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Whenever a search is being conducted for whatever reason, whether for a lost person or a crime search, the search leader will always direct the resources to look in the most likely place, i.e. the place with the highest probability of finding the subject/evidence.

This makes obvious sense – this is probability theory.

We always use search probabilities without even realising it, perhaps. We are looking in the most likely place with the resources most likely to find the subject.

Probabilities are relative expressions, they are not absolutes.

As an example of converting phraseology to mathematical percentages we can use the following scenario:

“The lost person has probably gone down Willow Hill to the forest. If we send all our search teams and dogs to check the copse then they will almost certainly find him. If that’s right we can go home soon because we’ll find him within the hour.”

Another way of saying this is……

“There’s an 80% probability the lost person has gone to the forest, a 90% chance the searchers will find him therefore there is a 72% probability that we will be successful.”

Probability v Phraseology

Percentages can be expressed in simple phrases:

100%

                                    Very unlikely

90%

80%

                                    Likely

70%

60%

50%                  Even chance

40%

30%

                                    Unlikely

20%

10%

                                    Very unlikely

0%

In using probabilities we compare the odds and trade one off against another. Numbers are relative expressions. 60% by itself is meaningless but we can say it is better then 50% but not as good as 70%.

The numbers merely give us a framework for applying the search theory. They are not precise.

The last chapter discussed some of the reasons for using mathematical data and numbers. It was suggested that we don’t have to use them. This is so, but it is undoubtedly the case that there are compelling reasons to use them.

Statistics and Databases – The Case For

Statistics are merely a group of numbers which are able to summarise information such as:

A database is a collection of a lot of individual results which can be placed in some sort of order. A database should collect only one category of information such as, in our case, elderly persons, hikers, etc. The larger the database then the more significant the information. For example 500 cases are better than 100, 50 or even 10.

The chapter dealing with ‘Lost Person Behaviour’ has already provided information contained within the statistical database for each category of lost person. The usefulness of such data is clear as a planning tool.

The application of these category databases is straightforward and an essential element of search planning.

We can, however, go much further if we wish and apply probability percentages of the actual search operation itself. These will be in the form of:

POA – Probability of Area – the chances of the subject being in a given area.

POD – Probability of Detection – the chances of the subject being detected if they were there.

POS – Probability of Success – of actually finding the subject in the area being searched.

These probability notations will be discussed in more detail later in this chapter.

The next section will concentrate on the databases compiled for each lost person category and how it is applied.

The search data is usually presented in the following format:

Median Distance

This is the middle value such that half the values within the set are smaller and half the values within the set are larger than the median value.

Mean Distance

This figure is sometimes used. It is the average value for all figures contained within the database. One rogue figure can ‘skew’ the entire distribution of the database and hence the search. The mean distance, is therefore rarely used.

When applying the figures to a map to establish the search area we are talking about the probability – the chance of an event occurring or someone behaving in an expected manner.

For example:

If numbers are to be used in a search operation then they need to be expressed in meaningful terms, e.g. percentages.

Applying Search Data to Maps – Steps

1.         On a suitable map mark the IPP

2.         Draw a circle on the map to indicate the median distance

3.         Mark a circle on the map to mark other zones such as 25%, 50%, 75% or MAX.

This is the theoretical search area. You should have very good reasons for searching beyond the maximum zone.

Each zone can also be referred to as a ‘probability zone’.

For a 75% POA we need look no further than the 75% zone.

For a 25% POA we need look no further than the 25% zone, and so on.

If the maximum zone is 94% then in 94% of previous cases the subject has been found within that distance. i.e. there is a 94% probability that the subject in the current case will be in this same size area.

This is only one step to applying the search data and therefore the search resources. The databases go much further and give percentages of places where the subject is likely to go or what resources are best to find them. For instance, in the elderly persons category percentages are given for the proportion of cases where the subject has gone up or downhill from the PLS.

In such a case the search manager would analyse the map and within the chosen probability zones would identify the downhill areas, these being where most elderly persons would go from the PLS. This then starts to give the search manager separate specific search sector/segments to search. These would then need to be prioritised. The next chapter on ‘Establishing the Search Area’ goes into this in detail.

This illustration shows the

IPP marked, along with the

Median and max zones.

The search manager has then

Identified an area of priority

and sectorised it into small,

more manageable sectors.

Back to Probability Theory……..

POA – The likelihood of the subject being in a particular area as opposed to another.

POD - The likelihood of locating the subject in a particular area using a certain type of resource in certain conditions.

POS – The probability of successfully finding the subject in that area with the given resources.

POS is arrived at simply by the following:

POA x POD = POS

This is what we do anyway; we are just quantifying it by using percentages.

Search Priority

We can use POS to enable us to find the subject/clue in the fastest possible time by using the most appropriate resource.

The application of percentages and statistics to the search operation will:

Probability of Detection (POD)

The scope of the search manager’s role in this handbook is to manage the search operation in the early stages of the search and through the first operational period. As most searches are concluded within this first operational period there is little need to have an army of search managers trained up to a level able to complete full mathematical calculations.

The following figures shown earlier in this handbook support the above statement:

MRC Statistics of times taken to locate the subject

It is anticipated that during the first operational period the search manager will be preparing for the second. This will require the attendance of a full search manager capable and qualified to the level where full POA/POD/POS calculations can be computed. These persons will, in the main, be POLSA’s within the Devon and Cornwall Force Area.

To enable the search manager/POLSA for the second and subsequent operational periods to take over the initial search manager must be in a position to fully brief their relief and provide him/her with the necessary calculations.

POA will already have been done with the completion of the consensus worksheet.

POS is not necessary in the early stages.

POD must be calculated in order that POS can be worked out. The knowledge of the levels of POS will enable the search manager/POLSA in the second and subsequent operational periods to focus and direct the search more efficiently.

POD can be applied to an area or resources and can be predictive or retrospective

Predictive POD

This is used as a planning tool using numbers derived from theoretical and experimental work. In most cases the theoretical figures have been calculated from previous studies and actual searches carried out. Predictive POD can help to direct which resources to deploy to ensure the highest possible POS.

Retrospective POD

This is the figure given by the search resource after they have completed their search and is given during the debrief.

This is the opinion as to how likely they would have been to find the subject in the area searched. It is the quantitative answer to the question ‘how well have you searched your area?’

A retrospective POD can vary greatly between searchers and may not always be accurate. A team leader may be reluctant to quote a figure of, say, 50%.

One way of asking your search resource to estimate their POD is to ask the relatively simple question ‘If there had been ten subjects in your search area how many of them would you have found?’

A lone dog handler in a very heavily vegetated area of forest may only reply ‘three.’

This would equate to a POD of 30%.

If on the other hand, a search team of six persons had to search a field of 30cm high grass and you asked the same question, they may well reply with an answer of ‘nine.’ This would be a POD of 90% and in these circumstances would not be unreasonable.

The logical step which follows these two examples may be that the same forest in the first example would be searched again by the six person search team. They may well then be able to come back with a retrospective POD of, say, 60%.

Although beyond the scope of this handbook, a cumulative POD for the two searches of 30% and 60% POD would be 72%. This is worked out using tables available to the search manager/POLSA.

The search manager uses each POD and subsequent POD/cumulative POD to work out where next to send his resources. It may well be that the mathematics would suggest a third search in the same area of woodland in order to raise the cumulative POD further.

For the search manager in the first operational period, it is sufficient for them to be able to provide the relief search manager with the POD for all areas searched. This would simply be recorded in the search documentation and any subsequent calculations could be continued later.

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