Quantitative Methods Part I Top Five Ideas from Statistics that help Project Management John C Goodpasture Square Peg Consulting www.sqpegconsulting.com www.johngoodpasture.com

Top five ideas from statistics that help project management The Bell Curve: In the long run, most real activities, like cost and schedule, have outcomes that cluster around an average according to a bell curve of probabilities Expected Value: In the face of uncertainty about the real world outcomes, the best single number to represent the average outcome is a risk-weighted average: Expected Value (EV) Distributions: Every project estimate—without exception—has some uncertainty about it, a distribution of possibilities, each possibility having a unique probability. Photo:Tom Gazpacho

The Bell Curve: In the long run, most real activities, like cost and schedule, have outcomes that cluster around an average according to a bell curve of probabilities

Expected Value: In the face of uncertainty about the real world outcomes, the best single number to represent the average outcome is a risk-weighted average: Expected Value (EV)

Distributions: Every project estimate—without exception—has some uncertainty about it, a distribution of possibilities, each possibility having a unique probability.

Top five ideas from statistics that help project management Monte Carlo: the best and fastest way to get a handle on your project is to simulate the outcomes Dependency bias: When otherwise independent actions become dependent upon each other, there is a bias towards extending the schedule

Monte Carlo: the best and fastest way to get a handle on your project is to simulate the outcomes

Dependency bias: When otherwise independent actions become dependent upon each other, there is a bias towards extending the schedule

The Bell Curve is ubiquitous—it’s everywhere! The bell curve—aka the Normal curve—is ubiquitous because of the Central Limit Theorem and the Law of Large Numbers CLT tells us that the sum of value set—like the sum of work-package costs—will be a value with probabilities that tend towards a bell curve LLN tells us that the average of the value set will tend toward the expected value and true mean of the population, even if the value set is only a ‘large enough’ sample The consequence of the LLN upon the CLT is that the EV of the bell curve is an excellent estimate of the true mean of the population The consequence of the CLT upon the LLN is that the bell curve provides additional information about the quality of the value set. Events or Measurements Outcome Values EV

The bell curve—aka the Normal curve—is ubiquitous because of the Central Limit Theorem and the Law of Large Numbers

CLT tells us that the sum of value set—like the sum of work-package costs—will be a value with probabilities that tend towards a bell curve

LLN tells us that the average of the value set will tend toward the expected value and true mean of the population, even if the value set is only a ‘large enough’ sample

The consequence of the LLN upon the CLT is that the EV of the bell curve is an excellent estimate of the true mean of the population

The consequence of the CLT upon the LLN is that the bell curve provides additional information about the quality of the value set.

Expected Value is the one go-to number for everyone Example: 10 work-packages 3-point estimates with probabilities, ~ 80-20 rule EV = value x probability* Variance** = Value probability x ( LLN EV – Value ) 2 Standard deviation = √( variance ) Expected value (budget): $549.7 84% confidence the budget will be < $549.7 + $40.8 = $590.5 EV + 1 standard deviation * Example: WP1 10% x (60 + 45) + 80% x 50 = 50.5 ** Example: WP1 80% x (55. – 50) 2 +10% x (55-60) 2 + 10% x (55-45) 2

Example: 10 work-packages

3-point estimates with probabilities, ~ 80-20 rule

EV = value x probability*

Variance** = Value probability x ( LLN EV – Value ) 2

Standard deviation = √( variance )

Expected value (budget): $549.7

84% confidence the budget will be < $549.7 + $40.8 = $590.5

EV + 1 standard deviation

Ban single-point estimates! It’s all about distributions There are no facts about the future—everything that hasn’t happened is only an estimate! “If you are going to predict, predict often…” Milton Friedman, Nobel laureate Every estimate should be placed within a range of possibilities Some possibilities are more probable than others Possibilities and probabilities constitute a distribution It’s rare that the real distribution is known or can be known It’s likely that reasonable 3-point estimates can be made 3-point estimates constitute a distribution Points in between would be handy to know, but not essential Its customary to connect the 3 points with straight lines, thereby the Triangular Distribution 3-point estimates can be used directly in simple arithmetic approximations that provide ‘good enough’ risk adjustments for estimates

There are no facts about the future—everything that hasn’t happened is only an estimate!

“If you are going to predict, predict often…” Milton Friedman, Nobel laureate

Every estimate should be placed within a range of possibilities

Some possibilities are more probable than others

Possibilities and probabilities constitute a distribution

It’s rare that the real distribution is known or can be known

It’s likely that reasonable 3-point estimates can be made

3-point estimates constitute a distribution

Points in between would be handy to know, but not essential

Its customary to connect the 3 points with straight lines, thereby the Triangular Distribution

3-point estimates can be used directly in simple arithmetic approximations that provide ‘good enough’ risk adjustments for estimates

Monte Carlo is a simulation technique that gives quick, useful answers Make a 3-point estimate for every outcome—work package or activity Most pessimistic, most optimistic and most likely Assume a distribution that fits the situation; most quick estimates are made with the Triangular distribution The choice of distribution is not as important as picking the three points since the Central Limit Theorem will tend to wash-out the distribution detail Run a simulation using a plug-in tool on your scheduler application* The outcome will tend to be bell-curve distributed in almost every case, so the interesting results are in the cumulative probability distribution—this is in effect a confidence data for your outcome, the so-called S-curve Photo John Goodpasture

Make a 3-point estimate for every outcome—work package or activity

Most pessimistic, most optimistic and most likely

Assume a distribution that fits the situation; most quick estimates are made with the Triangular distribution

The choice of distribution is not as important as picking the three points since the Central Limit Theorem will tend to wash-out the distribution detail

Everything stretches out when there are dependencies When there are dependencies, the distributions of each event interact At a milestone with paths joining: Probability ( milestone ) = P (path A) x P (path B) 90% confidence in each path leads to 81% confidence in the milestone To raise the milestone confidence, each path must be allowed to stretch out to the right—a phenomenon called ‘merge bias’ Dependencies can be created by resource conflicts With independent resources the schedule is 5 units With resources-to-task dependency, the schedule extends to 6 units Time 4 tasks, 2 resources

When there are dependencies, the distributions of each event interact

At a milestone with paths joining: Probability ( milestone ) = P (path A) x P (path B)

90% confidence in each path leads to 81% confidence in the milestone

To raise the milestone confidence, each path must be allowed to stretch out to the right—a phenomenon called ‘merge bias’

Dependencies can be created by resource conflicts

With independent resources the schedule is 5 units

With resources-to-task dependency, the schedule extends to 6 units

Read more about it! Quantitative Methods is a book about numbers and methods for applying them to practical situations in projects There is a good tutorial on statistics, accounting, balanced scorecard, and value The chapter on estimating is right out of my own experience The presentation on earned value makes EV really workable in day-to-day situations. If you do contracting, read the chapter on about doing risk management with contracts And, best of all, you can buy it at any on-line retailer, and read excerpts on google/books

Quantitative Methods is a book about numbers and methods for applying them to practical situations in projects

There is a good tutorial on statistics, accounting, balanced scorecard, and value

The chapter on estimating is right out of my own experience

The presentation on earned value makes EV really workable in day-to-day situations.

If you do contracting, read the chapter on about doing risk management with contracts

And, best of all, you can buy it at any on-line retailer, and read excerpts on google/books

I hope you liked what you saw here I hope you enjoyed this presentation. You can share it with your network There is a lot more information in the book, at my company website, and at my BLOG. See the cover page for links By the way, there is information on my other books and magazine articles at sqpegconsulting.com You can contact me from my company website; the information is all there

I hope you enjoyed this presentation.

You can share it with your network

There is a lot more information in the book, at my company website, and at my BLOG. See the cover page for links

By the way, there is information on my other books and magazine articles at sqpegconsulting.com

You can contact me from my company website; the information is all there