# About the Return on Investment of Test-Driven Development

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2 Conventional TDD Development Development LifeCycleBenefit NetReturn Quality Assurance Figure. Overview of benefit cost ratio calculation. 2 Model This section describes those formulas of our model which are necessary to understand the break-even analysis in Section 3. Appendix A contains a comprehensive description of the model formulas. 2. Return on Calculating the return on investment ROI means to add up all the benefits of the investment, subtract the cost, and then compute the ratio of the cost: ROI = LifeCycleBenefit If the investment pays off, the ROI is positive, otherwise negative. In our evaluation of TDD we focus on the benefit cost ratio BCR which is easily derived from the return on investment. BCR = LifeCycleBenefit = ROI + Studying the BCR instead of the ROI makes the breakeven analysis much simpler, see below. 2.2 Cost We first look at the investment cost. For the conventional project, the development phase includes design, implementation and test. The development phase of the TDD project is comprised only of test-driven development. As first empirical evidence suggests, we assume that the TDD project lasts longer than the conventional project. We call the ratio of the project durations the test-speed-disadvantage (). = Time Conv Time TDD. Since we assume that the development phase is shorter for the conventional project, the test-speeddisadvantage ranges between 0 and : 0 < <. Using productivity figures to explain the difference in elapsed development time between the two kinds of project, the TDD development is ( ) 00 % less productive than the conventional project. Finally, the investment is the difference between the development cost of the TDD project and the conventional project. 2.3 Life Cycle Benefit Now, we consider the benefit. Each development process is characterized by a distinct defect-removalefficiency (DRE). The defect-removal-efficiency denotes the percentage of defects a developer eliminates during development. Initially, a developer inserts a fixed amount of defects per thousands lines of code (initial-defect-density, IDD), but he eliminates DRE 00 % of the defects during the development process. From the increased reliability assumed for TDD, we have 0 < DRE Conv < DRE TDD <. The additional quality assurance (QA) phase of the conventional project compensates for the reduced defect-removal-efficiency of the conventional process. The only purpose of the QA phase is to remove all those defects found by TDD but not by the conventional process. The amount of defects to be removed in the QA phase is mainly characterized by DRE = DRE TDD DRE Conv. The benefit of TDD is equal to the cost of the QA phase for the conventional project. The benefit depends on 2

3 the effort (measured in developer months) for repairing one line of code during QA, which is characterized by DRT IDD QAEffort = WT QAEffort depends on the following: The defect removal time DRT. It describes the developer effort in hours for finding and removing one defect. The inital defect density IDD. The number of defects per line of code inserted during development. The working time WT. month of a developer. The working hours per The reciprocal of QAEffort is a measure for the productivity during the QA phase. 3 Results 3. Exploring the Benefit Cost Ratio As an example, we examine the benefit cost ratio of the following scenario. Factor DRT IDD WT Prod Value 0 h/defect 0. defects/loc 35 h/month 350 LOC/month Let and DRE vary. Figure 2 shows the benefit cost ratio plane spanned by the test-speeddisadvantage and the defect-removal-efficiency difference DRE. Values larger than 4 are cut off. 2.4 Benefit Cost Ratio The benefit cost ratio is the ratio of the benefit and the investment. Substituting the detailed formulas of our model given in Appendix A, the benefit cost ratio becomes BCR = QAEffort Prod DRE ( ), () where Prod is the productivity of the conventional project during the development phase measured in lines of code per month. Values larger than for the BCR mean a monetary gain from TDD, values smaller than a loss. 2.5 Break Even Setting the benefit cost ratio equal to, we get a relation between the test-speed-disadvantage of TDD and the reliability gain of TDD: = DRE = c c DRE +, or c = QAEffort Prod This relation characterizes the break-even point for TDD. If the difference between the defect-removalefficiencies is known, a lower bound for the test-speeddisadvantage can be calculated from which on the TDD project starts to be beneficial. DRE BCR Figure 2. Benefit cost ratio dependent on and Eff For large values of the test-speed-disadvantage ( > 0.9) the TDD project performs almost always better than the conventional project, even for a small defectremoval-efficiency difference. On the other hand, if the test-speed-disadvantage is very small ( < 0.2), TDD does not produce any benefit regardless how large the defect-removal-efficiency difference is. The following table shows some benefit cost ratios for selected values of and DRE. = 0.9 DRE BCR : : : = 0.3 DRE BCR 0.2 : : : :. 0.9 : 3

4 If the productivity of TDD is 0 % smaller than the productivity of the conventional project (left table), a 5 % better defect-reduction-efficiency suffices for TDD to break-even with the conventional process (.7 : ). If the productivity of TDD is much worse, say, 70 % smaller (right table), even a 80 % better defectreduction-efficiency does not lead to a gain as compared to the conventional process (BCR is :.). 3.2 Break Even Analysis With break even analysis, the ranges for and DRE can be identified where TDD is more beneficial than the conventional process. Figure 3 shows the intersection of the surface in figure 2 with the horizontal plane BCR =. Delta Efficiency [%] BCR < BCR > TestSpeedDisadvantage [%] Figure 3. and Eff plane for BCR = 00 The right half of the plane (BCR > ) corresponds to the parameter range of and DRE where TDD is superior over conventional development. Two observations can be made. First, assuming that practical values for DRE can not be larger than 20 %, the may not drop below 66 % for TDD, otherwise the TDD cost exceeds its benefit. Second, if the drops below 27 %, TDD does not have a chance to provide any financial return, regardless of how large the improved defect-removal-efficiency may be. 3.3 Varying other project parameters Figure 4 shows the different cost benefit break-even lines for varying values of the programmer productivity Prod. All other parameters are kept constant. Delta Efficiency [%] Prod=350 Prod=250 Prod= TestSpeedDisadvantage [%] Figure 4. Break even analysis for varying values for Prod The higher the initial productivity, the higher the chance for TDD to get a financial return over conventional development. This result is not intuitively obvious but, it can easily be derived from () and explained with figure as follows. The higher the productivity the shorter the elapsed development time for both TDD and the conventional project. If the elapsed time for the development phase decreases, the investment (difference between both development phases) also decreases, and thus the benefit cost ratio becomes larger. 4 Conclusions We propose an economic model for the return on investment of test-driven development. Our analysis of the break-even leads, all other parameters are kept constant, to the following conclusions: The return on investment of TDD depends to a large extend on the slower development of TDD and the higher quality code of TDD. Other factors like the effort for fixing a faulty line of code, or, the productivity of a developer using the conventional development process, have only minor impact on the return on investment of TDD. The calculation of the return on investment is independent of the project size, the number of developers, and the developer salary. Our model assumes an experienced TDD team. The additional cost for training which is necessary when first introducing TDD is ignored so far. 4

5 Finally, our model strengthens the need for actual empirical figures (or ranges) for the quality advantage and the loss of productivity of TDD, in order to get a comprehensive evaluation of the cost and benefit of TDD. References [] W. Humphrey. A discipline for software engineering. Addison-Wesley, 997. [2] M. Müller and O. Hagner. Experiment about test-first programming. IEE Proceedings Software, 49(5):3 36, Oct [3] M. Müller and F. Padberg. Extreme programming from an engineering economics point of view. In International Workshop on Economics-Driven Software Engineering Research (EDSER), Orlando, Florida, May [4] I. Sommerville. Software Engineering. Addison-Wesley, 995. A Appendix A. Factors in the Economic Model The following list explains the factors and their abbreviations used throughout the model. ProductSize Size of the project in lines of code. Prod The developer productivity measured in lines of code written per month. This figure includes design, coding, and testing. We assume that the productivity remains constant for all developers during the project. The average productivity ranges between 250 and 550 lines of code per month [4]. Salary Salary for the whole team per year. This factor is not further broken down as it turns out that our model is independent from the actual value for the salary. NumOfDev The number of developers working in the project. We assume that this number is fixed throughout the whole project. DRE TDD / DRE Conv The defect removal efficiency describes the percentage of defects a team removes during development. We assume that TDD has a higher defect removal efficiency than the conventional process. The test-speed-disadvantage accounts for the additional effort for using TDD during development as compared to the conventional process. DRT The defect removal time denotes the effort for finding and removing one defect during the QA phase measured in hours per defect. IDD The number of defects per thousand lines of code inserted during development is described by the initial defect density. A typical number is 00 defects per thousands lines of code []. A developer reduces this number of defects according to his defect removal efficiency. WT The working hours of a developer each month. A.2 Model Formulas For the conventional project, the development time is Time Conv = 2 ProductSize Prod NumOfDev. For the TDD project, the decreased productivity has to be taken into account: Time TDD = Time Conv During the QA phase, the conventional project has to compensate for the lower defect removal efficiency as compared to TDD: There have to be DRE = DRE TDD DRE Conv Defect = ProductSize IDD DRE defects removed during QA to get the same defect density as the TDD project. Thus, the time spent in the QA phase is Time QA = 2 DRT Defect WT NumOfDev The cost for both the TDD and the conventional project and the QA phase is Cost p = Time p Salary where p { TDD, Conv, QA }. A.3 Calculating the BCR The benefit cost ratio is defined as the ratio between the life cycle benefit and the investment (cost): BCR = LifeCycleBenefit Recall that the life cycle benefit equals the cost for the additional QA phase in the conventional process. BCR = Cost QA Cost TDD Cost Conv 5

6 The factor Salary can be canceled out. Hence, BCR = = Time QA Time TDD Time Conv Time QA Time Conv ( ). Further canceling of the factors 2, NumOfDev, and ProductSize leads to DRT IDD Prod DRE BCR = WT ( ) DRT IDD Prod DRE = WT ( ) DRT IDD DRE = Prod WT ( ) DRE = QAEffort Prod ( ). 6

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