ESTIMATING - FACT OR FICTION

INTRODUCTION

"Holy mackerel, this project is 80% over budget! This estimate has no relationship to reality!" This statement has probably been made at least once a day in the construction industry. Who usually utters these words? - Owners, architects, engineers, contractors, sub-contractors, construc­tion managers, bankers and probably a few others. When a budget is overshot the effect can range from mere annoyance to' anger, to litigation. Often reputations are marred and good business relationships severed. How does such a thing happen? Is it irresponsible design, incompetent budget preparation, greedy contractors, unrealistic owners, or is it just the nature of the beast? Thus the paramount question - is an estimate of a construction project fact or fiction? Perhaps if there were some understanding of the nature of the estimate, some of the problems associated with the question could be mitigated or greatly reduced.

PROBLEM

What is the effect of an estimated budget for a construction project that does not compare with the results of a bidding process? Perhaps three courses of action are available to the bill payer who has an overshot budget:

The latter course may have a few problems on the subject of who pays for the redesign and who is responsible for the new design.

Why the question? Perhaps the basis of this question revolves around what may be called a defective estimate.

A defective or bad estimate may be defined as an estimate that is different from an acceptable proposal by more than a reasonable amount, either in absolute monetary terms or percentages. It must be stated that the reasonable amount may, indeed, be in the eyes of the beholder. To be sure, this definition is not precise but it is believed that it represents the thinking and practice of most people in the construction industry today. It is also interesting to note that an estimate can be substantially higher than an acceptable proposal. In this instance the effect may not be adversarial between the various parties, though the difference may be substantial. One effect of this problem       is that   the owner or the

designer may not have included all the functional or other features that may have been desired on the project.

The following statement is a hypothesis that might explain some of the reasons for the differences between estimates of budgets and contract proposals:

THE ESTIMATING PROCESS IS INHERENTLY A STATISTICAL PROCEDURE. IF THIS IS TRUE, THEN CERTAIN STATISTICAL PRINCIPALS AND PROCESSES MAY BE USED TO UNDERSTAND THE NUMERICAL FORMULATION.

This hypothesis may also be applicable to contract bid proposals as well.

The basic equation for estimating the price of virtually any item of con­struction is formulated as c = pq, where c = unit price of an item, p = unit labor cost and q = unit quantity of the material. For a number of "n" items of "i"; the total cost of a system would be:

If the exact unit price is p and the exact quantity is q let = the percentage difference Between the exact value/quantity and the estimated value/quantity of a specific item. Then:

If it is assumed that 5% is the "D" for both quantity and price, by using Eq. (3) it can be shown that the price for the item "i" can be 10.25% higher to 9.75% lower that the exact price. For a building, such cost variations of combinations can be infinite. Some items would be plus and some minus. The "D" is also variable and can fluctuate considerably. Using this approach it should come as no surprise that a computation of an "exact" price is virtually impossible. This point is true unless there is no variability in unit price of anything (a most unlikely state of affairs).

When computing a construction cost, the estimator often believes he is computing p or q₀. The general procedure is to compute the quantities. Then some unit price of labor, material, or equipment that is associated with that particular quantity is used to calculate the price. This is done for all the cost items of the project. The total of these cost items is the project cost (adding profit and overhead, of course). There is often a perception that this cost is an exact cost. Most estimators, contractors, and knowledgeable owners understand the preciseness of such prices or bids. They appreciate the degree of accuracy or inaccuracy that is inherent in such computations and react accordingly by applying contingencies or by adding to profit via "gut feelings". Thus it might be stated, with conviction, an estimate is not fact but fiction, but the fiction is a fact.

The "D's" (percentage difference from exact values) can be estimated by the use of some simple statistical procedures and a few assumptions or definitions. Unfortunately good data that describes or quantifies estimating variability is lacking. As a start, it can be assumed that the exact value of either quantity or labor, is the arithmetic mean of a small population. Also assume that the "D" population, can be represented by a normal distribution curve. With these assumptions, various characteristics of the population, such as variances, standard deviations, etc., can be computed. A graphical depiction of the assumptions is shown in Fig. 1.

Why there should be a "D" for quantity estimates is most difficult to answer. It seems inconceivable that two people very often do not compute the same value of quantity of some cost item even if both have the same set of plans and specifications. Yet except for a most simple item, if five people compute a quantity of some item, the probability is virtually a certainty that all five will have a different amount. This phenomena has been tested experimentally (at least by the writer) and the results are consistent - all estimators come up with different values for the quantities. The range of variation may be small in some cases but there are still a number of different answers.

Fig. 2 shows some possible results of different estimators computing the quantity of concrete for a small project. Though the numbers herein are fictitious, the results can be considered a good simulation of actual practice.

Fig. 3 shows the results of a survey of eleven contractors who provided "bids" for labor only on a concrete wall 100 ft.long, 1 ft. wide, and 10 ft. high and had 1 ton of reinforcing steel. The statistical parameters are computed. The results show that for a 95% confidence level, the error in the unit price for form work is +/- 27% of the median, for concrete the error is +/­34% of the median, and for setting reinforcing steel the error is +/- 23% of the median. These results seem surprising considering the simple problem given to the eleven experienced contractors. Some of the data might have been disregarded as anomalies. Yet, considering what this paper is studying, it was deemed proper to use the data as it was provided. Some of the prices may have included certain financial provisions for equipment or small tools.

The unit cost of labor is generally conceded to be far more variable than other unit costs such as material or equipment. Even within a specific company, the individual estimators have variances on the unit labor cost due to accounting procedures, a personal perception of the project, and the general risk-taking attitudes of the estimators. If credible and substantial data were available and collated properly then "D's" for various cost items could be made available for analyses to be described. Another example of cost variances is to check the unit costs found in publications such as F.W. Dodge and R.S. Means.

Unit prices for materials are also variable. Examples of such diversity can easily be verified by calling different suppliers, or as a quick check, looking in the cost publications.

From this attack on the processes of estimating, it is obvious that at least four variables are not only possible but quite likely to occur: quantities of materials, prices of materials, productivity rates of labor and unit cost of labor. Unfortunately these are not the only variables in the estimating activity.

The fact that prices vary is confirmed by taking bids, particularly unit price bids. In fact, if the prices don't vary, collusion is often suspected.

Using the example in Fig. 2 and noting that there is a 95% probability of being within +/- 2.4% of the correct answer of quantity of a single item, it now is possible to estimate what impact this may have on a project of very modest size. The question is, if the probability of being within +/- 2.4% of the correct unit quantity is 95% for one item, what is the probability of having none to all items exactly correct on a specific project? Assume in this case that there are 40 quantity items to compute. For this calculation, the binomial or Bernoulli distribution function is very helpful.

From the Bernoulli equation, the probability of having all forty items correct to within +/- 2.4% (remember this is not the "exact" q ) is about 13%. Keep in mind that the confidence level is 95%. The most probable number of items being "correct" is 38, with a probability of about 27.6%. If the accuracy of the labor item is similar to the material item (this is most unlikely), then it is possible to compute the probability of both the quantity units and labor units occurring at the same time. This probability is about 7.6%. What this implies is that the probability of having exactly 38 items correct to within +/- 2.4% 95% of the time in the quantity and labor units is about 8%. It can be shown that the probability of having 25 items to 40 items correct is about 98%. This probability seems reasonable to work with for estimating until it is recognized that at the lower end of the scale only about one half of the items (about 25) will fall within a 2.4% error factor. The remaining items will have

errors that are higher. From an actual survey, the average error for the labor item of the three cost items is 28% (Fig.3). This error factor also has latitude that can be computed for the three cost items. Results of this computation suggest that 95% of the time (using three items only), the error will vary about +/- 49% of the mean. This observation is certainly significant. Using the labor items, the argument presented for the hypothetical concrete is still valid for a 95% confidence level except the error would be about +/- 28%. Going back to Eq. 3 and using +/- 2.4% for material and +/- 28% for labor, the price for the "i" th item can be 31% higher or 30% lower than the exact price - or somewhere in between. To complicate matters further, it also must be recognized that the absolute magnitude of the variance when translated to dollars can be most pervasive. For instance, on a project that has a budget of $1,000,000, an error or variance of the hardware item that is estimated to cost $2,500 could be 50% wrong and thus cause an annoyance of about $1,250. On the other hand an error of 10% in the electrical system that is budgeted for $150,000 ($15,000) could be very disturbing.

These calculations were based on a confidence level of 95% probability of being within 2.4% for concrete quantity and 28% for labor. If the confidence level is 90% for the same accuracy, then the probability of having exactly 38 items correct drops to about 14%. This simple analysis strongly suggests that to estimate to a very close tolerance is statistically very low. Thus, in actual practice, the variances of estimates as compared with contract prices should not be surprising.

If it is concluded that the hypothesis proposed, namely, that estimating may be statistical in nature and that the laws of probability can explain the differences between estimates and bids, then, is a procedure available that could present estimates that reflect those statistical parameters? This procedure could then be strongly compelling in convincing the bill payers to understand that the fact is - estimating should not be perceived as being exact. The answer to this question is -yes-. Range estimating is a method now available. Architects and/or construction managers should no longer provide estimates as a single figure. It has been the writer's

experience that those preliminary estimates are never forgotten but the caveats associated with them are.

RANGE ESTIMATING

Predicting numerical values for future events is a way of life in most organizations. Nearly everyone is on the "estimating merry-go-round" forecasting and re-forecasting costs, profits, return on investment and other performance criteria. All to often, however, the actual result differs significantly from the estimate. This difference is generally attributed to the vagueness of modern business, and rightly so. This is simply an admission that conventional techniques of estimating are often incapable of coping with real world problems.

The reason for this deficiency is fundamental. With most conventional estimating methods, the forecast of each element in the estimate must ultimately be represented as a single number, even though management may know beforehand that thousands of other values are possible. if there are more than a few such elements, the number of possible ways in which they can combine and cascade to the bottom line defies conventional analysis.

Paretto's law states that, as a general rule, a relatively small number of elements in a population will collectively account for a very large percentage of the overall measure of the population. For example, a fairly small percentage of people account for a very large percentage of the total personal wealth. Similarly, a fairly small percentage of items in an inventory will collectively account for a very large part of the total dollar value of the inventory. This phenomenon is often referred to as the "80/20 rule", the implication being that a rather large portion (e.g., 80%) of the overall measure of the population can be attributed to a rather small portion (e.g., 20%) of its elements.

There is an abundance of real world examples of Paretto's law. The area of project estimating is no exception. In fact, there are several different ways in which the Paretto effect manifests itself. The most obvious case is the fact that a relatively small number of elements in a project collectively account for a very large portion of its bottom line.    Another example:          a

relatively small number of elements will create the majority of problems for management.

The example of paramount importance is simply this: A fairly small number of elements in a project will collectively account for the greatest portion of the total potential VARIABILITY of its bottom line. It is this bottom line variability of course which sets up the primary uncertainty in all project estimates. Note that, in this all important example of Paretto's law, those relatively few elements which account for the greatest portion of the bottom line variability are, by the definition stated, "critical" elements. Thus, a very large percentage of the total uncertainty in a project is accounted for in the fairly small number of critical elements. In effect, this makes the problem manageable: relatively few items qualify for constant vigilance. All of the other project elements (the non-critical) deserve no more attention than they normally receive: the future performance of each can adequately be assessed with the conventional single-point "best estimate".

The manner in which data is provided depends upon the elements criticality. A range of possible values is assigned to each critical element of the project. The single-value estimate from the conventional estimate becomes the target estimate. In addition to the target estimate, the other components of the range are the lowest estimate, the highest estimate, and the probability factor.

The range is determined by specifying the lowest and highest values that the element can possibly assume. Since the attempt is assessed to capture the reality of the future as the range, the low and high should be relatively improbable numbers, so improbable, in fact, that there is only a 1% chance that the actual value could materialize higher than the high and a 1% chance that the actual value could materialize lower than the low. The range must necessarily be broad to allow for all that might occur to the individual critical element.

When conventionally estimating the future outcome of a line item such as labor costs, for example, the attempt is to forecast the outcome of all the factors that could possibly impinge upon the outcome of labor cost. We are, in essence, forecasting scope, productivity, labor rates, interest rates, weather, rework, material shortages, and other undefinable factors and their relationship to labor cost.

It is obviously infeasible to forecast each of these factors as labor is estimated. What is feasible is to consider these factors at their best case and worst case. If all the factors that could impact cost were to collectively combine at their worst case, what would be their net effect on cost? In essence, what is called for is the most pessimistic assessment of cost given the scenario painted by the worst case outcome of all the relevant factors. This highest estimate for cost would be a highly unlikely value because of the extremely low probability of all factors materializing at their worst case. Next, if we consider the outcome for labor cost, if all the relevant factors were to materialize at their best case, this optimistic scenario would produce the lowest estimate.

The span of possible values between these two boundaries defines the range for cost. Embedded within this range is the conventional, single-point estimate - the target estimate. Using this technique, the end product is a range of estimates and their probability of occurrence. Figures 4 and 5 show the results of such a computation. Figure 4 is a graphical representation of Fig. 5.

CONCLUSION

Is estimating fact or fiction? This short study suggests that it may be a little of both. If this is so, then conveying such information statistically is probably more realistic than provid­ing such cost information as a single figure.

ACKNOWLEDGMENT

This section of range estimating is indebted to Decision Sciences Corporation of St. Louis, Missouri.