# Risk Management with the Probability Times Impact Analysis

## Risk Management with the Probability Times Impact Analysis

It is good practice for the project management team to have a working understanding of statistical and numerical methods to apply to projects. Most of what we have discussed has been aimed at managing risk so that the project delivers business value and satisfies the business users and sponsors. Experienced project managers know that the number of identified risks in projects can quickly grow to a long list, a list so long as to lose meaning and be awkward and ineffective to manage. The project manager's objective is to filter the list and identify the risks that have a prospect of impacting the outcome of the project. For this filtering task, a common tool is the P * I analysis, or the "probability times impact" analysis.

### Probability and Impact

To this point we have spent a good deal of time on the probability development and analysis as applied to a project event, work breakdown structure (WBS) work package, or other project activity. We have not addressed to any great extent the impact of any particular risk to the project. Further, the product of impact and probability really sets up the data set to be filtered to whittle down the list. For example, a risk with a \$1 million impact is really a \$10,000 risk to manage if the probability of occurrence is only 1%. Thus, the attitude of the project manager is that what is being managed is a \$10,000 problem, not \$1 million.

The \$10,000 figure is the weighted value of the risk. Take note that in other chapters we have called the weighted value the expected value (outcome times probability of outcome). When working with weighted values, it is typical to sum all the weighted values to obtain the dollar value of the expected value of the risks under management. On a weighted basis, it is reasonable to expect that some risks will occur in spite of all efforts to the contrary and some risks will not come true. But on average, if the list of risks is long enough, the weighted value is the best estimate of the throughput impact.

Risk under management = (Risk \$value * Risk probability) (dollar value)

Average risk under management = (1/N) * (Risk \$value * Risk probability) (dollar value)

Risk under management = Throughput \$impact to project

From the Central Limit Theorem, if the list of risks is "long enough," we know that the probability distribution of the average of the risks under management will be Normal, or approximately so. This means that there is equal pessimism and optimism about the ultimate dollar value of risks paid. We also know that the variance of the average will be improved by a factor of 1/N, where N is the number of risks in the weighted list.

Throughput is a concept from the Theory of Constraints applied to project management. As in the critical chain discussion, throughput is the portion of total activity that makes its way all the way to project outcomes. The constraint in this case is risk management. The risks that make it through the risk management process impact the project. The dollar value of those impacts is the throughput of the risk possibilities to the project.

Obviously, the risk under management must be carried to the project balance sheet on the project side. If the expected value of the project plus the risk under management does not fit within the resources assigned by the business, then the project manager must take immediate steps to more rigorously manage the risks or find other offsets to bring the project into balance.

### Probability Times Impact Tools

There are plenty of ways to calculate and convey the results of a P * I analysis. A simple multicolumn table is probably the best. Table 8-1 is one such example. As there are multiple columns in a P * I analysis, so are there multiple decisions to be made:

• First, follow the normal steps of risk management to identify risks in the project. However, identified risks can and should be an unordered list without intelligence as to which risk is more important. The ranking of risks by importance is one of the primary outcomes of the P * I analysis.

• Second, each identified risk, regardless of likelihood, must be given a dollar value equal to the impact on the project if the risk comes true. Naturally, three-point estimates should be made. From the three-point estimates an expected value is calculated.

• The expected value is adjusted according to the risk attitude of the management team. The value of the risk if the risk comes true is the so-called "downside" figure of which we have spoken in other chapters. If the project or the business cannot afford the downside, then according to the concept of utility, the value of the risk is amplified by a weighting factor to reflect the consequences of the impact. The dollar value should be in what might be called "utility dollars" [6] that reflect the risk attitude of the project, the business, or executives who make "bet the business" decisions. [7]

• All risk figures are adjusted for the present value. Making a present value calculation brings into play a risk adjustment of other factors that are summarized in the discount factor.

• An estimate of probability of risk coming true is made. Such an estimate is judgmental and subject to bias if made by a single estimator. Making risk assessments of this type is a perfect opportunity for the Delphi method of independent evaluators to be brought into play.

• Finally, the present value of the impact utility dollars is multiplied by the probability of occurrence in order to get the final expected value of the risk to the project.

Table 8-1: P * I Display

Risk Event

Probability of Occurrence

Impact to Project if Risk Occurs

P * I

Vendor fails to deliver computer on time

50% chance of 5-day delay

\$10,000 per day of delay

P * I = 0.5 * 5 * 10,000 = \$25,000

New environmental regulations issued

5% chance of happening during project development

\$100,000 redesign of the environmental module

P * I = 0.05 * \$100,000 = \$5,000

Assembly facility is not available on time

5% chance of 10-day delay

\$5,000 per day of delay

P * I = 0.05 * 10 * 5,000 = \$2,500

Truck rental required if boxes exceed half a ton [*]

30% chance of overweight boxes

\$200 per day rental, 10 days required

P * I = 0.3 * 200 * 10 = \$600

[*]Truck rental risk may not be of sufficient consequence that it would make the list of risks to watch. Project manager may set a dollar threshold of P * I that would exclude such minor risk events.

Once the P * I calculations are made, the project team sets a threshold for risks that will be actively managed and are exposed to the project team for tracking. Other risks not above the threshold go on another list of unmanaged risks that are dealt with as circumstances and situations bring them to the forefront.

### Unmanaged Risks

Project managers cannot ordinarily devote attention to every risk that anyone can think of during the course of the project life cycle. We have discussed several situations where such a phenomenon occurs: the paths in the network that are not critical or near critical, the risks that have very low P * I, and the project activities that have very low correlation with other activities and therefore very low r2 figures of merit. The fact is that in real projects, low-impact risks go on the back burner. The back burner is really just another list where the activities judged to be low threats are placed. Nothing is ever thrown away, but if a situation arises that promotes one of these unmanaged risks to the front burner, then that situation becomes the time and the place to confront and addresses these unmanaged risks.

[6]Schuyler, John, Risk and Decision Analysis in Projects, Second Edition, Project Management Institute, Newtown Square, PA, 2001, pp. 35 and 52.

[7]Various types of utility factors can be applied to different risks and different cost accounts in the WBS. For instance, the utility concepts in software might be quite different from the utility concepts in a regulatory environment where compliance, or not, could mean shutting down company processes and business value. Generally, if the downside is somehow deemed unaffordable or more onerous than the unweighted impact of the risk, then a weight, greater than 1, is applied to the risk. The utility dollars = real dollars * risk-averse factor. For instance, if the downside of a software failure is considered to have 10 times the impact on the business because of customer and investor relationships than the actual dollar impact to the project, then the equation for the software risk becomes utility dollars = real dollars * 10.