Soft tennis originated in Japan after the introduction of lawn tennis in the nation. It is a modified version of lawn tennis that developed under the influence of Japanese culture. A few of the characteristic features of soft tennis are as follows: The rackets used are lighter than those used in lawn tennis, the balls are made with a soft membrane of natural rubber, and the doubles game is more popular than the singles game (Ida et al., 2005).

The first international soft tennis event was conducted in 1956 only among Korea (KOR), Chinese Taipei (CTP), and Japan (JPN), even though the game had been played for more than 50 years in KOR, CTP, and JPN by that time (Omote & Japan Soft Tennis Association [JSTA], 1985, 1986). The Japanese introduced soft tennis to the Korean Peninsula in approximately 1905 and to CTP in approximately 1907 (Omote & JSTA).

The first official international soft tennis event, the First Asian Soft Tennis Championship, was held in 1988, with the establishment of the Asian Soft Tennis Federation on February 6, 1988 (JSTA web site, a). After that, international events for soft tennis have been held regularly. There are four major international soft tennis events: the World Championships, Asian Games, East Asian Games, and Asian Championships. To date, 29 international soft tennis events have been held, with a total of 576 medals awarded to the players during these events.

Each soft tennis match consists of a sequence of seven or nine games; hence, the matches are generally played in a shorter amount of time than in tennis. Therefore, most players and coaches believe that the likelihood of uncertainty in the result of a match is very high. Despite a good understanding of the game, no studies have been conducted on factors that determine winning games in international soft tennis events; these events have a greater level of uncertainty regarding match results than do domestic events.

Most sports organizations announce their international rankings periodically on the basis of their original rating systems. For example, the International Tennis Federation, Association of Tennis Professionals, and Women's Tennis Association release the categorized rankings precisely, based on sex, age, and event. The rankings are calculated on an individual and national basis; however, these rankings only reflect the results. Therefore, players, coaches, and analysts need more useful information to help them win against their opponents.

Bernard and Busse (2004) clarified that the “host” is a better predictor than either the gross domestic product (GDP) or population for winning medals in the Olympic Games. The findings of many other studies were consistent with those of Bernard and Busse and reveal that the host is a strong predictor (Celik & Gius, 2014; Forrest et al., 2010; Hoffmann et al., 2004; Scelles et al., 2020; Vagenas & Vlachokyriakou, 2012), and a “home” advantage exists in the Summer (Balmer et al. 2003; Pettigrewa & Reicheb, 2016) and Winter (Balmer et al. 2001) Olympic Games.

In the context of players’ performance, home seems to be equivalent to host for encouraging players. Nevill et al. (1997) examined the home advantage effect at the Grand Slam tournaments held in 1993 and reported that players had an effective home advantage only at Wimbledon. However, using four regression models Holder and Nevill (1997), reported little evidence of a home advantage at Grand Slam tournaments. Koning (2011) used a modified logistic regression model in his study, which revealed that a home advantage exists among male professional tennis players, but not among females. To date, it is not clear whether or not there is a home advantage effect at Grand Slam tennis tournaments.

The type of court surface affects the game patterns (Hughes & Clark, 1995; O'Donoghue & Liddle, 1998) and strategies (Hughes & Franks, 2004) in Grand Slam tennis tournaments. A study by McHalea and Morton (2011) revealed a surface effect among the top-ranking players in the Association of Tennis Professionals tour. However, a study by Corral (2009) did not reveal any conclusive surface effects in Grand Slam tennis tournaments, except in female player competitions on grass courts. As for soft tennis, because the ball differs from that used in tennis, the effects of the court surface for soft tennis players will differ from tennis.

The study by Koning (2011) used data from 2000-2008 for men and from 2007-2008 for women, as far as we know, which is the longest duration of data capturing for any study on racket sports science, and examined the factors that may contribute to winning. Studies using data captured over long time periods can identify significant factors for winning, considering the rapid development of rackets, strings, and other equipment. Knowledge of factors that can help players win tournaments or international events can change the attitude of coaches toward the players and help evolve coaching methods for training them. However, only a few studies have been conducted investigating the number of medals awarded in racket sports in international events.

Fortunately, there is ample information on medals that have been awarded for international events in soft tennis. We summarized the results of four international events for soft tennis held between 1988 and 2019, citing the results described in the study by Omote and JSTA (1985) and on the website “Soft Tennis Homepage,” administrated by the second author (Tanaka, 2019). These data include the results of both individual and team competitions. Table 1 shows information about the international soft tennis events held and the court surfaces used that were analyzed in this study. However, no analysis has been performed on these wins yet. But in analyzing the information, several problems can be assumed. Tables 1, 2, and 3 show the information on events, court surface, the results of medal winning, and the times of host experienced. It seems clear that the data is biased, especially in medal distributions and the number of host experiences. However, while the number of medals won is a result of the competitions, the number of host experiences is considered factors for the number of medals won. This means we must keep these in mind and care must be taken in the analysis. Thus, we will conduct two-stage analysis to explore the factors that contribute to the awarding of medals.

Table 3 Information about host experienced times for the countries and regions.

Therefore, the purpose of this study was to identify the factors that play a role in winning international events in soft tennis. The analysis was performed carefully, as we analyzed potentially biased data.

Despite a history of medal races at international soft tennis events, there has been no investigation into them. Due to the low number of studies on soft tennis, we have little information about the factors that play a role in winning medals at international events. The data that we have include information on events, court surfaces, number of medals awarded to players, number of times a country hosted an event (Tables 1, 2, and 3), and number of international events attended (NIEA). Hence, it is inadequate to assume the factors that play a role in winning medals. Therefore, we need to employ an exploratory approach toward analyzing data, by outlining it first.

We propose that decision tree induction should be employed to obtain insights into soft tennis. A data mining technique can extract useful and previously unknown information from archived data (Ofoghi et al., 2013). Decision trees can also be used on datasets with missing values (Loh, 2008; Morgan et al., 2013). It is a non-linear technique and independent of selection of a prior data distribution (Kawabata, 2008). In addition, the results of decision tree induction can be expressed as a dendrogram, which could help coaches and analysts to interpret the relationships among variables. Further, this technique has the advantages of greater interpretability Hastie et al., 2009) and the ability to provide greater insights into factors influencing results than linear methods (Written & Frank, 2005). Decision trees have also been used for sports studies such as curling (Willoughby & Kostuk, 2005), participation in daily physical activity, sports of children with disabilities (Ross et al., 2021), food prediction during endurance sport competitions (Fister et al., 2014), match quarter outcome in elite women’s Australian rules football (Cust, 2019), and attacker-defender interactions in hockey (Morgan, 2013).

We applied decision tree induction for data analysis of the unbalanced provision of medals in soft tennis. The analysis was done carefully to avoid overfitting. We applied 10 times 10-fold cross-validation (Written & Frank, 2005). This procedure is reliable enough to produce an error estimate for most datasets. Further, we are trying to reconsider the “host” effect, as we do not have enough insight into the host effect yet. Therefore, we must compare the results with and without the host effect. Here we will define the host effect as equivalent to home advantage, because host and home are considered similar in the sense that they encourage to the player (see Figure 1).

Figure 1 An example of the decision tree nodes for total medals among the top four countries.

All raw medal distribution data were collated and analyzed using JMP 14.3 (SAS Institute Inc., North Carolina, USA). The aim of using the decision tree here was to comprehend the features of the data and identify the possible candidates of variables for subsequent analyses.

Results and discussion 1

Our first goal in the exploratory analysis is to determine whether host effects exist. The first split in our decision tree model was caused by the attribute “Country” and the “Host” for total medals won and gold medals won were observed only for KOR, JPN and CTP, and only for KOR and JPN, respectively.

Table 4 shows the results of 10 times 10-fold cross-validation analyses for (i) 10 countries and (ii) the top four countries (KOR, JPN, CTP, and China (CHN)). Table 5 presents the results of the confusion matrices showing the relationships between the host effect and total medals obtained, and the accuracy of our model and recall on host effect. Considering the host effect, the root mean square error and coefficient of determination (R ² ) values were close with or without the host in our model (Table 4). Confusion matrices indicated high accuracy to distinguish; however, recall values for both the ten countries and top four countries were very low (Table 5). Considering these results, the host was not deemed to be a factor for winning medals, but is a norm for international soft tennis events due to the data bias caused by exclusive host concentration (that is, the phenomenon that only certain countries are hosts. (Table 3). Therefore, “Host” is excluded here for the subsequent analysis.

The results of our decision tree model showed two interesting outcomes for winning medals. For CTP, the court surface type, namely whether the court surface is “Hard” or not, was the contributing factor for winning more medals. In terms of winning medals, NIEA was a significant predictor for every country that attended international events more than 16 times. The attribute “Event” here did not indicate any effects. This phenomenon implies the need to give systematic support to other countries via the International Soft Tennis Federation, which could yield more participants.

As a whole, all the attributes analyzed, except for “Event” and “Host”, seemed to be good predictors. However, “Event” was a significant predictor for KOR and JPN, who collectively occupy 64.5% of the medal tally. “Event” is likely to be the key for success at international events in soft tennis. Therefore, the exclusion of “Event” is inadequate here. Hence, the remaining three attributes (Court surface, Country, and NIEA) also have been applied to the subsequent analysis.

Methods 2

As collectively KOR, JPN, CTP, and CHN have won 93.2% of the awarded medals, analyzing the top four countries would make the de facto medal race analysis simpler. The aims of this section were to clarify the factors for winning medals in international soft tennis events more clearly and also to determine the factors that play a role in winning gold medals by analyzing the data of the top four countries that have won gold medals.

Considering the information provided in the RESULTS and DISCUSSION1 section, we proceeded more carefully with the analysis to avoid overfitting. In METHODS 2, we applied 10 times 10-fold cross-validation (Written & Frank, 2005) again.

Results and discussion 2

Figures 1 and 2 show examples of our decision tree model for total medals and total gold medals, respectively, among the top four countries. The first split in the model occurred when the attribute “Country” for KOR and JPN was equal to or greater than 4.603 for total medals. Considering the left side of the tree, as well as the RESULTS and DISCUSSION1 section, it is clear that CTP is winning more medals on hard courts, and during the 29 international competitions China has recorded better results in the last decade than in the last three decades. At the right side of the tree, the NIEA seems to be a good predictor for winning medals, but this was the result of an increased number of individual games played in international soft tennis events. Until 1991, only team and doubles events were played. Singles and mixed doubles were first played in 1992 and 2002, respectively. As those results, the number of total medals increased for KOR and JPN.

Figure 2 An example of the decision tree nodes for total gold medals among the top four countries.

Considering the left side of the tree in Figure 2, CTP has an advantage for winning gold medals on hard courts. Based on the right side of the tree, KOR has won more gold medals in the Asian Games and World Championships than in the Asian Championships and East Asian Games. This is possibly owing to the social structure in KOR. Players are given monetary rewards and virtually exempted from military service in KOR upon winning gold medals at the Asian Games and World Championships (Takahashi & Kiku, 2013).

Further, CTP has an advantage on hard courts, whereas KOR has an advantage on clay courts. On the other hand, JPN has won more gold medals at the Asian Championships than at other events.