Brooks’s Law: training costs, but not as much as you might think

Surely everyone involved in developing software has heard of Brooks’s Law. First presented in the eponymous chapter of Frederick P. Brooks, Jr.’s classic The Mythical Man Month, it states: “Adding manpower to a late software project makes it later.” This “law” is much beloved by software developers as a handy bucket of cold water with which to cool the ardor of overly enthusiastic managers and executives. Lately, however, I’ve been thinking about Brooks’s Law and rereading The Mythical Man Month and I’m no longer as impressed with Brooks’s analysis as I once was. This is the first in what I expect will be a series of posts discussing some of the reasons why.

When Brooks says that adding manpower makes a late project later, he doesn’t specify what he means by later. Later than it already is? Almost certainly, but so what? Later than your new wildly optimistic estimate? Probably, but again not all that interesting. The slightly paradoxical interpretation that makes Brooks’s Law such a perennial on amusing quotation lists is: later than it would have been if you had just left well enough alone.

Of the various reasons Brooks gives in the chapter “The Mythical Man Month” for projects running out of calendar time, the only one that has specifically to do with adding staff to an existing project is the cost of training the added staff. There are other costs associated with having a bigger team that such as potentially increased intercommunication costs and the need to repartition tasks. I’ll discuss those costs in later posts but for now I’m concerned only with whether Brooks’s own analysis of the costs of training holds water.

If we were to take Brooks’s Law as literally true, then we would have to believe that the costs of training new staff will always be higher than any capacity for productive work they might eventually develop. That seems unlikely. However, Brooks’s Law only refers to “late” projects so perhaps there’s something about being late that makes it true. Unfortunately, he doesn’t define “late” any more than he defines “later” so if we want to apply Brooks’s Law wisely we’re on our own — we need to ask, when can we get more done by adding staff than by not?

Much more often than Brooks lets on, it seems. In the section “Regenerative Schedule Disaster” Brooks uses a hypothetical project, originally estimated to be twelve person-months of effort and assigned to a three person team, to demonstrate how training costs affect our ability to speed up a project. In his scenario the project has been divided into four milestones, each of which should be completed in one calendar month by the team of three, i.e. three person-months per milestone. Unfortunately it takes the team two calendar months, or six person-months, to finish the first milestone, so there are only two months left to complete the remaining three milestones. Brooks then considers two sub-scenarios — one where only the first milestone was mis-estimated, in which case there are nine person-months worth of work left and two months in which to do it, and another where the underestimation was systematic so the three remaining milestones are all, like the first, six person-months of work leaving eighteen person-months of work. The question he then poses is, what happens if a manager attempts to get the project finished in the remaining two calendar months by adding staff.

In the first sub-scenario, a manager who ignores training costs would calculate that they need four and a half people to do nine person-months of work in two months. Rounding up to five, subtracting the three they’ve already got, and they add two people. In the second scenario, eighteen divided by two is nine, subtract the three they’ve got, and they’d need to grow by six. Brooks then analyzes the first sub-scenario, making the rather conservative assumption that it’ll take one month of full-time work by one of the existing team members to train the two newcomers before they’ll be able to do any work. Under that assumption, only two people will do productive work during the third month so only two more person-months of actual work will be done, leaving seven. In the fourth, and final, month, the new people will start contributing and the trainer can get back to real work but it’s too late — they’ll get five person-months worth of work done but with seven left to do the schedule is blown.

But there’s another way to look at it. With the two newcomers, the team managed to complete a total of thirteen person-months worth of actual (non-training) work, or almost 87% of the originally planned functionality (assuming the revised estimate of fifteen person-months for the whole project is correct.) What would have happened if they had heeded Brooks’s Law and just kept going with the original three-person team? They’d have completed only twelve person-months, or 80% of the originally planned effort. Or, if it’s more important to deliver 100% of the functionality as soon as possible, the original team would have needed another month, blowing the schedule by 25% while the augmented team would only need an additional two-fifths of a month, or about 10% over the original schedule.

In Brooks’s second sub-scenario, where the actual project size is assumed to be twenty-four person-months, the benefits of adding staff are even more pronounced. Assuming the same one-month of full-time training, the augmented team finishes almost 71% of the originally planned effort in four months compared to only 50% by the original team. Or they can finish the whole project in a bit less than five months total, extending the original schedule by about 20%, compared to the 100% by which to the original team would blow the original schedule.

The problem is not that adding staff to the project didn’t help; it’s that it didn’t help quite enough. You might ask, why not account for the training costs when figuring out how many new staff are needed? Brooks briefly considers that idea and rejects it on the grounds that the seven person team needed in the first sub-scenario to finish the remaining seven person-months worth of work after training would be too different in kind from a five person team for it to be feasible. That may be true but the question remains, what’s the alternative? Brooks considers attempts to finish the project on the original four-month schedule “disastrous” and recommends that we should instead “reschedule” or “trim the task”. Both of those are probably wise strategies but even with Brooks’s conservative assumptions about training time, the expanded team would still get more done needing either less of a schedule slip or less trimming of functionality.

At any rate, it’s not the case, in either sub-scenario, that training costs on their own would cause the project to finish later with additional staff than it would have without. Brooks does, however, make one important point when he says:

Notice by the end of the third month, things look very black. The [second] milestone has not been reached in spite of all the managerial effort. The temptation is very strong to repeat the cycle, adding yet more manpower. Therein lies madness. (pp. 24-5)

It is important not to lose one’s nerve. If you’ve already used up two months of a four-month schedule, it’s going to be queasy-making to reduce your productivity by a third for another whole month. If you do, you’ve got to stick with it to reap the benefits as your new workers get up to speed. It also suggests two bits of tactics. One: make sure you add enough new staff. If you’re going to take the hit of losing the output of one or more of your currently productive workers to training you want to make sure you get as big a return on that investment as possible — add as many people as you can afford and as you think can be trained in a reasonable amount of time. Second, make sure you invest enough in training. In his own reappraisal of Brooks’s Law Steve McConnell called Brooks’s assumptions about training costs “absurdly conservative” and they may be. But notice that even with those conservative assumptions the investment can still pay off quickly. It can be tempting to try to cheat, adding staff without explicit training, hoping they’ll somehow get up to speed on their own. If it works, great, but more likely they’ll just nibble away at the productivity of the current staff without ever becoming productive enough to offset the cost. Better to plan conservatively and then end the training ahead of schedule if they’re ready to get to fully productive work sooner than planned.

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