RWP − ERWP. This metric indicates whether stroke performance exceeds expectations (positive values) or falls below expectations (negative values).

Statistical analysis

This study used the Shapiro-Wilk normality test to assess the distribution of data in the sample [24]. Since the data did not follow a normal distribution (p < 0.05), nonparametric statistical methods were used. The Mann–Whitney U tests [25] were used to compare differences in stroke performance fluctuations, Kruskal–Wallis H tests were used to compare differences between games, and Dunn tests with a correction with Bonferroni were used to determine specific differences between games if significant differences existed between games. Effect sizes were measured using r to measure between-group differences [26] with strengths of small (r < 0.3), medium (0.3 ≤ r < 0.5), and large (r ≥ 0.5). Statistical test significance level was set at p < 0.05 [27]. The results are expressed as median and interquartile range. All data processing and statistical analyses were performed using Python 3.12, utilizing NumPy and Pandas for data manipulation and SciPy’s test module for statistical testing.

Results

Gender differences in SPF

Table 2 presents the differences in SPF between male and female players, with significant differences observed for Block against Topspin (p < 0.001, r = 0.270), Topspin against Block (p < 0.001, r = 0.027), Topspin against Flick (p = 0.029, r = 0.130), and Topspin against Topspin (p < 0.001, r = 0.052) in the topspin state; male players exhibited greater fluctuation when receiving serves, with significant differences observed for Push (p < 0.001, r = 0.176), Short (p = 0.018, r = 0.063), Topspin (p = 0.002, r = 0.099) and Twist (backhand flick) (p = 0.006, r = 0.091) against Pendulum, and also for Topspin against Reverse (p = 0.001, r = 0.168); in addition, significant differences were also observed for Flick and Push against Short (p < 0.01, r = 0.131 and 0.204) in the underspin state.

Table 2.

Comparison of SPF between male and female

Stroke technique	State → Behavior	Male (%) (n = 50)	Female (%) (n = 50)	Z	p	r
Serve	Init → Pendulum	9.4 [4.4–12.3]	8.9 [5.1–13.1]	0.190	0.850	0.003
	Init → Reverse	3.6 [2.8–11.5]	3.3 [2.7–12.5]	1.153	0.248	0.030
Block	Flick → Block	7.7 [2.0–12.9]	5.8 [2.6–13.0]	-0.262	0.802	0.039
	Topspin → Block	9.2 [5.0–14.7]	5.3 [2.5–9.7]	-9.717	<0.001	0.270
	Twist → Block	7.6 [4.4–12.0]	6.2 [3.8–09.4]	-1.027	0.307	0.113
Flick	Pendulum → Flick	10.0 [5.5–17.8]	8.3 [3.5–13.2]	-1.424	0.155	0.114
	Reverse → Flick	8.3 [2.8–13.7]	9.3 [3.0–13.2]	0.481	0.634	0.055
	Short → Flick	9.1 [2.8–13.0]	5.9 [2.0–9.6]	-3.069	0.002	0.204
Push	Pendulum → Push	9.2 [5.6–14.2]	7.6 [3.0–11.8]	-5.696	<0.001	0.176
	Reverse → Push	7.9 [3.6–11.8]	7.7 [3.0–9.9]	-1.626	0.104	0.084
	Push → Push	8.7 [5.0–12.3]	7.2 [2.2–16.7]	-0.233	0.818	0.024
	Short → Push	8.4 [4.6–13.0]	6.3 [1.6–10.8]	-3.220	0.001	0.131
Short	Pendulum → Short	9.3 [5.4–12.7]	9.1 [2.1–13.6]	-2.369	0.018	0.063
	Reverse → Short	6.4 [2.4–12.9]	5.7 [2.9–13.0]	-0.503	0.615	0.027
	Short → Short	9.2 [5.2–12.7]	8.3 [1.9–13.8]	-1.776	0.076	0.071
Topspin	Pendulum → Topspin	8.0 [5.5–13.5]	8.0 [4.1–12.4]	-3.146	0.002	0.099
	Reverse → Topspin	8.9 [4.9–14.3]	7.4 [3.3–12.2]	-3.272	0.001	0.168
	Block → Topspin	10.1 [6.2–13.8]	6.1 [4.9–14.3]	-6.047	<0.001	0.270
	Flick → Topspin	9.5 [3.8–14.2]	6.9 [2.9–12.2]	-2.178	0.029	0.130
	Push → Topspin	7.9 [3.7–12.8]	7.5 [3.7–11.3]	-1.914	0.056	0.045
	Short → Topspin	7.6 [4.0–12.2]	8.1 [5.0–11.7]	0.190	0.849	0.008
	Topspin → Topspin	8.1 [3.6–13.2]	7.7 [3.7–11.6]	-5.236	<0.001	0.052
	Twist → Topspin	8.4 [4.5–15.5]	8.5 [3.7–13.4]	1.388	0.165	0.044
Twist	Pendulum → Twist	10.2 [4.4–16.2]	9.5 [4.9–13.9]	-2.730	0.006	0.091
	Reverse → Twist	10.5 [4.4–16.9]	7.1 [3.4–11.5]	-1.848	0.065	0.117
	Short → Twist	6.6 [4.7–11.6]	8.7 [5.6–11.7]	-1.086	0.278	0.080

Values are presented as median and interquartile range of the absolute fluctuation values. Bold values indicate statistical significance (p < 0.05)

Overall, male players show greater fluctuations in stroke technique behavior than female players, especially in the topspin technique, while female players show greater stability in most stroke behaviors.

Competitive level differences in SPF

Table 3 shows the differences in SPF between the top 20 players and others. The results indicate that the top 20 players were more consistent in their stroke performance than the others across all states, except Flick against Reverse and Push against Short. Significant differences were found for Reverse in serving behavior (p < 0.001, r = 0.241), Push (p < 0.001, r = 0.163; p = 0.007, r = 0.170), Short (p < 0.001, r = 0.287; p = 0.010, r = 0.111), Topspin (p < 0.001, r = 0.229) and Twist (p = 0.001, r = 0.300) against different serving states, Topspin against multiple states (p = 0.002, r = 0.097; p = 0.004, r = 0.241; p < 0.001, r = 0.077; p = 0.036, r = 0.104, Flick and Short against Short (p = 0.004, r = 0.314; p < 0.001, r = 0.283) and Block against Topspin (p = 0.001, r = 0.162).

Table 3.

Comparing male players’ SPF between the top 20 and others

Stroke technique	State → Behavior	top 20 (%) (n = 50)	others (%) (n = 50)	Z	p	r
Serve	Init → Pendulum	5.3 [1.9–8.4]	4.9 [3.2–8.8]	1.528	0.127	0.033
	Init → Reverse	4.6 [3.2–8.8]	8.3 [3.0–10.0]	7.155	<0.001	0.241
Block	Flick → Block	5.3 [4.6–7.1]	7.6 [1.4–12.3]	0.159	0.916	0.040
	Topspin → Block	4.7 [2.0–9.6]	7.6 [3.1–12.2]	3.300	0.001	0.162
	Twist → Block	3.5 [1.7–5.1]	6.8 [4.1–10.8]	1.121	0.310	0.324
Flick	Pendulum → Flick	6.2 [1.9–10.7]	8.8 [4.6–13.6]	1.483	0.139	0.160
	Reverse → Flick	5.0 [1.6–12.3]	3.6 [1.3–9.3]	-0.812	0.423	0.117
	Short → Flick	5.0 [2.1–10.3]	11.9 [7.7–13.3]	2.898	0.004	0.314
Push	Pendulum → Push	3.8 [1.9–5.9]	5.3 [2.2–9.8]	3.790	<0.001	0.163
	Reverse → Push	4.2 [1.9–6.3]	5.7 [1.9–10.0]	2.719	0.007	0.170
	Push → Push	4.0 [1.5–7.5]	3.9 [2.6–10.5]	0.899	0.372	0.113
	Short → Push	5.4 [2.7–9.1]	4.8 [2.8–7.5]	-1.936	0.053	0.111
Short	Pendulum → Short	5.8 [3.3–8.1]	5.9 [3.7–10.7]	2.579	0.010	0.111
	Reverse → Short	4.5 [2.7–9.2]	8.4 [5.1–11.0]	3.602	<0.001	0.287
	Short → Short	6.2 [4.9–8.1]	7.6 [5.9–14.0]	4.552	<0.001	0.283
Topspin	Pendulum → Topspin	3.5 [1.9–7.9]	5.4 [2.0–9.4]	1.226	0.220	0.053
	Reverse → Topspin	4.9 [2.4–6.7]	7.1 [4.1–12.1]	3.753	<0.001	0.229
	Block → Topspin	3.8 [1.8–7.3]	5.3 [2.6–14.2]	2.854	0.004	0.241
	Flick → Topspin	4.4 [2.6–15.6]	8.0 [3.4–11.4]	1.519	0.129	0.126
	Push → Topspin	4.6 [2.0–7.2]	4.7 [2.7–8.3]	3.024	0.002	0.097
	Short → Topspin	4.2 [1.9–8.9]	5.3 [3.4–8.5]	1.762	0.078	0.116
	Topspin → Topspin	4.3 [2.2–8.6]	5.2 [3.0–8.6]	6.035	<0.001	0.077
	Twist → Topspin	6.0 [2.1–10.5]	6.6 [3.7–10.6]	2.096	0.036	0.104
Twist	Pendulum → Twist	7.9 [2.9–10.7]	6.5 [2.6–12.0]	0.487	0.626	0.026
	Reverse → Twist	6.1 [2.7–10.9]	10.7 [7.5–13.7]	3.179	0.001	0.300
	Short → Twist	4.3 [2.7–11.6]	6.1 [3.4–11.9]	1.055	0.296	0.148

Values are presented as median and interquartile range of the absolute fluctuation values. Bold values indicate statistical significance (p < 0.05)

The top 20 players performed more consistently than other players in most serving, receiving, and offensive stroke transitions. The highest differences were observed in receiving and offensive techniques based on topspin, suggesting that technical stability in these areas may be a key factor in distinguishing excellent male players.

Table 4 shows the comparison of SPF between female top 20 players and others. The results showed that top 20 players were more consistent in their serving behavior than the others for both Pendulum and Reverse (all p < 0.01, r = 0.063 and 0.112), as well as in Topspin (p < 0.001, r = 0.288; p < 0.001, r = 0.161; p < 0.001, r = 0.081; p = 0.046, r = 0.245; p < 0.015, r = 0.122) and Twist (all p < 0.05, r = 0.144, 0.188 and 0.280) against multiple states. However, others showed a more consistent pattern of stroke fluctuation in Push against pendulum (p = 0.001, r = 0.117) with significant differences.

Table 4.

Comparing female players’ SPF between the top 20 and others

Stroke technique	State → Behavior	top 20 (%) (n = 50)	others (%) (n = 50)	Z	p	r
Serve	Init → Pendulum	4.8 [2.0–8.3]	5.1 [2.7–10.5]	3.123	0.002	0.063
	Init → Reverse	5.4 [5.4–6.7]	10.2 [1.8–13.5]	2.695	0.007	0.112
Block	Flick → Block	6.8 [3.6–8.5]	7.3 [5.6–9.5]	0.964	0.347	0.182
	Topspin → Block	4.6 [2.2–8.0]	4.0 [2.1–8.1]	-0.537	0.592	0.019
	Twist → Block	3.9 [1.4–6.7]	5.7 [2.5–11.2]	1.635	0.103	0.197
Flick	Pendulum → Flick	7.5 [5.6–9.4]	5.4 [3.5–8.9]	-1.112	0.267	0.106
	Reverse → Flick	10.8 [9.4–11.8]	6.0 [4.2–16.4]	-0.127	0.915	0.023
	Short → Flick	4.9 [3.6–8.0]	3.9 [2.2–12.0]	-0.270	0.789	0.023
Push	Pendulum → Push	4.9 [1.8–10.7]	3.6 [1.0–7.6]	-3.432	0.001	0.117
	Reverse → Push	7.9 [1.5–10.2]	5.6 [2.8–8.7]	-0.576	0.566	0.054
	Push → Push	3.1 [2.7–8.0]	7.2 [3.0–7.5]	0.619	0.549	0.111
	Short → Push	7.3 [0.9–10.4]	5.2 [4.1–10.2]	1.064	0.288	0.092
Short	Pendulum → Short	5.2 [2.3–9.3]	5.5 [2.1–8.0]	-0.916	0.360	0.042
	Reverse → Short	4.1 [2.6–9.3]	5.7 [2.5–8.1]	-0.063	0.951	0.005
	Short → Short	4.0 [1.8–6.9]	3.8 [1.5–9.8]	0.600	0.549	0.033
Topspin	Pendulum → Topspin	5.1 [2.7–6.8]	4.5 [1.6–9.1]	0.981	0.327	0.046
	Reverse → Topspin	6.2 [3.9–11.0]	11.8 [8.1–16.7]	2.006	0.046	0.245
	Block → Topspin	3.7 [2.3–6.0]	6.5 [4.0–9.2]	5.443	<0.001	0.288
	Flick → Topspin	4.2 [2.6–5.8]	6.6 [2.8–12.2]	1.928	0.054	0.169
	Push → Topspin	4.1 [2.2–6.6]	5.5 [2.9–9.0]	4.751	<0.001	0.161
	Short → Topspin	3.0 [1.4–5.9]	3.9 [2.1–9.0]	2.434	0.015	0.122
	Topspin → Topspin	3.9 [1.8–6.8]	4.8 [2.2–7.4]	4.910	<0.001	0.081
	Twist → Topspin	5.2 [2.6–7.8]	4.7 [2.3–7.2]	-1.874	0.061	0.079
Twist	Pendulum → Twist	3.2 [1.9–6.2]	5.9 [3.4–9.3]	6.537	<0.001	0.280
	Reverse → Twist	3.5 [1.7–7.9]	4.5 [2.1–10.3]	2.450	0.014	0.144
	Short → Twist	2.7 [1.3–4.2]	4.3 [1.7–8.2]	2.157	0.031	0.188

Values are presented as median and interquartile range of the absolute fluctuation values. Bold values indicate statistical significance (p < 0.05)

Compared with other players, the top 20 players showed better stability in their serves and topspin technique behavior, indicating that stability in offensive techniques and serving are key factors in becoming an excellent female player.

Game-wise differences in performance deviation

In this study, “game” refers to an individual game within a match (e.g., first game, second game, etc., in accordance with ITTF terminology). The analysis included all available games from the sampled matches, rather than a fixed number of games. Consequently, the number of observations naturally differs between games: early games (e.g., the first and second) contain data from all 100 matches, whereas later games (e.g., the fifth) contain data only from matches that reached a deciding game. This implies that SPF values observed in later games primarily characterise fluctuations in stroke performance during prolonged, high-pressure matches.

Figure 3 illustrates the changes in performance deviation for male players across games (n = 50), where significant differences between games were found in the four stroke technique behavior transitions of Flick and Topspin against Reverse, Short against Pendulum, and Topspin against Topspin.

Fig. 3.

Comparison of performance deviation across games in male players. Legend: The box and dashed lines of the box plot indicate the maximum, minimum, median, first quartile, and third quartile, with connecting lines to indicate significance between games, *: p < 0.05, **: p < 0.01, ***: p < 0.001

In Flick against Reverse, the performance deviation in the second game was positive and significantly higher than the negative deviations in the fourth (p < 0.05, r = 0.559) and fifth (p < 0.001, r = 0.759) games; in Topspin against Reverse, a significant difference was found between the first and the third games (p < 0.05, r = 0.237); in Short against Pendulum, a significant performance drop was observed between the first and the fifth games (p < 0.05, r = 0.178); Additionally, in Topspin against Topspin, performance declined in the deciding phase, where the first, second, and third games were all found to be significantly different from the fifth game (All p < 0.01, r = 0.078, 0.075 and 0.66).

It is worth noting that, as mentioned above, the peculiarities of tiebreaker matches mean that changes in performance deviation across games do not follow a strictly monotonic trajectory (e.g., game by game). Instead, significant fluctuations are mainly observed in specific pairwise comparisons, especially between the early and decisive phases of the match. This suggests that changes in stability are context-dependent rather than linearly cumulative.

Figure 4 displays the performance deviation for female players across games (n = 50), where significant differences among games were found in the stroke technique behavior of Topspin and Short against Pendulum and Topspin against Topspin.

Fig. 4.

Comparison of performance deviation across games in male players. Legend: The box and dashed lines of the box plot indicate the maximum, minimum, median, first quartile, and third quartile, with connecting lines to indicate significance between games, *: p < 0.05, **: p < 0.01, ***: p < 0.001

In the state against Pendulum, the Topspin behavior showed a more positive performance deviation in the second game, which was significantly different from the fourth game (p < 0.05, r = 0.231);in the Short behavior, the performance deteriorated in the fifth game, showing significantly lower deviations than in the first (p < 0.05, r = 0.188) and second games (p < 0.01, r = 0.191);In addition, the performance deviation in the first game was higher (better) in the Topspin against Topspin, which was significantly different from the declining performance in the fourth (p < 0.01, r = 0.095) and fifth games (p < 0.05, r = 0.090).

Discussion

As mentioned previously, previous studies on fluctuations in table tennis performance have relied heavily on psychological or outcome-oriented indicators [15–17], particularly score-based double moving averages used to assess match momentum. While these macro-methods are effective in identifying when a player is at an advantage or disadvantage, they are unable to capture the technical stability of the stroke in a given tactical situation (e.g., how performance fluctuations occur at the level of actual technical execution). Therefore, this study constructs SPF metrics that focus on analyzing the consistency of stroke technical behavioral performance across tactical situations, thereby addressing the shortcomings of existing assessment methods. For example, two players may receive similar scores, but their SPF values may be significantly different, revealing potential differences in their consistency and adaptability. This methodological shift not only overcomes the limitations of traditional analyses based on simple metrics, but also provides a more refined tool for understanding and monitoring technical and tactical consistency. In addition, the model can identify which stroke techniques are more prone to fluctuations in specific match situations, thus providing a clearer explanation of how fluctuations occur, and how interactions between players can affect the pattern of stroke performance in specific match scenarios.

Practical significance of SPF differences

Since this study used a large sample size (N = 29,406), many of the stroke behaviors were statistically significant even with small effect sizes. Thus, the p-values alone may overestimate the substantial importance of certain behaviors. In order to better relate the statistical results to coaching practice, we used a stratified effect size interpretation approach, considering r > 0.2 as a medium effect, which may be relevant in an applied elite-level sport setting. Within this framework, findings with effect sizes above 0.2 (e.g., Twist against Pendulum in the comparison between top-20 and other female players) were considered primary targets for adjustment. When statistically significant results with effect sizes above 0.2 were observed, they indicated that there was a large technical inconsistency and that targeted training was needed to strengthen stroke technique in order to improve skill levels. Conversely, findings that were statistically significant but had a small effect size (r < 0.1) were considered secondary adjustment targets. In elite-level sporting scenarios, where the results of matches often depend on the accumulation of small advantages, these small fluctuations are not inconsequential but may require a focus on tactical-level adjustments (e.g., stroke technique selection) rather than a single stroke technique-enhancing training session. This tiered perspective can provide coaches with valuable training information to more rationally set training goals: first addressing erratic hitting behaviors with higher effect sizes, then optimizing volatile hitting behaviors with lower effect sizes to improve players’ overall competition level.

Gender-based comparison of SPF

As shown in Fig. 2, SPF values were generally higher for male players than for female players across a variety of stroke patterns, suggesting larger fluctuations in stroke levels for male players in similar technical-tactical situations. Although most of these differences had small effect sizes (r < 0.10) and thus limited practical significance, some of the stroke maneuvers (e.g., Block against Topspin and Topspin against Block) showed small to medium effects, suggesting that gender differences in stability are more pronounced in specific contexts. From a theoretical perspective, these findings can be explained in terms of both tactical tendencies and motor skill control.

At the overall performance level, male players tend to score more game-winning points, but also score more losing points, many of which are of an offensive nature [8]. At the technical and tactical level, male players are more likely to employ aggressive offensive techniques, whereas female players rely relatively more on control and defensive-oriented strategies [18, 19, 28]. Offensive strokes typically require higher racket speeds and more precise timing of the stroke; as ball speed increases, the location of the drop point becomes more sensitive to small errors in angle and timing, which reduces tolerance and amplifies the variability of the stroke action [29]. In the SPF framework, this implies that when the stroke action is less than perfect, aggressive, power-oriented strokes are more prone to larger deviations between RWP and ERWP, whereas conservative, drop-oriented strokes are likely to produce smaller fluctuations around their expected probability of making a winning stroke.

Thus, rather than simply implying poorer technique, the higher SPF of male players may partly reflect a different risk-reward model: greater tactical aggressiveness comes at the expense of stroke consistency. By adopting a more conservative and control-oriented stroke pattern, female players may be able to keep the range of fluctuations in their own performance within a smaller range of expected levels. For coaches, these results emphasize that the high SPF of male athletes should be interpreted in terms of both technical stability and tactical risk-taking: depending on the characteristics of the player, interventions could consider readjusting the tactical balance between frequency of attack and control.

Competitive level comparison of SPF

In terms of competitive level, the results in Tables 3 and 4 show that the top 20 ranked athletes in the world, both male and female are generally lower in SPF than the others. This pattern was most pronounced in serving, receiving and attacking techniques, suggesting that higher ranked players were more consistent in their execution of these three types of technical movements. At the same time, the effect sizes for many of the between-group differences were very small (r < 0.10), suggesting that despite being statistically significant on a large data set, their practical application is limited. However, a small proportion of batting maneuvers had small to moderate effect sizes (r > 0.20; e.g., Twist for higher ranked players), and these differences are more meaningful from an application perspective, reflecting differences in stroke stability.

Prior research has shown that high level table tennis players possess faster ball speeds, higher stroke accuracy and more repeatable stroke kinematics than low level players [30], and that the top 20 players have more favorable technical and tactical choices in serving, receiving and attacking strokes, and that these choices are more reliably executed in the rally. From a motor control perspective, they were better able to stabilize task-related outcome variables such as ball speed, ball landing, and spin, despite inherent differences in joint and muscle coordination [31]. In addition, high-quality serve and serve receive are key determinants of match outcome [20]. In addition, the offensive technique has been one of the most commonly used techniques in both male and female competitions [19], suggesting that superior consistency demonstrated in all three techniques appears to be a distinguishing characteristic of top players.

Game-wise variations in performance deviation

Figures 3 and 4 show the transitions in stroke behavior for both male and female players whose performance deviations differed significantly from game to game. Most of the stroke patterns did not differ significantly across games, suggesting that players’ overall stroke performance was relatively stable. However, two “state → behavior” transitions (Topspin against Topspin and Short against Pendulum) showed a lower-than-expected trend across games for both male and female players, suggesting that the performance of these stroke behaviors declined as the match progressed. Although the magnitude of the effect of these changes is usually small, they are systematic and occur in technically difficult stroke patterns, and are therefore important for understanding performance under fatigue and stress.

Short is a controlled technique that relies heavily on fine motor control of racket angle and stroke timing. In high-intensity matches, with the gradual depletion of physical and mental resources, as well as the increasing importance of each point and the tactical pressure exerted by the serving side [32], these factors reduce the accuracy of these fine adjustments and increase the instability of the Short [14]. In contrast, Topspin against Topspin represents a high-speed counter pattern, with both players generating high racket speeds and rapid interplay. The accumulation of physical fatigue in strongly-opposed rallies reduces stroke speed and accuracy and increases the rate of errors [33], which in turn exacerbates the disparity between expected and actual results in such high-intensity rallies [21].

Practical applications of SPF

Taken together, these findings highlight the contribution of the SPF framework to data-driven, contextualized tactical coaching by quantifying fluctuations in stroke performance at the level of specific “state → behavior” patterns, allowing coaches to focus on a player’s most volatile technical and tactical behavior by looking beyond global outcome statistics. In fact, SPF analysis can be extracted from coded game video without the need for special equipment and can be aggregated into simple tables or visual dashboards. Coaches can use these outputs to quickly identify stroke behaviors that need to be adjusted, design targeted training tasks that correspond to the tactical situations in which the instability occurs (e.g., specific serve-receive patterns), and monitor whether consistency at the stroke level improves with repetitions or over time. Thus, the SPF framework provides a concise and easy-to-use tool for personalized coaching and match preparation of elite table tennis players.

Limitation

Although the current study proposes a method to quantify the performance fluctuations of stroke behavior, it still suffers from several limitations. First, the current model only considers stroke technique, omitting characteristics such as ball position, spin, speed, and score state. These unobserved variables can be confounding factors; for instance, the higher SPF values of male players may be influenced by the fact that they employ riskier tactics (e.g., faster speeds or Extreme ball position) rather than just their own technical inconsistencies, which may exaggerate the observed gender difference. Therefore, future research should aim to incorporate these multidimensional metrics in order to better distinguish technical and tactical environmental factors from pure performance stability. Second, the model has not yet been able to accurately model the sequential dependencies (specifically, the strict stroke-by-stroke interactions within a rally), making it difficult to reveal the specific details of the variations in the ups and downs of a player’s performance during a match. In addition, high-level players have smaller SPF values. This does not mean that smaller variances are the reason for their higher ERWP. On the contrary, according to the model calculations, their superior technical and tactical skills are more likely to lead to higher ERWP values. Therefore, whether the victory in a match is mainly due to the player’s excellent technical and tactical abilities or the stability of their performance remains to be further explored. Third, although strokes are inherently clustered within players, we analyzed stroke behavior as the unit of analysis to capture subtle fluctuations in “state → behavior” that are masked at the player level. To mitigate the significance inflation associated with large samples, we prioritized findings with meaningful effect sizes (r > 0.2) and combined them with standard significance tests to ensure their relevance. Additionally, with respect to multiple pairwise comparisons (e.g., comparisons between different stroke techniques), we did not apply a global family-wise error rate correction across the multiple Mann–Whitney U-tests to avoid an overly conservative increase in Type II errors in this exploratory analysis. However, we prioritized findings with higher effect sizes (r > 0.2) to reduce the risk of over-interpreting spuriously significant results and to ensure that findings were of practical relevance. Finally, regarding the model structure, the context vector used in this study generalizes the rally history to a normalized frequency distribution, which effectively captures the tactical composition of the rally, but it acts as a memory-reduction approximation that compresses strictly sequential information. Consequently, the model may not be able to fully capture complex temporal dependencies or specific sequential patterns in the rally. Future research could address this limitation by exploring order-sensitive architectures such as Hidden Markov Models (HMMs) or deep sequential models such as Long Short-Term Memory Networks (LSTMs) to more realistically model the dynamics within rallies.

Conclusion

This study developed a context-based Markov chain model and proposed the SPF index to quantify fluctuations in stroke performance in elite table tennis competitions. Crucially, SPF measures stability relative to a player’s baseline technical and tactical level, not stability independent of ability. Accordingly, the results of the study showed that there were significant differences in the fluctuation of some key stroke behaviors among players of different genders and levels, and that female players generally exhibited more stable performance; top 20 players showed significantly less fluctuation in their stroke performance in serving, receiving, and offensive techniques, reflecting stronger behavioral consistency. In addition, some stroke behaviors (Short against Pendulum and Topspin against Topspin) showed measurable performance decline during the course of the match. Practically, by observing the SPF in specific stroke behaviors, coaches can identify the points with the greatest fluctuations in performance during a match and implement targeted training or tactical adjustments to maintain stability in competitive situations.

Authors’ contributions

WY conceptualized the study, wrote the manuscript, analyzed the data, and prepared the figures. ZZ collected the dataset and co-wrote the discussion section with model. HZ conceptualized the study and developed the computational models. ZZ supervised the project. XX supervised the project and revised the manuscript. All authors have read and approved the final manuscript.

Funding

This work received no external funding.

Data availability

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

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.