# The Conundrum of Three Point Estimation and PERT

Is an estimate based on multiple points more accurate than a single estimate?

If we go with conventional wisdom then it certainly would seem so. A mean of more than one estimate is likely to give us better result.

In project management, there is a three-point estimation technique. It calculates the expected duration based on three different estimates. It calculates the mean of three different estimates to determine the final estimate. This technique can also be used for estimating cost and resources.

Although it would seem that a mean of three points will give us better results but does it have a scientific basis. Letâ€™s find out.

History of Three Point Estimation

The three-point estimation method evolved from Program Evaluation and Review Technique (PERT). IT was first developed by US Navy in 1958. It is commonly used with Critical Path Method (CPM) that is was introduced in 1957.

PERT was developed to support U.S. Navy's Polaris nuclear submarine project. It was developed primarily to simplify the scheduling and planning of large and complex projects. Over the time, it has found application in many other industries.

PERT tries to find the time needed to complete each project activity and tries to determine the minimum duration of a project.

Two Ways to do Three-Point Estimation

The three-point estimation technique is used when there is very limited information. It is used to construct an approximate probability distribution that represents the outcome of future events.

While normal distribution can be used for the approximation purposes but that is not always the case. PERT uses Beta distribution for calculating the result. Another way to find the result is through triangular distribution. Both probability distribution techniques can be used depending on the application.

Three-point estimation used three different estimates to arrive at a result:

- Optimistic Duration (O): It represents the best-case scenario or the minimum possible time required to complete an activity. It assumes everything will proceed better than what is normally expected. This estimate is the most ideal scenario in which everything will run perfectly.
- Pessimistic Duration (P): It represents the worst-case scenario or the maximum possible time required to complete an activity. It assumes everything that can go wrong will go wrong (not including major catastrophes). In this estimate you are confronted with undesirable conditions or events.
- Most Likely Duration (M): It represents the realistic scenario or the best estimate of the time required to complete an activity. It assumes everything will proceed as normal.

Based on these the above three estimates expected duration is calculated.

Expected duration is the mean estimate of the time required to complete an activity. It is the average duration that an activity would require if it was repeated many times over an extended period of time.

By calculating the mean of three points, we reduce the risk of going wrong.

The two methods to do three-point estimation include:

Triangular Distribution

It calculates the average or mean of three estimates by using the following formula:

E = (O + M + P)/3

PERT Beta Distribution

This distribution gives more weight to the most likely scenario while calculating the mean or average. It uses the following formula:

E = (O + P + 4*M)/ 6

Examples

Scenario I

O=9, M=12, P=18

Triangular Distribution

E = (O + M + P)/3

E = (9 + 12 + 18)/3

E = (39)/3

E = 13

PERT Beta Distribution

E = (O + P + 4*M)/6

E = (9 + 18 + 4*12)/6

E = (9 + 18 + 48)6

E = (75)/6

E = 12.5

Scenario II

O=9, M=15, P=18

Triangular Distribution

E = (9 + 15 + 18)/3

E = (42)/3

E = 14

PERT Beta Distribution

E = (9 + 18 + 4*15)/6

E = (9 + 18 + 60)/6

E = (87)/6

E = 14.5

We can draw two observations from the above calculations.

- If most likely is closer to the optimistic value than the mean is greater than most likely duration. On the other hand, if most likely is closer to the pessimistic value than the mean is less than most likely duration.
- The results from beta distribution are closer to the most likely duration than they are from triangular distribution.

Conclusion

Three-point estimation is best done by doing some research about the activity or by contacting an expert. The main thing is to find reasonable estimates for optimistic, most likely and, pessimistic. It is a good idea to record notes for basis of each estimate. Think about the conditions that are likely to occur when the activity is undertaken.

Some important points to note:

- This estimation is more accurate than analogous and parametric estimation
- This estimation allows a consideration for uncertainties and risk.
- This estimation is usually used when there is not enough historical data, or when you are using more subjective data.

There is no correct method to three-point estimation. Both triangular and beta distribution methods are valid methods. Your chosen method will depend on the nature of your work and your organizational processes. You can try to experiment with both the methods and find out which method is giving you better results.

References and further reading:

- How to Use PERT Formula?
- How to Use Standard Deviation Using PERT Formula?
- How to Use PERT and CPM together?
- The Ultimate Guide to Critical Path Analysis

Image courtesy: pixabay.com

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