Last time out, we determined that mucking with the estimate to account for variance and surprises in projects is in several ways wanting. This time, we’ll make some choices about the tasks and the projects, and see where those choices might take us.

Leave Problem Tasks Incomplete; Accept Missing Features

There are a couple of variations on this strategy. The first is to Blow The Whistle At 100. That is, we could time-box the entire project, which in the examples above would mean stopping the project after 100 hours of work no matter where we were. That might seem a little abrupt, but we would be done after 100 hours.

To reduce the surprise level and make things a tiny bit more predictable, we could Drop Scope As You Go. That is, if we were to find out at some point that you’re behind our intended schedule, we could refine the charter of the project to meet the schedule by immediately revising the estimate and dropping scope commitments equivalent to the amount of time we’ve lost. Moreover, we could choose which tasks to drop, preferring to drop those that were interdependent with other tasks.

In our Monte Carlo model, project scope is represented by the number of tasks that we attempt. After a Wasted Morning, we drop any future commitment to at least three tasks; after a Lost Day, we drop seven; and after a Black Cygnet, we drop 15. We don’t have to drop the tasks completely; if we get close to 100 hours and find out that we have plenty of time left over due to a number of Stunning Successes, we can resume work on one or more of the dropped tasks.

Of course, any tasks that we’ve dropped might have turned out to be Stunning Successes, but in this model, we assume that we can’t know that in advance; otherwise, there’d be no need to estimate. In this scenario, it would also be wise to allocate some task time to manage the dropping and picking up of tasks.

I’ve been a program manager for a company that used a combination of Blow The Whistle and Drop Scope As You Go very successfully. This strategy often works reasonably well for commercial software. In general, you have to release an update periodically to keep the stock market analysts and shareholders happy. Releasing something less ambitious than you hoped is disappointing. Still, it’s usually more palatable than shipping late and missing out on revenue for a given quarter. If you can keep the marketers, salespeople, and gossip focused on things that you’ve actually done, no one outside the company has to know how much you really intended to do. There’s an advantage here, too, for future planning: uncompleted tasks for this project represent elements of the task list for the next project.

Leave Problem Tasks Incomplete; Accept Missing Features AND Bugs

We could time-box our tasks, lower our standard of quality, and stop working on a task as soon as it extends beyond a Little Slip. This typically means bugs or other problems in tasks that would otherwise have been Wasted Mornings, Lost Days, or Black Cygnets, and it means at least a few dropped tasks too (since even a Little Slip costs us a Regular Task).

This is The Perpetual Beta Strategy, in which we adjust our quality standards such that we can declare a result a draft or a beta at the predicted completion time. The Perpetual Beta Strategy assumes that our customers explicitly or implicitly consent to accepting something on the estimated date, and are willing to sacrifice features, live with problems, wait for completion of the original task list, or some combination of all of these. That’s not crazy. In fact, many organizations work this way. Some have got very wealthy doing it.

Either of these two strategies would work less well the more our tasks had dependencies upon each other. So, a related strategy would be to…

De-Linearize and Decouple Tasks

We’re especially at risk of project delays when tasks are interdependent, and when we’re unable to switch the sequence of tasks quickly and easily. My little Monte Carlo exercises are agnostic about task dependencies. As idealized models, they’re founded on the notion that a problem in one area wouldn’t affect the workings in any other area, and that a delay in one task wouldn’t have an impact on any other tasks, only on the project overall. On the one hand, the simulations just march straight through the tasks in each project equentially, as though each task were dependent on the last. On the other hand, each task is assigned a time at random.

In real life, things don’t work this way. Much of the time, we have options to re-organize and re-prioritize tasks, such that when a Black Cygnet task comes along, we may be able to ignore it and pick some other task. That works when we’re ultimately flexible, and when tasks aren’t dependent on other tasks.

And yet at some point, in any project and any estimation effort there’s going to be a set of tasks that are on a critical path. I’ve never seen a project organized such no task was dependent on any other task. The model still has some resonance, even if we don’t take it literally.

A key factor here would seem to be preventing problems, and dealing with potential problems at the first available opportunity.

Detect and Manage The Problems

What could we do to prevent, detect, and manage problems?

We could apply Agile practices like promiscuous pairing (that is, making sure that every team member regularly pairs with every other team member). Such things might to help with the critical path issue. If each person has at least passing familiarity with the whole project, each is more likely to be able to work on a new task while their current one is blocked. Similarly, when one person is blocked, others can help by picking up on that person’s tasks, or by helping to remove the block.

We could perform some kind of corrective action as soon as we have any information to suggest that a given task might not be completed on time. That suggests shortening feedback loops by constant checking and testing, checking in on tasks in progress, and resolving problems as early as possible, instead of allowing tasks to slip into potentially disastrous delays. By that measure, a short daily standup is better than a long weekly status meeting; pairing, co-location and continuous conversation are better still. Waiting to check or test the project until we have an integration- or system-level build provided relatively slow feedback for low-level problems; low-level unit checks reveal information relatively quickly and easy.

We could manage both tasks and projects to emphasize information gathering and analysis. Look at the nature of the slippages; maybe there’s a pattern to Black Cygnets, Lost Days, or Wasted Mornings. Is a certain aspect of the project consistently problematic? Does the sequencing of the project make it more vulnerable to slips? Are experiments or uncertain tasks allocated the task time that they need to inform better estimation? Is some person or group consistently involved in delays, such that training, supervision, pairing, or reassignment might help?

Note that obtaining feedback takes some time. Meetings can take task-level units of times, and continuous conversation may slow down tasks. As a result, we might have to change some of our tasks or some part of them from work to examining work or talking about work; and it’s likely some Stunning Successes will turn into Regular Tasks. That’s the downside. The upside is that we’ll probably prevent some Little Slips, Wasted Mornings, Lost Days and Black Cygnets, and turn them into Regular Tasks or Stunning Successes.

We could try to reduce various kinds of inefficiencies associated with certain highly repetitive tasks. Lots of organizations try to do this by bringing in continuous building and integration, or by automating the checking that they do for each new build. But be aware that the process of automating those checks involves lots of tasks that are themselves subject to the same kind of estimation problems that the rest of your project must endure.

So, if we were to manage the project, respond quickly to potentially out-of-control tasks, and moderate the variances using some of the ideas above, how would we model that in a Monte Carlo simulation? If we’re checking in frequently, we might not be able to get as much done in a single task, so let’s turn the Stunning Successes (50% of the estimated task time) into Modest Successes (75% of the estimated task time). Inevitably we’ll underestimate some tasks and overestimate others, so let’s say on average, out of 100 tasks, 50 come in 25% early, 49 come in 25% late. Bad luck of some kind happens to everyone at some point, so let’s say there’s still a chance of one Black Cygnet per project.

Once again, I ran 5000 simulated projects.

Remember that in the first example above, half our tasks were early by 50%. Here, half our tasks are early by only 25%, but things overall look better. We’ve doubled the number of on-time projects, and our average project length is down to 114% from 124%. Catching problems before they turn into Wasted Mornings or Lost Days makes an impressive difference.

Detect and Manage The Problems, Plus Short Iterations

The more tasks in a project, the greater the chance that we’ll be whacked with a random Black Cygnet. So, we could choose your projects and refrain from attempting big ones. This is essentially the idea behind agile development’s focus on a rapid series of short iterations, rather than on a single monolithic project. Breaking a big project up into sprints offers you the opportunity to do the project-level equivalent of frequent check-ins in on our tasks.

When I modeled an agile project with a Monte Carlo simulation, I was astonished by what happened.

For the task/duration breakdown, I took the same approach as just above:

I changed the project size to 20 tasks. Then, to compensate for the fact that the projects were only 20 tasks long, instead of 100, I ran 25000 simulated projects.

A few points of interest. At last, we’re estimating to the point where almost half our the projects are on time! In addition, more than 80% of the projects (20443 out of 25000, in my run) are within 15% of the estimate time—and since the entire project is only 20 hours, these projects run over by only three hours. That affords quick course correction; in the 100-hours-per-project model, the average project is late by three days.

Here’s one extra fascinating result: the total time taken for these 25000 projects (500,000 tasks in all) was 573,410 hours. For the original model (the one above, the first in yesterday’s post), the total was 619,156.5 hours, or 8% more. For the more realistic second example, the total was 736,199.2 hours, or 28% more. In these models, shorter iterations give less opportunity for random events to affect a given project.

So, what does all this mean? What can we learn? Let’s review some ideas on that next time.

In the last post, I talked about the asymmetry of unexpected events and the attendant problems with estimation. Today we’re going to look at some possible workarounds for the problems. Testers often start by questioning the validity of models, so let’s start there.

The linear model that I’ve proposed doesn’t match reality in several ways, and so far I haven’t been very explicit about them. Here are just a few of the problems with the model.

• The model tacitly assumes that all tasks have to be done in a specific order.
• The model tacitly assumes that all tasks are of equal significance.
• The model leaves out all notions of tasks being independent or interdependent with respect to each other.
• The model assumes that once we’re into a Wasted Morning, a Lost Day, or a Black Cygnet, there’s nothing we can do about it, and that we won’t do anything about it.

In particular, the model leaves out control actions that could be applied by managers or by the people performing the tasks, control actions that could be applied to the tasks, the project, the context, or to the estimates. Let’s start with the latter.

Pad The Estimates So We’re Half Right

Here’s the chart of yesterday’s first scenario again:

Under the given set of assumptions, and assuming random distribution, we come in late a little over 90% of the time. To counter this, we could add some arbitrary percentage to our estimates such that half the time we’ll come in early, while the other half of the time we’ll (still) come in late. In that case, we’d want to pick a median value.

When I used the data from the Monte Carlo simulation and sorted the project lengths, I found that Project 2500, the one right in the middle, has a length of 122 hours. So: pad the estimate by 22%, and we’ll be on time 50% of the time.

There are two problems with this. The first is that there’s still significant variability in terms of how late.  Second, the asymmetry problem is the same for projects as it is for individual tasks: our big losses have a greater magnitude than our big wins. Even if we go for the average project length, rather than the median (the average 123.83 hours, is a couple of hours longer), fewer projects will go over the estimated time, but early projects will tend to be more modestly early, while the late ones will be more extremely late. None of this is likely to be acceptable to someone who values predictability (that is, the person who is asking us for the estimate).

Pad The Estimates So We’re Almost Always Right

Someone who likes predictability would probably prefer our projects to come in on time 95% of the time. If we wanted to satisfy that, based on the same set of assumptions, we would do the best estimating job we could, then pad our estimate by 58%, to 158 hours.

One problem with that strategy is that work tends to expand to fill time available, and people will start to work at a slower pace.

One the other hand, if people keep the regular pace up, 82% of our projects are going to come in at least 10% early, and 42% of our projects will come in 25% early! In such a case, we’ll probably face political backlash and be urged to less conservative with our estimates. By the math, we really can’t win under this set of assumptions.

Pad The Team

Rather than padding the estimate of time, we could build slack into the system by having extra people available to take on any surprises or misunderstandings. But note Fred Brooks’ Law, which says that adding people to a late project makes it later. That’s because of at least two problems: the new people need to be brought up to speed, and having more connections in a system tends increases the communication burden.

So maybe we’ll have to change something about the way we manage the project. We’ll look at that next.

There has been a flurry of discussion about estimation on the net in the last few months.

• Ward Cunningham tweeted, “Estimating is the non-problem that know-nothings spent decades trying to solve.”


• Pradeep Soundararajan wrote a long blog post on test effort estimation.


• A fellow named Nathaniel posted an interesting perspective on successful estimates on the Terralien Web site.


• Jens Schauder posted 8 Reasons Why The Estimates Are Too Low.


• Andre Dhondt weighed in more recently with Estimation Causes Waste, Slack Creates Value. (Actually I disagree. Slack doesn’t create value, but does add something to favourable conditions in which value can be created. An appropriate amount of slack provides opportunity to reduce threats to value.)
  

All this reminded me to post the results of some number-crunching experiments that I started to do back in November 2009, based on a thought experiment by James Bach. That work coincided with the writing of a Swan Song, a Better Software column in which I discussed The Black Swan, by Nassim Nicholas Taleb.

A Black Swan is an improbable and unexpected event that has three characteristics. First, it takes us completely by surprise, typically because it’s outside of our models. Taleb says, “Models and constructions, those intellectual maps of reality, are not always wrong; they are wrong only in some specific applications. The difficulty is that a) you do not know beforehand (only after the fact) where the map will be wrong, and b) the mistakes can lead to severe consequences. These models are like potentially helpful medicines that carry random but very severe side effects.”

Second, a Black Swan has a disproportionately large impact. Many rare and surprising events happen that aren’t such a big deal. Black Swans can destroy wealth, property, or careers—or create them. A Black Swan can be a positive event, even though we tend not to think of them as such.

Third, after a Black Swan, people have a tendency to say that they saw it coming. They make this claim after the event because of a pair of inter-related cognitive biases. Taleb calls the first epistemic arrogance, an inflated sense of knowing what we know. The second is the narrative fallacy, our tendency to bend a story to fit with our perception of what we know, without validating the links between cause and effect. It’s easy to say that we know the important factors of the story when we already know the ending. The First World War was a Black Swan; September 11, 2001 was a Black Swan; the earthquake in Haiti, the volcano in Iceland, and the Deepwater Horizon oil spill in the Gulf of Mexico were all Black Swans. (The latter was a white swan, but it’s now coated in oil, which is the kind of joke that atracygnologists like to make). The rise of Google’s stock price after it went public was a Black Swan too. (You’ll probably meet people who claim that they knew in advance that Google’s stock price would explode. If that were true, they would have bought stock then, and they’d be rich. If they’re not rich, it’s evidence of the narrative fallacy in action.)

I think one reason that projects don’t meet their estimates is that we don’t naturally consider the impact of the Black Swan. James introduced me to a thought experiment that illustrates some interesting problems with estimation.

Imagine that you have a project, and that, for estimation’s sake, you broke it down into really fine-grained detail. The entire project decomposes into one hundred tasks, such that you figured that each task would take one hour. That means that your project should take 100 hours.

Suppose also that you estimated extremely conservatively, such that half of the tasks (that is, 50) were accomplished in half an hour, instead of an hour. Let’s call these Stunning Successes. 35% of the tasks are on time; we’ll called them Regular Tasks.

15% of the time, you encounter some bad luck.

• Eight tasks, instead of taking an hour, take two hours. Let’s call those Little Slips.


• Four tasks (one in 25) end up taking four hours, instead of the hour you thought they’d take. There’s a bug in some library that you’re calling; you need access to a particular server and the IT guys are overextended so they don’t call back until after lunch. We’ll call them Wasted Mornings.


• Two tasks (one in fifty) take a whole day, instead of an hour. Someone has to stay home to mind a sick kid. Those we’ll call Lost Days.


• One task in a hundred—just one—takes two days instead of just an hour. A library developed by another team is a couple of days late; a hard drive crash takes down a system and it turns out there’s a Post-It note jammed in the backup tape drive; one of the programmers has her wisdom teeth removed (all these things have happened on projects that I’ve worked on). These don’t have the devastating impact of a Black Swan; they’re like baby Black Swans, so let’s call them Black Cygnets.

That’s right: the average project, based on the assumptions above, would come in 24% late. That is, you estimated it would take two and a half weeks. In fact, it’s going to take more than three weeks. Mind you, that’s the average project, and the notion of the “average” project is strictly based on probability. There’s no such thing as an “average” project in reality and all of its rich detail. Not every project will encounter bad luck—and some projects will run into more bad luck than others.

So there’s a way of modeling projects in a more representative way, and it can be a lot of fun. Take the probabilities above, and subject them to random chance. Do that for every task in the project, then run a lot of projects. This shows you what can happen on projects in a fairly dramatic way. It’s called a Monte Carlo simulation, and it’s an excellent example of exploratory test automation.

I put together a little Ruby program to generate the results of scenarios like the one above. The script runs N projects of M tasks each, allows me to enter as many probabilities and as many durations as I like, puts the results into an Excel spreadsheet, and graphs them. (Naturally I found and fixed a ton of bugs in my code as I prepared this little project. But I also found bugs in Excel, including some race-condition-based crashes, API performance problems, and severely inadequate documentation. Ain’t testing fun?) For the scenario above, I ran 5000 projects of 100 randomized tasks each. Based on the numbers above, I got these results:

Here are some of the interesting things I see here:

• The average project took 123.83 hours, almost 25% longer than estimated.


• 460 projects (or fewer than 10%) were on time or early!


• 4540 projects (or just over 90%) were late!


• You can get lucky. In the run I did, three projects were accomplished in 80 hours or fewer. No project avoided having any Wasted Mornings, Lost Days, or Black Cygnets. That’s none out of five thousand.


• You can get unlucky, too. 469 projects took at least 1.5 times their projected time. Two took more than twice their projected time. And one very unlucky project had four Wasted Mornings, one Lost Day, and eight Black Cygnets. That one took 217 hours.

This might seem to some to be a counterintuitive result. Half the tasks took only half of the time alloted to them. 85% of the tasks came in on time or better. Only 15% were late. There’s a one-in-one-hundred chance that you’ll encounter a Black Cygnet. How could it be that so few projects came in on time?

The answer likes in asymmetry, another element of Taleb’s Black Swan model. It’s easy to err in our estimates by, say, a factor of two. Yet dividing the duration of a task by two has a very different impact from multiplying the duration by two. A Minor Victory saves only half a Regular Task, but a Little Slip costs two whole Regular Tasks.

Suppose you’re pretty good at estimation, and that you don’t underestimate so often. 20% of the tasks came in 10% early (let’s call those Minor Victories). 65% of the tasks come right on time (Regular Tasks). That is, 85% of your estimates are either too conservative or spot on. As before, there are eight Little Slips, four Wasted Mornings, two Lost Days, and a Black Cygnet.

With 20% of your tasks coming in early, and 15% coming in late, how long would you expect the average project to take?

That’s right: even though your estimation of tasks is more accurate than in the first example above, the average project would come in 47% late. That is, you thought it would take two and a half weeks, and in fact, it’s going to take more than three and a half weeks. Mind you, that’s the average, and again that’s based on probability. Just as above, not every project will encounter bad luck, and some projects will run into more bad luck than others. Again, I ran 5,000 projects of 100 tasks each.

Over 5000 projects, not a single project came in on time. The very best project came in just over 5% late. It had 18 Minor Victories, 77 on-time tasks, four Little Slips, and a Wasted Morning. It successfully avoided the Lost Day and the Black Cygnet. And in being anywhere near on-time, it was exceedingly rare. In fact, only 16 out of 5000 projects were less than 10% late.

Now, these are purely mathematical models. They ignore just about everything we could imagine about self-aware systems, and the ways the systems and their participants influence each other. The only project management activity that we’re really imagining here is the modelling and estimating of tasks into one-hour chunks. Everything that happens after that is down to random luck. Yet I think the Monte Carlo simulations shows that, unmanaged, what we might think of as a small number of surprises and a small amount of disorder can have a big impact.

Note that, in both of the examples above, at least 85% of the tasks come in on time or early overall. At most, only 15% of the tasks are late. It’s the asymmetry of the impact of late tasks that makes the overwhelming majority of projects late. A task that takes one-sixteenth of the time you estimated saves you less that one Regular Task, but a Black Cygnet costs you an extra fifteen Regular Tasks. The combination of the mathematics and the unexpected is relentlessly against you. In order to get around that, you’re going to have to manage something. What are the possible strategies? Let’s talk about that tomorrow.