The Mathematical Value of Function Points

"Anything you need to quantify can be measured in some way this is superior to not measuring it
all." – Gilb’s Law(1).

To assess the value of function points (any variety), it is important to step back and address
two questions.  The first is “What are function points (in a macro sense)” and secondly “Why do we measure?”

Function points are a measure of the functional size of software. What are IFPUG Function
Points? IFPUG Function Points (there are several non-IFPUG variants) are a measure of the functionality delivered by the project or application. The measure is generated by counting features and functions of the project or application based on a set of rules. In this case, the rules for counting IFPUG Function Points are documented in the IFPUG Counting Practices Manual. Using the published rules, the measure of IFPUG Function Points is a consistent and repeatable proxy for size. Consistency and repeatability increase the usefulness of estimating and measurement. An analogy for the function point size of a project is the number of square feet of a house when building or renovating. Knowing the number of square feet provides one view of the house, but not the other attributes, such as the number of bedrooms. A project function point count is a measure of the function size a project while an application count is a measure of the functional size of the application. 

The question of why do we measure is more esoteric. The stated reasons for measuring often
include:

  • To measure performance,
  • To ensure our processes are efficient,
  • To provide input for managing,
  • To estimate,
  • To pass a CMMI appraisal,
  • To control specific behaviour, and
  • To predict the future.

Douglas Hubbard (2) summarizes the myriad reasons for measuring into three basic categories.  
1. Measure to satisfy a curiosity.
2. Measure to collect data that has external economic value (selling of data).
3.Measure in order to make a decision.

The final reason, to make a decision, is the crux of why measurement has value in most organizations. The decision is the driver to the value of counting function points. The requirements for making a decision are uncertainty (lack of complete knowledge), risk (a consequence of making the wrong decision) and a decision maker (someone to make the decision).  

The attribute of uncertainty is the direct reflection that there exists more than one possible outcome for a decision. Represent the measurement of uncertainty as a set of probabilities assigned to the possible outcomes. For example, there are two possibilities for the weather tomorrow, precipitation or no precipitation. The measurement of uncertainty might be expressed as a 60% chance of rain (from the statement we can infer a 40% chance of no rain). Define risk as the uncertainty that a loss or some other “bad thing” will occur.  In this case, the risk might be that we intend to go picnic if it does not rain and must spend $30 for food the day before that will perish if we can't go on the picnic.  
Measurement of risk is the quantification of the set of possibilities that combines the probability of occurrence with the quantified impact of an outcome.  We would express the risk as a 60% chance of rain tomorrow with a potential loss of $30 for the picnic lunch that won't be eaten. In simplest terms, we measure so we can reduce the risk of a negative outcome. In our picnic example, a measure would have value if it allows us to reduce the chance that we spend $30 for a picnic on a rainy day.

A simple framework hybridized from Hubbard’s How to Measure Anything or determining the value of counting function points to support decision making is:

  • Define the decision.
  • Determine what you already know (it may be sufficient).
  • Determine if knowing functional size will reduce uncertainty.
  • Compute the value of knowing functional size (or other additional information).
  • Count the function points if they have economic value.
  • Make the decision!

The Process and an Example:

1. Define the decision.

Function points provide useful information when making some types of decisions. Knowing the size of the software delivered or maintained would address the following questions:

  • How much effort will be required to deliver a set of functionality?
  • Given a potential staffing level, is a date or budget possible?
  • Given a required level of support, is staffing sufficient?

Summarizing the myriad uses of function points into four primary areas is useful for understanding where knowing size reduces uncertainty.

a) Estimation: Size is a partial predictor of effort or duration. Estimating projects is an important use of software size. Mathematically, the effort is a function of size, behaviour, and technical complexity. All parametric estimation tools, home-grown or commercial, require project size as one of the primary inputs. The simple parametric model that equates effort to size, behavior and complexity are an example of how knowing size reduces uncertainty.
b)Denominator: Size is a descriptor that is generally used to add interpretive information
to other attributes or as a tool to normalize other attributes. When used to normalize other measures or attributes, size is usually used as a denominator. Effort per function point is an example of using function points as the denominator. Using size as a denominator helps organizations make performance comparisons between projects of differing sizes. For example, if two projects discovered ten defects after implementation, which had better quality? The size of the delivered functionality would have to be factored into the discussion of quality.  
c) Reporting: Collect the measures needed to paint a picture of project performance,
progress or success. Leverage measurement data for Organizational report cards and performance comparisons. Use functional metrics as a denominator to synchronize many disparate measures to allow comparison and reporting.
d) Control: Understanding performance allows project managers, team leaders, and project team members to understand where they are in an overall project or piece of work and, therefore, take action to change the trajectory of the work. Knowledge allows the organization to control the flow of work in order to influence the delivery of functionality and value in a predictable and controlled manner.

2. Determine what you already know (it may be enough).

Based on the decision needs, the organization may have sufficient information to reduce
uncertainty and make the decision. For example, if a table update is made every month, takes 10 hours to build and test, then no additional information is needed to predict how much effort is needed to make the change next month. However, when asked to predict a release of a fixed but un-sized backlog, collect more data.

3. Determine if knowing functional size will reduce uncertainty.

Not all software development decisions will be improved by counting function points (at
least in their purest form). Function point counting for work that is technical in nature (hardware and platform related), non-functional in nature (changing the color of a screen) or an effort to correct defects rarely provides significant economic value.

4. Compute the value of knowing the functional size (or other additional information).

One approach to determining whether measurement will provide economic value is to calculate the expected opportunity loss. As a simple example assume a high profile $10M project, estimated to have a 50% chance of being on a budget (or below) and a 50% probability of being 20% over budget.  
In table form:

Mathematical Value of Function Points

The expected opportunity loss is $1M (50% * 2M, very similar to the concept of Weighted Shortest Job First used in SAFe®). In this simple example, if we had perfect information we could make a decision to avoid a $2M over budget scenario.  The expected value of perfect information is $2M. If counting function points and modeling the estimate improves the probability of meeting the budget to 75% then the expected opportunity loss is $500K (a 50% reduction).

5. Count the function points if there is economic value.

Assuming that the cost of the function point count and the estimate is less than the improvement in the opportunity loss, there is value to counting function points.  The same basic thought process is valid to determine whether to make any measure.

6. Make the decision!

Using the reduction of uncertainty make the decision. For example, if the function point count and estimate based on that count reduce our uncertainty that we can meet the estimate by 50% we would be more apt to decide to do the project and to worry less about the potential ramifications to our career. 

Conclusion

While the scenario used to illustrate the process is simple, the basic process can be used to evaluate the value of any measurement process. The difference in the expected gain and the expected value or the percentage not spent on measurement is the value of the function point count. Modeling techniques
such as Monte Carlo Analysis and calibrated estimates are useful to address more robust scenarios in addition to the use of historical data. Counting function points reduces the amount of uncertainty so that we can make better decisions. If this simple statement is true, we can measure the economic value of counting function points.

Sources

1. Demarco, Tom and Lister, Tim. Peopleware: Productive Projects and Teams (3rd Edition). 2013.
2. Hubbard, Douglas. How to Measure Anything. (Third Edition). 2014. Wiley. 

Download

The report can downloaded here.

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