- Quantify the possible outcomes for the project and their probabilities
- Assess the probability of achieving specific project objectives
- Identify risks requiring the most attention by quantifying their relative contribution to overall project risk
- Identify realistic and achievable cost, schedule, or scope targets, given the project risks
- Determine the best project management decision when some conditions or outcomes are uncertain.

Quantitative Risk Analysis generally follows the Qualitative Risk Analysis process. Quantitative Risk Analysis should be repeated after Risk Response Planning, as well as part of Risk Monitoring and Control, to determine if the overall project risk has been satisfactorily decreased. (Refer to Section 11.4.2 in the PMBOK)

**Note:** You quantify the risks with numbers, values, and data. Quantification of the risk can lead to time and cost contingencies for the project, priority of the risks, and an overall risk score. Monte Carlo simulations are typically associated with quantitative risk analysis. Quantitative risk analysis relies on hard numbers. Each risk is assigned a score and not a high, medium, low ranking. You can remember quantitative analysis as the “N” in quantitative and the “N” in numbers.

**Risk Quantification **PMI® defines risk quantification as evaluating risks and risk interactions to assess the range of possible project outcomes. The primary objective of risk quantification is to use a set of structured tools to help decide which risk events warrant a response strategy of some kind. Risk quantification essentially helps in comparing and evaluating options.

**Probability Distributions**

**Expected Monetary Value**

EMV is a statistical technique that calculates the average outcome when the future includes scenarios that may or may not happen. A common use of this technique is within decision tree analysis. Modeling and simulation are recommended for cost and schedule risk analysis because it is more powerful and less subject to misapplication than expected monetary value analysis. To illustrate the expected monetary value concept, suppose that a game of chance can be played for $1.00. It is a very simple game. The bettor pays $1.00 and has a chance to win $50.00. The bettor may also win $2.00 or no money at all. The dollar amounts and probability of winning are as follows:

The bettor would like to know, before actually paying a dollar, what the expected winnings are. The expected value of winnings is the sum of the winning amounts multiplied by their respective probability of occurrence, or”

($50.00 * 0.01) + ($2.00 * 0.10) + ($0.00 * 0.89) =

$0.50 + $0.20 + $0.00 =

$0.70.

Because the bettor can only expect winnings on the average of seventy cents and pays one dollar to play the game, the net payoff is a negative thirty cents. One might believe that most individuals, when forced to face this logic, would choose not to play. However this is a very realistic example of gambling and risk. Many individuals would play this game; because they are willing to accept the risk of losing $1.00 in order to take a chance at winning $50.00. These individuals are risk-prone. The individual who follows the basic logic of this example and does not play is said to be risk-averse.

Expected value is a statistical assessment of project value, not a prediction of final revenue or cost. Generally, in project risk assessment, we assess the best case and the worst case to determine the boundaries. Final actual value will probably fall between the two. The EMV is generally used as input to further analysis (for example, in a decision tree) because risk events can occur individually or in groups, in parallel or in sequence.

**Decision-Tree Analysis**

A decision tree is a method to determine which of two decisions is the best to make. The purpose of the decision tree is to make a decision, calculate the value of that decision, or to determine which decision costs the least. Solving the decision tree provides the EMV (Expected Monetary Value) for each alternative, when all the rewards and subsequent decisions are quantified.

This notion of expected value is prerequisite to the following discussion on decision-tree analysis. Decision-tree analysis attempts to break down a series of events into smaller, simpler, and more manageable segments. Many similarities exist between decision-tree analysis and more complicated forms of management and risk analysis, such as PERT and CPM. All three forms of analysis presume that a sequence of events can be broken down into smaller and smaller segments, to more accurately represent reality.

**Modeling / Simulation**

Project simulations allow the project team to play “what-if” games without affecting any areas of production. The Monte Carlo technique is the most common simulation.

**Monte Carlo Analysis**

A technique that computes, or iterates, the project cost or project schedule many times using input values selected at random from probability distributions of possible costs or durations, to calculate a distribution of possible total project cost or completion dates. This method, also used in Project Time Management, is typically a computer program to estimate the many possible variables within a project schedule. Monte Carlo simulations predict probable risks, not an exact risk.

**Note:** Monte Carlo analysis is considered a superior approach to analyzing the schedule when compared to PERT or CPM. This is true because PERT and CPM fails to account for path convergence and, as a result, tend to underestimate project durations. Another important point is that the choice of statistical distribution used in the Monte Carlo routine can have important effects on the results of the simulation.