Modified Handball in Physical Education: Investigating Opportunities for Inclusion and Relatedness

Abstract

This paper addresses the challenge of assessing relatedness and functional interdependence through connecting passes within invasion games, which may offer valuable pedagogical insights into gameplay for accessibility and inclusiveness. Hence, the purpose of this paper is twofold. Firstly, it presents preliminary work on the methodology for computing open passing lanes and derived metrics, integrating spatiotemporal data analysis with event data. Secondly, using a within-subject design, it investigates how modified handball games influence game play opportunities. Data were collected during handball matches in a pre-teens Physical Education (PE) class with mixed-skill-level teams. Game actions (e.g., passes, receptions, and shots) were manually recorded through systematic observation of video footage, while players’ positional data were captured with ultra-wideband technology. Findings provide evidence that employing a numerical advantage (one player up) enhances overall opportunities for individual attacking actions (i.e., more passing, catching actions, and goal-scoring opportunities) and relational actions (i.e., more open passing lanes) compared to equal numbers. Conversely, equal numbers with individual marking appeared more challenging, as fewer secure passing lanes were observed, and the ball possessor spent more time with the ball before releasing it. The developed approach holds promise for studying designed games to enhance inclusion and learning opportunities for all.

1. Introduction

Team games in physical education teach provide opportunities for learning social inclusion, enabling students to internalize essential life skills [1]. They offer a rare chance to learn teamwork and ethics in practice, including fair play, knowing how to behave when winning and losing, and developing resilience in defeat. These games are unique in the sense that the practice and learning opportunities of each student depend on the other students—things in any collective sport: if someone is labelled less sport-competent, their teammates tend to exclude him/her from play, such as by not passing him/her the ball. A Norwegian study [2] found that students who did not receive the ball reported feelings of exclusion, alienation, unwantedness, and demotivation. These exclusionary behaviors can also cause students with self-perceived low game competence to adopt strategies of avoidance and self-exclusion [3,4], such as “avoiding the ball”, “reducing effort”, “social dizziness”, “faking soreness”, “warming the bench”, or “forgetting gym clothing” [4] (p. 1). So, equal opportunity or inclusion is a problem that PE teachers must address in daily classes.

Despite widespread acceptance of inclusivity as an essential contemporary teaching principle, national and international advocacy movements such as the Salamanca Declaration by UNESCO [5], doubts and difficulties remain about what inclusivity really means and how it should be practiced in team sports. These uncertainties can be further understood through DeLuca’s [6] identification of four competing perspectives on inclusion, whose conceptions range from maintaining the status quo to fostering social justice and embracing student diversity in a more transformative way: (a) normative perspective—this is directed towards the hegemonic level and suggests that everyone can learn, but they have to be assessed by the same yardstick; (b) integrative perspective—this view holds that everyone can learn, but students of different statuses learn separately at their level. Assessment can be specific to each level, but the reference level of the hegemonic level is maintained; (c) dialogical perspective—recognizing the difference in capabilities between different students, advocates learning through co-participation, interaction and collaboration between students of different statuses, including socio-economic, cultural, gender, race, ethnicity, religion, country or region of origin, or with disabilities; (d) transgressive perspective—this is antagonistic to ableism, to normative hegemony. It requires everyone to learn everything they can learn and to learn with everyone, collaborating with everyone. Learning is not understood as standardized; everyone needs to recognize and try to understand each other in solving problems and overcoming jointly achievable challenges, and in the possibilities of joint creation and in the perception of personal transformation and the relationship of reciprocity.

Although teaching team sports is culturally and pedagogically valued, it has been argued that the traditional approach is often delivered with low expectations for game tactical understanding, skill development, and enjoyment, particularly for less-skilled students and girls [7]. The traditional physical PE curriculum and team-teaching practices frequently fail to accommodate diversity, leading to the exclusion and marginalization of certain student groups (e.g., [2,8,9]). Additionally, if teachers do not actively intervene, the competitive nature of institutionalized team sports, combined with a performance-oriented perspective in schools, can exacerbate inequalities, allowing higher-skilled students to dominate while others feel excluded [7].

Over the past 40 years, a wealth of information has been accumulated about game-based approaches that empower teachers to design games where students can actively participate and engage in their creation according to their possibilities. At the heart of those approaches is the Teaching Games for Understanding (TGfU) model [10]. The proponents of the TGfU argue that all students can actively participate in games through carefully tailored modifications such as representation, exaggeration, and adaptation. The adjustments should facilitate meaningful play by aligning game elements and tactical problems with students’ skills, ensuring everyone can engage, learn, and contribute effectively [11].

Teachers can facilitate game involvement by explicitly instructing students to be inclusive or modifying the rules to encourage a more collective game [1]. Hence, when designing and implementing game modifications, as they inevitably influence learning opportunities and gameplay experiences, the opportunities for play involvement and interaction are critical considerations. Specifically, in heterogenous groups or mixed-gender classes, girls and perceived ‘weaker’ players are at risk of being marginalized, ignored, or excluded by those who dominate the game (the ‘game owners’).

Therefore, adjusting elements such as rules (including object/ball characteristics), time–space, number of players, and the ratio between attackers and defenders is essential for promoting inclusion and accommodating students of varying abilities, genders, and game sense. In essence, teachers are challenged and advised to co-create, with their students, games that bind all players—even the low-skilled ones—to engage with one another whilst still resembling the original sport, thus fostering interconnectedness and positive interdependence to successful play [12]. However, with numerous possibilities for modifying traditional invasion team sports, it is essential to investigate how key game modifications impact the students’ opportunities to be involved, play, and learn. In this work, we are specifically interested in investigating how key handball game modifications might influence relational and functional dependencies among attackers, thereby creating a more inclusive gameplay environment. Although Olympic indoor handball is played in a seven-a-side format, a multitude of tactical structures can emerge during both the transitional and positional phases of the game, as well as their sub-phases. To introduce children to handball, various small-sided game forms, or ‘mini’ versions of the institutionalized game, have been developed and implemented around the globe. While some sporting cultures, such as those in Scandinavian countries, emphasize numerical advantages and confine the defensive pressure to empower children’s inclusion, others prioritize the full-court pressure defense to trigger individual movement and transitional play [13,14].

Thus far, research on inclusive and exclusive behaviors in team games in PE has been primarily based on notational analysis (such as engagement rates and success) or interviews [1,2,15]. Observational finding studies have suggested that low-skilled students are disadvantaged in mixed-ability competitive games [16]. However, there is a lack of research on how to modulate the game dynamics and competition to foster a more inclusive play.

With tracking technologies and wearable microsensors inundating our daily lives, we can now monitor physical activities with unprecedented accuracy and convenience. Combining spatiotemporal tracking data with event data is considered the most promising approach for gaining deeper insights into player and team tactical behaviors [17]. Existing contributions have primarily focused on soccer, examining tactical performance by analyzing specific actions and tactics related to the spacing and timing of co-players and opponents [18].

In this study, we are particularly interested in investigating how modified handball games create opportunities or obstacles for inclusive play experiences by analyzing the ball handler’s pass actions and the involvement opportunities, based on the concept of being available to receive a pass. This leads us to the challenge of quantifying the effectiveness of a player’s positioning or co-positioning to support the ball carrier by getting ‘open’ for a pass or free-to-attempt scoring, which we will refer to as ‘Availability’ (for more, see [19]). Additionally, we were interested in quantifying the number of passing lanes available to the ball possessor and the time required to release the ball to investigate the complexity and difficulty of the game problems posed.

In modifying and engineering handball games for teaching purposes with a focus on inclusion, several guiding assumptions were adopted to create a rich, inclusive, fair, and challenging game environment. These assumptions were framed within the dialogical and transgressive perspectives of inclusion [6] and incorporated general recommendations [20] as well as handball-specific practical recommendations [21].

(a)

Reduced and shaped game forms sampled from the full game are projected to create more opportunities for involvement in ball action (catching, passing, and shooting), as having fewer players allows everyone more chances to handle the ball.

(b)

The soft ball is assumed to ensure easy catching for all players and safe saving or blocking actions by the goalkeeper. Its non-bouncing nature is expected to encourage players to discover an open receiver and pass rather than dribble, thereby promoting a more collaborative passing game.

(c)

The complexity of the full game can be simplified by sampling and isolating different phases (transitional or positional) and exaggerating their corresponding tactical problems and challenges. The game becomes potentially more inclusive when using the four vs. three mini handball structure, with an advanced goalkeeper (an empty goal) and zone defense, which emphasizes positional play and provides more time and space to execute tactical decisions. In contrast, the equal numbers game form (three vs. three) with mandatory player-to-player defense emphasizes transition play, creating a more dynamic environment and increasing decision-making challenges.

(d)

By incorporating shaped scoring rules that overvalue “collective scoring” (all players must touch the ball) and prioritize each player’s first successful goal in the game, a more inclusive gameplay experience is being developed.

(e)

Students learning within the game can be differentiated by implementing variations in tactical challenges (symmetric versus asymmetric numbers and different action constraints, with varying levels of defensive pressure).

(f)

Since heterogeneous grouping strategies can lead to some players dominating the action (by scoring in most of their team’s attacking attempts) while others are marginalized by being placed in the goalkeeping position, a positional swapping system between shooter and goalkeeper was implemented.

Rooted in the teaching assumptions that shaped this pedagogical experience, key research questions were formulated:

• What is the value of the developed methodologies in uncovering affordances for action and interaction through the manipulation of game constraints in a pedagogical context?
• How do variations in the attack/defense ratio (both even and uneven numbers), along with levels of defensive pressure and inclusion-focused rules, impact the participation and engagement of all students, particularly marginalized groups such as girls and low-skilled players, in a mixed-skill PE game competition?
• How does the availability of passing lanes affect the time required to release the ball and movement at ball reception, and what do these factors indicate about the complexity of the game?

In summary, this research addresses the challenge of evaluating team games, specifically handball, focusing on opportunities for game involvement and interactions—such as passing and receiving—that are significant for assessing their accessibility and inclusiveness potential. It pursues two interlinked aims. Firstly, it presents a preliminary work on computing open passing lanes and derived metrics that integrate spatiotemporal data analysis with event data. Secondly, it uses a within-subject design to explore how modified handball game forms impact students’ gameplay opportunities.

2. Materials and Methods

2.1. Context and Participants

This study is part of a larger research project aimed at empowering preservice teachers as practitioner researchers towards inclusive PE practices, focusing on invasion team games.

This specific work stems from a teaching experience during the 2022–2023 academic year, dedicated to training PE preservice teachers (PSTs), involving a university teacher educator and specialist in handball didactics. The study was conducted in an intra-class tournament where intentional gameplay configurations were used to create a more engaging handball play experience. It involved a class of 16 students (ages 11–12), consisting of 11 boys and 5 girls, who participated in the matches.

The tournament organization and instructional interventions during the games were collaboratively prepared and discussed by the group of six PSTs responsible for the activity and the university teacher educator in a micro-teaching context. Four mixed-ability teams, each consisting of four student-players, were formed. The classroom teacher, the full-year PE teacher, established the teams to ensure they were balanced in terms of game performance.

Data collection occurred at the end of the 9th lesson of a handball unit (with each lesson lasting 90 min). In the first four lessons of the unit, the students mainly learned to solve game problems based on numerical advantage (such as 4vs.3+GK, 3vs.2+GK, 2vs.1+GK, 2vs.1+1+GK); between the 5th and 8th lessons, game problems with equal numbers were also addressed (such as 3vs.3+GK and 2vs.2+GK with supporters), incorporating different space constraints according to the learning needs. In all games and tasks, soft balls (size 2) were used to discourage dribbling and ensure safety for the goalkeepers. Throughout the entire unit, aspiring PE PSTs were actively engaged in planning, observing, adapting, and analyzing as part of their training. They were intentionally tasked with addressing inclusion challenges to enhance their preparation and problem-solving skills to deal with student diversity.

The school principals and the class PE teacher were fully informed about the study. Written consent was obtained from the students and their guardians, who explicitly agreed to use wearable sensors and video recordings during the class.

This research adhered to the principles of the Declaration of Helsinki for conducting research with human participants and was approved by the local Ethics Committee (2023).

2.2. Description of the Used Game Forms

Two distinct game forms (GF) were played, where key rule modifications were introduced, which included changes in the ratio of attackers to defenders, as well as changes in the defensive and goalkeeper (GK) behavior:

–

Uneven game form: 4vs.3+GK: The player in the goalkeeping position actively participated in the attack, creating a numerical advantage (4 attackers vs. 3 defenders. Defensive transition: Upon losing possession of the ball, the players were instructed to immediately sprint back to their goal area line before participating in defensive actions. This strategy was intended to provoke a more low-pressure defense and lined-up formation.

–

Even game form: GK+3vs.3+GK: Full-court pressure with goalkeeper’s support up to the midcourt line was implemented. Defensive transition: Upon losing possession of the ball, the players were instructed to only exert pressure in half-court (their defensive field).

In all cases, a small-sized court (20 m by ≈ 27 m) was used with a 5 m goal area line. A soft ball (size 2) was used to discourage dribbling and encourage cooperative play (connecting passes) instead of individual play. Special scoring rules were used in both forms to encourage more collaborative play. As such, if a goal was scored after all team players had touched the ball, three points were awarded; otherwise, only one point was given. Also, the first goal of each player was awarded three points.

A mandatory swap rule was enforced, meaning that whenever a team scored a goal, the player who scored (the shooter) immediately swapped positions with their team’s goalkeeper. Each match lasted 10 min, with a break of about 5 min between them. Additionally, the team compositions remained constant throughout all the games.

2.3. Data Collection, Synchronization and Treatment

The data were collected during a single 90 min class at the cooperating school facilities using two data sources: spatiotemporal data (including x, y positions of the student-players) obtained with the local position system and event data collected manually.

At the beginning of the session, each student-player was equipped with a wearable device (i.e., a tag) commercially available tracking system (WIMU™; Realtrack Systems SL, Almería, Spain) based on ultra-wideband (UWB) technology. Previous work on the validation of this tracking system for handball found mean absolute measurement errors below 10 centimeters (for more details, see Bastida-Castillo, et al. [22]). The devices were used to determine a participant’s two-dimensional positions (with a frequency range of 20 Hz). For the identification and tracking of the tag positions, an 8-antennae system was installed around the tournament space, and the calibration process was done according to the company.

Every game had a (.csv) file with 2-D coordinate data extracted with the help of the manufacturer’s tracking device software. Although the exported files were labelled raw data, it is important to mention that the software applied a hidden signal filtering process before making the raw data available for export; therefore, no additional data filtering processes were implemented. A preprocessing step was conducted to address missing spatiotemporal data using interpolation methods, specifically cubic splines.

Additionally, the session was video recorded using two cameras (with 25 fps), providing a full view of the class space. The same handball expert (a member of the research team) analyzed all the matches using slow-motion replays as needed while embedding the images with codes/flags corresponding to a given event (conducted by designated rules—per event) with the help of a subtitle video editor software (open-source). Afterward, an events list was generated with the corresponding timestamp and saved in an Excel file format. This process allowed the use of the manually logged game status flag (game starts and game ends) for data synchronization before they could be processed together. We also made use of the ball status flag, which indicates when a given player catches the ball and releases the ball, to determine the ball’s location on the court (x, y), and whether the ball is being grabbed or on a fly. The event data were then synchronized with the positional raw data.

2.4. Methodological Procedures for Systematic Observation

Whenever a student was directly involved with the ball (such as passing, catching, saving, or intercepting), was the intended recipient of a pass but failed to receive it (due to an unsuccessful catch, interception, or overthrow), or even participated in a finishing attempt (as either a shooter or goalkeeper), it was annotated using the observational categories outlined in

Table 1. Events observational criteria adapted from Gréhaigne et al. [23].

Events	Description
Ball conquered	Player intercepts a pass or recaptures a ball after an unsuccessful shot on goal or after a loss catch by the other team.
Received pass	Two different types were considered: (1) appropriate reception—when a player receives the ball from a teammate and does not immediately lose control of it; and (2) inappropriate reception (dropped pass)—when a player receives a catchable pass but fails to immediately secure the ball (strikes the ground or goes out of bounds).
Neutral pass	A pass executed without defensive pressure, which does not truly put the other team in threat, a typical pass executed to move up court or to organize the attack without defensive interference.
Offensive pass	A pass executed under defensive pressure, or a pass which puts pressure on the other team, such as leading to threatening situation or shooting opportunity.
Uncatchable pass	A pass that the teammates cannot catch as a consequence of the thrower’s technical and/or decision-making errors.
Shot *	Two different types were considered: goal and failed/unsuccessful shot.
Saving *	In the goalkeeper role, “saving” refers to the player successfully preventing the ball from entering the goal.
Overlooked scoring opportunity *	A situation where a player fails to recognize and take advantage of a chance to score.

* These categories were included or subdivided to more detailed observations (such as a failed shot).

.

The categories were adapted from the Sports Performance Assessment Tool [23]. Subsequently, composite variables or indices were calculated from the manually collected event data for each student-player:

–

Rate of on-ball actions: the number of ball engagement actions (ball receptions, stealing the ball, passing, and shots) per minute of play.

–

Rate of offensive balls: the number of on-ball threatening actions (offensive passes, assists and shots) per minute of play.

From a collective point of view, the game balance between the attack and defensive play was established using the following ratios:

–

Game Balance_Goal: number of goals/number of attacks

–

Game Balance_Shots: number of shots/number of attacks

The intra- and inter-observer rater agreement of the manual notational data events was assessed using 25% of the data (one 10 min match). Intraclass correlation coefficients were employed to quantify the agreement, revealing an average of 99% for intra-observer reliability and 95% for inter-observer reliability across all categories.

2.5. Preliminary Work on Computing Open Passing Lanes and Derived Metrics

The method used to estimate the existence of passing lanes is purely kinematic and utilizes the spatiotemporal data (x, y) of the players and the ball (when in a player’s possession). For each passing situation, we evaluated if there was a zone from the ball carrier any other team member that had no adversaries in it. That exclusion zone guarantees that the pass cannot be intercepted. This defines a passing lane whenever a triangle zone around the line segment between the ball handler and the receiver has no opponent inside (as illustrated in Figure 1). At any given point in space, the aperture angle is given by

$$\theta =\arctan \left({\displaystyle \raisebox{1ex}{$v_{opponent}$}\!\left/ \!\raisebox{-1ex}{$v_{ball}$}\right.}\right)$$

(1)

The first adjustable parameter is the ball velocity (V_ball), defined for simplicity as the mean velocity of the fastest 10% (90th percentile) recorded passes, although future work should consider the fastest pass executed by each player. The ball speed was considered constant at 9.18 m/s. A passing lane was defined as an opportunity to execute a straight pass in the x–y plane without opponent intervention, excluding lob or bounce passes.

Table 2. Descriptive data regarding passing and movement velocity computed for each team.

	Passing Velocity (m/s)		Movement Velocity (m/s)
Game form	Uneven game [Mean ± SD]	Even game [Mean ± SD]	Uneven game [Mean ± SD]	Even game [Mean ± SD]
Team A	6.28 ± 1.61	6.32 ± 1.73	1.37 ± 0.17	1.14 ± 0.12
Team B	6.58 ± 1.73	5.91 ± 1.89	1.32 ± 0.13	1.10 ± 0.09
Team C	6.53 ± 1.91	5.69 ± 1.71	1.07 ± 0.11	1.02 ± 0.22
Team D	6.37 ± 1.60	6.26 ± 1.57	1.05 ± 0.09	1.12 ± 0.10
Overall [Mean ± SD]	6.42 ± 1.69	6.03 ± 1.76	1.20 ± 0.19	1.09 ± 0.14

displays the players’ mean moving velocity and ball velocity derived from the experimental data.

The second parameter is each opponent’s moving velocity (V_opponent). This is more complex as it depends on the range. As an example, below (Figure 2b—right side) is a composite plot of an arm moving 0.5 m in 0.1 s (5 m/s) plus Usain Bolt’s 100 m dash world record velocity-displacement profile (starting from blocks) plus a 0.146 s reaction time (data adapted from Helene and Yamashita [24]). The real velocity profile of a student-player is much slower but equally complex, so we simply used a constant average value obtained in our data that was defined at 6.15 m/s, representative of the mean speed of all student-players (v = 1.15 m/s) plus the moving arm speed (v = 5 m/s). We just assumed that the opponent could immediately start moving at that average velocity and ignore the reaction time and if he/she was already moving or not. The line patterns marking the exclusion zone in Figure 2a are matched with the opponent’s velocity profiles of Figure 2b. The significant differences between the computed ball interception areas started to appear for passes longer than 10 m, which in our data set, represented 4.08% of total passes.

Then, the angle between the receiver (R), the passer (P), and the opponent (O) is calculated at the passer’s vertex, given by:

$$\mathrm{\alpha }=\arccos \left({\displaystyle \frac{\overrightarrow{\mathrm{PR}}\cdot \overrightarrow{\mathrm{PO}}}{\overrightarrow{\mathrm{PR}}\overrightarrow{\mathrm{PO}}}}\right).$$

(2)

Hence, a passing lane is defined as open for every receiver if the corresponding α (see Equation (2)) for every opponent is equal or greater than the defined θ (see Equation (1)), or if the opponent is behind a perpendicular line that crosses the endpoints of the line segment $\overline{\mathrm{PR}}$, i.e., the opponent is behind the receiver or behind the passer. If the receiver is inside the area (e.g., the goalkeeper), the passing lane is automatically defined as ‘closed’.

For every passing situation when the ball carrier holds the ball, we, then, computed the following variables:

–

Number of passing lanes: average number of available passing lanes during all instances of ball possession (i.e., no opponents within the passing lane).

–

Availability (A_%): fraction of time a player can receive a pass during teammate ball possession (i.e., ’open’ status).

–

Ball possession time (B_time): the average time (in seconds) a player possesses the ball.

–

Slow move with the ball (SMB_%): fraction of time a ball possessor holds the ball while moving at a very slow speed (below 0.8 m per second); in other words, it represents the proportion of the total ball possession time spent by a player standing still or barely moving (i.e., stationary status).

2.6. Comparison with Expert Decisions on Open Passing Lanes

It was decided to compare the number of computed open passing lanes against those estimated by human observers. This was conducted for 48 passing situations from the video of two different matches. The typology of situations chosen for comparison was similar to Dick, et al. [19]. Both the experts and model were instructed to identify the ‘Availability’ in situations where the ball handler possessed the ball for at least 0.5 s, and in different types of situations encompassing a spectrum of anticipated availability from none to full availability in transition and positional offensive phases. For each passing situation, the experts were instructed to indicate how many available passing lanes existed for each passer, ranging from zero to three.

Both our study and previous research [19] achieved similar observer–model correlation coefficients in assessing players’ availability. The coefficients ranged from 0.641 to 0.739 in our case, and, in theirs, from 0.638 to 0.769. However, there was a slight difference in the agreement between experts. Our study showed a marginally lower correlation (0.736) compared to Dick, et al. [19] (0.740–0.842). One potential explanation for our model vs. observer correlation results is that using fixed parameters for all situations could have been too restrictive. Additionally, comparing our model directly to human experts requires caution. Our study relied on video recordings from a single angle and distance to the court, which limited depth perception and made distinguishing between available and unavailable players difficult. This limitation is well recognized, prompting the growing use of technology-driven models in sports, such as automatic goal-line technology and semi-automatic offside detection in soccer, to replace or assist subjective human judgment.

2.7. Statistical Analysis

The data processing treatment and plot creation were performed using a custom script in Python 3.11.3 with the help of the following packages: Numpy [25], Seaborn [26], Pandas [27], and Matplotlib [28]. For the statistical tests, the SPSS software was used (IBM SPSS Statistics for Windows, Version 29.0.2.0, Armonk, NY, USA: IBM Corp).

To ensure data met the assumptions of parametric tests, normality was assessed using the Shapiro–Wilk test. While most variables (number of pass lanes, A_% SMB_%, velocity at ball reception, and velocity at ball passing): exhibited normal distribution, the variable B_time was the only variable with non-normal distribution. Consequently, appropriate statistical tests (parametric or non-parametric) were employed for repeated measures comparison. Normally distributed data were analyzed using the paired-samples t-test with a significance level of 0.05. Hedges’ g with a 95% confidence interval was used to estimate the effect size for these comparisons. For the B_time variable, the Wilcoxon signed-rank test was performed, and Cohen’s d_z, following Field [29], served as the effect size measure.

3. Results

The results section presents measurements of both on-ball involvement (time with the ball, number of receptions, passes, and shots on goal) and opportunities for involvement based on off-ball positioning (availability to receive a pass or creation of passing lanes) across two different simplified handball game forms: uneven (4v3+GK) and even game form (GK+3v3 +GK).

A total of 1591 event data (on-ball actions) were collected and coded manually across the four observed matches. The data were then aggregated to produce descriptive analytical statistics for each dependent variable and for each student (unit of observation) when playing the different game forms.

Table 3. Descriptive data regarding the observed matches.

Game Form		Teams	Attacks	Completed Passes	Finishing Attempts	Goals	GK Saves (%)	Game BalanceGoals	Game BalanceShots
			(n/min)	(n/min)	(n/min)	(n/min)
Uneven	Match 1	C	1.6	7.3	1.2	0.0	75%	0%	75%
		D	1.5	10.5	1.4	0.3	64%	20%	93%
	Match 3	A	1.9	9.7	1.3	0.6	31%	32%	68%
		B	1.9	11.7	1.6	0.5	44%	26%	84%
Even	Match 2	C	1.9	6.9	0.9	0.4	44%	21%	47%
		D	1.9	5.5	1.2	0.7	17%	37%	63%
	Match 4	A	1.9	9.8	1.0	0.25	25%	13%	53%
		B	1.8	8.4	1.0	0.25	75%	14%	57%

summarizes the descriptive analytical statistics regarding the observed individual and group interactions through successful passing, as well as the game balance, in each match.

When comparing both game forms (

Table 4. Individual game actions’ (per minute) differences between even and uneven game form.

		Uneven Form 4vs.3+Gk	Even Form Gk+3vs.3+Gk	t	p-Value	ES a (95% CI)
Variables		[Mean ± SD]	[Mean ± SD]
Catchable passes		2.5 (±0.8)	1.9 (±0.7)	2.989	0.005 *	0.709 [0.171; 1.229]
Received passes		2.3 (± 0.7)	1.8 (±0.6)	3.496	0.002 *	0.829 [0.269; 1.370]
Goal scoring opportunities		0.4 (±0.3)	0.3 (±0.2)	2.038	0.030 *	0.484 [−0.019; 0.972]
Rate of offensive balls		0.9 (±0.5)	0.9 (±0.3)	−0.308	0.381	−0.073 [−0.538; 0.394]
Rate of on-ball actions		5.6 (±1.6)	4.5 (±1.4)	3.261	0.003 *	0.774 [0.224; 1.304]

* Significant differences (p < 0.05); ^a Hedges’ g.

), a major game-play involvement in relational skills, such as passing and receiving, was observed when using numerical advantage, as well as an incremental number of goal-scoring opportunities. In the ‘attack balls’ variable, no differences were found between the different configurations of play.

The descriptive statistics for player availability to receive the ball, the number of available passing options, the velocity at ball reception and release (fraction of time moving very slowly or standing still), and the time needed to decide with the ball (pass or shot) per game form tested are presented in

Table 5. Differences between even and uneven game form configurations based positional data.

Computed Variables	Uneven Game Form 4vs.3+Gk		Even Game Form Gk + 3vs.3+Gk		t	p-Value	ES a, b (95% CI)
	[Mean ± SD]	CV (%)	[Mean ± SD]	CV (%)
Nr. of passing lanes	1.82 ± 0.27	14.59	1.02 ± 0.26	25.28	8.285	<0.001 *	1.966 b [1.118, 2.793]
Availability (A%)	60.03 ± 10.09	16.79	34.44 ± 8.80	25.55	6.740	<0.001 *	1.599 b [0.855, 2.322]
Ball possession time (s)	1.33 ± 0.27	22.45	1.88 ± 0.67	34.94	−3.206	<0.001 *	−0.805 a
SMB%	53.82 ± 15.73	29.23	62.33 ± 16.81	26.94	−2.923	0.011 *	−0.693 b [−1.210, −0.158]
Velocity at ball reception (m/s)	1.29 ± 0.19	14.80	1.16 ± 0.14	12.37	3.388	0.004 *	0.807 b [0.262, 1.412]
Velocity at ball passing (m/s)	1.27 ± 0.19	14.92	1.15 ± 0.16	13.52	2.971	0.01 *	0.705 b [0.168, 1.224]

* Significant differences (p < 0.05). ^a Cohen’s d_z. ^b Hedges’ g.

. The results indicate significant differences in all variables between the two game forms played.

4. Discussion

The physical–perceptual and social–interactive dimensions of situated gameplay experience have primarily been examined through direct observation of gameplay behaviors, focusing on individual on-ball involvement (touches) and interactions with teammates (such as passing and receiving). While these approaches primarily focus on ball play, exploring opportunities for involvement—connecting what occurred with what could have occurred—might offer a more comprehensive perspective on marginalization, exclusion, or inclusion. It is important to distinguish between gameplay situations where a player theoretically can pass to any teammate and situations where options are restricted, and risks are amplified. Specifically, we were interested in exploring how game involvement, such as receiving a pass, correlates with the receiver’s availability or ‘openness’ to successfully catch the ball, which was expected to be influenced by varying levels of defensive pressure that can be adjusted or regulated by the teacher.

To our knowledge, this is the first study to integrate spatiotemporal tracking data with event data to examine how students interact in team games within PE teaching. By incorporating the concept of ‘Availability’ into our analysis, we aimed to enhance the standard observational methods (i.e., notational analysis) used to explore how various pedagogically modified small-sided handball game forms accommodate student diversity. It specifically aimed to investigate the number of available passing lanes, off-ball positioning to create passing opportunities (distinguishing between ‘open’ and ‘closed’ receiver status), and the resulting interactions through passes or situations of systematic exclusion (such as when a player, though available, does not receive the pass). From a methodological perspective, this work explores new avenues of game observation in the complex dynamics of team interrelations and interdependent behaviors.

4.1. Data-Driven Tool for Game Play Assessment

Commonly used handcraft game assessment tools (e.g., [30]) are primarily focused on how players disposed of the ball (including the appropriateness of their decision) and the resulting outcome and much less emphasis on the co-positioning of off-ball attackers to create space or game options. Additionally, this process heavily depends on the observer’s ability to capture and evaluate these game actions in real-time, or it becomes very time-consuming if done offline through systematic video analysis. Yet, when teachers observe students playing, they also look for and intentionally instruct pupils to move into empty spaces to support the ball carrier and to be a target player for passing, so in a certain way, they are using the concept of ‘Availability’ [19]. So, based on the concept of ‘Availability’, we investigated the ball possessor’s playing options and a player’s availability to be a target player (receiver).

Pass accuracy models based on kinematic parameters have already emerged in sports research and are growing [18,19,31,32,33,34,35]; these models have a probabilistic output nature and are mainly built on physics-based [31,32,33,34,35] or machine-learning principles [18,19], and they are trained with vast amounts of publicly available data. The main aim of these models lies in finding where the ball should go next, so that the team is closer to scoring a goal without jeopardizing the momentum gained, i.e., finding the most secure pass options whilst being the most rewarding and threatening for the opposition [36,37]. However, the impact of each kinematic parameter in some models, such as the machine-learning ones, is quite complex to interpret, and their reproducibility is sometimes impractical, consequently being infamously called ‘black-box’ models [38]. Additionally, as expected, the derived metrics obtained from these models do not easily fit into the pedagogical criteria for evaluating game accessibility and inclusiveness in PE.

Our preliminary methodological efforts were, then, focused on developing measurement procedures to estimate open passing lanes by integrating game events (ball control and release) with spatiotemporal coordinate data, aiming for game evidence (i.e., outcomes) that would be easy to interpret. The approach used is very similar to the ‘pass risk’ displayed in Cakmak et al. [32], regarding the kinematic parameters; however, our model incorporates arm movement velocity, which is critical for intercepting the ball in handball. We assumed a constant full-body average movement velocity, whereas the model in Cakmak et al. [32] defined a minimum velocity required to intercept the ball and, then, calculated the probability of a certain player reaching that minimum velocity needed based on previous player velocity data. In our model, the concept of ‘Availability’ is very similar to the “openness of the passing lane” defined by Steiner et al. [33] (p. 3). The authors considered the angle between the three involved ‘agents’ in the passing situation (passer, receiver, and opponent) to quantify the receiver’s degree of availability or openness. However, in our model, a threshold angle based on kinematic parameters was set to distinguish between available and non-available passing lanes. Ultimately, concepts from Cakmak et al. [32] and Steiner et al. [33] were considered, along with critical parameters specific to handball, such as the arm’s and ball’s velocities, to compute the receiver’s availability. The significant conceptual difference from all models cited above is that ours presents binary outputs instead of a probability of pass success; it aims to answer the question, ‘Is there an open passing lane or not?’

4.2. Effects of ‘Uneven’ and ‘Even’ Modified Handball Game Forms on Inclusion

Using DeLuca’s [6] dialogical and transgressive perspectives of inclusion as a framework, this study sought to take a step towards bridging the gap between educational theory in team sports and its practical application. The approach focused on creating and co-creating an inclusive game environment where all students could learn through game-play engagement, interaction, and collaboration. Students were deliberately encouraged to rely on, recognize, understand, and support one another while solving game-related problems, overcoming challenges, and working together to achieve team goals. Through rules manipulation, students were compelled to distribute the ball, build up plays, and score goals collaboratively.

Accordingly, our primary research question focused on how different contextual circumstances regulated by the rules affect game participation and inclusion opportunities, potentially allowing us to address the diverse learning needs of the class.

Specifically, we were interested in examining how reduced handball game forms (4-a-side) and intentional modifications in the balance between attackers and defenders (symmetric and asymmetric numbers) influence students’ on-ball involvement and opportunities for participation in PE class settings. In both cases, the pedagogical aim was to enhance the intensity of teammates’ interdependence by making passing the primary method to progress towards the goal. This was achieved using fewer players per team, a soft ball that did not bounce easily, and a maximum of three steps with the ball (according to official rules). The game forms differed not only in the ratio between attackers and defenders (three-on-three versus four-on-three) but also in the type of defensive behavior employed (individual versus zone defense). The ‘even’ game form was intended to encourage more off-ball initiatives, such as one-on-one maneuvers, to become unmarked, while the ‘uneven’ form aimed to promote wider positioning and passing (as postulated by Estriga [39]). Both situations emphasized the importance of off-ball positioning in supporting the ball carrier and making joint efforts (passing and moving forward or wide to be ‘open’ for a pass) to achieve the team’s goals.

It is noteworthy that, in Portugal, where this study was conducted, the PE curriculum recommends a well-known five-a-side version of the game (commonly referred to as mini-handball) with individual marking, where bouncing is considered an essential motor skill to master. However, in the observed games, to discourage individual play and dominance by the most skilled players, dribbling was inhibited using a non-bouncing ball. Additionally, ‘collective scoring’ was highly valued and stimulated by awarding more points if all players touched the ball before finishing. In fact, the use of bouncing balls along with individual marking is expected to encourage individual play, typically involving one-on-one dribbling to break away. Consequently, these circumstances may not foster collaborative problem-solving among students, potentially leading to a poorer game experience (as defined by Hastie [16]).

It is also important to mention that both game forms were deliberately designed and progressively implemented during the unit [39] to create rich and diverse learning environments. This approach aimed to maximize students’ opportunities for participation, learning, and enjoyment. The interchange between ‘even’ and ‘uneven’ forms used in the intra-class competition was adopted as a strategy to introduce variation in-game dynamics, skills, and movement, thereby enhancing the learning process and increasing the challenge.

A recommended criterion in competitive engineering is to create a proper dynamic difficulty balance (not too hard or too easy) or game balance (between attack and defense) to foster a stimulating learning environment [40,41]. Regarding game balance based on goals (ratio between the number of attacks and goals), the obtained values were below the recommended ratio (40–59%, [41]), likely due to the goalkeepers’ success (with cases reaching 75% efficiency). Interestingly, the obtained game balance ratios based on the number of scoring attempts were higher than the minimum of the proposed ratio. This lack of shooting efficiency suggests that incorporating more shooting tasks would enhance the class’s game skills development.

The findings clearly indicate that games based on numerical advantage increased the number of catchable passes by 27% (with a medium effect size) and successful receptions by 24% (with a large effect size), aligning with our expectations. The same occurred when assessing players’ availability to be a target player; the numerical advantage increased the frequency that a player was available to receive a ball while a teammate had the ball by 55%. Additionally, we searched into the average number of open passing lanes each player had. The results showed that, in numerical advantage, the players had about 1.82 (±0.27) secure (open) passing options, which represented an increase of 57% when compared to numerical equality with only 1.02 (±0.26) passing options. The addition of an attacking player significantly increased the number of open passing options and enhanced team interdependence and relatedness through passing. We believe that the instruction of goalkeeper support at half-court in the even play form helped minimize the differences between game forms in terms of these co-operation variables.

In sports analytics, particularly for team sports like football (soccer) [19,33] and hockey [34], a player’s ‘Availability’ (or ‘openness’) is a metric already being investigated. This reflects their ability to effectively position themselves to support the attacking flow, which is crucial for building an attack. However, developing this skill and getting the most out of it requires ongoing teamwork and implicit learning through regular gameplay practice, potentially supplemented by explicit teaching on how to unmark from defenders and become a viable receiving option. Therefore, the game form must scaffold each student’s ability to position themselves as an open passing option and ensure they receive passes during the game; otherwise, students may feel that their efforts are in vain.

Thus, to explore the relationship between the number of created passing lanes (or time being in an ‘open’ position) and the number of passes received, Figure 3 visually represents the results for both game forms. Each point on the graph represents a specific player’s time spent in an ‘open’ position and the number of passes they received while playing the game form in question. It is possible to observe not only that there are two almost pure clusters of students based on the game forms but as well, as seen by the regression lines, the ‘uneven’ game form rewarded the students that had more time available with more passes received per minute than the ‘even’ game form.

Figure 4 explores the relationship between time spent in an ‘open’ positioning and passes received per minute by comparing expected and actual passes received. It also examines potential gender biases by separating boys and girls. Interestingly, both genders seem equally excluded (‘exclusion zone’), but only boys tended to consistently be included (‘inclusion zone’) in the game.

4.3. Understanding the Impact of Game Modifications on Game Complexity and Decision-Making

When designing inclusive and challenging games, teachers should carefully consider the passer’s decision-making process, including how many open and secure passing lanes, as well as how much space–time, should be provided to meet students’ developmental needs without making the game too difficult, complex, or easy.

To explore this issue, we analyzed how the availability of passing lanes, influenced by changes in game constraints, affects both the time required to release the ball and the movement at ball reception. Additionally, we investigated what these factors might reveal about the game’s complexity for different students.

We specifically analyzed the time the players had the ball and how that time was spent: whether standing still/moving slowly or actively moving. Notably, when facing high-pressure defense in an equal numbers (three-on-three) scenario, the time required to release the ball was significantly longer compared to the power play (four-on-three). Moreover, in the ‘even’ form, there was a higher proportion of time spent in a ‘stationary’ overhead throwing position, and players exhibited lower velocity when receiving and passing the ball. These findings suggest that in closely marked situations, players take more time to decide and execute passes. The increased time in a ‘stationary’ overhead throwing position may result from opponents pressuring them to protect the ball immediately, which leads to slower actions to avoid turnovers and reduces available passing opportunities. This defensive strategy disrupts the flow of play and makes fast effective transitions harder to achieve.

The lower velocity observed during ball reception and passing in the ‘even’ form may indicate more challenges or troubles in finding open positions to receive the ball. This could also be due to a lack anticipation and faking movement skills to be ‘open’, preferably moving towards goal.

Figure 5 shows the relationship between the number of ‘open’ passing lanes and the time needed to release the ball for boys and girls. Surprisingly, in boys (Figure 5a), the mean ball throwing position time increased or remained stable as the number of ‘open’ passing lanes increased. In contrast, for girls (Figure 5b), the opposite trend appeared, with the ‘even’ game form showing the most significant impact.

Most likely, for girls, the increase in game complexity (specifically, the more advanced ‘even’ game form)—characterized by fewer passing options, increased uncertainty, and time pressure to decide and execute actions—substantially lengthens the time required to pass the ball, indicative of hesitation. In contrast, this does not seem to occur to the same extent for boys. However, these comparisons should be interpreted cautiously due to potential confounding factors. For instance, dominant players, typically boys, often dictate the game’s pace, potentially creating situations where they have numerous passing options while maintaining high ball possession, possibly by deliberately delaying their passes.

4.4. Methodological Limitations and Issues for Further Improvement

From a game assessment perspective, the implemented model for computing ‘Availability’ is currently very naïf, but simple and practical. Future improvements will depend on incorporating additional kinematic parameters, such as the z-coordinates of the players and the ball, as well as the players’ orientation, whether a defender is already running to intercept the ball path before its release, and their ability to change direction quickly. More accurate estimations of individual parameters, such as arm speed, reaction time, and movement velocity to reach different distances will also be beneficial.

Our model’s simplicity assumes linear ball trajectories, excluding the possibility of accounting for bounced or lob passes. In soccer, some models already incorporate ball motion dynamics to better estimate the success probability of long lob passes or account for ground friction in ground passes (see [19,31,35] for more detail). These models typically assume the ball departs and arrives at ground level, excluding situations where the ball does not depart from the ground (e.g., passes made with the head), with angles and velocities of release being the only degrees of freedom considered. However, in ball-grabbing sports, such as handball, basketball, or rugby, the heights of departure and arrival also pose as degrees of freedom that can be computationally demanding to address.

The concept of ‘Availability’ should also be slightly adjusted to account for particular situations, such as if two teammates are both open to receive the ball but one is eclipsing the other, the model considers two passing options when, in reality, there is only one functional available passing option.

The binary output nature of the model has some pros and cons; it enables computation of the number of open passing lanes that each ball handler has at their disposal, or the time a student/player is ‘open’ to receive a pass, which are metrics that are easy to interpret and bring great pedagogical value in the PE gameplay assessment context. Nonetheless, it cannot differentiate, from multiple open passing lanes, which one is the safest or the most appropriate tactically. Based on positional data, future analyses should focus on space creation through off-ball positioning and shooting opportunities.

4.5. Practical Implications and Further Research

While using advanced analysis tools in daily PE classes may not always be feasible, they can significantly enhance PE teacher training, targeted interventions, and research.

In PE teacher training, these tools can raise awareness among future teachers about creating inclusive games that meet all students’ learning needs, including assessing how different game forms impact student involvement, interaction, and learning. They might help future teachers develop skills to design inclusive, engaging, and educational games, ensuring meaningful participation for every student. Additionally, these tools enhance PSTs’ ability to identify and create challenging and inclusive gameplay environments.

For targeted interventions, implementing these tools provides comprehensive data to refine teaching strategies and game forms, making them more effective, inclusive, or challenging.

In research, incorporating these tools can offer deeper insights into team sports dynamics in educational settings. Conducting PE practitioner research with these tools allows for observing games, collecting and analyzing data, and developing pedagogical knowledge. This kind of research can lead to evidence-based improvements in PE teaching strategies, promoting inclusiveness, relatedness, and engagement. By analyzing game and task data, teachers can better understand team game dynamics and the impact of modifying game rules and tasks. This approach helps identify game forms that better promote student engagement and inclusiveness, leading to more positive PE experiences for all students.

Furthermore, gathering feedback on students’ experiences with various game forms can provide valuable insights into the perceived inclusiveness, challenge, and enjoyment of team activities. Additionally, the findings of the present study highlight the importance of future research to investigate how learning outcomes—such as game knowledge, skill development, and inclusion—are influenced by different game forms, learning tasks, and teacher interventions.

5. Conclusions

Our preliminary focus was on evaluating the inclusiveness and relational potential of modified team games at school by combining notational and spatiotemporal data. We considered the number of open passing lanes available to the ball possessor as a key criterion in our analysis, aiming to design games that engage and support low-skilled students. Additionally, we examined the time and space provided for decision-making (whether to pass or shoot and which receiver to choose) and the execution of actions (passing or shooting) in relation to the situational constraints’ complexity.

Clearly, this methodology is a promising tool for understanding how modified games impact learners’ opportunities for action, focusing on their involvement and playing possibilities. It also offers pedagogical insights into how specific space–time constraints in invasion team games drive individual actions and collective gameplay.

Regarding the design of ‘mini’ handball games to address student diversity, our study provides evidence that employing a numerical advantage (even just one player up) enhances overall opportunities for individual and group actions, thereby increasing relational and interdependent actions among teammates. Specifically, utilizing a power play alongside constraints, like ‘no dribbling’, promotes functional dependency among teammates, leading to more passing and receiving actions and facilitating goal-scoring attempts for all learners. While equal numbers appear beneficial for challenging more skilled learners, it is crucial to ensure that participation among less-skilled learners is not compromised, and opponents are evenly matched (e.g., the best defender guards the best attacker and vice versa). Further, by altering the degree of game complexity, less and more skilled learners are challenged differently, which might be pedagogical a tool to addressing their diverse learning needs.

Undoubtedly, further research is necessary to explore how defensive behavior and ball types influence the development of functional dependencies among teammates in mixed-skill level handball practices within PE classes.