# Eight to Late

Sensemaking and Analytics for Organizations

## The reference class problem and its implications for project management

### Introduction

Managers make decisions based on incomplete information, so it is no surprise that the tools of probability and statistics have made their way into management practice. This trend has accelerated somewhat over the last few years, particularly with the availability of software tools that simplify much of the grunt-work of using probabilistic techniques such as Monte Carlo methods or Bayesian networks. Purveyors of tools and methodologies and assume probabilities (or more correctly, probability distributions) to be known, or exhort users to determine probabilities using relevant historical data. The word relevant is important: it emphasises that the data used to calculate probabilities (or distributions) should be from situations that are similar to the one at hand. This innocuous statement papers over a fundamental problem in the foundations of probability: the reference class problem. This post is a brief introduction to the reference class problem and its implications for project management.

I’ll begin with some background and then, after defining the problem, I’ll present a couple of illustrations of the problem drawn from project management.

### Background and the Problem

The most commonly held interpretation of probability is that it is a measure of the frequency with which an event of interest occurs. In this frequentist view, as it is called, probability is defined as the ratio of the number of times the event of interest occurs to the total number of events. An example might help clarify what this means: the probability that a specific project will finish on time is given by the ratio of the number of similar projects that have finished on time to the total number of similar projects undertaken (including both on-time and not-on-time projects).

At first sight the frequentist approach seems a reasonable one. However, in this straightforward definition of probability lurks a problem: how do we determine which events are similar to the one at hand? In terms of the example: what are the criteria by which we can determine the projects that resemble the one we’re interested in? Do we look at projects with similar scope, or do we use size (in terms of budget, resources or other measure), or technology or….? There could be a range of criteria that one could use, but one never knows with certainty which one(s) is (are) the right one(s). Why is it an issue? It’s an issue because probability changes depending on the classification criteria used. This is the reference class problem.

In a paper entitled The Reference Class Problem is Your Problem Too, the philosopher Alan Hajek sums it up as follows:

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified.

Incidentally, in another paper entitled Conditional Probability is the Very Guide of Life, Hajek discusses how the reference class problem afflicts all major interpretations of probability, not just the frequentist approach. We’ll stick with the latter interpretation since it is the one used in project management practice and research… and virtually all the social and natural sciences to boot.

### The reference class problem in project management

Let’s look at a couple of project management-related illustrations of the reference class problem.
First up, consider the technique of reference class forecasting which I’ve discussed in this post. Note that reference class forecasting technique is distinct from the reference class problem although, as we shall see in less than a minute, the technique is fatally afflicted by the problem.

What’s reference class forecasting? To quote from the post referenced earlier, the technique involves:

…creating a probability distribution of estimates based on data for completed projects that are similar to the one of interest, and then comparing the said project with the distribution in order to get a most likely outcome. Basically, [it] consists of the following steps:

1. Collecting data for a number of similar past projects – these projects form the reference class. The reference class must encompass a sufficient number of projects to produce a meaningful statistical distribution, but individual projects must be similar to the project of interest.
2. Establishing a probability distribution based on (reliable!) data for the reference class. The challenge here is to get good data for a sufficient number of reference class projects.
3. Predicting most likely outcomes for the project of interest based on comparisons with the reference class distribution.

Now, the key assumption in reference class forecasting is that it is possible to identify a number of completed projects that are similar to the one at hand. But what does “similar” mean? Clearly the composition of the reference class depends on the similarity criteria used, and consequently so does the resulting distribution. Reference class forecasting is a victim of the reference class problem!

The reference class problem will affect any technique that uses arbitrary criteria to determine the set of all possible events. As another example, the probability distributions used in Monte Carlo simulations (of project cost, duration or whatever) are determined using historical data. Again, typically one selects projects (or tasks – if one is doing a task level simulation) that are similar to the one at hand. Defining “similar” is left to common sense or expert judgement or some other subjective approach. Yet, by the most commonly used definition, a project is a “temporary endeavor, having a defined beginning and end, undertaken to meet unique goals and objectives”. By definition, therefore, we never do the same project twice – at best we do the same project differently  (and the same applies to tasks). So, despite ones best intentions and efforts, historical data can never be totally congruent to the situation at hand. There will always be differences, and one cannot tell with certainty that those differences do not matter.

Truth be told, most organizations do not retain data on completed projects – except superficial stuff that isn’t much use. The reference class problem seems to justify the position of this slack majority. After all, why bother keeping data when one isn’t able to use it to predict project performance. This argument is wrong-headed: although one cannot use it to calculate probabilities, historical data is useful because it keeps us from repeating our errors.  Just don’t expect the data to yield reliable quantitative information on probabilities.

Before I close this piece, I should clarify that there are areas in which the reference class problem is not an issue. In physics, for example, the discipline of statistical mechanics is founded on the principle that the average motion of large collections of molecules can be treated statistically. Clearly, there is no problem here: molecules are indeed indistinguishable from each other, so it is clear that a particular molecule (of a gas in a container of carbon dioxide, say) belongs to the reference class of all carbon dioxide molecules in that container. In general this is true of any situation where one is dealing with a large collection of identical (or very similar) entities.

### Conclusion

The reference class problem affects most probabilistic methods in project management  and  other areas of the social sciences. It is a problem because it is often impossible to know beforehand  which attributes of the objects or events of interest are the most significant ones. Consequently it is impossible to determine with certainty whether or not a particular object or event belongs to a defined reference class.

I’ll end with an anecdote to illustrate my point:

Some time ago I was asked to provide estimates for design work that was superficially similar to something I’d done before. “You’ve done this before,” a manager said, “so you should be able to estimate this quite accurately.”

As many best practices and methodologies recommend, I used a mix of historical data and “expert” judgement (and added in a dash of padding) to arrive at (what I thought was) a robust estimate. To all you agilists out there, an incremental approach was not an option in this case.

I got it wrong – badly wrong. It turned out that the unique features of the project, which weren’t apparent at first, made a mockery of my estimates. I didn’t know it then, but I’d fallen victim to the reference class problem.

Finally, it should be clear that although my examples are project management focused, the arguments are quite general. They apply to all areas of management theory and practice, and indeed to most areas of inquiry that use probabilistic techniques. To use the words of Alan Hajek:  the reference class problem is your  problem too.

Written by K

May 13, 2010 at 11:42 pm

### 14 Responses

1. […] This post was mentioned on Twitter by Pat and Sara BROCA, Kailash Awati. Kailash Awati said: The reference class problem and its relevance to (project) management: http://bit.ly/bbd463 […]

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2. K,
Another superb contribution. I’ve forwarded this to several “like minded” PMs and a few that haven’t a clue about probabilistic modeling in the project domain.

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Glen B Alleman

May 14, 2010 at 10:27 am

• Glen,

When I was working in physics I used to think that the reference class problem was a nitpicky non-issue. It was only when I started working with probabilities in PM and the social sciences that I realised just how big a problem it can be.

Thanks for the feedback – much appreciated!

Regards,

Kailash.

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K

May 14, 2010 at 6:34 pm

3. […] Techniques such as reference class forecasting have been proposed to improve estimation for projects where incremental approaches are not possible (infrastructural projects, for example). However, this technique is subject to the reference class problem. […]

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4. […] How does one decide on what makes up the population of all events. This is sometimes called the reference class problem. […]

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5. […] actually dissimilar in ways that are critical. I’ve seen this happen over and over again. See my post on the reference class problem for a discussion of an estimation technique that is prone to incorrect analogical […]

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6. […] The particular customer may differ in important ways from those used in estimating the probability.This is a manifestation of the reference class problem. […]

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7. […] the one at hand, but actually differs in critical ways.  See my posts on false analogies and the reference class problem for more on this […]

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8. […] be sure that the historical tasks are similar to the one at hand in ways that matter (this is the reference class problem).  As Shim Marom warns us in this post, all our predictions depend on the credibility of our […]

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9. […] gets to one of the big problems with probability distributions which Kailash tells me is called the Reference class problem. How can you pick a representative sample? In some situations completely random might actually be […]

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10. […] question to answer, it is critical as far as the relevance of the estimate is concerned. See my post on the reference class problem for more on this […]

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11. […] Before closing this section, I should mention that the reference class problem has implications for many professional disciplines. I have discussed its relevance to project management in my post entitled, “The reference class problem and its implications for project management”. […]

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12. […] This is essentially the support interpretation (interpretation 3 above).  However, although this seems reasonable, there is a problem: tasks that are superficially similar will differ in the details, and these small differences may turn out to be significant when one is actually carrying out the task.  One never knows beforehand which variables are important. For example, my ability to finish a particular task within a stated time depends not only on my skill but also on things such as my workload, stress levels and even my state of mind. There are many external factors that one might not even recognize as being significant. This is a manifestation of the reference class problem. […]

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13. […] In the world of software development we are asked to exhibit the same assessment skills with the appreciation that our reference class might not be obvious up front – i.e we might be having a Reference Class Problem. In a nutshell, this problem “…arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified ” (from The Reference Class Problem is Your Problem Too, in Kailash Awati’s The reference class problem and its implications for project management). […]

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