Why 5 by 5 risk maps are meaningless and perhaps even dangerous

A 5 x 5 risk maps (sometimes called heat maps) for risks that are represented by the product of likelihood and impact ratings on one to 5 scales is meaningless because multiplication of ordinal measures is mathematically meaningless. Ordinal ratings do not have interval or ratio meanings. So, for example, the difference between a 5 and 4 does not have the same meaning as the difference between a 3 and 2. More importantly, the ratio of a 4 to a 2 does not have the same meaning as the ratio between a 2 and a 1.  

Since multiplication of ordinal numbers is mathematically meaningless, the position of the points on the typical risk map resulting from the multiplication of two ordinal ordinal 1-5 axes are meaningless.  This is reflected in the rectangular regions of the typical risk map, rather than a curved (hyperbolic regions) that represent products of ratio scale measures of likelihood and impact.

Other drawbacks of traditional heat maps based on 1 to 5 estimates of likelihood and impact are:
Risks in a yellow region might actually be higher than those in a red region;
Risks in a green region might actually be higher than those in a yellow region;

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