![]() This point is seriously counter-intuitive (to me anyway) and merits a proof, which Cox provides and I discuss below. there is the possibility of making ranking errors. Look at that statement again: it implies that risk matrices can incorrectly assign higher qualitative rankings to quantitatively smaller risks – i.e. the other one is high or low), then there is a non-zero chance of making an incorrect ranking because some points in the cell with the higher qualitative rating have a lower quantitative value of risk than some points in the cell with the lower qualitative ranking. ![]() But there’s more: if one of the ratings is medium and the other one is not (i.e. “That’s obvious,” I hear you say – and you’re right. In doing this, analysts make the implicit assumption that the categorisation provided by the qualitative assessment ranks the risks in correct quantitative order. The standard solution is to use a qualitative scale, where instead of numbers one uses descriptive text – for example, the probability, impact and risk can take on one of three values: high, medium and low (as shown in Figure 1 below). This is typically where the problems start: for most risks, neither the probability nor the impact can be accurately quantified. This formula looks reasonable, but is typically specified a priori, without any justification.Ī risk can be plotted on a two dimensional graph depicting impact (on the x-axis) and probability (on the y-axis). Risk: In many project risk management frameworks, risk is characterised by the formula: Risk = probability x impact. Note that the above scales for probability and impact are arbitrary – other common choices are percentages or a scale of 0 to 10. It can also be quantified as a number between 0 (lowest severity) and 1(highest severity). Impact (termed “consequence” in the paper): This is the severity of the risk should it occur. It is quantified as a number between 0 (will definitely not occur) and 1 (will definitely occur). Probability: This is the likelihood that a risk will occur. Let’s begin with some terminology that’s well known to most project managers: Developing an understanding of these points will enable project managers to use risk matrices in a more logically sound manner. As I discuss later, this is essentially due to the impossibility of representing quantitative rankings accurately on a rectangular grid. Second, and possibly more important, is that the arguments presented in the paper show that it is impossible to maintain perfect congruence between qualitative (matrix) and quantitative rankings. ![]() This conclusion was surprising to me, and I think that many readers may also find it so. Cox shows – using very general assumptions – that there is only one sensible colouring scheme (or form) of these matrices. Typically these matrices are constructed in an intuitive (but arbitrary) manner. First, 3×3 and 4×4 risk matrices are widely used in managing project risk. Since the content of this post may seem overly academic to some of my readers, I think it is worth clarifying why I believe an understanding of Cox’s principles is important for project managers. ![]() This post is devoted to an exposition of these principles and their consequences. In a paper entitled, What’s wrong with risk matrices?, Tony Cox shows that the qualitative risk ranking provided by a risk matrix will agree with the quantitative risk ranking only if the matrix is constructed according to certain general principles. ![]() There is a widespread belief that the qualitative ranking provided by matrices reflects an underlying quantitative ranking. Such rankings are often used to prioritise and allocate resources to manage risks. These matrices provide a qualitative risk ranking in categories such as high, medium and low (or colour: red, yellow and green). One of the standard ways of characterising risk on projects is to use matrices which categorise risks by impact and probability of occurrence. ![]()
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