Creating effective teams by means of mathematical modelling
Created by Rune Huntley Andersen, February 2022
The use of teams in organisations has enlarged rapidly the past 30 years, in correlation with the vast amount of more complex tasks in almost any industry. This development has augmented the requirements in management, since additional factors have altering influence on the work process, compared to individuals working solitarily. It requires insight in the process of people collaborating, to achieve a common goal. Nonetheless there’re scarce information about the process of achieving a high performing team, or effective team, from a managerial perspective.
A lot of literature and theories about group creation, group dynamics and group development has been utilized over the years, which widens the scope of the subject. Though, much of the literature available erects from the same origin, which can therefore be summed to a more general model for team effectiveness.  This article intends to review the relevant literature to outline the current knowledge of creating teams and examine the factors influencing on team effectiveness. This is outlined through the general model, which describes the determining factors in team effectiveness.
Even though the literature illuminates a lot of factors determining team effectiveness, the applicability in practice is not so clear. This article intends to examine two different approaches to acquire team effectiveness, to review the potential of using mathematical models for estimating team effectiveness. Devine & Phillips developed a meta-analysis to investigate the link between cognitive ability in teams and the performance of the team, to create a hands-on scheme for predicting team effectiveness. This study focuses on the abilities of the team members as individuals, and are therefore not considering the context, which, in the team effective model, is stated to be a huge factor for team effectiveness. T. Meridith Ross & Eric C. Jones have conducted a more holistic framework which has led to a more substantial mathematical process for predicting team effectiveness.  These studies constitute the aim of the discussion for this article, while assessing if mathematical modelling is a valid method for constructing and evaluating teams, to achieve effectiveness.
Creating effective teams
Work groups and teams are widely used in almost every kind of labour activity across the world, which is why teams are regarded as an essential part of most companies and organisations. A common definition of a team is that it consists of individuals who are working interdependently, in a joint effort in which synergy effects emerge, whereas groups are independent individuals who interact and exchange information to achieve a particular goal. The definition of a team by Robbins, Judge and Campbell is given as “A group whose individual efforts result in performance that is greater than the sum of the individual inputs”.  This definition refers to the synergy effect mentioned in the broader definition. Since teams are such valued parts of most organisations, several studies have been conducted with the interest of optimising the performance of teams, by analysing the influencing factors.
Much of the research that has been conducted about teams, has led to several methods, concepts, and models. These models are mainly created as linear frameworks with the purpose of predicting the input-parameters leading to team effectiveness.  McGrath is a predominant psychiatrist who worked out the framework known as the I-P-O model.  This concept introduces three factors influencing team effectiveness and the correlation between. The three factors are input-process-output (I-P-O). This framework was used to explain the influence of different input factors and the team’s interaction process on the team’s performance. The input-variables include the following four aspects: individual factors, team factors, environmental factors, and target factors, whereas the process-variables include interpersonal relation, conflict levels, commitment, and resource monitoring. McGrath’s work has inspired a lot of the later concepts and theories about team performance and team effectiveness, by evaluating the interconnection between different personal traits in a team. The framework by McGrath therefore recurs in most of the later developed theories and concepts in some form.  Although the framework is widely acknowledged, it is today seen as insufficient to describe teams, since it lacks to capture the emerging consensus about teams being complex and adaptive systems. 
“In another sense, however, the convergence on consensus regarding the utility of I-P-O models as a guide to empirical research fails to capture the emerging consensus about teams as complex, adaptive systems. Indeed, the I-P-O framework is insufficient for characterizing teams”
This is exemplified by the very linear approach to describing a team’s process. It lacks more detailed information about the input parameters, which is not always a straightforward process.
“I-P-O framework tends to suggest a linear progression of main effect influences proceeding from one category (I, P, or O) to the next. However, much of the recent research has moved beyond this.” 
The underlying pattern of having several input factors influencing team performance is nevertheless still well recognised, but with a stronger acceptance of the complex processes that can erect during the different stages. Understanding the complex processes is an important aspect of project management, when working with teams. It therefore seems necessary to evaluate team effectiveness from a more holistic and detailed approach that is capable of controlling and handling the complex behaviour of the parameters. It’s also vital to understand the distinctive workflow and characteristics of different kinds of teams, since they require various motivational components, given as the aforementioned input factors, to achieve effectiveness.  Robbins, Judge and Campbell defines the four most common types of teams you’re likely to find in organisations as: problem-solving teams, self-managed work teams, cross-functional teams, and virtual teams.  Robbins, Judge and Campbell has summarised what is currently known about the influencing factors on team effectiveness in a relatively focused model, which is named the “team effectiveness model”. 
Team effectiveness model
The term team effectiveness in the model is regarded as both objective measures of the team’s productivity, managers’ rating of the team’s performance and aggregate measures of team member satisfaction.  This is a broad scope of the outcome, which is in accordance with the rather complex understanding of rating a team’s efforts. In the team effectiveness model , the key components of effective teams are subsumed into four general categories, Context, Composition, Work design and Process, respectively. These four categories cover some of the same aspects as the input variables in the IPO-model but represents them as solely influencing parameters and therefore not describing the procedural effect. The parameters in the model are a representation of the factors that are known today, to have an influence on team performance. In the following, each component will be described and summarised according to the definition by the authors.
The contextual factors include adequate resources, leadership and structure, climate of trust and performance evaluation and reward systems. The adequate resources refer to the organisational support to the team, where timely information, proper equipment, adequate staffing, encouragement, and administrative assistance is vital for a team to succeed. A scarcity of resources reduces the ability of the team to work effectively. The leadership and structure refer to the structurisation of who do what and appeals to clarity regarding adequate sharing of workload between the different team members. A formal leader is often necessary, but this is dependent on the type of team. Nevertheless, for delegating tasks a facilitator in the team is required, for keeping a streamlined workflow. A climate of trust implies both trust in the leader and the interpersonal trust between team members. This is a vital condition to achieve individuals taking more risks and simultaneously increase team cohesiveness. This is typically initiated by great leadership, but it also depends on the mutual understanding among team members. The performance evaluation and reward systems must reflect team performance and not reward the individual performance, to achieve team commitment, which is the foundation for a high performing team. Individual evaluations and incentives have the possibility to interfere with the group development.
The team composition category includes abilities of members, personality of members, allocation of roles and diversity of members. The abilities of members refer to the individual skills and abilities each member can provide to the team. It’s stated, that for a team to perform effectively, the following three types of skills are necessary within a team: technical expertise, problem-solving and decision-making skills, and interpersonal skills. The right mixture is said to be crucial. If not weighed correctly, it causes lower team performance. Nevertheless, it’s been shown that it’s very much task dependent, since research have shown that high-ability teams, as an example, tend to perform better when the task is complex. The personality of members can to a large degree be put in relation to the Big 5 personality model . Three of the traits from the big 5 are suggested to be especially important. Teams that possess higher levels of conscientiousness and openness to experience tend to deliver a greater performance. Additionally, the opposite result is achieved with teams containing disagreeable members (neuroticism). The allocation of roles is based on the early work on team roles by Dr Meredith Belbin (BSPI) , which states that successful teams contain all nine different roles, with the possibility of one team member fulfilling multiple roles. The nine roles have different forces and weaknesses which theoretically, with the right composition, could eliminate the team’s weaknesses and allow for optimal collaboration. The diversity of members is by many regarded as an advantage. Nonetheless, evidence has shown that differences such as race/ethnicity, gender and age tend to have negative effects on a team’s performance.  Although these effects tend to decline over time, there’s minimal evidence that the performance increases due to member diversity. The size of teams should generally be considered as the minimum number of people who can complete the task. Most effective teams consist of five to nine members. Teams of too many members tend to suffer from social loafing , whereas smaller teams tend to achieve a better team cohesiveness and mutual accountability, which increase the performance. The member preferences cope with the individual’s view on teamwork versus working solitarily. If a team member prefers working solitarily but are required to participate in teamwork, it can cause a threat to the morale of the team. Therefore, teams should only consist of people interested in working collaboratively.
The work design category reflects the Job characteristics theory (JCM-model) developed by Hackman and Oldham, which includes autonomy, skill variety, task identity and task significance. The autonomy refers to the opportunity for the members to work independently having the freedom to plan the work themselves, which increase member responsibility and returns a higher level of task motivation. The skill variety refers to the degree the tasks require different activities, and various skills are needed. A high degree of skill variety tends to increase intrinsic motivation for the members. Task identity describes to what degree a piece of work requires completion of a whole or if it only involves completion of parts of a whole. People tend to value full completion instead of smaller parts. The task significance relates to the impact the task has for either the organisation or even the society. People tend to be more motivated when doing meaningful work. 
The process variables include common plan and purpose, specific goals, team efficacy, mental models, conflict levels and social loafing. Having a common plan and purpose within a team is crucial for achieving effectiveness. It is important for every member to feel belonged within the teamwork, therefore they must conform with the common plan and purpose whilst being able to adapt to changes, when it's necessary. Specific goals have the purpose of maintaining the members’ focus, while making it possible to measure the performance. Therefore, the goals must be specific, measurable, and realistic. Team efficacy relates to the team’s confidence, which is important for achieving success. To achieve team confidence, management could facilitate smaller successes e.g. milestones, which could lead to an increase in confidence levels. The confidence is very record based, which is why team efficacy often increase with time, if the team is successful. The mental models relate to the team members’ comprehension and beliefs about solving the task, which means that the performance of the team suffers, if there is uncertainty about how to solve the task. Teams with members having different mental models can reduce the effectiveness as well. Conflict levels has been given a lot of awareness over the years and been analysed by means of several models. Task related conflicts have shown to improve team effectiveness, whereas conflicts regarding interpersonal issues almost always are dysfunctional for a team. Therefore teams must develop an appropriate level of task related conflict, since that can lead to better decisions. Social loafing occurs when a team member provides an insignificant amount of work to support the common goal, and in that way coasts on the group’s effort. In effective teams this is avoided by holding each team member accountable, both on an individual level and on team level.
The possibility of predicting team effectiveness and its limitations
In recent years researchers have used mathematical modelling with the aim of predicting or even achieving team effectiveness. This seems like a difficult task due to the complexity of the interconnection between the parameters stated in the team effectiveness model. Nevertheless, there’s a need for a practical tool managers can use, to achieve high performing teams, since it could save costs and therefore be of great value to any organisation.
There has been a variety of approaches, which has resulted in different outcomes. One study was focusing on the connection between cognitive ability of team members and the team performance.  Specifically, it was investigated to what degree the cognitive ability, measured as highest member score, lowest member score, mean score and standard deviation of scores, influenced the team performance. “Given the critical role of member interdependence in most work groups, it seems likely that the performance of few (if any) work groups would be determined solely by the actions of a single member”  With this approach the analysis neglects the concept of synergy effects, since the hypothesis is that having individual members with great cognitive ability, would increase team performance. One of the findings from the study was that there was an indication that the mean level of cognitive ability within a team, leads to higher team performance, whereas the highest and lowest score was rather insignificant. Nonetheless, the results are very context based, and since the specific task characteristics, the organisational setup and other parameters that are included in the team effectiveness model, was not considered, it’s a rather uncertain conclusion. According to the team effectiveness model, an effective team should contain members with both technical expertise, problem-solving expertise, decision-making skills, and interpersonal skills.  Besides, teams should only be used if it benefits the solving of a given task. Assuming that the cognitive ability of a single member would increase team effectiveness, could imply that the member would be better off working solitarily, which neglects the need for teamwork. Therefore, it would be a waste of resources using multiple employees on the task. Nevertheless, the mean score of cognitive ability, could be an important indicator, dependent on the task that needs to be done. But when dealing with teams, all the members’ traits must be evaluated, since having one or more disagreeable members in a team, decrease the effectiveness of the team, no matter the skills and traits of the others.  Besides, rating variables on a mean value of cognitive ability, opens the opportunity for outliers, which could cause lower effectiveness, since more conscientious members would have to perform not only their own task, but also take more responsibility of the individual tasks for the lower conscientious members.  Therefore, it’s fair to presume that there are several limitations to estimating team effectiveness from such a narrow perspective, even though it shows some approving results. This supports the narrative of teams being such complex structures, that it require a more holistic analysis.
Another approach has been applied by Ross & Jones, which contains a theoretically developed model to predict team effectiveness quantitively.  The procedure is to identify standardised variables and find correlations between the variables to form a model. They assert team effectiveness by means of performance, behaviour, attitude, team member style and corporate culture.
This approach therefore implies a more holistic scope for predicting team effectiveness. The standardised variables  comply with the factors denoted in the team effectiveness model, to a large degree. The correlations between the different standardised variables were based on questionnaires, interviews and observations made by Hans J. Thamhain, involving 180 projects. With this approach, the authors succeeded in finding a method for predicting team effectiveness quantitatively.  Nevertheless, even though the model is based on well recognised input variables, the interrelation between these constitutes the complex part. As noted, the correlation is based on questionnaires and interviews, though it is not stated where these are executed. There could be significant cultural differences in the way workers value and perceive different aspects of teamwork. This could imply differences in leadership style, collaboration, and other variables.  Besides from that, the model neglects the importance of team size, which could have a huge impact according to the team effectiveness model. The type of team would rationally similarly have an impact on the correlation between the variables, since some teams presumably requires certain ways of communication or reward structures, as an example. This method would also require managers to acquire a lot of knowledge about every aspirant, before setting up the team, if this were to be used as a predicting model, and not “only” an evaluation strategy. Nevertheless, this approach shows great potential as a way to be able to predict team effectiveness. In time, when more data about the correlation between the different variables has been collected, the model could become a great and desirable resource to project managers and organisations, since managers would be able to select individual team members, to enhance the performance of a given team.
In this article, the complexity of constructing effective teams, has been illuminated. The affecting parameters are in such big numbers with a variety of intercorrelation, which makes it extremely challenging to standardise and specify a prediction method for effectiveness. Nevertheless, much of the affecting parameters have been investigated and theorised separately, which constitutes the foundation and enables further investigation and theorisation of team effectiveness. This allows project managers to at least try to optimise the parameters individually, but requires in-depth knowledge about a variety of behavioural and motivational theories as well as securing the contextual parameters. The affecting parameters on team effectiveness spans over a variety of different domains, which roughly can be mapped into four categories including context, composition, process and work design. The intercorrelation between the affecting parameters is constituting the most complex aspect, when trying to evaluating or predicting team effectiveness. With the aid from mathematical modelling the intercorrelation between these parameters, is closer to be determined. Several studies have been conducted with the aim of achieving complete determination of this intercorrelation, with promising results that indicate a rather strong correlation. Nonetheless, the methods don't seem to be sufficient for application yet, since it lacks a deeper insight into how one individual’s characteristics influence on the overall team effectiveness. If the future research determine these measures and increase the precision of estimating the correlation between the affecting parameters, projects managers would be able to apply these methods to collect candidates that could form an effective team for a specific task.
 Robbins, Judge, & Campbell. (2010). Organizational behaviour (13th ed.). Pearson Education.
This book has been utilised to clarify and provide a deep insight into the knowledge of work teams. In the book they describe several managerial issues or challenges with working with teams in organisations. For this article, the most important inspiration has been on the variables affecting team effectiveness and the explanation of different types of work teams. The authors of this book also provided the "team effectiveness model", which has acted as a central aspect of this article. In addition the book contributes to a broad range of managerial topics with in depth description of several methods on conflicts, communication, leadership etc.
 Devine, D. J., & Philips, J. L. (2001). Do Smarter Teams Do Better. Small Group Research, 32(5), 507–532. https://doi.org/10.1177/104649640103200501
In this article, the authors have done an analysis on the correlation between cognitive ability and team performance. In the article the process of the analysis is deeply described and serves as a highly relevant reference, since it gives an insight in one approach to predict team effectiveness mathematically. The point of bringing this reference is to analyse an approach that questions the knowledge known today about team effectiveness and compare results with more recent knowledge.
 Meredith Ross, Jones, & Adams. (2008). Can team effectiveness be predicted?, 248–268. https://www.researchgate.net/publication/235307866_Can_team_effectiveness_be_predicted
This article proposes an approach to predicting team effectiveness, that is more aligned with recent knowledge, when it comes to the influencing factors and variables. This article is interesting and highly relevant since it builds on huge amounts of previous frameworks and concepts and involve a great deal of research data. It contributes with a holistic perspective on how to predict team effectiveness, which can form the future research in the topic.
 E. McGrath, Arrow, & L. Berdahl. (2000). The Study of Groups: Past, Present, and Future, 4(1), 95–105. https://www.researchgate.net/publication/258180855_The_Study_of_Groups_Past_Present_and_Future
 P. Morgeson, D. Aiman-Smith, & A. Champion. (1997). Implementing work teams. Recommendations from Organizational Behaviour and Development Theories, 4, 1–44. ISBN: 0-7623-0173-2
 S. Goodman, C. Ravlin, & Argote. (1986). Current Thinking About Groups. Setting the Stage for New Ideas, 4, 1–19. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.475.9943&rep=rep1&type=pdf
- ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 Robbins, Judge, & Campbell. (2010). Organizational behaviour (13th ed.). Pearson Education.
- ↑ 2.0 2.1 2.2 Devine, D. J., & Philips, J. L. (2001). Do Smarter Teams Do Better. Small Group Research, 32(5), 507–532. https://doi.org/10.1177/104649640103200501.
- ↑ 3.0 3.1 3.2 3.3 3.4 Meredith Ross, Jones, & Adams. (2008). Can team effectiveness be predicted?, 248–268. https://www.researchgate.net/publication/235307866_Can_team_effectiveness_be_predicted
- ↑ 4.0 4.1 4.2 4.3 Ilgen, D. R., Hollenbeck, J. R., Johnson, M., & Jundt, D. (2005). Teams in Organizations: From Input-Process-Output Models to IMOI Models. Annual Review of Psychology, 56(1), 517–543. https://doi.org/10.1146/annurev.psych.56.091103.070250
- ↑ 5.0 5.1 Y. Wang. (2018). Overview on the Team Interaction Process. Open Journal of Social Sciences, 6, 1–11. https://doi.org/10.4236/jss.2018.612001
- ↑ Janse, B. (2022, February 3). Job Characteristics Model (Hackman and Oldham). Toolshero. https://www.toolshero.com/human-resources/job-characteristics-model/