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Objective Mathematical Frameworks for Organisation Development (OD) and HR

Updated: Sep 18, 2020

Technology and Applications already coined the "UBER" of OD and HR by clients

The measurability and objectivity of OD and HR have always been contentious. While various other organisational aspects, e.g. finance and engineering, can be measured and manipulated for optimal value, the same is not always true for OD and HR.

KontextIt, through continuous research, has developed what is probably the first objectively measurable OD and HR approach addressing the core of Organisation Effectiveness, Efficiency and Risk. The design requirements of, or vulnerabilities in the appropriateness, quality and strength of key organisational issues, can be determined and expressed in objective numerical numbers and percentages for easy compare and contrast evaluation. With one glance the Executive, Board, OD, HR and Change teams are able to see where the actual problems are that impact the organisation’s ability to deliver on its mandate and bottom-line results.

Already referred to as the "UBER" of OD and HR, the suite of technologies and applications put the power for change and optimization back into the hands of the organisation and its people.

Background to the development of the Mathematical Model and the Objective Delivery-Fitness Dashboard

Research information was gathered from work done over 27 years on 5 continents, multiple organisations, with application of various organisational models and the introduction of applied mathematics. This resulted in the development of a reliable framework of work where the intent and current quality of work and people can mathematically be measurement and expressed. In the process the focus has radically moved away from the input-based organisation towards a clear delivery-based organisation. Delivery-based does not necessarily equate what is sometimes referred to as output-based. Delivery-based definition is e.g. Profitable Business, while “having a Business Plan in place” is often seen as an output; similar to Business Growth being a deliverable with “having a Strategic Plan in place” often seen as an output. The latter, in both cases, clearly being input activities in the process towards a Profitable Business or Business Growth. Current input based organisations can however still be evaluated on the mathematical model.

This delivery-based work design approach and its objective mathematics can determine an organisation’s required design upfront and/or evaluate its current design to ensure the organisation’s relevance and appropriateness in strategy, setup and design.

The mathematical and delivery-based approach comes at a significantly reduced cost and demonstrated value when compared to traditional large scale change projects. As a result of making things visible through numbers, it enables a process of joint decision-making regarding interventions. It also utilizes and builds on the internal strength of companies resulting in further cost containment due to joint process, joint controls and company accountability in affecting actual value delivery.

Continuous research and development of the frameworks and the supportive mathematics have resulted in a number of applications of which the Organisation Delivery-Fitness Dashboard is but one of a suite of applications.

The Organisation delivery Fitness Dashboard application

The Dashboard integrates a number of applications to provide a one page, critical view of the status of health of the organisation. The detail, in the background, facilitates the immediate recognition of issues to address that will enable the organisation to deliver optimally. This dashboard has, as a result of its ability to define issues, also become a vehicle to track the impact and relevance of change.

The Dashboard emerged from application of the mathematical model in quantifying the current status of the organisation and comparing it to the required appropriateness. In a one page summary the company can get a view of the Status of Health (appropriateness, strength and quality) of a company’s “hardware” in relation to e.g.:

  • Strategy,

  • Roles and Structure,

  • Teams,

  • People.

These processes, when applied in a cascaded approach throughout the organisation, assist in identifying performance and delivery risks in relation to:

  • The pitch appropriateness, strength and quality of strategy and operational plans;

  • Structural and role design appropriateness and alignment with strategy, as well as:

  1. Structural design strength and quality;

  2. Role delivery strength and quality;

  3. Appropriateness of role relationships (reporting structure) with clear indicators of overlaps/underlaps, the magnitude thereof, in reporting relationships.

  • Team alignment (executive to operating teams) and

  • People alignment to their respective role delivery accountabilities.

This dashboard allows for immediate identification of areas of performance and delivery risk and the calculation of the degree of seriousness in deviation, as expressed in numerical numbers and percentage risk. The detail supporting this dashboard also demonstrate where the problems are and already suggests possible solutions. Targeted and appropriate interventions can then be developed to remove these risks, or leverage strengths, to enable optimal organisational value delivery.

This targeted approach, in addition to a delivery-based approach, builds on the philosophy that organisations internally have people with the appropriate knowledge and skill to make organisations successful. This approach assists in focusing internal capacity and strength on the issues of importance. This focus ensures the optimal shaping and managing of performance and delivery risks to affect value delivery. When people are focused on what needs to be delivered, understand and apply their own full scope of influence and context in their roles towards that delivery, the organisation achieves its intent and value delivery objectives.

The format of the Dashboard can be adapted to suite the organisation’s unique setup, character and style. The measurements are done against a global standard of work and work in context.

Mathematical Application to Strategy

Each and every individual strategic objective, as well as the comprehensive whole, can be mathematically measured, against a global framework, for its relevance, strength and quality. These strategies can then again be mathematically measured against competitor/market/industry trends or requirements, also measured against the global framework, to determine the relevance, strength and quality of the company’s strategic drivers. The percentage deviation, from the required, then demonstrates the severity of risk this deviation poses to the organisation, be it no risk, moderate, or severe risk. This clarity around risk enables focused corrective action to restore and strengthen company strategy to what it should be. Moderate to severe risks can be redefined without interfering with the no-risk areas. What is absent from the strategy and need to be there, can also be defined. If these deviations, or absences, are not addressed, it will inevitably result in the devaluing of company intent as well as its actual value delivery and effectiveness. Mathematical measurement clearly differentiates what needs be done to increase effectiveness and optimal value delivery.

Mathematical Application to structure

Mathematical objective measurement of:

  • Vertical management reporting structure;

  • Horizontal role/team structure, e.g. Executive team, Business teams, Operations Teams;

  • Actual job structure (job design) and grading;

  • Horizontal content and vertical context job grading differentiation.

to determine relevance, strength, quality and the alignment with strategic as well as operational intent, objectives and effectiveness.

  • Vertical Management: The tolerable distance between vertical reporting roles, in mathematical terms, have been calculated against a global framework and norms. This prevents overlaps or gaps that could interfere with organisational effectiveness. This enables optimally designed, mathematically validated, vertical structures that allow for full accountability, employee engagement and optimal value delivery.

  • Horizontal Team/Role Structure: Mathematically validated appropriateness, strength and quality of team design compared to strategic and operational imperatives. Deviations indicate the level of risk that, if not corrected, will result in non-delivery of strategy, operational objectives and targets.

  • Job Structure (Job/Role design): Mathematically validated appropriateness, strength and quality of role design, as well as determining the degree of role internal consistency. This enables the shaping or redesign of roles for optimal value delivery. Mathematical measurement clearly demonstrate in percentages:

  1. Relevance – how aligned is the role to delivery requirements;

  2. Internal consistency - delivery that belongs, does not belong, should or should not belong in a role;

  • Horizontal Content and Vertical Context Job Grading: Measuring the delivery field on more than one axis to differentiate value contribution between roles in companies.

Mathematical Application to Broader HR

Mathematical measurement in relation to:

  • Delivery based Job Grading;

  • Succession Management;

  • Career Management and Coaching;

  • Manpower planning;

  • Recruitment and placement.

All the above areas can be objectively mathematically measured to enable objective alignment, planning and management, thereby ensuring optimal value delivery success of the company. Room for error in subjective judgement is eliminated through the mathematical processes that support objective decision-making. The magnitude of risk can be quantified in percentage risk to the company, thereby assisting management to appreciate the risk severity to delivery and achievement of bottom-line results.

Bringing mathematical measurement to organisational qualities has opened the field to understand and manage a substantial number of previously subjective processes more effectively. With this knowledge organisations can take charge of affecting required changes themselves, thereby becoming self-sustainable in bringing about the changes required. Measurements of the company are done against global norms, competitor trends, as well as against itself. Responding appropriately ensures the company remains relevant, effective and sustainable in achieving its strategic intent, operational and strategic objectives as well as its value delivery.

Practical Examples of Applications

Practical application example of the high-end Fitness Dashboard mathematics

Dashboard Interpretation:

Executive Level

  • Strategy, green and at a -6% variance still within acceptable limits.

  • There are problems with the design of the Executive Roles (Horizontal Design) that will negatively impact the achievement of strategy if not addressed. (-21% red). The current role design is a weakness in the executive setup and eventual delivery value of the executive team as a whole, as well as specific executive members in particular. Roles will have to be re-designed to ensure appropriate value delivery at executive level. The Excel Dashboard Workbook highlights the specific roles that results in the negative variance. Individual role detail can be investigated to determine reasons for inappropriate design to take necessary steps for redesign and change.

  • Executive Vertical Design, i.e. the combined 2 or 3 layers that constitute the Senior Management layer, is within acceptable limits.

  • At executive level there is some risk, albeit moderate risk, in terms of the Executive team’s Contextual Insight Strength in steering the company forward. The Excel Dashboard Workbook gives detail on each individual and also highlights where the risks are to the overall strength of contribution of the team, as well as specific optimal role contributions.

Operations Level

  • Visible on the Dashboard is the Operational Plan’s own internal consistency (-9%). In this regard the plan is somewhat below what it should be and therefore posing a moderate risk to the achievement of the Operational Plan.

  • The operational plan also does not fully support the achievement of company strategic objectives (-14% - orange). The plan is moderately out of sync with the requirements of and needed support to the strategic plan. The Operations plan therefore needs a review both in terms of its:

  1. lack of support to the Strategic Plan and;

  2. lack of internal consistency and strength

in working towards the achievement of the Operations Plan. The Excel Dashboard

Workbook highlights the specific areas for reconsideration to ensure appropriate


  • Senior Operational Roles (Horizontal Design) experience similar inadequate design problems (-36%) that will not only impact the Operational Plan achievement, but will also negatively impact company strategy achievement. The Excel Dashboard Workbook highlights the specific roles that results in the negative variance.

  • Operations Vertical Design, i.e. the combined 2 or 3 layers that constitute the Management layer, is within acceptable limits.

  • The combined Contextual Insight Strength of the team, to take the operations forward, is within acceptable limits.

  • The combined Contextual Insight Strength of the team, to take the operations forward, is within acceptable limits.

Production Level

  • There is a serious over-design in the Vertical Design structures of the Production layer (+88%). This will result in amongst others:

  1. role confusion,

  2. abdication of accountability,

  3. duplication of work,

  4. unnecessary red-tape, with the resultant,

  5. incurring of huge cost to company and,

  6. interference with effectiveness and efficiency of delivery.

  • The Plan at Production Level is on par and in support of the overall operations plan. It needs to be specified that measurement is always against the optimal. While the operations plan may not be up to par, we know what the optimal plan should be and it is with this level that the production plan is compared.

  • The Horizontal Role and Team Design strength is on par with the required delivery plan.

  • The Team and Individual Contextual Insight strengths, at production level, clearly indicate a depth of contextual strength. The implication is that there are enough people with suitable strength to deliver the value required at production level. It is however critical to address the over-design of structure to ensure the optimal deployment of this rich resource. It is also possible that some individuals are underutilized when considering the value they can potentially deliver.

Practical Examples of Drilling Down into some Detail

By drilling down into some detail, the ease with which issues can be identified and changed becomes clear.


(This is an example of a different company than the one quoted under Dashboard Interpretation above)

We start with a mathematical analysis of the existing strategy. This analysis puts the company in the high risk (red) category – a -23% gap between current and ideal. This called for a critical review of strategy to determine:

  • What is appropriate (that which contributes to the optimal required strength – the high 400’s;

  • What may not be appropriate in this strategic plan, but merely management efficiency – (the 200’s and 300’s). This is not to say that in others strategic plans this may however be appropriate in strength. The nature of the organisation and how it wants to position itself will determine this.

  • And what is absent from the strategy – (the 600’s not currently featuring in the strategy).

It is clear that aspects of this strategy are purely management operational issues, not belonging in strategy, while high-end issues critical to the strategy are glaringly absent.

The mathematical applications can clearly assist in strengthening strategy.It can also be used to direct strategic processes and strategic thinking towards the design of optimal strategy.This is done by upfront deciding the required strength, based on the contextual work themes, and deliberately designing strategy with the appropriate content – a different approach to strategic planning.


(This is an example of a different company than the one quoted under Strategy above)

A systematic evaluation of current structure (top to bottom), as well as roles (top to bottom), can be done to determine the relevance and strength of design and setup in support of strategy. This will highlight team structure design strength as well as individual role design strength in support of strategy.

From the above it is clear that service roles in particular were completely inadequately designed for appropriate value delivery and support to the business. The total team design strength, as a result, is critically below what is required. This raises serious risks of the structure (designed roles) not supporting strategy. The measurement confirmed the need for services roles to be reconfigured. Similar mathematical detail within each role furthermore highlights the areas of adjustment required to enable appropriate value delivery.

Mathematics of the Organisation’s Vertical Structure

In this example the mathematical model clearly highlights the vertical pre-redesign problems in the organisation (see Figure 1) as well as the post-redesign quantification status (see Figure 2).


The traditional approach of design merely shows how hierarchical positions fit together in the structure. The quantified approach demonstrates the stretch of each position, from its lowest to highest point. The quantification clearly shows the value destructive layering within the organisation (Figure 1). Quantified values indicate substantial, even complete overlaps between roles in the structure. This inevitably results in e.g. role confusion and lack of clear accountability with resultant abdication of accountabilities.

Figure 1:

From this layout the overlaps, resulting in operational ineffectiveness and inefficiency, are made visible through quantification of the roles. The percentage overlaps are determined in the background workbook that forms part of the Dashboard. This assists in determining which roles need to be removed and which to be reconfigured to ensure the optimal vertical structure for optimal delivery.

Post-redesign quantification (figure 2).

The mathematical model is used to specify the context of the roles upfront to ensure optimal value and minimal overlap. This results in the removal of value destructive layering. Notice the perfect quantified values of roles with no overlaps on the side. This is optimal.

Figure 2:


The Contextual Insight strength of the team and individual team members are evaluated and mathematically converted to determine the likelihood of the appropriate deliverables being achieved. This is to ensure an alignment from strategy, through structure and role right down to team and individual contextual insight. This gives the organisation the biggest opportunity to deliver real value aligned with purpose and objectives.

In itself the following table tells its own story.

The contextual insight strength of the team as a whole has the potential of the team pulling things through. A detailed analysis, however, provides a different picture of the team. It was clear that deliverables in a key role like MRM will most likely not be achieved as the current incumbent may find it exceedingly difficult to comprehend the nature of the challenge in role. This also applied to Finance. One GM may be in the process of becoming disconnected from his role as the role no longer challenges the scope of the contextual issues he would enjoy dealing with. Another individual may be on the way of becoming disconnected in about 3 – 5 years (Environmental) as the score already indicates insight beyond his current role requirements.

Value of the OD/HR Dashboard

  • Required strength of organisation delivery can be determined upfront. The mix of what strategy, roles, structure and people should be, and the strength thereof, can also be determined upfront to ensure the appropriate ingredients at the right strength are in place to guarantee organisation delivery. This can be compared with the construction of a building: deciding what to build, what material needs to go into this at what strength and what mix to construct something that satisfy the plan and ensure an enduring construction. Accurate objective numerical specification upfront or evaluation in retrospect is done to construct or change an organisation fit for delivery. Whether up front or in retrospect, the appropriate design and development of delivery focused strategies, structures and roles can be done while being guided and supported by the mathematical processes.

  • Visibility and objectivity in measuring all the elements crucial to organisation delivery-fitness to ensure alignment from strategy, through roles and structures to teams and individuals.

  • Vulnerabilities to the organisation are expressed in percentage gap and risk, thereby indicating the degree of seriousness with which deviations should be considered.

  • Areas of vulnerability are clearly defined and can be clearly demarcated - therefore no need for weakly defined, large scale, costly interventions. Change can be focused around areas of critical vulnerability.

  • Vulnerable areas can reasonably quickly and cost-effectively be reconfigured as the detail and measurements, in the Dashboard Workbook that builds up to the Dashboard, highlights the areas for corrective action. We have seen substantial reductions in intervention cost and even more so when the organisation takes charge of the processes. Interventions, as a result of its targeted nature, clearly contribute to the delivery success and bottom-line of the organisation.

  • People alignment with role and role ownership also drives engagement of people with role delivery and the organisation’s delivery success.

  • The impact of and the process towards affecting change can be measured and tracked to ensure value.

  • The approach is one of pragmatism where areas that need to change are highlighted while staying clear of areas that are within acceptable limits. This guards against subjecting areas of effectiveness to change thereby upsetting organisation delivery value

  • Test-retest can be done to determine the effectiveness of refocused changes.

  • We focus on enabling the organisation to become masters of their own destiny by providing them with the tools to design and reconfigure the organisation for appropriate delivery.

It is clear that this mathematical (numerical) objective process assists in the clarity with which issues of delivery can be identified. It also assists in defining what delivery is required within what context. This knowledge increases the ownership and value contribution of incumbents.

What are those Critical Steps:

In a start-up organisation, or an organisation than wants to take a zero-based approach, the following steps will be critical:

  1. Deciding upfront what the intent or purpose of the organisation is and the game-plan of delivery it wants to follow to position itself and guarantee delivery success. This qualitative decision can then be expressed in a quantitative value.

  2. The quality of ingredients required, as in strategy, structure, teams and people, can be numerically specified. The numerical specification will guide the content that needs to be built into each of these (strategy, roles, structure, teams and people) to ensure the relevance, appropriateness, strength and quality thereof.

  3. The focus in all phases of the process is the building of delivery-based organisations, from strategy, to roles and structures, to teams and people and the mathematical tracking of all these elements for quality delivery.

  4. A continuous comparison to the optimal requirement will ensure the shaping of the optimal ingredients for optimal value contribution.

  5. Appointment of appropriately aligned people at all levels to take charge and affect delivery on all levels.

  6. A dashboard to consistently ensure optimal alignment of the current with requirement. This alignment, in mathematical terms, runs through purpose, strategy, roles. structure, teams and people to ensure comprehensive alignment at all times for optimal delivery.

In an operating organisation, the following steps will be critical:

  1. Determine the purpose and delivery game-plan of the organisation to understand how the organisation wants to position itself for delivery.

  2. Develop the dashboard of measurements for all the elements of the organisation to compare/contrast what is versus what should be on the ground for delivery success.

  3. Identify the areas of critical risk and the degree of severity.

  4. At times corrective action can be taken by focusing on the quantitative values within the content, making the change less radical but very effective. Other initiatives, of more substantial impact, need to be decided upon and optimally implemented for value delivery. The quantitative values will continuously guide the process to ensure delivery-based solutions of the right quality and strength that contributes to the development of a delivery based-organisation. This will also imply having to reconfigure various aspects, e.g. roles, into delivery based format and language.

  5. The Dashboard will, as in the case of the start-up organisation, ensure the continuous alignment of all aspects of the organisation to enable optimal value delivery at all levels in the organisation.

Through the application of the mathematical approach to organisation design and other HR issues (not covered in this chapter), issues in the OD and HR space can be objectively measured in numbers and percentages. The findings these numbers and percentages represent are of critical relevance to the bottom-line delivery of the organisation.OD/HR can with confidence have a presence and make a convincing value contribution at the boardroom table and executive levels in the organisation.

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