Gross Estimates

The “Brooks” Formula

Patrick Boens

12/05/2010

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1. Background

2. Context & Objectives

3. Formula

1. Base

2. Updated

1. Developers’ focus

2. Supervision

3. Contingency

4. Deployment

Agenda

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Background

• Frederick Brooks is a Software Engineer and Computer Scientist, best-known for managing the development of IBM 0S/360.

• Author of the famous “The Mythical Man-Month”, a book about Software Engineering and Project Management.

• He had mistakenly added more workers to a project falling behind schedule, considering the equivalence of “resources” and “time” (Man-Month).

• In his book, he presents a simple formula for software estimates, a formula he considered to be invalid in subsequent editions.

• Still, this formula is a very good basis for early estimates.

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Context & Objectives

• Early stages of a project (inception, initiation)

• Gross != precise it gives an idea, a rough estimate (no equivalence with COCOMO II for example)

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Base Formula

• Effort = 1/3 specs + 1/6 code + 1/4 ut + 1/4 it … where

- specs = requirements + analysis

- code = build

- ut = unit tests

- it = integration testing

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Updated Formula

• Some refinements are needed in order to cope with “Prince 2” sort of slicing:

- Specs = Requirements + analyses (BA, FA, TA) = 1/3 = 4/12

- Code = Code + Unit tests = 1/6 + 1/4 = 5/12

- Tests = Integration Testing + Functional Testing* = 1/4 = 3/12

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*UAT is not included (not a concern of IT)

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Updated Formula

• Supervision effort (PM and Team Leader work) not included

• Contingency not included

• Deployment effort not included

• The formula becomes:

- Specs = Requirements + analyses = 1/3 = 4/12

- Code = Code + Unit tests = 1/6 + 1/4 = 5/12

- Tests = Integration Testing + Functional Testing = 1/4 = 3/12

- + supervision + contingency + deployment effort

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Updated formula: Developers’ focus

• Developers focus on:

- Specs = Requirements + analyses = 1/3 = 4/12

- Code = Code + Unit tests = 1/6 + 1/4 = 5/12

- Tests = Integration Testing + Functional Testing = 1/4 = 3/12

- + supervision + contingency + deployment effort

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Updated formula: Supervision

• Supervision is often seen as a percentage of the overall project (± 15%*)

• Example: Specs + Code + Tests = 100 mdays Supervision = 15 mdays

• Total effort = 100 mdays + 15 mdays = 115 mdays

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* Although acceptable, a more precise formula exists to calculate the Supervision effort. we’ll see this in a minute

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Updated formula: Contingency

• Contingency is a way to foresee what’s impredictable. Statistically, 17% contingency is used. This percentage must be adapted to the context of your project, based on the degree of uncertainty.

• Example: Specs + Code + Tests + Supervision = 115 mdays Contingency = 20 mdays

• Total effort = 100 mdays + 15 mdays + 20 mdays = 135 mdays

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Updated formula: an example

• Imagine a developer’s evaluation of 50 mdays, and now calculate the overall effort 1/12 = 10 mdays

› specs = 4/12 = 40 mdays

› code = 5/12 = 50 mdays

› tests* = 3/12 = 30 mdays

• Effort = 40 mdays + 50 mdays + 30 mdays = 120 mdays

• Supervision = 120 mdays x 15/100 = 18 mdays

• Contingency = 138 mdays x 17/100 = 23 mdays

• Deployment = x mdays (say, 5) Total effort = 161 mdays + 5 mdays = 166 mdays

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* UAT not included

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Updated formula: the bottom line

• You started with 50 mdays and you ended up with 166 mdays!

• This sounds funny: an experienced Project Manager said that he always multiplied the developers’ evaluations by PI 50 mdays x 3.141592 = 157 mdays! ... which is close enough to the end result (it remains a gross figure!)

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* UAT not included

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Supervision Effort : ≠ 15%

• Time and team size must be balanced (theoretical view). A project of 6 months should be worked out with 6 people (team size and duration are equilibrated = square root). Always favor “more time” instead of “more people” (get back to Brooks’ findings).

• A PM is needed for the whole duration of the project. If a month work is 20 days of work, you need the PM during 6 x 20 days, x% of his time.

• The direct span of control is about 6 people* for a project of 3 months, you need the PM half of his time; for a 6 months project, you need him full-time.

• Getting back to our example of 50 mdays of developers’ estimates we have calculated an effort of 120 mdays 120 / 20 = 6 SQRT(6) = 2.45 team of 2 people and timeline of 3 months ( 2 x 20 x 3 = 120 mdays) (ideal view) PM is needed 33% of his time (2 persons for a possible span of 6) during 3 months Supervision effort = 3 x 20 x 1/3 = 20 mdays (instead of 18 mdays with 15%).

• Contingency of 17% (120 + 20 ) mdays x 17/100 = 24 mdays

• Deployment (5 mdays) Total effort = 120 + 20 + 24 + 5 = 169 mdays remember, you started from 50!

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* Software industry