## Second and third cuts to develop an estimate

More detail can be associated with Table 10.1 outcomes using 'second- and third-cut' refinement of 'first-cut' estimates without significantly altering the intended message, as illustrated in Table 10.3.

The second-cut probabilities of Table 10.3 are typical of the effect of still working to one significant figure, but pushing an estimator to provide more detail in the distribution tails. The probability associated with the central value of 10 months drops from 0.5 to 0.3 to provide the probability to fill out the tails. It might be argued that if the second cut is unbiased, the first cut should have had a 0.3 probability associated with 10 months. However, this implies probability values for 8, 10, and 12 months of 0.3, 0.3, and 0.4, which sends a different message. Further, we will argue later that most probability elicitation techniques are biased in terms of yielding too small a spread. The design of the process described here is explicitly concerned with pushing out the spread of distributions, to deliberately work against known bias.

The third-cut probabilities of Table 10.3 are typical of the effect of pushing an estimator to provide still more detail in the tails, using a 20-division probability scale instead of 10, working to the nearest 0.05. A further slight decline in the central value probability is motivated by the need for more probability to fill out the tails.

Table 10.3—Second-cut and third-cut examples delay (months) probability of each delay, given a delay occurs

Table 10.3—Second-cut and third-cut examples delay (months) probability of each delay, given a delay occurs

 first cut second cut third cut 4 0.05 6 0.1 0.10 8 0.2 0.2 0.15 10 0.5 0.3 0.25 12 0.3 0.2 0.20 14 0.1 0.15 16 0.1 0.10 conditional expected delay 10.20 10.60 10.60 expected delay 2.04 2.12 2.12

It is worth noting that the expected values for each successive cut do not differ significantly. If expected value were the key issue, the second cut would provide all the precision needed and the first cut would suffice for many purposes. The difference in expected values between cuts is a function of the skew or asymmetry of the distribution, which is modest in this case. Extreme skew would make more intervals more desirable.

It is worth noting that the variance (spread) increases as more detail is provided. This is a deliberate aspect of the process design, as noted earlier. It is also worth noting that the third cut provides all the precision needed for most purposes in terms of variance.

Further, it is worth noting that any probability distribution shape can be captured to whatever level of precision is required by using more intervals: the simple scenario approach involves no restrictive assumptions at all and facilitates a trade-off between precision and effort that is clear and transparent.

A range of well-known, alternative approaches to providing more detailed estimates are available, which may or may not help in a given situation. Some of these approaches are considered below.

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