Abstract
Managing projects with multiple risks and uncertainties is central to the art of project management. How do you predict possible events one month in the future, let alone for the entire duration of a project? How long will the project take given many uncertainties in the project scope? Are your suppliers still going to be in business? What would the project cost given the uncertainties in financing? When assessing risks and uncertainties, project managers often rely on intuition rather than logic and comprehensive analysis. There are so many analytical techniques and tools, some of which are very complex and require a lot of effort to perform and others that are very industry specific. However, there are some very easy to use and very effective methods for risk management and risk analysis. One of them is expected value analysis. This analysis is more of a mental exercise rather than a strict and formal project management process. At the same time, going through the expected value thinking process may significantly improve the quality of decisions.
At the time of uncertainties and risks, the most
important thing is not to lose a head.
Marie Antoinette (allegedly)
Which Risk is the Most Dangerous?
We must be able to assess the probability and impacts of project risks properly. Which risk is greater: a delay in project financing or a low-quality component? Here is an example: As you go about your life at home, at work, and even on vacation, you are surrounded by a myriad of risks. When you step out your door, having managed to avoid a house fire, you could be hit by debris from a plane flying overhead or struck by a falling branch. According to official statistics, 600 Americans each year fall out of bed and die (Kluger, 2006). When you wake up, you are at risk for a heart attack and poisoned toothpaste. When you go to work, you might collide with a lamp pole while driving or die in a car accident. Finally, having successfully avoided all of these risks, you arrive at work and discover that there is now a risk that your project will be over budget by 5%. Compared with the risks with lethal consequences, which you have just avoided, the over-budget project should be your least concern. Nevertheless, for some reason, you are more preoccupied with project delays and far less with traffic accidents. You might ask how we made this assumption. In fact, 411 people died from electrocutions in the United States in 2001, or 0.63 per million (Wrong Diagnosis, 2008). At the same time, we were unable to find any official statistics on how many project managers died due to budget overruns.
Many of the difficulties that we cause for ourselves in projects, and in our lives in general, occur because we are not able to rationally assess risks. In this paper, we are going to learn some of the basics about risk analysis.
Are You Afraid of Falling Asteroids?
How do you rank project risks? Which project risk represents a greater danger to your project scope, duration, and budget? Do you think asteroids represent a real danger? Should we do something to protect earth against asteroids? Here are a few facts about asteroids:
- The probability that a big asteroid will hit Earth between now until the end of Earth’s lifetime equals 1.
- There are no confirmed human deaths due to asteroid impacts.
- The chance of been killed by an asteroid on an annualized basis is somewhere between the chance of being killed by a shark attack and bee stings (Lynch, 2008).
This means that if you are concerned about been killed by a shark or a bee, you should be concerned about asteroids as well.
What we are illustrating here is our analysis of this risk. We determined the probabilities for a risk and compared the probabilities of these risks with others; by doing this, we were able to put the information regarding a potential asteroid impact into perspective. Based on this information, we can make an informed decision regarding how we should view this risk. As it happens, the risk of asteroid impacts is a real one and scientists are looking at ways to reduce the probability, although blowing it up with a nuclear blast, as in the movie “Armageddon,” does not appear to be a good idea. More likely, in the event that a large asteroid’s orbit takes it into close proximity to Earth, it may be possible to deflect it using either a nuclear blast or by hitting it with a heavy fast-moving probe. So, we are not completely doomed!
The problem with risk is that people often do not perform the necessary level of analysis and even when they do, the results may not be very intuitive. To further complicate things, different people and organizations have different risk attitudes about risk, which also affects their decisions.
What is Risk Attitude?
Built between 1985 and 1989, the Sayano–Shushenskaya hydroelectric power station, on the Yenisei River in Siberia, was the sixth largest hydroelectric power station in the world, with three times the power generation capacity of the Hoover Dam (Exhibit 1).
Exhibit 1: The Sayano–Shushenskaya hydroelectric power station
Why are we talking about it in the past sense? On 17 August 2009, the Sayano–Shushenskaya hydroelectric power station violently broke apart, flooding the turbine hall and engine room. The ceiling of the turbine hall collapsed, 9 of 10 turbines were damaged or destroyed, and 75 people were killed (Demchenko, Krasikov, et. al. 2009). The entire plant output of 6400MW, a significant portion of the supply to the local grid, was lost, leading to widespread power failure in the local area and forcing all major users in the regions (e.g., aluminum smelters) to switch to diesel generators.
How did this happen? As it turns out, turbine 2 had had a long history of problems prior to the 2009 accident. The turbine underwent a number of repairs, most recently between January and March 2009 in response to an elevated vibration emanating from it. By the beginning of July, the vibration had exceeded specification and continued to increase with accelerated speed. On the night of 16-17 August, the vibration level jumped substantially. By the following day, the vibration levels were extreme and now registering with seismic instruments in the plant. During attempts to shut it down, the rotor inside the turbine was pushed up, which, in turn, created pressure pushing up on the turbine cover.
At 08:13 local time, there was a loud bang from turbine 2. The turbine cover shot up and the 920-ton rotor shot out of its seat. Water spouted from the cavity of the turbine into the machinery hall. As a result, the turbine hall and rooms below were flooded. At the same time, an alarm was received at the power station’s main control panel, and the power output fell to zero, resulting in a local blackout. The steel gates to the water intake pipes of turbines, weighing 150 tons each, were closed manually by opening the valves of the hydraulic jacks keeping them up. Seventy-four people were later found dead, while 1 person was listed as missing, but probably also dead.
Turbine 2 had major structural defects since its installation. Some of these defects were known well before the accident. A former power station director actually warned about the potential problem ten years before the accident. Nevertheless, the automatic system which was designed to shut off water flow in case of high vibration was not engaged. Before the accident, when vibration increased dramatically, it was possible to perform an emergency shutdown of the turbine by shutting down water. But, apparently, in this case the people who were operating the station did not understand the potential risk impact of a turbine failure. In other words, the people who were trying to fix the problem before the accident and those who operated the troublesome turbine had a high risk tolerance: they were willing to accept higher level of risk.
People always have an attitude toward risk. David Hillson and Ruth Murrey-Webster (Hillson & Murrey-Webster 2007) suggested a spectrum of risk attitudes (Exhibit 2 and Exhibit 3). The vertical axis of the charts represents uncertainty; the horizontal axis represents different individuals or groups.
Exhibit 2: Risk Attitudes
Not only individuals but also groups, such as companies, will possess a certain attitude toward risk (Hillson and Murrey-Webster 2008). For example, the street gangs from West Side Story were risk seeking. Apparently, the same could be said for the banks and financial companies in the center of the 2008 sub-prime mortgage crisis. Here is an interesting coincidence: both the gangs and many of the financial companies were from New York City, and the risk-seeking activities they both engaged in came to a bad end.
Some organizations, especially large companies in traditional areas such as oil and gas and manufacturing, are risk averse. They significantly reduce activities during downturns in the economy, even though it will potentially lead to losses over the next few years. The management of organizations is comprised of individuals who have their own risk attitudes; at the same time, the attitude of an organization will affect the risk attitudes of members of the organization.
Exhibit 3: Spectum of Risk Attitudes
Risks versus Opportunities in Project Management
Remember the movie My Blue Heaven, starring Steve Martin and Rick Moranis? Vincent ‘Vinnie’ Antonelli (Steve Martin) is a former Mafia figure turned informant. While under the witness protection program in the suburbs, Vinnie becomes engaged in various criminal activities. The truck which is supposed to bring him supplies for his criminal businesses, actually delivers empty water jars. “Somebody see a problem, I see an opportunity,” notes Vinnie and he decides to use the jugs to collect donations from his community toward the construction of a youth sports facility. In reality, his intent is to pocket the proceeds.
In spite of his bumbling, Vinnie was absolutely right: in many cases, opportunities accompany threats. For example, a downturn in the economy can cause severe hardships, but it also presents an opportunity for many to successfully invest, start new businesses, or learn new technologies. Project delays are an opportunity to review issues, regroup, and improve management not only for current projects, but future projects as well.
Most people know that risks and opportunities are related but this seems to be counterintuitive. How can threats be converted to opportunities? Here is one explanation. In the same way we are surrounded by a myriad of threats, we are surrounded by a myriad of opportunities. In most cases, we are so preoccupied with threats that we don’t analyze the opportunities. Here is an observation. In the Risk Management chapter in A Guide to the Project Management Body of Knowledge (PMBOK® Guide)(2008) , the focus is primarily on the management of threats, but in fact treats threats and risk almost synonymously. There is no equivalent section on managing opportunities, although opportunities are mentioned. There are a number of risk analysis and risk management groups or societies, but they are almost all thought of as being preoccupied with threats.
Opportunities do not always coincide with risks. Sometimes the impact of a risk is quite severe and any opportunity cannot completely compensate for losses; however, it is important to remember that even in bad situations, there is room for opportunities.
Introduction to Expected Value Convent
Questions regarding lotteries are pretty common fodder for us, when people realize that our field touches on topics like risk and decision analysis. “So, if I buy lottery tickets and I know the chances of winning are supposedly really small, am I just throwing away my money or is there some way to boost my chances?” Needless to say, we are never short of advice, and it mostly follows along these lines, “You would most likely get a better return using other investment vehicles, like a savings account or bonds. On the other hand, lotteries can be really fun as long as winning is not part of your retirement planning. So, if you want to have it as part of your entertainment budget, go ahead, knock yourself out.” When really pressed, we may digress into a more detailed discussion on expected value and whether anyone can justify playing the lottery, but by that point, most of our audience will have moved on.
Let us assume that you bought 20 scratch-and-win lottery tickets. What would be the total return for all tickets if the price for one ticket is US$1? In other words, if you spent US$20, how much should you expect in return? In fact, over the past several years, we have been conducting experiments on this exact subject. When we have our presentations on risk and decision analysis, we buy US$20 worth of scratch-and-win lottery tickets, which we randomly handed out to attendees. During the presentation, we have the attendees check their tickets, and the results have been very consistent. After spending US$20 for tickets, the payout has usually ranged from US$7–12, we have never won more than we spent on the tickets.
The theory behind this is very straightforward. Only a certain percentage from the ticket sales revenue goes toward prizes, which is normally around 50%. So, the overall chance to win a lottery is around 50%, and the rest is used to pay costs for marketing and sales, but the vast majority of the owner’s take is pure profit that usually gets funnelled into public goods or charities, so we do not feel so badly about the extended losing streaks that are common for those who play the lottery. “If it wasn’t for the lottery, we would have to pay more taxes.” Sort of like a bitter medicine with a tiny bit of honey. In this case, US$0.50 is the expected value of playing one game. So, why would people play under such measly payout conditions? Quite simply, really, because there is a small chance to win a prize that is exponentially larger than the cost of the tickets. It is because of the potential for the large payout we would also argue that playing the lottery is a rational behavior. When discussing this with an acquaintance who participates in an office lottery pool, who also happens to be both a professional statistician and avid gambler, he said “Of course I now about all the odds, but somebody is winning!" Therefore, in each particular game, you may win more or less than the expected value. Risk takers hope that they will receive more than the expected value. Risk-averse people see the equation from the other side, and believe that the chances are that they will receive less than the expected and therefore do not play.
Expected value is not the prize you expect to win. If there is a million-dollar lottery, the expected value is not the prize; rather, expected value is an indicator or measure that will help you make better choices in uncertain situations. Expected value is calculated by multiplying each possible outcome by its probability of occurrence and then summing the results. Expected value can be calculated based on any parameters that are possible to measure, such as cost, price, duration, or number of units.
Here is a small test for you. Conrad White, the former CFO of Efron, Inc. who served time for fraud and embezzlement now needs to decide on a career. Which project should bring him more value?
- Accept the invitation of his prison buddy Robin Hoode, and rob the bank at Parkland Boulevard and 10th Street. The chance of being caught is 80%. The potential payout is US$200,000.
- Become an Autumnfield city council person. The salary is US$80,000, but to get elected, Conrad needs to spend US$30,000 for the posters and mail campaign “Conrad White for Change” and “Vote for Honesty and Accountability”.
- Become the food critic for the Autumnfield Sun, which pays an annual salary of US$20,000.
When you multiply the probability of the payout of each one of Conrad White’s alternative projects, you would get an expected value for the alternative. The alternative with the highest expected value (the city council person position) would bring Conrad White the most money.
Situations in which we can use simple expected value calculations arise all the time. When you buy a sofa in a furniture store for US$1000, the salesman will probably offer you damage insurance for around US$50. Without insurance, let’s estimate that it would cost you US$200 to repair any damage. In addition, the chance that your sofa will be damaged so that it will require a repair is 10%. In this scenario, the expected value of a repair is US$200 X 10% = US$20, which is significantly less than insurance cost. Therefore, unless you have five boys who like to bounce up and down on your sofa with swords, forks, and scissors, you should probably pass on the insurance.
Expected value will help you decide on a course of action in more complex cases. For example, lawyers use expected value when they make recommendations to their clients regarding any legal actions. Would it be better to take a plea bargain and plead guilty to lesser charges or face the chance that you might lose at trial? Oil companies use expected value to calculate the volumes of oil and gas they can produce given the uncertainties in petroleum reserves. Sales managers can use expected value to estimate sale figures. Governments are supposed to use expected value to estimate potential tax revenue. Because most governments are pathologically in debt, whether they understand the concept is open to question, or perhaps they just use unrealistic probabilities (100%) when performing expected value analysis on revenues.
For project managers, expected value is a simple and very effective analytical technique that can help us reduce the effects of many project illusions. It is mostly a simple mental exercise and is part of the Project Risk Management Process described in the PMBOK® Guide, chapter 11 (Project Management Institute, 2008). How much will the project cost given the chance of delay? Since there is always a chance that a supplier may not be able to deliver components on time, which supplier should you choose?
Let’s return to our discussion on lotteries. If your idea of winning is making more money than you spent, then our recommended strategy is “Don’t do it.” However, if you find that you cannot help yourself, here is another suggestion. Pick a number that appears to be non-random (e.g., 1, 2, 3, 4, 5…). This will not increase your chances of winning, but if you win, you will be less likely to share the prize with someone else. Why? Most people think that these numbers are not random enough and don’t select patterns. In reality, 1, 2, 3, 4, 5 is as random as any other combination of numbers.
How People Ignore Expected Value
The advantage of expected value is that you do not need to perform any complex calculations. You simply multiply the probabilities on possible outcomes for different scenarios and then compare the results. Even though it is simple, people do not bother to do these calculations even though substantial sums may be at risk.
In 2005, administrative law Judge Roy L. Pearson filed a civil case in the District of Columbia. He claimed that a dry-cleaning company had lost his trousers. Over a period of time, the owners of the dry-cleaning business made three settlement offers of US$3000, US$4600, and US$12,000, respectively, all of which were rejected by Pearson. Claiming the shop’s “satisfaction guaranteed” sign misled customers Pearson sought US$1500 for every day the dry-cleaning operation was in business, over a four-year period of time, which totalled US$54 million. Needless to say, the case generated a significant amount of attention and ridicule. Fortune magazine listed the case at #37 in its “101 Dumbest Moments in Business” of 2007 (Fortune, 2007). Eventually, after years of working its way through the legal system, a federal court rejected Pearson’s appeal (Alexander, 2009). Pearson must have been a real risk taker. What was the chance that he would be successful in getting US$54 million for a lost pair of pants? We imagine that he was probably angling for a lavish settlement rather than public humiliation. One can always make the case that Pearson did perform an expected value analysis, it was just that his assumptions must have been horribly skewed; maybe he should have had a job working for the government providing tax revenue forecasts. In any event, Pearson’s poor decision regarding the expected value of his legal actions only managed to increase the misery, not only for himself, but for the unfortunate owner of the dry-cleaning business. As it actually turned out, the pants in question were never really lost; the dry cleaners had merely temporarily misplaced them.
Although it might surprise some of our leaders, union leaders often have a good understanding of the underlying business situation facing their employers and use this knowledge to negotiate realistic compensation packages. On the other hand, there are also many examples in which they ignore expected values and reality. In 2007, union members employed by the Greyhound Bus Company in Western Canada went on strike (Komarnicki, 2007). One week into the strike, after it had caused millions of dollars in lost revenue and wages, the union accepted a new offer from the company. Notably, this offer was less than the original offer that had initially sent the union to the picket line. Union leaders probably were so overwhelmed by their membership’s negative emotions toward management that they acted rashly without first performing an analysis that should have included an expected value for their final decision.
Intentionally or unintentionally, overlooking expected value analysis is very common in project management. Large construction projects may have to go through an environmental assessment, which could be a long and very expensive process that would significantly delay the project and, hence, increase project cost. A valid question might be to ask: What value does the assessment actually bring to the project? Does it actually protect the environment or would it be better to just save the money spent on the assessment and spend it on activities that actually protect the environment? It is possible to make a calculation based on the expected value principle, but the validity of the bureaucratic procedures are rarely scrutinized.
Incorrect Probability and Incorrect Expected Value
There is another issue with adoption of the expected value approach. How can we be sure that the estimated probabilities and outcomes are correct? For example, you have decided to purchase a new home and have two options (Exhibit 3):
Exhibit 3: Estimating Probabilities
- You can purchase a home for US$300,000 but it will require an additional US$100,000 for renovations.
- You can purchase a brand new home for US$500,000
If everything was straightforward, the first option would be the obvious choice; even taking into account the hassles of managing the renovations, you would save US$100,000. But, in reality, nothing is ever this straightforward. Although the home sales price is determined, the cost of renovations is subject to multiple uncertainties. Because you would like to make the renovations at as low a cost as possible, you may dismiss evidence that the costs could be significantly higher. The contractor has warned you that they have no idea what shape the house is in until they start removing some of the flooring and walls to reveal the underlying wood frame. The house could be in pristine condition, but there is a chance, given the age of the house, that there will be significant rot, outdated plumbing, or electrical systems that are not up to current building codes. If any of these conditions is present, it will drive up the cost of the renovations, and if more than one of these conditions is present, which is likely given the age of the home, it will significantly drive up the cost. In the end, you determine that there is really only a 20% chance that the cost will be US$100,000, and an 80% chance that the cost will be US$325,000. Therefore, the expected cost of the renovations would be:
20%* US$200,000 + 80%* US$325,000 = $300,000.
After this analysis (option 2) buying a new home becomes much more attractive than option 1, which is why it is so important that probabilities are estimated as accurately as possible. If you underestimated the probability that the house would require more extensive renovations, not only would you be out of pocket for a lot more money, but you would have to live with the reality that you paid an extra US$100,000 for living in a worn-out home, an issue that would probably become a popular topic of discussion with your spouse. So, performing expected value analysis before making decisions not only saves projects but can do wonders for your marriage as well.
Following is an example of the same problem with assessing probabilities but for a much larger project. The “Big Dig “is the unofficial name of the Central Artery/Tunnel Project (CA/T), a transportation megaproject in Boston and is a good example in which the expected value analysis would have contributed to better, less costly decisions (Exhibit 4).
Exhibit 4: “Big Dig” Project in Boston
The “Big Dig,” at the time, the dubious distinction of being the most expensive highway project in the United States. Originally, in 1985, the total project cost was estimated at US$2.8 billion (in 1982 dollars), but by 2006, the total accumulates costs were over US$14.6 billion (US$8.08 billion in 1982 dollars) (Kwak, 2008). Cost overruns were mostly attributed to politics, added scope, and problems with oversight. In particular, inflation and growth in scope added US$2.7 billion, environmental compliance added US$3.0 billon, and an accelerated schedule added US$0.6 billion. One issue that arose during the project was that the project management plan had been based on inadequate survey of the central artery. To save time and money, project planners took a risk and did not perform a detailed survey of this key feature of the project. With great hindsight, we can now say that, as in many cases, this attempt to save money led to spending more. The failure to perform a comprehensive survey had a direct cost of US$26 million to tax payers and perhaps much more due to indirect effects. Another serious issue was related to the large number of water leaks in the tunnels. The contractors used a proven technology, called “slurry wall panel,” to create the tunnels, but in this particular case, the technique led to approximately 1100 leaks, which needed remediation. Risks were not only technical in nature, but political as well. Local politicians were in an uproar when they discovered the water leakage in the tunnels. In reality, the extent of the leakage was insignificant and did not pose any threat to the integrity of the tunnels. Nevertheless, the project team was forced to bend to accommodate the concerns of the politicians, and the contractors were ordered to seal all of the leaks. In the end, it was the cumulative effect of all these events that caused the huge cost overruns. Expected value analysis of different technological scenarios would potentially discover the level of exposure these risks represented and help the project team select a better plan for the project.
Conclusions
Our assessment of project risk probabilities and impact depends on our risk attitude. People have different attitudes toward risk: they can be risk tolerant, risk seeking, risk averse, or risk addicted. In project management, opportunities often exist alongside threats; they are often overlooked and not analyzed. Expected value analysis is an easy to use analytical technique that helps make better choices. It requires small calculations, which can be done without any specialized tools. Even simple expected value analysis is not always properly performed by project managers, and, as a result, project managers take unnecessary risks.
