Delphi and group estimation

A software estimate is a prediction about the future. Software developers were not the first people to formalize processes for making predictions about the future. Starting in the last 1940s, the RAND Corporation’s Delphi project created what became known as the Delphi method, e.g., An Experiment in Estimation, and Construction of Group Preference Relations by Iteration.

In its original form experts were anonymous; there was a “… deliberate attempt to avoid the disadvantages associated with more conventional uses of experts, such as round-table discussions or other milder forms of confrontation with opposing views.”, and no rules were given for the number of iterations. The questions involved issues whose answers involved long term planning, e.g., how many nuclear weapons did the Soviet Union possess (this study asked five questions, which required five estimates). Experts could provide multiple answers, and had to give a probability for each being true.

One of those involved in the Delphi project (Helmer-Hirschberg) co-founded the Institute for the Future, which published reports about the future based on answers obtained using the Delphi method, e.g., a 1970 prediction of the state-of-the-art of computer development by the year 2000 (Dalkey, a productive member of the project, stayed at RAND).

The first application of Delphi to software estimation was by Farquhar in 1970 (no pdf available), and Boehm is said to have modified the Delphi process to have the ‘experts’ meet together, rather than be anonymous, (I don’t have a copy of Farquhar, and my copy of Boehm’s book is in a box I cannot easily get to); this meeting together form of Delphi is known as Wideband Delphi.

Planning poker is a variant of Wideband Delphi.

An assessment of Delphi by Sackman (of Grant-Sackman fame) found that: “Much of the popularity and acceptance of Delphi rests on the claim of the superiority of group over individual opinions, and the preferability of private opinion over face-to-face confrontation.” The Oracle at Delphi was one person, have we learned something new since that time?

Group dynamics is covered in section 3.4 of my Evidence-based software engineering book; resource estimation is covered in section 5.3.

The likelihood that a group will outperform an individual has been found to depend on the kind of problem. Is software estimation the kind of problem where a group is likely to outperform an individual? Obviously it will depend on the expertise of those in the group, relative to what is being estimated.

What does the evidence have to say about the accuracy of the Delphi method and its spinoffs?

When asked to come up with a list of issues associated with solving a problem, groups generate longer lists of issues than individuals. The average number of issues per person is smaller, but efficient use of people is not the topic here. Having a more complete list of issues ought to be good for accurate estimating (the validity of the issues is dependent on the expertise of those involved).

There are patterns of consistent variability in the estimates made by individuals; some people tend to consistently over-estimate, while others consistently under-estimate. A group will probably contain a mixture of people who tend to over/under estimate, and an iterative estimation process that leads to convergence is likely to produce a middling result.

By how much do some people under/over estimate?

The multiplicative factor values (y-axis) appearing in the plot below are from a regression model fitted to estimate/actual implementation time for a project involving 13,669 tasks and 47 developers (data from a study Nichols, McHale, Sweeney, Snavely and Volkmann). Each vertical line, or single red plus, is one person (at least four estimates needed to be made for a red plus to occur); the red pluses are the regression model’s multiplicative factor for that person’s estimates of a particular kind of creation task, e.g., design, coding, or testing. Points below the grey line are overestimation, and above the grey line the underestimation (code+data):

3n+1 programs containing various lines of code.

What is the probability of a Delphi estimate being more accurate than an individual’s estimate?

If we assume that a middling answer is more likely to be correct, then we need to calculate the probability that the mix of people in a Delphi group produces a middling estimate while the individual produces a more extreme estimate.

I don’t have any Wideband Delphi estimation data (or rather, I only have tiny amounts); pointers to such data are most welcome.

Estimate variability for the same task

If 100 people estimate the time needed to implement a feature, in software, what is the expected variability in the estimates?

Studies of multiple implementations of the same specification suggest that standard deviation of the mean number of lines across implementations is 25% of the mean (based on data from 10 sets of multiple implementations, of various sizes).

The plot below shows lines of code against the number of programs (implementing the 3n+1 problem) containing that many lines (red line is a Normal distribution fitted by eye, code and data):

3n+1 programs containing various lines of code.

Might any variability in the estimates for task implementation be the result of individuals estimating their own performance (which is variable)?

To the extent that an estimate is based on a person’s implementation experience, a developer’s past performance will have some impact on their estimate. However, studies have found a great deal of variability between individual estimates and their corresponding performance.

One study asked 14 companies to bid on implementing a system (four were eventually chosen to implement it; see figure 5.2 in my book). The estimated elapsed time varied by a factor of ten. Until the last week this was the only study of this question for which the data was available (and may have been the only such study).

A study by Alhamed and Storer investigated crowd-sourcing of effort estimates, structured by use of planning poker. The crowd were workers on Amazon’s Mechanical Turk, and the tasks estimated came from the issue trackers of JBoss, Apache and Spring Integration (using issues that had been annotated with an estimate and actual time, along with what was considered sufficient detail to make an estimate). An initial set of 419 issues were whittled down to 30, which were made available, one at a time, as a Mechanical Turk task (i.e., only one issue was available to be estimated at any time).

Worker estimates were given using a time-based category (i.e., the values 1, 4, 8, 20, 40, 80), with each value representing a unit of actual time (i.e., one hour, half-day, day, half-week, week and two weeks, respectively).

Analysis of the results from a pilot study were used to build a model that detected estimates considered to be low quality, e.g., providing a poor justification for the estimate. These were excluded from any subsequent iterations.

Of the 506 estimates made, 321 passed the quality check.

Planning poker is an iterative process, with those making estimates in later rounds seeing estimates made in earlier rounds. So estimates made in later rounds are expected to have some correlation with earlier estimates.

Of the 321 quality check passing estimates, 153 were made in the first-round. Most of the 30 issues have 5 first-round estimates each, one has 4 and two have 6.

Workers have to pick one of five possible value as their estimate, with these values being roughly linear on a logarithmic scale, i.e., it is not possible to select an estimate from many possible large values, small values, or intermediate values. Unless most workers pick the same value, the standard deviation is likely to be large. Taking the logarithm of the estimate maps it to a linear scale, and the plot below shows the mean and standard deviation of the log of the estimates for each issue made during the first-round (code+data):

Mean against standard deviation for log of estimates of each issue.

The wide spread in the standard deviations across a spread of mean values may be due to small sample size, or it may be real. The only way to find out is to rerun with larger sample sizes per issue.

Now it has been done once, this study needs to be run lots of times to measure the factors involved in the variability of developer estimates. What would be the impact of asking workers to make hourly estimates (they would not be anchored by experimenter specified values), or shifting the numeric values used for the categories (which probably have an anchoring effect)? Asking for an estimate to fix an issue in a large software system introduces the unknown of all kinds of dependencies, would estimates provided by workers who are already familiar with a project be consistently shifted up/down (compared to estimates made by those not familiar with the project)? The problem of unknown dependencies could be reduced by giving workers self-contained problems to estimate, e.g., the 3n+1 problem.

The crowdsourcing idea is interesting, but I don’t think it will scale, and I don’t see many companies making task specifications publicly available.

To mimic actual usage, research on planning poker (which appears to have non-trivial usage) needs to ensure that the people making the estimates are involved during all iterations. What is needed is a dataset of lots of planning poker estimates. Please let me know if you know of one.