Help Needed: Probability Problem in Risk Management Calculcations

[Moose Winooski]

TL;DR Summary

How to figure out the probability of multiple outcomes from a single event

Hello all!

I hope I have come to the right place, and I appreciate any help! My first disclaimer is that I am not a math professional of any sort, I am not bad at it but I just wanted to start with that so if I ask a stupid question, it's because I am ignorant mostly. What I work in is risk management, specifically health and safety.

My problem is this, I don't like and have never really felt comfortable with communicating risk from a 2-dimensional point of view (e.g. likelihood is between 1-2 years, and the consequence is a permanent disability). For those that are familiar with risk, your typical 5x5 heat map.

My issue with this is a "Risk Event" can have a range of possible outcomes. If you think of a car accident, the outcomes can range from minor bumps and bruises to death... and I would like to, in a visual way, represent the probability of many outcomes. (e.g. Bumps and bruises 22% chance, Hospitalisation 48% chance, Permanent disability 20%, Death 10%).

To add to my problem in many cases I probably won't have good external or internal data to already represent this... but I may have multiple "Risk Inputs" so if I go back to my car accident example there would be the inputs of speed, weather, road conditions, driver experience etc... that I could use as "dials" to shift the probability of the outcomes. I also assume that I would have to "weight" these inputs and that would add some subjectivity but I don't think I could be any more accurate?

So in a nutshell, is there a way I can visualise a Risk Event that shows a bunch of grouped outcomes and their probabilities while also having the ability to highlight that "if we increase the speed" then it shifts the numbers?

Cheers, M

 

[Mark44]

My issue with this is a "Risk Event" can have a range of possible outcomes. If you think of a car accident, the outcomes can range from minor bumps and bruises to death... and I would like to, in a visual way, represent the probability of many outcomes. (e.g. Bumps and bruises 22% chance, Hospitalisation 48% chance, Permanent disability 20%, Death 10%).

I see things in terms of a function with several input parameters and a single output in the range of 0 through 1.

To add to my problem in many cases I probably won't have good external or internal data to already represent this... but I may have multiple "Risk Inputs" so if I go back to my car accident example there would be the inputs of speed, weather, road conditions, driver experience etc... that I could use as "dials" to shift the probability of the outcomes. I also assume that I would have to "weight" these inputs and that would add some subjectivity but I don't think I could be any more accurate?

What I have in mind is something like this:
$$R(S, W, C, E, \dots) = \frac{S + W + C + E + \dots}{S_{max} + W_{max} + C_{max} + E_{max} \dots}$$
Here R = Risk, S = Speed, W = Weather, C= (road)Condition, E = (driver)Experience.

The max numbers are there so that the resulting output value is in the range 0 ... 1. This is just a first cut at a possible solution, so might need to be extensively modified. Also, one might need to take into account that some risk factor levels could virtually guarantee a serious accident, if not outright fatalities. If I were doing this I would try to set something up in a spreadsheet and play with it.

 

[FactChecker]

My first disclaimer is that I am not a math professional of any sort, I am not bad at it but I just wanted to start with that so if I ask a stupid question, it's because I am ignorant mostly. What I work in is risk management, specifically health and safety.

You should be aware that risk management is a very complicated mathematical problem. Insurance companies hire and support actuaries to do the calculations that they need. There are several levels of Actuary certification that require you to pass tests that are heavily mathematical and become very hard. I have read that in all of India there is only one person who has passed them all and is certified at the highest level.

 

[Stephen Tashi]

(e.g. Bumps and bruises 22% chance, Hospitalisation 48% chance, Permanent disability 20%, Death 10%).

It isn't clear whether you intend those outcomes to be mutually exclusive. For an example, a person who suffers permanent disability might also suffer bumps-and-bruises unless you intend bumps-and-bruises to mean " only bumps-and-bruises and not one of the other listed outcomes".

 

[Moose Winooski]

Thanks all,

@Stephen Tashi - For the most part, when dealing with risks it's like passing through gates... so if we were talking about $$$ you might have an algorithmic scale of like Loss $0-10k... Loss $10k-100k... Loss $100k-$1M etc... With the most likely being perhaps the 10-100k... but that doesnt mean that the other "bands" have a 0% probability

@FactChecker - Yes very aware, I am looking for something in between subjective 5x5 risk matrix likelihood/consequence comparison to full-blown actuary level analysis as I don't have the time/resources to make that a practical option

@Mark44 - With your formula would all of the variables need to have consistent value ranges? Like would it break if I made speed a range of options from 0-300 and road condition 0.0-1.0 to represent a percentage?