Expected Utility and Agile

Mar 30, 2016

Selling Agile

When convincing others to adopt agile practices, I have often found it useful to discuss those practices in terms of risk reduction. For example, we can talk about continuous integration in terms of reducing the “schedule risk” that results from performing all the integration at the end.

Unfortunately, selling agile in this way has a major disadvantage, which is that people tend to associate reduced risk with reduced cost, even though that is not really a valid association. In fact, I’m not sure that there’s any reason to expect agile to be less expensive in the “everything goes well” case, because there is an increase in certain repetitve activities like planning and integration. Thinking about this problem led me to start thinking about choosing agile in terms of utility theory, which is used in economics to try to explain how humans actually make decisions.

Expected Value

The expected value, or the mean, is very easy to understand and use; unfortunately it does not really consider risk.

Imagine that we have some software work that we can choose to perform either using agile practices or using a more traditional approach. To keep things simple, we’ll decide that the value of the project is the same either way, and we’re not highly concerned about schedule or about getting an early working version, so we just care about performing the work at the lowest cost.

This may seem like an over-simplified assumption, but there are plenty of plausible examples, like having the software ready for a new car or airplane; in many cases software is not the schedule driver on that kind of effort, and there is no where for an early version to run. So the only remaining advantage to agile is the ability to try out working code in a simulated environment, which is a risk reducer but not value from the end user’s perspective.

But even in this case, we buy the idea that agile practices will reduce risk. So we might say that if we use our traditional approach, the project will cost $1m with a standard deviation of $500k, and if we use an agile approach, the project will cost $1m with a standard deviation of $200k.

At this point, in a lot of organizations, we would just report the expected value, which is the average expected cost. (For that matter, in a lot of organizations we would only be coming up with a single number estimate, so we wouldn’t be able to quantify the lower risk, much less put it in terms of standard deviation.)

If we only look at the expected value we don’t have any reason to prefer the agile approach; in fact, we might avoid it because people quite rightly prefer not to change for no reason. (“And the Gods of the Copybook Headings said: ‘Stick to the Devil you know.’”.)

While this is a contrived example, I have absolutely seen similar situations, where a team suggests process improvement with the intent of reducing variability, only to be asked for some justification in terms of lower cost. And what tends to happen is that software teams that “know” agile is a move in the right direction will sometimes agree to lower their estimates, because a better process must mean that there will be cost savings, right?

Risk Aversion

The problem with the above way of approaching things is that, in the terms of economists, we’ve taken a “risk neutral” strategy to comparing the two approaches. And while it is true that some economics argue that companies should take a risk neutral strategy, because over time successful projects will balance out unsuccessful ones, in practice large projects that fail can have unrecoverable negative impacts, and if anything we software estimators tend to underestimate risk.

So in practice we probably want to have a risk averse strategy. This means that we would potentially be willing to pay more if it means we reduce the potential downside.

To see how this works, consider a simple example. You are on a game show and the host is offering you a choice. You can flip a coin; if the coin is heads you win $100k, but if it’s tails, you get nothing. Or, you can walk away with $25k right now. Depending on your level of risk aversion, you may choose to flip the coin at this point. But before you flip the coin, the host increases the “sure thing” offer to $40k. At this point, even though your expected value is higher with the coin flip, most people would take the money.

This is the primary insight of utility theory, which is that ordinary statistics doesn’t explain how people really behave, because they don’t consider their comfort with risk. (On the other side, a person who loves to gamble will spend hours taking risks with a negative expected value, because of the small chance of a big payout.)

Expected Utility

So how does utility work in practice? There are different types of equations, but the simplest uses an exponential function.

In this equation, c is whatever we want more of, and u(c) is the “utility” or benefit we receive from having a certain amount of c. (To express a desire for reduced cost, we would just use the negative of the cost.) The variable a is our level of risk aversion. Settling on this can be very challenging; it is usually done through “games” such as the one described above, where people are asked which of two scenarios they would choose. This is repeated until a reasonably consistent value is achieved.

Also, since our ability to acquire c is uncertain, we need to extend this utility function with the notion of “expected utility”. This is the equivalent to expected value, except instead of just finding the mean for c, we are finding the mean for the utility function u(c) given the distribution of possible outcomes for c.

Unfortunately, we have introduced some additional unknowns here, because in addition to finding a utility function, which is challenging, we also need to know the distribution of c, which is challenging. Here again some simplifying assumptions can help. For example, for a normally distributed c, our expected utility function is:

This function will increase as long as this increases:

Looking at this expression, it is easy to see that in our earlier example, we would have a higher expected utility where we have a lower standard deviation. And we can determine the value of the risk reduction by choosing a risk posture and then setting the expression equal in the two scenarios. For example, for a risk aversion value of a = 0.5, we would be willing to pay up to $75k more for the reduction in standard deviation of $300k.


If we really believed that we should be risk averse, we would be willing to accept an approach that is more expensive as long as it is sufficiently lower in risk. In that case, it would be possible for the agile practitioner to say, “switching to agile practices may be more expensive, because we will be performing planning and integration in small increments. However, it will reduce risk and therefore is worth doing.”

Of course, to say that, there are a few things we might be expected to produce, such as an estimate of risk before and after changing to agile, and some sense of whether the additional expense is worth it, given our risk posture. I’m interested in exploring the concept further to see if there would be a reasonable way to quantify these items and to provide an intuitive explanation for them. However, while I’m interested in what the concept of expected utility says we should do, I’m not convinced that it would be terribly useful. It’s challenging enough to explain agile practices using analogies to assembly lines. Bringing in utility functions is not likely to make the explanations easier.