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Probability theory: applicability in risk and uncertainty management

July 12, 2010

Probability theory: applicability in risk and uncertainty management

The argument that “probability theory is at the heart of risk and uncertainty management” sounds logical and appropriate in layman terms. However, an empirical analysis of the risk and uncertainty management shows that probability theory has limited role in both concepts. There is a clear difference between risk and uncertainty whereby risk being product of likelihood of an event occurring and impact of that impact on the objectives. The uncertainty concept is the difference between desired and emergent outcome.

The concept of risk, uncertainty and probability has been explained in this document. Using examples of financial, reputation and project risks, it is demonstrated that although probability theory plays a critical role in assessing risk and uncertainty it is not alone at the hear of risk and uncertainty management.



Quite often similarities are drawn between risk and uncertainty management by generalists, sometimes to extend of clubbing them together as a single concept as you may notice in “The Basics” by Leitch (Leitch, 2003). This generalisation leads to common belief that probability theory is equally useful in both risk and uncertainty management.

This article attempts to understand the key difference between the concept of risk, uncertainty and how probability theory plays a role in managing them. Using examples from financial, reputation and project risks, it is demonstrated how probability applicability varies in context of risk and uncertainty management. On the onset it is critical to understand that applicability here does not mean just the validity but also the degree of importance the probability concept has within the context.

Defining uncertainty and risk

Since ages people have been fascinated by the desire to know what future holds for them and have been using various means like interpretation of dreams, study of historic pattern and past experience to predict future (Trippett, 1982). All predictions of future come associated with the concept of uncertainty and this uncertainty makes prediction of future a difficult task. This close association of uncertainty with future and growing interest of people to understand future has motivated extensive research in uncertainty and its management (Hillson & Murray-Webster, 2007).

As suggested by Hillson & Murray-Webster (2007), there are two extreme schools of thoughts on the concept of uncertainty with one suggesting that universe by nature is mysterious and prediction is a futile exercise. While the other school suggests that advancement in technology and knowledge enables one to predict future more accurately thereby removing uncertainty. Hillson & Murray-Webster (2007) suggest that the concept of uncertainty relies on two key points namely;

Variability: a situation where the outcome of a measured factor can be within a given range. It can also be referred as objective uncertainty as suggested by theory of individual choice under uncertainty (Machina, 2004).

Ambiguity: a situation where the outcome can either happen or not or something totally different may happen in future. As per the theory of individual choice under uncertainty, this is also known as subjective uncertainty (Machina, 2004).

As defined by Oxford English Dictionary (O.E.D., 2008), “uncertainty is (1) the state of being uncertain, (2) something that is uncertain or causes one to feel uncertain”. This definition suggests uncertainty as a negative entity. However, holistic review of uncertainty demonstrates that uncertainty with its variability and ambiguity elements only refers to possible differences in expected outcome and final results without any negative or positive implications.

The definition of risk is more open for interpretation and applied in various ways by different group of people (Bracken, Bremmer, & Gordon, 2008). The Royal Society of Britain in its 1983 report titled ‘Risk Assessment’ stated risk “as the probability that a particular adverse event occurs during a stated period of time, or results from a particular challenge” (Adams, 1995). There are various other definitions of risk but generally all suggest risk as adverse or undesirable outcome of an event. This negative connotation implies risk as a threat but in recent times there has been increasing focus on treating risk as neutral or even something which can have positive outcome (Hillson & Murray-Webster, 2007).

Despite differences, there is common acceptance that risk is associated with uncertainty and it comes with consequences (Hillson & Murray-Webster, 2007). Paul (Hopkin, 2002) suggested that risk is a “circumstance, action, situation or event (CASE)” which has the capability to impact on key factors acting as dependencies of core processes of the organisation. This leads to us the concept that risk is product of probability or likelihood and potential impact. In more simple terms, risk is “an uncertainty that could affect one or more objectives” or “uncertainty that matters” (Hillson & Murray-Webster, 2007).

This relative context of uncertainty in risk sets the uncertainty concept apart from risk. For example, there can be an uncertainty around tropical rainfall in India for a particular year but it will have no impact on a farmer in Brazil and therefore is not a risk for the Brazilian farmer. However, for an Indian farmer this uncertainty can result into a potential crop loss which makes the uncertainty a risk.

Understanding probability theory

Probability theory has evolved over ages since it was 1st introduced by Galileo as part of his observations on the dice game (Webb, 1996). Primarily considered as part of mathematical studies, probability theory aims at studying and explaining the pattern arising from random experiments which can be executed repeatedly and where the outcome is uncertain (Gut, 2005).

As with risk and uncertainty, there have been various definitions offered for probability and the debate still continues around their interpretation and validity in context of risk or uncertainty (Cheeseman, 1985). These definitions often come with their own calculi for uncertainty model which is based on certain assumptions which lead to confusion (Cheeseman, 1985). Broadly, in the frequentist interpretation probability arranges set of observations as per the likelihood concept as against arrangement by degree of belief suggested by Bayesians and many other approaches (Ben-Haim, 2004).

As suggested above, there are many definitions for probability and their respective interpretation. Probability simply indicates potential outcome based on study of pattern or past historical data. There is no guarantee that the suggested outcome may occur as there can be a sale or no sale at all. Sale of goods does not depend on frequency but on taste and choice of people along with other circumstances. This lack of personal judgement context in probability theory acts as a limitation of this theory. This argument is very well supported by the approach taken by many Keynesians that there are many situations where real uncertainty exists and no amount of statistical analysis can provide accurate indicators for future (Davidson, 1991).

Role of attitude in risk management

The introduction of the perception concept to risk brings attitude into the picture. Attitude drives the way in which risk is managed by organisations and individuals (Hillson & Murray-Webster, 2007). It is important to note here that attitude refers to actions of individuals or groups driven by perception of a certain situation.

Risk management is set of activities carried out by individuals, groups or organisations using management policies and practices based on the perception of analysis (Bracken, Bremmer, & Gordon, 2008). Risk management can be defined as steps involving defining, identifying, analysing, processing, evaluating and communicating risk (Chapman, 1997).

Human factor plays an important role in risk management as it is not done by machines or robots as risk management requires human judgement (Hillson & Murray-Webster, 2007). Qualitative risk assessment considers the probability and the impact on the objectives in both positive and negative aspects using human perception. While the quantitative risk analysis focuses on application of mathematical models to identify risk (Hillson & Murray-Webster, 2007).

Examples of risk management

Having looked at the definitions of risk, uncertainty, the concept of probability and how attitude plays a key role in risk management, let us know understand how probability plays a varying role in practical risk management.

Financial risk

In last 30-40 years, financial risk management has led to development of application of various statistical and probability models (Thomas, 2000). In advanced economies like US and UK, individuals are credit scored to assess the risk involved in lending. Banks use credit scores, given on basis of historical records leading to understanding the probability of default, while accepting or rejecting lending requests. Records of millions of such transactions are stored for future analysis. These records help the banks understand details of the customer but without the knowledge of how the behaviour would have been if the lending was provided without scores. This introduces a bias towards people who have got bad credit scores and stand no chances of getting lending (Thomas, 2000).

To overcome this limitation, banks have now introduced behavioural scoring along with economic condition consideration. Statistics have shown that economic conditions alter customer behaviour (Thomas, 2000). This development shows that probability theory is very useful in scenario where all other conditions are similar. However changing economic environment alters customer behaviour resulting in varying behavioural score.

Reputation risk

Positive reputation attracts people and therefore companies can charge premium. Reputation risk management is emerging as a growing field within risk management domain. However, not much is being done in real risk management sense as most managers’ focus on managing threats to reputation that have already surfaced (Eccles, Newquist, & Schatz, 2007).

Media coverage determines the reputation of the organisation to greater extent and the analysis of BP’s reputation based on articles appearing in media during 2003-2006 period suggest that perception plays a very important role in reputation risk (Eccles, Newquist, & Schatz, 2007). As noted in the study, the ratio of negative to positive was 1:2 during 2003 and 2004 but during 2005 it increased to 1:1 and further in 2006 it reversed to 2:1 ratio. Probability theory will suggest that possibility of reputation damage is equal in all situations however the study shows that perception played a major role in the real extent of damage.

Project risk

Uncertainty management is increasingly used in project management to bring balanced approach to opportunity and threat management. Uncertainty management includes not just managing threats, opportunities and their implication but also identifying and managing all sources of uncertainty which develop the perception of threats and opportunities (Ward & Chapman, 2003). In the same paper, they (Ward & Chapman, 2003) have suggested various sources of uncertainty in projects including “variability associated with project parameters, design and logic, objectives, priorities and relationships between partners”.

Previous track record of a company in complete the project within the time specified at the beginning does not necessarily indicate that all future projects will complete as per schedule. This is primarily because uncertainty is depended upon elements of the project management as mentioned earlier (Ward & Chapman, 2003). This clearly demonstrates that probability theory plays minimal role in determining the desired outcome in project risk or uncertainty management.


In this article we have seen that risk and uncertainty have different scope and meaning. Uncertainty as defined by many focuses on potential difference between desired outcome and final result. Risk is product of likelihood of an event happening and its potential impact on the objectives.

There are various schools of thought on probability theory and it can be stated as model to predict outcome based on study of pattern in similar conditions. The degree and usability of probability theory differs in each context of risk and uncertainty management. Therefore, it is critical to understand the limitations of probability.

Risk and uncertainty management involve not just management of threats and opportunities but all sources of uncertainties that drive the perception. The importance of perception and therefore attitude of individuals, groups and organisations towards risk and uncertainty management makes concept of probability a mere tool in understanding the potential outcomes. It does not in itself complete the entire scope of risk and uncertainty management.

Therefore, it can be said that probability theory is part of risk and uncertainty management but certainly not alone at the heart of the concept. Risk and uncertainty management involves much more analysis than probability itself.



Adams, J. 1995: Risk. London: UCL Press Limited.

Ben-Haim, Y. 2004: Uncertainty, probability and information-gaps. Reliability Engineering and System Safety
, 85, 249–266.

Bracken, P., Bremmer, I., & Gordon, D. 2008: Managing Strategic Surprise. Cambridge: Cambridge University Press.

Chapman, C. 1997:Project risk analysis and management – PRAM the generic process. International Journal of Project Management
, 15 (5), 273-281.

Cheeseman, P. 1985: Defense of Probability. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence (pp. 1002-1009). Menlo Park: SRI International.

Davidson, P. 1991: Is Probability Theory Relevant for Uncertainty? A Post Keynesian Perspective. The Journal of Economic Perspectives
, 5 (1), 129-143.

Eccles, R. G., Newquist, S. C., & Schatz, R. 2007, February: Reputation and its risks. Harvard Business Review , pp. 104-114.

Gut, A. 2005: Probability: A Graduate Course. London: Springer.

Hillson, D., & Murray-Webster, R. 2007: Understanding and Managing Risk Attitude (2nd ed.). Burlington: Gower Publishing Company.

Hopkin, P. 2002: Holistic Risk Management in Practice. London: Witherby & Co. Ltd.

Kendrick, T. 2008: Strategic risk management. 2008 MBA Risk Management unit lectures (pp. 6-7). Norwich: Norwich Business School.

Leitch, M. 2003, March 18: The basics (of risk and uncertainty management). Managed Luck web site: (Accessed on 23 October 2008)

Machina, M. J. 2004: Almost – objective uncertainty. Economic Theory
, 24, 1-54.

O.E.D. 2008: AskOxford: uncertainty. Oxford English Dictionary web site: (Accessed on 23 October 2008)

Thomas, L. C. 2000: A survey of credit and behavioural scoring: forecasting financial risk of lending to consumers. International Journal of Forecasting
, 16 (2), 149-172.

Trippett, F. 1982, April 26: Looking for Tomorrow (and Tomorrow). Time Magazine .

Ward, S., & Chapman, C. 2003: Transforming project risk management into project uncertainty management. International Journal of Project Management
, 21, 97–105.

Webb, P. 1996: Probability theory. Probability theory Info web site: (Accessed on 25 October 2008)

2 Comments leave one →
  1. January 7, 2013 9:17 am

    Hi Sagar

    Three points:

    1) I’ve changed the text of my article, “The Basics” that you cite, so it may no longer say the thing you were referring to.

    2) Just to be clear, what I was actually doing when ‘clubbing together’ the words risk and uncertainty was not to equate the two terms, but just to collect together all management concerned with ‘risk’ or ‘uncertainty’, interpreted any way you like, or any mixture. I just wanted to talk to anyone with any interest in that general area.

    3) The definition of ‘probability’ you have gone with is a frequentist one where, in effect, the word probability is being used as a synonym for ‘long run relative frequency’. Since your article above was written I have written a book called “A pocket guide to risk mathematics” that discusses the interpretation of probability and various mistakes in practice that can flow from this area. You may find it helpful.

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