Performance Factors of Foreign Players Contributing to Team Success in Korean Women’s Volleyball

2.1. Study Design

This study employed a time-series forecasting approach using the NeuralProphet model to identify performance trends and assess the relationship between foreign players’ offensive performance indicators and team ranking patterns. Time-series analysis is a predictive method that utilizes data collected over time to forecast future trends and has been widely applied across various fields, including medicine, economics, media, and the natural sciences [20].

Traditionally, classical forecasting models such as ARIMA and SARIMA have been widely used for time-series prediction [21]. However, these models are primarily designed to capture linear relationships and often exhibit reduced forecasting accuracy when applied to increasingly nonlinear and volatile datasets [22]. Consequently, machine learning and deep learning approaches, including LSTM, Transformer-based architectures, and NeuralProphet, have gained considerable attention due to their ability to model complex temporal dynamics [23]. Among these methods, NeuralProphet is particularly suitable for the present study because it combines the interpretability of the Prophet framework with the forecasting capabilities of neural networks. Specifically, NeuralProphet can explicitly model trend and seasonality while effectively accommodating nonlinear temporal variations, making it well-suited for sports performance data. As an extension of the original Prophet framework developed by Facebook's Data Science team, NeuralProphet incorporates neural network components to enhance its ability to model complex, nonlinear, and nonstationary patterns. Empirical studies have demonstrated that NeuralProphet achieves 55–92% higher forecasting accuracy than Prophet in short- and medium-term predictions [24].

Building on these methodological advances, the present study applied the NeuralProphet model to analyze and forecast offensive performance indicators in the Women’s Professional Volleyball League (KOVO) from the 2015–2016 to 2024–2025 seasons. Specifically, the model predicts one-year-ahead values for team-level indicators, attack efficiency rate and average number of blocks per set, as well as foreign-player-specific indicators, including attack efficiency rate, attack share rate, and average number of blocks per set.

2.2. NeuralProphet Model Configuration and Training

This study reconstructed all collected weekly data to reflect the structural characteristics of the Women’s Professional Volleyball League (KOVO), which operates during distinct seasonal and off-season periods and holds matches at least once a week. Before model training, all date variables were converted to the datetime format required by NeuralProphet, and records containing missing values or invalid observations were excluded from the analysis. Since the league begins and ends at approximately the same time each year, yearly seasonality was enabled to capture annual cyclical fluctuations. In contrast, weekly and daily seasonalities were disabled because match schedules do not follow a fixed weekday pattern and are not organized on a daily basis.

Since the variation in each indicator does not exhibit a consistent periodic pattern but instead fluctuates based on match conditions and team strength, the seasonality_mode was set to “multiplicative” to capture proportional rather than absolute changes in the seasonal components. This configuration reflects the nature of volleyball performance, where relative variations are more meaningful than absolute values.

The learning rate was fixed at 0.01 to prevent potential overfitting and to ensure the model's generalization capability, thereby reducing prediction bias that could arise from the limited number of matches per season. The NeuralProphet model was trained using the complete historical dataset (2015–2016 to 2024–2025) to maximize the utilization of available temporal information for forecasting the subsequent 36 weeks. Additionally, to prevent temporal leakage, all input variables were constructed using only information available prior to the target prediction point. Consequently, future observations were excluded from the training process, preserving the temporal order of the data and minimizing contamination from future information. All analyses were conducted using Python (version 3.10) with NeuralProphet (version 0.9.0). All other model parameters were maintained at their default settings.

2.3. Data Collection

To forecast offensive indicators for the upcoming season of the Women’s Professional Volleyball League (KOVO), this study collected match statistics from the KOVO DB BANK spanning the 2015-2016 through 2024-2025 seasons.

Among the many offensive metrics used in volleyball, such as total points, attack attempts, open attacks, serves, blocks, and spikes, the present study focused on three key offensive indicators: attack efficiency rate, attack share rate, and average number of blocks per set.

Traditional performance indicators often emphasize the number of successful attacks; however, these measures do not fully capture offensive effectiveness because they exclude failed attempts, such as attack errors and blocked shots [25]. To address this limitation, Shondell and Reynaud [26] proposed the attack efficiency metric, which subtracts attack errors and blocked attempts from successful attacks and then divides the result by the total number of attack attempts. This index allows for a more comprehensive evaluation of offensive performance at both the player and team levels [27].

The attack share rate represents the proportion of total team attack attempts by a specific player [28]. This metric provides a quantitative assessment of players’ levels of offensive involvement and tactical importance within the team structure [29]. Similarly, the average number of blocks per set measures the ratio of successful blocks to the total number of sets played, thereby reflecting a team’s tactical deployment and strategic efficiency [30].

The top-ranking and bottom-ranking teams for each season were defined as the first-place and last-place teams in the regular season, respectively, as shown in Table 1. Although the foreign player system was introduced in 2006, teams initially recruited foreign players through a free contract system, under which clubs directly signed players of their choice. However, beginning with the 2015-2016 season in the women’s league, a tryout-based recruitment system was implemented and has continued to the present [31]. To ensure consistency with the current foreign player recruitment structure, this study collected data starting from the 2015-2016 season.

The foreign players included in the analysis are summarized in Table 2. Under the KOVO foreign player system, each team is allowed to register only one foreign player per season. However, if a foreign player was unable to continue competing due to injury or unsatisfactory performance, the player could be replaced by another foreign player during the season. Since foreign players in the KOVO Women's League primarily occupy offensive positions, this study focused on their offensive performance indicators.

The dataset comprised all official KOVO match records of foreign players from both top- and bottom-ranking teams during the 2015–2016 to 2024–2025 seasons. Since all official match records meeting the inclusion criteria were collected, no missing values were identified in the team-level dataset. In the foreign-player dataset, matches in which the registered foreign player did not participate were treated as missing because no valid individual performance data were available. Consequently, missing values accounted for less than 2% of all observations, with missing data occurring more frequently among bottom-ranking teams than top-ranking teams. Because these missing values reflected actual player non-participation rather than measurement error, no data imputation was performed, and the missing values were retained throughout the analysis.

2.4. Model Performance Evaluation

The predictive performance of the model was evaluated using the Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE), as summarized in Table 3. MAE and RMSE are widely used and well-established metrics for assessing prediction accuracy in time-series forecasting studies because they quantify the magnitude of prediction errors while offering complementary perspectives on model performance [32]. The MAE represents the average of the absolute differences between predicted and actual values, providing an easily interpretable measure of average prediction error. In contrast, the RMSE is the square root of the mean squared error and places greater emphasis on larger prediction errors [33].

MAE and RMSE values approaching zero indicate higher predictive accuracy [34]. For percentage-based performance indicators, such as attack efficiency rate and attack share rate, previous studies have suggested that MAE values below 10 and RMSE values below 15 are indicative of acceptable forecasting performance [35]. Therefore, these metrics were used to evaluate the predictive accuracy of the forecasting models employed in this study. All MAE and RMSE values met the predefined criteria for acceptable forecasting performance, despite variations across performance indicators.

3.1. Attack Efficiency Rate

The forecasted attack efficiency results for the top-ranking and bottom-ranking teams in the upcoming season are presented in Fig. (1) and Table 4, respectively. The top-ranking teams were predicted to have attack efficiency values ranging from 27.084-32.959%, whereas the bottom-ranking teams were expected to achieve values between 22.357% and 26.025%.

The forecasted attack efficiency results of foreign players on both the top-ranking and bottom-ranking teams are presented in Fig. (2) and Table 4, respectively. Foreign players on the top-ranking team were predicted to achieve attack efficiency values between 26.181% and 38.163%, whereas those on the bottom-ranking teams were expected to achieve values ranging from 20.396-28.762%.

The negative values shown in Fig. (2) correspond to actual observations in the dataset. Because attack efficiency is calculated by considering both successful and unsuccessful attacks [34], negative values may result when unsuccessful attacks and blocked attacks exceed successful attacks. Therefore, negative attack-efficiency values indicate poor offensive efficiency rather than data abnormalities and reflect the actual performance characteristics observed during matches.

3.2. Attack Share Rate

The forecasted attack share values of foreign players on the top-ranking and bottom-ranking teams are presented in Fig. (3) and Table 5, respectively. Foreign players on the top-ranking teams were predicted to have attack share values ranging from 22.281-28.699%, whereas those on the bottom-ranking teams were expected to have values ranging from 23.216-33.694%.

3.3. Average Number of Blocks Per Set

The forecasted average number of blocks per set for the top-ranking and bottom-ranking teams in the upcoming season is presented in Fig. (4) and Table 6, respectively. The top-ranking teams were predicted to achieve values between 2.413 and 3.081, whereas the bottom-ranking teams were expected to range from 1.705-2.642.

The forecasted average number of blocks per set for foreign players on the top-ranking and bottom-ranking teams is presented in Fig. (5) and Table 6, respectively. Foreign players on the top-ranking teams were predicted to achieve an average of 0.279-0.789 blocks per set, whereas those on the bottom-ranking teams were expected to achieve a range of 0.109-0.247 blocks per set.

4.1. Attack Efficiency Rate

The forecasting results revealed a consistent difference in attack efficiency rates between top-ranking and bottom-ranking teams. This finding suggests that differences in competitive tiers may be reflected not only in the quantity of offensive opportunities but also in the effectiveness with which those opportunities are converted into points. Previous studies have identified offensive efficiency as one of the most influential performance indicators associated with successful volleyball performance [36]. In this context, the higher forecasted attack efficiency values observed among top-ranking teams may reflect a greater capacity to sustain effective offensive execution throughout a season. Collectively, these findings suggest that offensive efficiency is a distinguishing performance characteristic across competitive tiers in the Women’s Professional Volleyball League.

4.2. Attack Share Rate

Although foreign players on bottom-ranking teams were expected to account for a larger proportion of total attack attempts, their attack efficiency remained lower than that of foreign players on top-ranking teams. This finding suggests that a greater concentration of offensive opportunities among foreign players does not necessarily translate to higher offensive effectiveness. Furthermore, the relatively lower attack-share rates combined with higher attack efficiency observed in top-ranking teams may indicate a more balanced distribution of offensive responsibilities within the team structure. Therefore, differences in attack-share patterns seem to reflect contrasting offensive utilization characteristics across competitive tiers.

4.3. Average Number of Blocks Per Set

The forecasting results also demonstrated higher blocking values among top-ranking teams and their foreign players. Unlike attack-share rates, blocking performance exhibited a pattern similar to that observed for attack efficiency, suggesting that front-court performance characteristics may differ systematically across competitive tiers. Given that blocking serves as both a defensive and transitional performance indicator in volleyball [37], the observed differences may reflect broader performance characteristics associated with higher-ranking teams. Moreover, the higher blocking values forecasted for foreign players on top-ranking teams suggest that their contribution extends beyond offensive production and encompasses multiple aspects of match performance. These findings highlight the multidimensional role of foreign players within successful team environments.