The Effect of Situational Variables on Women’s Rink Hockey Match Outcomes

: The main objective of the present study was to develop a concise predictive model to determine the likelihood of winning in female rink hockey based on various situational variables. Additionally, the study aimed to assess the individual impact of each predictor on match outcomes. The analysis encompassed a dataset of 840 matches during five consecutive seasons (from 2018–2019 to 2022–2023) in the Spanish first division ( OkLiga ). Employing the comprehensive method of all possible regressions, the most effective predictive logistic model for match outcomes was identified. This entire model featured five categorical predictor variables ( match location , team level , opponent level , scoring first , and match status at halftime ) and one binary outcome variable ( match outcome ). Subsequently, the final model, which exhibited a sensitivity and specificity surpassing 80% for a cut-off point of 0.439, emerged. This model was applied to predict winning a match in 18 frequent situations determined from a two-step cluster analysis. Within this predictive framework, match status at halftime emerged as the most influential predictor impacting the match outcome, followed by opponent level , team level , and match location . The implications of our findings extend to rink hockey coaches and practitioners. Recognizing the significant impact of situational variables on match outcomes empowers them to customize game plans and design more specific strategies, thereby enhancing game understanding and elevating the overall performance.


Introduction
In recent times, there has been a rising interest in the analysis of sports performance, leading to an increase in studies examining various match variables across different sports.Rink hockey, a team sport featuring two teams of five players competing on a rectangular court measuring 40 × 20 m and surrounded by a one-meter-high barrier, is no exception, and the number of studies about this topic has grown considerably [1].However, it is worth noting that only a limited number of these studies have specifically addressed female teams.
Similar to many other team sports, match analysis has gained significant acceptance among players, coaches, and sports scientists due to the growing professionalization of sports [2,3].This practice is considered essential for evaluating and enhancing sports performance.Match analysis serves as a valuable tool for providing an objective assessment of the opponents' strengths and weaknesses [4].Additionally, it plays a crucial role in developing players' technical and tactical knowledge, fostering critical thinking, improving decision-making skills, and boosting overall confidence [5].
Situational variables are one of these indicators of performance.This term encompasses various match and situational conditions capable of exerting a substantial influence on performance at a behavioral level [6].Situational variables, such as match location, match status, or match time, have been established as pivotal determinants of performance, particularly in the analysis of game-related statistics, significantly impacting both team and player performance [7,8].Since rink hockey, much like other team sports, is impacted by strategic elements, it is logical to suggest that situational variables play a role in shaping the performance of both teams and players [6].Furthermore, the particular regulations of rink hockey, divided into two halves of 25 min each, with the option of two timeouts per team, allow for the adaptation of tactics and strategies based on game constraints and situational variables.
Probably the most analyzed topic in male rink hockey teams has been game location [1].This phenomenon, termed Home Advantage (HA), represents the perceived edge that teams have when playing on their home turf compared to away matches, typically estimated at around 60%, aligning with trends observed in other team sports [9].In rink hockey, previous investigations have proved the existence of HA, determining its effect to be around 60%.To illustrate this, Gómez et al. [10] and subsequently Arboix-Alió and Aguilera-Castells [11] documented HA rates of 58.32% and 59.80%, respectively, in the Spanish League (OkLiga).Likewise, in the Portuguese League, Arboix-Alió et al. [12] identified a HA value of 60.88%.
Other variables that have been examined include "scoring the first goal" [13], the crown effect [14], the impact of goalkeeper performance [15][16][17], and the influence of setpieces [18].Furthermore, as it happens with other team sports [8,19], it appears that the cumulative effect of various situational variables (e.g., playing at home, scoring first, and winning at halftime) tends to amplify their impact on the final outcomes of rink hockey matches [20].
However, there is currently no knowledge of such studies involving female rink hockey players.To address these gaps and acknowledge the lack of studies on women's rink hockey, a further investigation is needed to determine whether situational variables similarly affect the performance of female teams as they do in the case of their male counterparts.As a result, this study aimed to build a parsimonious model to predict the likelihood of winning a match, utilizing various situational variables.The secondary objective was to assess the significance of each predictor in determining match outcomes and to identify how these factors might influence match results in professional female rink hockey.

Sample
The sample comprised 840 matches spanning five consecutive seasons, from 2018-2019 to 2022-2023, within the Spanish first division (OkLiga).The OkLiga follows a balanced schedule, with each team participating in one home game and one away game.Data collection procedures involved sourcing match information from the official website of the Spanish Rink Hockey Federation, accessible at www.fep.es(accessed on 4 July 2023).

Design and Procedures
Table 1 shows the recording of a total of five categorical predictor variables and one binary outcome variable.Not won (0) The analyzed team lost or tied the match Won (1) The analyzed team won the match Predictor Match location (MatLoc) The analyzed team played away Home (1) The analyzed team competed on their field Team level (TeaLev) Relegation (1) The analyzed team finished between 12th and 14th position Remained (2) The analyzed team finished between 5th and 11th position Champions (3) The analyzed team finished between 1st and 4th position Opponent's level (OppLev) Champions (1) The opponent's team finished between 1st and 4th position Remained (2) The opponent's team between 5th and 11th position Relegation (3) The opponent's team between 12th and 14th position Scoring first (ScoFir) No (0) The analyzed team was not the first to score in the match Yes (1) The analyzed team was the first to score in the match Match status at halftime (MatStaHal) Loses (1) The analyzed team was losing at halftime Draws (2) The analyzed team was drawing at halftime Wins (3) The analyzed team was winning at halftime Note.In the logistic regression model, the category with the lowest numerical code within each variable (e.g., the category "not won" in the match outcome variable) was treated as the reference category.

Statistical Analysis
A descriptive analysis (involving absolute and relative frequencies) and an inferential analysis (in which confidence intervals for proportions were calculated using the Wilson method) were carried out on the categorical variables.
The method of all possible regressions was employed to determine the optimal predictive logistic model for the match outcome [21,22].In the original full model, there were five situational predictors (MatLoc, TeaLev, OppLev, ScoFir, and MatStaHal), alongside one binary outcome (MatOut).However, the multiplicative term TeaLev × OppLev was omitted due to the emergence of collinearity issues, which resulted in a substantial rise in the mean-variance inflation factor (mean VIF) from 1.79 to 4.04 when this term was included.The criteria employed for selecting the best predictive logistic model included the following aspects: (a) the parsimony principle [23]; (b) a large value of the area under the receiver operating characteristic (ROC) curve (AUC); (c) a small value of Akaike information criterion (AIC) [24]; (d) a good fit in the Hosmer-Lemeshow test (p > 0.10) [25]; (e) balanced sensitivity (Se) and specificity (Sp) for a cut-off point of 0.5; and (f) a non-significant difference between the ROC curve of the full model and the candidate sub-model (p > 0.05).
After selecting the best predictive model, its reliability was assessed through crossvalidation.Subsequently, an examination was conducted to ensure that this model met several key assumptions, with the respective statistical criteria indicated in parentheses: (a) absence of influential observations (2.0 Delta chi-squared influence statistic, ∆χ 2 > 3.84; and Delta-D influence statistic, ∆Dev > 3.84) [26]; (b) absence of collinearity (variance inflation factor, VIF < 5); and (c) presence of equi-dispersion (residual mean deviance, RMD ≈ 1).It is worth noting that the assumption of linearity between the predictors and the logit was not assessed since all the predictors in this study were categorical in nature.
Following the verification of the selected model's diagnostics, its parameters were estimated, and an evaluation of its overall goodness-of-fit was conducted.This assessment included a likelihood ratio test and the calculation of several pseudo-R 2 indices, including Cox-Snell, Nagelkerke, and adjusted McFadden.Subsequently, the model equation was employed to predict the probability of winning a match under 18 common scenarios, which were determined through a two-step cluster analysis.In this clustering analysis, two fixed clusters were defined, employing a log-likelihood distance measure and Schwarz's Bayesian criterion as the clustering criterion.Finally, the optimal cut-off point, based on the ROC curve, was determined to achieve a balance between sensitivity and specificity, maximizing the selected model's performance.
The two-step cluster analysis was conducted using IBM SPSS Statistics v. 20.0 software (SPSS Inc., Chicago, IL, USA).All other statistical analyses were carried out using Stata/IC v. 17.0 software (StataCorp, College Station, TX, USA), employing the following commands: proportions (for estimating proportions and calculating Wilson confidence intervals), allsets (for identifying the best subset for logistic regression and computing AIC, AUC, Se, Sp, and Hosmer-Lemeshow goodness-of-fit for each subset), roccomp (for assessing the equality of ROC curves), crossfold (for performing cross-validation), predict (for computing influence statistics), estat vif (for calculating VIF), logit (for reporting coefficients of the logistic model), lrtest (for conducting the likelihood ratio test), fitstat (for reporting pseudo-R 2 indices), contract (for determining the frequency of each combination of predictor values), lincom (for making predictions and calculating confidence intervals for each prediction), and dtroc (for computing the optimal cut-off point based on the ROC curve).

Results
Table 2 displays both the absolute and relative frequencies of the six categorical variables incorporated into the full model.The Wilson method was used to compute the 95% confidence interval for a proportion (95% CI for π).Note.n = number of observations; CI = confidence interval; LL = lower limit; UL = upper limit.
A total of 31 models were estimated using the method of all possible regressions.Table 3 presents the top five models based on the AIC criteria.The full model, which comprised five situational predictors (MatLoc, TeaLev, OppLev, ScoFir, and MatStaHal), had the lowest AIC (1238.7)and the highest AUC (0.9163).However, the third model in Table 3 was chosen as the best predictive model for several reasons.It was a more parsimonious model than the first model because it excluded the ScoFir predictor and had a lower AIC (1245.7)and a higher AUC (0.9143).Additionally, it exhibited a balanced Se (78.9%) and Sp (88.1%) for the cut-off point π = 0.5, demonstrated a good fit in the Hosmer-Lemeshow test (p = 0.145), and only had a non-significant 0.20% decrease in the AUC compared to the full model (p = 0.116).In contrast, the remaining models in Table 3 were not selected as the best predictive model because they did not meet certain selection criteria.For instance, the second model had a significant p-value in the Hosmer-Lemeshow test, while the fourth and fifth models experienced a significant decrease in the AUC compared to the full model.Regarding the reliability of the chosen model, cross-validation yielded a pseudo-R 2 Mean = 0.528, while bootstrap resampling resulted in an AUC of 0.908.Both of these values affirm the model's true predictive capability when applied to external samples.Concerning the diagnostic assessment of the selected model, 205 observations were identified, which accounted for 12.2% of the total, with notable influence statistics.However, it was opted not to exclude them from the model because they had been accurately recorded.Furthermore, no evidence of collinearity was found among the predictors, with the mean VIF standing at 1.51.It was also observed a slight infra-dispersion between the observed and expected variance (RMD = 0.73).Consequently, the standard errors of the model coefficients were marginally overestimated, leading to a slight increase in the type II error (β).
Table 4 displays the parameters of the chosen model, including their b coefficients, odds ratios (exponentials of the b coefficients), confidence intervals, and p-values.The global likelihood ratio test demonstrated that the set of parameters within the estimated model significantly predicted the match outcome (χ 2 LR = 1082.9,df = 7, p < 0.001).The pseudo-R 2 measures revealed that the estimated model accounted for between 46.1% and 63.6% of the variability in the data (R 2  Cox−Snell = 0.475, R 2 Nagelkerke = 0.636, R 2 adjMcFadden = 0.461).The odds ratios (ORs) indicated that several factors increased the chances of winning the match: playing at home (in comparison to playing away), having a high-level team (in contrast to a low-level team), facing a low-level opposing team (versus a high-level opponent), and either drawing or winning at halftime (compared to losing).Among these factors, match status at halftime had the most substantial impact on the match outcome (χ 2 LR = 342.3,df = 2, p < 0.001), followed by the opponent's level (χ 2 LR = 176.0,df = 2, p < 0.001), team level (χ 2 LR = 175.0,df = 2, p < 0.001), and match location (χ 2 LR = 9.5, df = 1, p = 0.002).Subsequently, the logistic function presented below was employed to predict the likelihood of winning the match in 18 common scenarios of the analyzed competition: Table 5 displays the 18 predictions.As an example, the first prediction can be interpreted as follows: When a team of the same level plays an away game against an opponent of the same level and loses at halftime, the probability of winning the match is estimated to be 0.105 (95% CI: 0.075 to 0.145).This specific scenario was the most frequently observed in the analyzed competition, occurring 91 times, which accounts for 5.42% of the total occurrences.Note.Pr(MatOut = Won) = probability of winning a match; CI = confidence interval; LL = lower limit; UL = upper limit; n = number of observations.
The optimal cut-off point, determined by the ROC curve, was found to be π = 0.4396.At this cut-off point, a high ability to detect both match victories (Sensitivity, Se = 85.6%) and non-victories (Specificity, Sp = 82.6%)was achieved, resulting in an overall correct classification rate of 83.9%.Therefore, the sensitivity and specificity values were more balanced for the π = 0.4396 cut-off point (Se = 85.6,Sp = 82.6%)compared to the π = 0.5 cut-off point (Se = 78.9%,Sp = 88.1%).

Discussion
The main aim of this study was to create a parsimonious model to predict the winning probability in female rink hockey according to different situational variables and evaluate the contribution of each predictor to the match outcome.As far as we know, this study is the first to examine the interactive effects of situational variables in female rink hockey.
Our key findings indicate that match status at halftime had the most significant impact on match outcomes, followed by the opponent's level, team level, and match location.While there are no comparable studies available for direct comparison, our findings align with those of Arboix-Alió et al. [20] for a sample of male rink hockey.Moreover, these findings follow the trend of other team sports [27,28], confirming that situational variables play a crucial role in team performance, supporting the idea that match analysis is essential in enhancing sports performance in team sports.

Match Status at Halftime
Match status at halftime emerged as a powerful predictor of match outcomes in female rink hockey.Teams that were drawing or winning at halftime had a significantly higher likelihood of winning the match compared to teams that were losing (OR = 20.56).This result aligns with previous rink hockey research in male competitions [20] and with studies in other team sports, demonstrating the significance of a positive halftime performance in determining the final match result [8].Halftime provides an opportunity for coaches to evaluate their team's performance, make necessary adjustments, and motivate players for the second half.Maintaining a strong defensive position during halftime may also reduce the likelihood of conceding goals and increase the chance of securing a positive outcome.
In addition to the straightforward goal differences reflected in the final match outcome, the advantage of winning at halftime can be attributed to tactical and psychological factors.Similar to other team sports, when a team secures a substantial lead, they may adopt playing tactics that aim to control the game pace and maintain their advantage.Similar to what has been reported in football [29], rink hockey teams might choose to employ a ball retention tactic.This involves deliberately slowing down the tempo of the game and adopting a more controlled approach to play.By doing so, teams aim to maintain their lead and effectively manage any goal differences that may arise during the match.This strategic decision allows teams to exert a greater control over the flow of the game and minimize the risk of conceding goals to the opposition.
Moreover, the psychological aspect plays a significant role in the performance of teams playing the second half with a lead of one or more goals.According to the cognitive activation theory of stress, competition-induced changes in androgens levels can influence athletes' behavior in subsequent interactions, depending on the current outcome [30].This hormonal response difference between winners and losers has been documented in various physically competitive situations [31] and may also explain the performance disparity between winning and losing teams observed in this study.In the context of rink hockey, previous research by Arboix-Alió et al. [18] found that players demonstrated a significantly better success in free direct hits when leading by two goals (OR = 2.4) and in penalties when winning by three or more goals (OR = 3.83).Conversely, players were less effective when losing by two goals (OR = 0.38).This indicates that a lead provides players with enhanced confidence and focus, leading to an improved performance in critical situations.Similarly, Sousa et al. [15] reported that, when a team had a lead of two or more goals over the opponent, the effectiveness of the opponent goalkeepers decreased by 45% compared to matches with a tied status in the Portuguese male rink hockey first division.This suggests that being in a winning position positively impacts the attacking team's effectiveness, as they are better able to capitalize on scoring opportunities.

Team Level and Opponent's Level
The second most influential predictor was the level of teams and opponents.Matches involving teams with a high level had a significantly higher probability of winning compared to matches featuring teams with a low level.This finding underscores the importance of team strength and competitive balance in female rink hockey.In closely contested matches between two high-level teams, the outcome may be more unpredictable, whereas matches between unevenly matched teams may result in more one-sided outcomes.
Based on the present results, it can be observed that this influence of teams' level on match outcomes has a higher effect on female than in male rink hockey [20].The reason can be attributed to the presence of a higher level of bias in female competitions in comparison to male competitions, likely stemming from the higher varying budgets of female teams competing in the same division [32].This budget disparity leads to higher-level heterogeneity compared to rink hockey male leagues, where both professional and amateur athletes participate in the same competitions.This advantageous situation, referred to as the "drag effect" [33], provides certain rink hockey teams with a significant edge, while others do not benefit from prominent professional structures, further increasing the difference in level between clubs.

Match Location
The probability of winning the match when playing at home was higher than when playing away (OR = 1.56).This finding corroborates the presence of HA in women's rink hockey, an effect that was reported to be 54.33% by Arboix-Alió et al. [12] in the female Portuguese rink hockey league.
Comparing the present results with their male counterparts, the match location in rink hockey has a lesser influence on females than on males (OR = 2.311) [20].Moreover, these outcomes are in line with expectations, as the existing literature from various sports also presents indications of higher HA values in men's teams.For instance, in football, Pollard and Gómez [34] assessed the HA effect across 26 European countries and discovered elevated HA values across all leagues for male teams.Similar patterns were observed in sports such as water polo [35], softball, and field hockey [36].
Numerous potential explanations can account for the disparities observed between sexes in relation to factors associated with HA effect, such as crowd influence, referee bias, territorial protection, and psychological aspects [35].Although there may not be overt reasons for some of these factors to diverge between male and female players, the higher attendance at men's competitions could play a role in amplifying the HA effect in male sports [34].
Another angle to consider for the lower levels of HA observed in women's sports could be the fluctuations in testosterone levels among males before matches, with a more pronounced increase when playing at home [37].According to Wolfson et al. [38], females experience a lesser rise in testosterone levels that remains consistent regardless of the playing location, since the feeling of territorial protection associated with the "home" environment is more potent in males than in females, leading to elevated testosterone levels and a heightened disposition for aggressive and dominant performance [37].

Scoring First
Finally, scoring the first goal of the match was not a significant predictor.As in men's hockey, although the likelihood of winning a match increased when teams secured the first goal, its impact did not emerge as a decisive situational variable influencing the match outcome [20].
In contrast, studies on other team sports, such as football, have demonstrated the significance of scoring the first goal.García-Rubio et al. [39] uncovered a noteworthy 3.36-fold increase in the odds ratio of winning for teams that achieved the initial goal.The absence of statistical significance in the current study may be attributed to the distinctive nature of rink hockey as a higher-scoring sport compared to football [40].
The distinctive attributes of rink hockey may elucidate the observed disparities among the various predictors.For instance, in rink hockey, the impact of scoring the first goal does not hold the same decisive weight as in other team sports characterized by a lower frequency of goals.Nevertheless, emerging as the most influential factors for victory are leading at halftime and the team's overall performance level.Notwithstanding these findings, it becomes evident that the cumulative effect of these variables significantly bolsters the likelihood of winning a match.For instance, the combined scenario of being a top team playing at home, along with securing a lead at halftime and facing a Relegation team, confers a remarkable probability of clinching victory in the match.
It is essential to acknowledge the limitations of this study to provide a comprehensive interpretation of the findings.Firstly, the sample was limited to matches from the Spanish first division (OkLiga).Consequently, future investigations should aim to validate our findings within diverse rink hockey competitive environments, including other national championships (such as the Italian and Portuguese leagues) or lower tiers of competition (grassroots sports or minor leagues).Additionally, exploring potential variations in these game variables based on the significance of the match (European or World Championships, or Euroleague) could provide intriguing insights.Additionally, while the study focused on situational variables, other factors, such as individual player performance, team formations, and tactical decisions, may also influence match outcomes.Future research could incorporate these additional variables to develop more comprehensive predictive models.

Conclusions
The present study underscores the notable influence of situational variables on the outcomes of female rink hockey matches.The results demonstrate the significance of match location, team level, opposing team level, and match status at halftime as predictors of match results.While these findings provide insights into specific aspects of performance scenarios, coaches and practitioners can leverage this information to shape more coherent training plans aligned with the dynamics of the game.The exploration of situational variables offers a wealth of information to bolster decision-making processes surrounding game strategies, player lineups, offensive tactics, team behavior, and set-pieces, contingent on factors like time remaining, team requirements, opponent characteristics, game momentum, and venue conditions.
Furthermore, this study holds the potential to assist staff members in crafting tailored practices that align with specific competition stages or simulate varying scenarios encompassing score advantages or deficits.These hypothetical scenarios could aid coaches in evaluating players' reactions under pressure, ultimately elevating performance in highstakes situations.Hence, enhancing psychological preparedness could prove instrumental in optimizing sports performance, particularly when grappling with the inherent pressures of competitive team sports.
Note.AUC = area under the ROC curve; AIC = Akaike's information criterion; ROC = comparison of models with ROC curves (chi-squared test); Se = sensitivity for cut-off point 0.5; Sp = specificity for cut-off point 0.5; p HL = significance of the Hosmer-Lemeshow test.

Table 1 .
Properties of the analyzed variables.

Table 2 .
Descriptive and inferential analyses of the categorical variables.

Table 3 .
Statistics and goodness-of-fit indices for the five models with the lowest AIC.

Table 4 .
Parameters of the selected model to predict the match outcome.

Table 4 .
Cont.Wald = significance of parameter β with the Wald test; OR = odds ratio (exponential of coefficient b); p LR = significance of parameter β with the partial likelihood ratio test.The logistic regression equation below was constructed based on the b coefficients listed in Note. b = regression coefficient b; LL = lower limit; CI = confidence interval; UL = upper limit; p

Table 5 .
Predictions of the probability of winning a match in 18 frequent situations.