**Three point estimating can be done in two ways – one is by applying Beta Distribution technique, which uses PERT (Program Evaluation and Review Technique) formula and other is by applying Triangular Distribution technique, which calculates simple average.**

Just like any other estimation technique, 3-point estimation can be used for estimating duration or cost of a task (work package, activity, or even entire project).

In this article you will find the definitions, explanations, and examples of Beta and Triangular distribution 3-point estimating techniques.

*The PMBOK Guide does not use the term PERT. It just talks about Beta and Triangular distribution formulas.*

## Why is Three Point Estimating Required?

Risks are inherent in any estimation. 3-Point Estimate helps in mitigating project risks.

In single point estimating, a single value of task estimate is determined, which can be fairly inaccurate for the complex tasks. The accuracy of a single point estimate can be improved by finding three different values. These values helps us in establishing a range, which reduces the project risk and improves confidence.

These 3 different values are

- Optimistic Value (O)
- Pessimistic Value (P)
- Most Likely Value (M)

In 3-Point estimation, expected value of a task is determined by calculating the statistical mean of 3 different values.

Let us look at the two popular methods and their formulas to arrive at the expected value (mean).

## Simple Average Using Triangular Distribution

The mean of three estimated values is determined by the following formula.

E_SA=(O+P+M)/3

### Example and Calculation

Let us consider an example to see how these formulas work. Let us assume that we have to estimate time it takes to go from point A to point B. There could be 3 different Scenario:

**Optimistic** Scenario – Roads would be free of any traffic congestion and there will be no stopping at Traffic signals

**Pessimistic** Scenario – There would be serious traffic bottlenecks ( may be due to a major accident) or there will be some unscheduled stops (may be due to vehicle breakdown)

**Most Likely** Scenario – There would be regular traffic conditions

Let us assume that our 3 estimates (Optimistic, Pessimistic & Most Likely) were 45 minutes, 225 minutes and 90 minutes respectively. Putting these values in the formulas, we get

E_SA=(45+225+90)/3

E_SA=120 minutes

It essentially means that, in most cases, the trip will require 120 minutes or less.

You can also read about the standard deviation that is applied on the triangular distribution mean to find out a range of estimates.

## PERT Formula Using Beta Distribution

PERT formula is an approximation of the Beta Distribution equation. It calculates a weighted average instead of simple average.

The mean of three estimated values is determined by the following formula.

E_PERT=(O+P+4×M)/6

### Why have they given 4 weights to M in the PERT Formula?

PERT formula is based on probability theory and statistics. Specifically PERT is based on Beta Distribution. Historically, 3-point estimation originated from PERT.

PERT was initially developed by US Navy to take care of scheduling uncertainties. The formula mentioned above is a close approximation of mean found by the Beta Distribution. PERT is often used along with CPM (Critical Path Method) for determining moderate risk project schedule.

### Example and Calculation

Let’s use the same three values from the above example and put them in the PERT formula.

E_PERT=(45+225+4×90)/6

E_PERT=105 minutes

It essentially means that, in most cases, the trip will require 105 minutes or less.

You will notice that PERT estimates are more close to ‘Most Likely’ value. Some Project Managers believe that a PERT Estimate yields better results but I am yet to see a definitive research suggesting this.

You can also read about the standard deviation that is applied on the PERT mean to find out a range of estimates.

### A note on PMP® Exam

PMP exam has many formula based questions. Some of these questions are based on 3-Point Estimate. Many of these questions can be solved by using either PERT formula or Simple Average formula. Usually these questions are relatively easy to solve. The underlying concept, itself, is very simple. However, I have observed many PMP Aspirants get confused by this topic. During PMP Exam training, many students ask questions like “Is 3-point estimation same as PERT?”, “Why are there 2 different formulas for arriving at 3-Point estimate?”, “Which formula should be used to solve the questions in the PMP exam?” et. el.

I believe this confusion comes mainly due to the different terminology used by different Project Management authors. My humble suggestion is that if you are a PMP® Aspirant then you should follow terminology from PMBOK Guide. All others sources of the information like books, websites and blogs (including this one) should be read with a bit of skepticism. You should follow other sources only if you find the information contained in these sources is conformant with the PMBOK Guide.

I believe, both PMP aspirants and Project Management practitioners should use PMBOK Guide to understand Project Management Terminology. PMI is trying to standardize Project Management terminology. Many experts from various different areas have contributed content for PMBOK Guide. The Guide is thoroughly reviewed before it is published. It is also updated with current trend and latest developments in Project Management.

### Concluding Remarks

Estimation is one of the most basic concepts of Project Management. In fact poor and improper estimation is one of the main causes of challenged projects. There are many ways to Estimate. Some of these estimation techniques are specific to an industrial domain like software size estimation techniques. While other techniques can be applied to any kind of projects (or daily life activities) e.g. Analogous and Parametric Estimation.

### Over To You

Which formula do you use to determine 3-Point Estimate in your projects? Why do use one method over the other? Please leave a comment.

### PMP Exam Formulas

I have also compiled a PMP Formulas Cheat Sheet. It contains 45 formulas and 57 abbrviations. It will help you in your exam prep. You can freely download the PMP Formulas Sheet for your studies. It is the best and most comprehensive cheat sheet based on the PMBOK Guide 6th edition.

If you are looking beyond a cheat sheet, then I would suggest you to buy detailed PMP Exam Formula Study Guide by Cornelius Fichtner. It contains detailed explanations of all the formulas along with examples and 105 practice questions.

**Disclosure**: This article contains affiliate links - it means that, if you buy from any of these links, then I will receive a small commission that would help me in maintaining this blog for free. However, for you, there is no extra cost. I recommend only those products that I believe will definitely help the certification aspirants.

PERT is one type of 3-point estimating. PERT assumes that the underlying distribution is a beta distribution. The “simple average” that you mention assumes a triangular distribution.

Thanks for enabling me to understand these strategies.

True. Triangular dist.

simplified…easy to understand…thanks !

I get it – Thanks!

Great explanation, thank you.

Thanks Paul

Thank you so much! Awesome explanation and easy to understand.

Thanks Patty.

Unquestionably believe that which you stated. I say to you, I certainly get irked while people consider otherwise, that they just do not know about. Will be back to get more. Thanks

Thanks Tara

i have read ur article but i m not understanding how did u calculated confidence level.

Hi Sonali, Confidence level is derived from probability theory. You can search for “z score tables” to determine the Confidence level (probability values).

Fabulous, what a website it is! This article provides helpful information to us, keep it up.|

Thanks MArinir

If we have to select one project out of three projects. Which project will we select by using 3-point estimate? We have O,P,ML estimated cost for all the three. So which project will have less risk?

Hi Qurban,

3-point estimation is not a Project Selection Method. You should read about various project selection methods like IRR, NPV, BCR etc.

BR

I have to agree with your statement.

Thanks John

How do you calculate the pessimistic and optimistic values??

Hi Hugh,

Most of the time, PMs tend to go with most likely estimates. But projects have inherent risks – both threats & opportunities. We should understand & evaluate these risks while estimating optimistic & pessimistic values respectively.

Just remember the English meaning meaning of Optimistic & Pessimistic before doing the estimation. Pessimistic estimation would mean that almost everything will go wrong while Optimistic estimation would mean that everything will go right.

Hope it helps.

Hi Praveen,

A. BOTTOM-UP ESTIMATING

1. Bottom-up estimating is at activity level estimating and roll-up for budget.

B. TOP-DOWN ESTIMATING

2. Analogue Estimating

3. Parametric Estimating

4. Heuristic and learning curve estimate (Though not in PMBOK)

C. THREE-POINT ESTIMATING

a. Simple Average

b. PERT Calculations

These estimates are for improving estimating accuracy and reducing risks.

They improve single-point estimate.

They can be used for:

c. Activity level estimate

d. Whole project level estimates

My question is whether THREE-POINT Estimating can be categorized as top-down or bottom-up estimating?

The ans is neither. top-down and bottom-up can be used for any form of estimating. basic forms of estimating are – expert judgement, analogous (in old literature it is incorrectly called top-down), and parametric.

hi can i ask what the meaning of 4 in the mean formula? why most likely time must multiply by 4

Hi Zaitun, As written in the article, the formula is a close approximation of Mean found by Beta Distribution.

For more on beta distribution, you can check – https://en.wikipedia.org/wiki/Beta_distribution

BR, Praveen.

Awesome issues here. I am very glad to see your post. Thank you so

much and I’m having a look ahead to contact you. Will drop a mail

How to know which formula to use between the simple average and PERT?

Hi Chandra, Just follow your org. guidelines. BR, Praveen.