Estimating Methods for Projects
There is no single method that applies to all projects. Estimating is very domain specific. Construction, software, pharmaceuticals, packaging, and services, just to name a few of perhaps hundreds if not thousands of domains, have unique and specific estimating methodologies. Our intent is to discuss general principles that apply universally. Project managers are in the best position to adapt generalities to the specific project instance.
Estimating Concepts
The objectives of performing an estimate are twofold: to arrive at an expected value for the item being estimated and to be able to convey a figure of merit for that estimate. In this book we will focus on estimating deliverables on a WBS. The figure of merit we will use is the confidence interval that is calculable from the statistical data of the underlying distribution of the expected value of the estimate.
Most estimating fits into one of four models as illustrated in Figure 38:

Topdown value judgments from the business side of the project balance sheet conveyed to the project team

Similarto judgments from either side of the project balance sheet, but most often from the business side

Bottomup factsdriven estimates of actual work effort from the project side of the project balance sheet conveyed to the project sponsor

Parametric calculations from a costhistory model, developed by the project team, and conveyed to the project sponsor
Figure 38: Estimating Concepts.
Naturally, it is rare that a project would depend only on one estimating technique; therefore, it is not unusual that any specific project team will use all the estimating methods available to it that fit the project context. However, let us consider them one by one.
TopDown Estimates
Topdown estimates could be made by anyone associated with the project, but most often topdown estimates come from the business and reflect a value judgment based on experience, marketing information, benchmarking data, consulting information, and other extraproject information. Topdown estimates rarely have concrete and verifiable facts of the type needed by the project team to validate the estimate with the scope laid out on the WBS.
Working with topdown estimates requires the steps shown in Table 33. Project risks are greatest in this estimating methodology, and overall cost estimates are usually lowest. In its purest form, topdown estimating foregoes the quantitative information that could be developed by the project team regarding the project cost. Usually, if there is an independent input to cost developed by the project team, the purpose of such an independent input from the project side is to provide comparative data with the topdown estimate. Such a comparison serves to establish the range or magnitude of the risks of being able to execute the project for the topdown budget. Because risks are greatest in topdown estimating, the risks developed in response to topdown budgets require careful identification, minimization planning, and estimation before the project begins. Risks are quantified and made visible on the project side of the project balance sheet.
Step 
Description 

Receive estimates from the business 
Estimates from the business reflect a judgment on the investment available given the intended scope and value to the business. 
Interview business leaders to determine the intended scope 
Scope is the common understanding between the business and the project. Interviews provide the opportunity to exchange information vital to project success. 
Verify assumptions and validate sources, if any 
The business judgment on investment and value is based on certain assumptions of the business managers and may also include collateral information that is useful to the project manager. 
Develop WBS from scope 
WBS must contain all the scope, but only the scope required by the business sponsors. 
Allocate topdown resources to WBS 
Allocation is a means of distributing the investment made possible by the business to the elements of scope on the WBS. 
Cost account managers identify risks and gaps 
Cost account managers have responsibility for elements of the WBS. They must assess the risk of performance based on the allocation of investment to the WBS made by the project manager. 
Negotiate to minimize risks and gaps 
Once the risks are quantified and understood, a confidence estimate can be made of the probability of meeting the project scope for the available investment. Negotiations with the business sponsors narrow the gap between investment and expected cost. 
Topdown estimate to the business side of project balance sheet 
The business makes the judgment on how much investment to make. This investment goes on the business side of the project balance sheet. 
Expected value estimate and risks to project side of balance sheet 
Once the allocation is made to the WBS, there is opportunity for the project manager to develop the risks to performance, the expected value, and the confidence of meeting the sponsor's objectives. 
A common application of the topdown methodology is in competitive bidding to win a project opportunity as a contractor to the project sponsor. In this scenario, the topdown estimate usually comes from a marketing or sales assessment of what the market will bear, what the competition is bidding, and in effect "what it will take to win." If the topdown estimate is the figure offered to the customer as the price, then the project manager is left with the task of estimating the risk of performance and developing the risk management plan to contain performance cost within the offered price:
Topdown offer to do business = Independently estimated cost of performance offered + Risk to close gap with topdown offer
From the steps in Table 33, we see that the project manager must allocate the topdown budget to the WBS. Doing so involves the following quantitative steps:

Develop the WBS from the scope statement, disregarding cost.

By judgment, experience, prototyping, or other means, determine or identify the deliverable of least likely cost, or the deliverable that represents the smallest "standard unit of work." Give that deliverable a numerical cost weight of 1 and call it the "baseline" deliverable, B. This procedure normalizes all costs in the WBS to the cost of the least costly deliverable.

Estimate the normalized cost of all other deliverables, D, as multiples, M, of the baseline deliverable: D_{i} = M_{i} * B, where M is a random variable with unknown distribution and "i" has values from 1 to n. "n" is the number of deliverables in the WBS.

Sum all deliverable weights and divide the sum into the available funds to determine an absolute baseline cost of the least costly deliverable.
($Topdown budget)/(∑M_{i}) = Allocated cost of baseline task B

A "sanity check" on the cost of B is now needed. Independently estimate the cost of B to determine an offset, plus or minus, between the allocated cost and the independent estimate. This offset, O, is a bias to be applied to each deliverable in the WBS. The total bias in the WBS is given by:
Total cost bias in WBS = n * O

Complete the allocation of all topdown budgets to the deliverables in the WBS according to their weights.

It is helpful at this point to simplify the disparate deliverables on the WBS to an average deliverable and its statistics. We know from the Central Limit Theorem that the average deliverable will be Normal distributed, so the attributes of the Normal distribution will be helpful to the project manager:
Average deliverable cost = α_{d} = (1/n) * ∑ [D_{i} + (M_{i} * O)]
σ^{2} of average deliverable = (1/n) * ∑[(D_{i} + O)  α_{d}]^{2}, and
σ of average deliverable = √(1/n) * ∑[(D_{i} + O)  α_{d}]^{2}
It is easier to calculate these figures than it probably appears from looking at the formulas. Table 34 provides a numerical example. In this example, a $30,000 topdown budget is applied to a WBS of seven deliverables. An offset is estimated at 23% of the allocated cost. Immediately, it appears that there may be a $6,900 risk to manage (23% of $30,000). However, we see from the calculations employing the Normal distribution that the confidence of hitting the topdown budget is only 24%, and with the $6,900 risk included, the confidence increases to only 50%. At 68% confidence, the level needed for many firms to do fixed price bidding, the risk increases significantly. Clearly if the risk is to be reduced, then the scope will have to be downsized or the budget increased, or more time given to estimating the offsets in order for this project to go forward.
WBS Element 
Weight, M_{i} 
Allocated Budget, D_{i} 
Allocated Budget + (M_{i} * O) 
Distance^{2} (d  average d)^{2} 

a 
b 
c 
d 
e 
1  
1.1.1 
8 
$10,435 
$12,835 
57,204,324 
1.1.2 
5 
$6,522 
$8,022 
7,564,208 
1.1.3 
1 
$1,304 
$1,604 
13,447,481 
1.2.1 
2 
$2,609 
$3,209 
4,254,867 
1.2.2 
2.5 
$3,260 
$4,010 
1,591,202 
1.3.1 
1.5 
$1,957 
$2,407 
8,207,691 
1.3.2 
3 
$3,913 
$4,813 
210,117 
Totals: 
23 
$30,000 
$36,900 
92,479,890 
Given: Topdown budget = $30,000 Evaluated least costly baseline deliverable, B = $1,304.35 Estimated independent cost of B = $1,604.35 Calculated baseline offset, O, = $300 = $1,604.35  $1,304.35 

n = 7 ∑ M_{i} = 23 ∑ D_{i} = ∑(M_{i} * B) = $30,000 Average deliverable, average d, with offset = $36,900/7 = $5,271 Variance, σ^{2} = 92,479,890/7 = 13,211,413 Standard deviation, σ = $3,635 

Confidence calculations: Total standard deviation of WBS = √7* σ^{2} = √92,479,890 = $9,616 24% confidence: WBS total ≤ $30,000 ^{[*]} 50% confidence: WBS total ≤ $36,900 68% confidence: WBS total ≤ $36,900 + $9,616 = $46,516 

^{[*]}From lookup on singletail standard Normal table for probability of outcome = ($36,900 $30,000)/$9,616 = 0.71σ below the mean value. Assumes summation of WBS is approximately Normal with mean = $36,900 and a = $9,616. 
Once the risks are calculated, all the computed figures can be moved to the right side of the project balance sheet. Let us recap what we have so far. On the business side of the project balance sheet, we have the topdown budget from the project sponsors. This is a value judgment about the amount of investment that can be afforded for the deliverables desired. On the right side of the balance sheet, the project manager has the following variables:

The estimated "fixed" bias between the cost to perform and the available budget. In the example, the bias is $6,900.

The average WBS for this project and the statistical standard deviation of the average WBS. In this example, the average WBS is $36,900 (equal to the budget + bias) and the standard deviation is $9,616.

And, of course, the available budget, $30,000.
As was done in the example, confidences are calculated and the overall confidence of the project is negotiated with the project sponsor until the project risks are within the risk tolerance of the business.
SimilarTo Estimates
"Similarto" estimates have many of the features of the topdown estimate except that there is a model or previous project with similar characteristics and a cost history to guide estimating. However, the starting point is the same. The business declares the new project "similar to" another completed project and provides the budget to the new project team based on the cost history of the completed project. Of course, some adjustments are often needed to correct for the escalation of labor and material costs from an earlier time frame to the present, and there may be a need to adjust for scope difference. In most cases, the "similarto" estimate is very much like a topdown estimate except that there is usually cost history at the WBS deliverable level available to the project manager that can be used by the project estimating team to narrow the offsets. In this manner, the offsets are not uniformly proportional as they were in the topdown model, but rather they are adjusted for each deliverable to the extent that relevant cost history is available.
The quantitative methods applied to the WBS are not really any different from those we employed in the topdown case except for the individual treatment of the offsets. Table 35 provides an example. We assume cost history can improve the offset estimates (or provide the business with a more realistic figure to start with). If so, the confidence in budget developed by the business as a "similar to" is generally much higher.
WBS Element 
Allocated Budget from Cost History, D_{i} 
Offset 
Allocated Budget + (M_{i} * O) 
Distance^{2} (d  average d)^{2} 

a 
b 
c 
d 
e 
1  
1.1.1 
$10,435 
$200 
$10,635 
39,813,357 
1.1.2 
$6,522 
$100 
$6,422 
4,396,315 
1.1.3 
$1,304 
$300 
$1,604 
7,401,948 
1.2.1 
$2,608 
$50 
$2,658 
2,778,889 
1.2.2 
$3,261 
$75 
$3,186 
1,297,618 
1.3.1 
$1,957 
$100 
$2,057 
5,145,994 
1.3.2 
$3,913 
$200 
$3,713 
374,491 
Totals: 
$30,000 
$275 
$30,275 
61,208,612 
Given: Topdown budget = $30,000 Evaluated least costly baseline deliverable, B = $1 ,304 

N = 7 ∑ M_{i} = 23 ∑ D_{i} = ∑(M_{i} * B) = $30,000 Average deliverable, average d, with offset = $30,275/7 = $4,325 Variance, σ^{2} = (1/7) * (61,208,612) = 8,744,087 Standard deviation, σ = $2,957 

Confidence calculations: Total standard deviation of WBS = √61, 208,612 = $7,823 46% confidence: WBS total ≤ $30,000 ^{[*]} 50% confidence: WBS total ≤ $30,275 68% confidence: WBS total ≤ $30,275 + $7,823 = $38,098 

^{[*]}From lookup on singletail standard Normal table for probability of outcome = ($30,275  $30,000)/$2,957 = 0.09σ below the mean value. Assumes summation of WBS is approximately Normal with mean = $30,275 and σ = $2,957. 
BottomUp Estimating
So far we have seen that the project side of the balance sheet is usually a higher estimate than the figure given by the business. Although there is no business rule or project management practice that makes this so in every case, it does happen more often than not. That trend toward a higher project estimate continues in bottomup estimating.
Bottomup estimating, in its purest form, is an independent estimate by the project management team of the activities in the WBS. The estimating team may actually be several teams working in parallel on the same estimating problem. Such an arrangement is called the Delphi method. The Delphi method is an approach to bottomup estimating whereby independent teams evaluate the same data, each team comes to an estimate, and then the project manager synthesizes a final estimate from the inputs from all teams.
The starting point for the estimating team(s) is the scope statement provided by the business. A budget from the business is provided as information and guidance. Parametric data developed from cost history are assumed to be unavailable. In practice, parametric data in some form are usually available, but we will discuss parametric data next.
Best practice in bottomup estimating employs the "npoint" estimate rather than a single deterministic number. The number of points is commonly taken to be three: most likely, most pessimistic, and most optimistic (thus the expression "threepoint estimates"). A distribution must be selected to go with the threepoint estimate. The Normal, BETA, and Triangular are the distributions of choice by project managers. The BETA and Triangular are used for individual activities and deliverables; the Normal is a consequence of the interaction of many BETA or Triangular distributions in the same WBS. However, if there are deliverables with symmetrical optimistic and pessimistic values, then the Normal is used in those cases.
Table 36 provides a numerical example of bottomup estimating using the BETA distribution. Recall that the Triangular distribution will give more pessimistic statistics than the BETA. Although individual deliverables are estimated with somewhat wide swings in optimistic and pessimistic range, overall the confidence of hitting a lower number with greater certainty is higher.
WBS Element 
Most Likely Estimate 
Most Pessimistic Offset 
Most Optimistic Offset 
BETA Expected Value 
BETA Variance 

1  
1.1.1 
$11,000 
$3,000 
$1,000 
$11,333 
444,444 
1.1.2 
$6,800 
$4,000 
$700 
$7,350 
613,611 
1.1.3 
$1,500 
$800 
$300 
$1,583 
33,611 
1.2.1 
$3,000 
$2,000 
$500 
$3,250 
173,611 
1.2.2 
$3,100 
$1,800 
$750 
$3,275 
180,625 
1.3.1 
$1,800 
$800 
$300 
$1,883 
33,611 
1.3.2 
$3,700 
$1,900 
$600 
$3,917 
173,611 
Totals: 
$32,591 
1,653,124 

Business desires project outcome = $30,000 

Average deliverable from BETA = $32,591/7 = $4,656 Variance, σ^{2} = 1,653, 124/7 = 236,161 Standard deviation, σ = $486 

Confidence calculations: Total standard deviation of WBS = √1, 653,124 = $1,286 50% confidence: WBS total ≤ $32,591 ^{[*]} 68% confidence: WBS total ≤ $32,591 + $1,286 = $33,877 

^{[*]}Assumes approximately Normal distribution of WBS summation with mean = $32,594 and σ = $1,286. 
Parametric Estimating
Parametric estimating is also called model estimating. Parametric estimating depends on cost history and an estimate of similarity between that project history available to the model and the project being estimated. Parametric estimating is employed widely in many industries, and industryspecific models are well published and supported by the experiences of many practitioners. ^{[12]} The software industry is a case in point with several models in wide use. So also do the general industry that builds hardware, as well as the construction industry, environmental industry, pharmaceuticals, and many others have many good models in place. The general characteristics of some of these models are given in Table 37.
Estimating Application 
Model Identification 
Key Model Parameters and Calibration Factors 
Model Outcome 

Construction 
PACES 2001 
Covers new construction, renovation, and alteration Covers buildings, site work, area work Regression model based on cost history in military construction Input parameters (abridged list): size, building type, foundation type, exterior closure type, roofing type, number of floors, functional and utility space requirements Media/waste type: cleanup facilities and methods 
Specific cost estimates (not averages) of specified construction according to model Project costs Life cycle costs 
Environmental 
RACER 
Handles natural attenuation, free product removal, passive water treatment, minor field installation, O&M, and phytoremediation Technical enhancements to over 20 technologies Ability to use either system costs or userdefined costs Professional labor template that creates task percentage template 
Programming and budgetary estimates for remedial environmental projects 
Hardware 
Price H® 
Key parameters: weight, size, and manufacturing complexity Input parameters: quantities of equipment to be developed, design inventory in existence, operating environment and hardware specifications, production schedules, manufacturing processes, labor attributes, financial accounting attributes 
Cost estimates Other parameter reports 
SEER H® 
WBS oriented Six knowledge bases support the WBS elements: application, platform, optional description, acquisition category, standards, class Cost estimates are produced for development and production cost activities (18) and labor categories (14), as well as "other" categories (4) 
Production cost estimates, schedules, and risks associated with hardware development and acquisition 

NAFCOM (NASA Air Force Cost Model) Available to qualified government contractors and agencies 
WBS oriented Subsystem oriented within the WBS Labor rate inputs, overhead, and G&A costs Integration point inputs Test hardware and quantity Production rates Complexity factors Test throughput factors Integrates with some commercial estimating models 
Estimates design, development, test, and evaluation (DDT&E) flight unit, production, and total (DDT&E + production) costs 

Software 
COCOMO 81 (waterfall methodology) 
Development environment: detached, embedded, organic Model complexity: basic, intermediate, detailed Parameters used to calibrate outcome (abridged list): estimated delivered source lines of code, product attributes, computer attributes, personnel attributes, project attributes (with breakdown of attributes, about 63 parameters altogether) 
Effort and duration in staff hours or months Other parametric reports 
COCOMO II (object oriented) 
Development stages: applications composition, early design, post architecture (modified COCOMO 81) Parameters used to calibrate outcome (abridged list): estimated source lines of code, function points, COCOMO 81 parameters (with some modification), productivity rating (Stage 1) 
Effort and duration in staff hours or months Other parametric reports 

Price S 
Nine categories for attributes: project magnitude, program application, productivity factor, design inventory, utilization, customer specification and reliability, development environment, difficulty, and development process 
Effort and duration in staff hours or months Other parametric reports 

SEERSEM 
Three categories for attributes: size, knowledge base, input Input is further subdivided into 15 parameter types very similar to the other models discussed 
Effort and duration in staff hours or months Other parametric reports 
Most parametric models are "regression models." We will discuss regression analysis in Chapter 8. Regression models require data sets from past performance in order that a regression formula can be derived. The regression formula is used to predict or forecast future performance. Thus, to employ parametric models they first must be calibrated with cost history. Calibration requires some standardization of the definition of deliverable items and item attributes. A checklist specific to the model or to the technology or process being modeled is a good device for obtaining consistent and complete history records. For instance, to use a software model, the definition of a line of code is needed, and the attributes of complexity or difficulty require definitions. In publications, the page size and composition require definition, as well as the type of original material that is to be received and published. Typically, more than ten projects are needed to obtain good calibration, but the requirements of cost history are model specific.
Once a calibrated model is in hand, to obtain estimates of deliverable costs the model is fed with parameter data of the project being estimated. Model parameters are also set or adjusted to account for similarity or dissimilarity between the project being estimated and the project history. Parameter data could be the estimated number of lines of software code to be written and their appropriate attributes, such as degree of difficulty or complexity. Usually, a methodology is incorporated into the model. That is to say, if the methodology for developing software involves requirements development, prototyping, code and unit test, and system tests, then the model takes this methodology into account. Some models also allow for specification of risk factors as well as the severity of those risks.
Outcomes of the model are applied directly to the deliverables on the WBS. At this point, outcomes are no different than bottomup estimates. Ordinarily, these outcomes are expected values since the model will have taken into account the risk factors and methodology to arrive at a statistically useful result. The model may or may not provide other statistical information, such as the variance, standard deviation, or information about any distributions employed. If only the expected value is provided, then the project manager must decide whether to use some independent evaluation to develop statistics that can be used to develop confidence intervals. The model outcome may also specify or identify dependencies accounted for in the result; as we saw in the discussion of covariance, dependencies change the risk factors.
Table 38 provides a numerical example of parametric estimating practices in the WBS.
WBS Element 
Deliverable 
Units 
Quantity 
Parametric Cost 
Model Expected Value 
Model Standard Deviation, σ 
Calculated Variance, σ^{2} 

1  
1.1.1 
Software code 
Lines of code 
5,000 
$25 
$125,000 
$25,000 
625,000,000 
1.1.2 
Software test plans 
Pages 
500 
$400 
$200,000 
$10,000 
100,000,000 
1.1.3 
Software requirements 
Numbered items 
800 
$100 
$80,000 
$12,000 
144,000,000 
1.2.1 
Tested module 
Unit tests 
2,000 
$100 
$200,000 
$30,000 
900,000,000 
1.2.2 
Integrated module 
Integration points 
1,800 
$50 
$90,000 
$3,500 
12,250,000 
1.3.1 
Training manuals 
Pages 
800 
$400 
$320,000 
$4,000 
16,000,000 
1.3.2 
Training delivery 
Students 
900 
$500 
$450,000 
$5,000 
25,000,000 
Totals: 
$1,465,000 
1,822,250,000 

Average deliverable from model = $1,465,000/7 = $209,286 Variance, σ^{2} = 1,822,250,000/7 = 260,321,429 Standard deviation, σ = √260.321 ,429 = $16,134 

Confidence calculations: Standard deviation of total expected value = √(1 ,822,250,000) = $42,687 50% confidence: WBS total ≤ $1 ,465,000 ^{[*]} 68% confidence: WBS total ≤ $1,465,000 + $42,687 = $1,507,687 

^{[*]}Assumes approximately Normal distribution of WBS summation with mean = $1 ,465,000 and σ = $42,687. 
^{[12]}A current listing of some of the prominent sources of information about parametric estimating can be found in "Appendix E, Listing of WEB Sites for Professional Societies, Educational Institutions, and Supplementary Information," of the Joint Industry/Government "Parametric Estimating Handbook," Second Edition, 1999, sponsored by the Department of Defense. Among the listings found in Appendix E are those for the American Society of Professional Estimators, International Society of Parametric Analysis, and the Society of Cost Estimating and Analysis.