Paul M. Jones

We've all heard of Fred Brooks' law regarding the mythical man-month. (If you have not heard of it, stop reading this and go read The Mythical Man Month). The rule is this:

Adding manpower to a late software project makes it later.

He concludes his essay with these words:

The number of months of a project depends on its sequential constraints. The maximum number of men depends on the number of independent subtasks. From these two quantites one can derive schedules using fewer men and more months. (The only risk is product obsolescence.) One cannot, however, get workable schedules using more men and fewer months.

Once a development project has started, and appears to be taking longer than desired, adding more developers will make the project more-late. Brooks explains that there are two reasons for this:

1. It takes at least one developer, often more, to brief, train, educate, and otherwise inculcate the new developers into the project. That developer is unproductive during this time, and so are the new developers.

2. The amount of communication between everyone on the project increases exponentially with each new developer added, but the amount of productivity only increases linearly.

But exactly how bad is the falloff in productivity? "Adding people will make it more late", but just how much later will it be? Is there a way to predict the schedule effects of adding developers?

Point 1 (the training of the new developers by one or more existing developers) is relatively easy to model. If you add one new developer, and it takes one existing developer a week to train him, then you just added at least a week to the schedule when neither of them is productive. The existing developer got no productive work done, and neither did the new one.

After that, the developers have to make up the lost time. To discover the effect of point 2 above (the communication costs involved once a new developer is in place), I plugged some numbers into a spreadsheet. The communication costs are quite dramatic.

Below is a table representing a one-developer project, along with the communication costs and resulting schedule compression when adding developers. I'll give some narrative about the table afterwards, and then close with some very strong caveats.

Do not interpret this as science; at best, it is an initial guide to expectations, subject to further revision as I explore the topic more deeply.

In the first row, we have the baseline case. One developer doesn't have to talk with anyone else, so there are no communication costs. By default, his productivity rate is 100% of whatever he would normally do, so his output is also at 100%. If the one-man project is estimated to take 10 weeks, then it takes 10 weeks (a time factor of 100%).

Now, let's say we add another developer. The first thought is that the project should now take half as long (5 weeks). But! Although we have now two developers, they have to spend time talking to each other and coordinating their activity. That means we have 2 "units" of development happening, but an additional "unit" of communication. Some of the combined effort of the two developers is spent talking to each other. Instead of getting 100% more productive output (two developers instead of one), they are together only about 33% more productive. That means the remaining project time won't be cut to 50%; instead, it will be reduced to 75% at best. (And to boot, if we spent a week training the new developer, it means we need to add that week to the schedule as well.)

It only gets worse from there. 3 developers means 3 lines of communication (i.e., each one has to talk to the other two developers). That will cut the remaining project duration down to 67% of the previously scheduled time. Adding the third developer only gained us 8 percentage points of duration savings over having two developers. At this point we have tripled the cost of development, but only save 33% of remaining project time, not counting the time lost in training the new developers.

4 developers is 6 lines of communication, and a schedule compression of 63% (i.e., only 4 percentage points better than 3 developers). 5 developers is 10 lines of communication, for a schedule compression of 60%. No matter how many developers we add to the single-developer programming job, it looks like we will never cut the remaining project time in half.

I find this rather depressing.

Now, some very strong caveats:

1. We presume the work being performed in the situation modeled above has to be done sequentially. If the work can be done concurrently or in parallel without additional planning, training, or communication, we can probably ignore the diminishing returns indicated by the table, since the developers don't have to talk to each other.

2. The amount of time spent in communication is assumed to be equal to the amount of time spent developing work product. We can game this a little bit by changing the "communication" column to some percentage of the number of communication links. This would show much better numbers, but my intuition tells me that it would not map to reality; it is my experience that just as much time is spent coordinating (and then regaining "flow") as is spent developing work product.

3. Each developer is presumed to be roughly as productive as each other developer. However, even the most productive developers will eventually be overwhelmed by the volume of communications, and if they spend time training new developers, their productivity drops to zero for that period.

4. The developer(s) being added are presumed beforehand to be familiar with the project, its history, and its idiosyncrasies. If the developers are not already so familiar, it means the one or more of the developers already working on the project has to stop working and spend time bringing the new developer(s) up to speed. That makes the productivity reduction even more dramatic, and is a key factor in making the late project later.

Finally, some conclusions:

• I think caveat #4 above is really important in relation to Brooks' Law. It makes me think that the above table probably describes the best case scenario when adding developers; i.e., if nobody has to train the new developer, then you don't lose the training time, but you still don't get twice as much productivity from adding a second developer.

• Caveat #4 also implies to me that, if we want to compress the development schedule, the time to add developers is at the beginning of a project, not later on, so that they all learn the project as they go. But even then, it won't result in enough schedule compression to warrant adding more than one or two extra developers to a single-developer project.

I said earlier, and I'll say again now: This is not science. It is the beginning of an exploration of how to reliably manage resources and make schedule predictions. If you have questions, concerns, insights, alternative analysis, or experiences you would like to share on this topic, please leave a comment below.

The central tension in the software process comes from the fact that we must go from an informally identified need that exists in-the-world to a formal model that operates in-the-computer.

From "Beyond Programming" by Bruce Blum, as quoted in "The Design of Design" by Frederick P. Brooks Jr.

It is time to question the meaning of the words “education reform” and the investment in reforming the current system. Once the automobile was invented, there was no need for “buggy whip reform” or “horse turnaround plans.” Mr. Khan, and those like him, have exposed the current system for the obsolete monopoly that it is. This article lays waste to the idea of “reforming” the current system. The best thing we can do is rapidly manage the transition to an entirely new education model.

via Chicago Boyz » Blog Archive » The Worth of Khan.

This afternoon James Jay Lee, a crazy person with a gun, a bomb, and an anti-human manifesto inspired by Al Gore’s An Inconvenient Truth, took hostages at the offices of the Discovery Channel in Silver Spring. He was shot and killed by police. The hostages were freed, unharmed.

How many Tea Party types have done this? Oh right, *zero*. Via Gun-wielding ecoterrorist calls for reduction in human population, gets wish | The Daily Caller - Breaking News, Opinion, Research, and Entertainment.

... [I]f you look at a Marxist Utopia -- say, Cuba -- what you’ll see is basically a plantation. At the top, you’ve got the Massa and his family -- Fidel, Raul, et al. -- followed by various layers of overseers -- the Communist Party apparat, the secret police -- and House Negroes -- e.g., the state-controlled media -- all living off the surplus labor of the Field Negroes, whose produce is disposed of not according to their own desires (that would be capitalism!) but according to their betters’. This, we’re told is for the best, since they aren’t smart enough to make their own decisions anyway, and the Massa looks after them with food, housing, and health care. Slaveholders even defended their system as more humane and less exploitative than atomistic capitalism, conveniently ignoring the role of the lash, just as apologists for Marxism conveniently ignore the role of the gulag.

Oh how I *hate* the damned Communists. Via Instapundit » Blog Archive » DAVE KOPEL: Obama Is Too A Christian..

In one camp are conservative Christians and their champion, the Texas State Board of Education; in the other are politically radical multiculturalists and their de facto champion, President Barack Obama. The two competing visions couldn’t be more different. And the stakes couldn’t be higher. Unfortunately, whichever side wins -- your kid ends up losing.

That’s because this war is for the power to dictate what our children are taught -- and, by extension, how future generations of Americans will view the world. Long gone are the days when classrooms were for learning: now each side sees the public school system as a vast indoctrination camp in which future culture-warriors are trained. The problem is, two diametrically opposed philosophies are struggling for supremacy, and neither is willing to give an inch, so the end result is extremism, no matter which side temporarily comes out on top.

Both visions are grotesque and unacceptable -- and yet they are currently the only two choices on the national menu.

via Zombie » Ideological War Spells Doom for America’s Schoolkids.

While for the most part the Texas State Board of Education is in fact admirably defending patriotism, they unfortunately drag some ideological baggage into the meeting room as well, and do here and there attempt to push conservative and/or Christian viewpoints into the curriculum. Maybe not as much as their critics charge, and they’re not always successful, but they try. And try. And try.

And it is this attempt on the part of the TSBE to overreach which frustrates me to no end. Because every time they push back too hard, they look just as partisan as the leftists they’re trying to counteract. Which gives the media and the liberal critics a valid basis on which to criticize Texas’ attempt (and thus any attempt) to salvage a patriotic curriculum.

Furthermore, the conservative board members of the TSBE have in a few cases gone too far and ended up distorting historical fact to match their own wishful thinking for a Christian nation. When you want to rectify your opponent’s twisting of the facts, it’s never good to overtwist them yourself in the opposite direction. It might work when negotiating the price of a used car, but in an argument about the nature of truth it only serves to undermine your position.

via Zombie » What’s the Matter with Texas?.

There are a lot of folks who think that a border fence is part of the "solution" for illegal immigration in the US. The problem with fences is that they work both ways. A fence now might seem like a good idea to keep people out; call me paranoid, but at some point in the future, I fear the same fence might also be used to keep people in.

The very phrase “insecure borders” conjures an image of government failing at its most fundamental responsibility--namely, protecting citizens from invading marauders. People see in their minds’ eyes an America increasingly at risk of being conquered by foreigners, leaving Americans at the mercy of invading rapists, plunderers, and murderers.

Immigrants, however, aren’t invaders, much less warriors in a conquering army.

...

For perspective, ask if America’s borders were insecure until 1921 when, with the Emergency Quota Act, Uncle Sam first began seriously to restrict the number of immigrants allowed into the United States. Were Americans, until just 90 years ago, living in peril of their lives and livelihoods because U.S. borders were "insecure"?

...

In fact, the security of American borders--if by this phrase we mean genuinely decreased risks to Americans’ persons and property--would almost certainly rise with open borders.

via Secure in Freedom | The Freeman | Ideas On Liberty.

Socialism: Quick, what's the murder capital of the world: Kabul? Juarez? Try Caracas, Venezuela, a city whose dictator, Hugo Chavez, has made murder a means of extending his control.

The silent protest at Monday night's Miss Universe Pageant in Las Vegas was invisible to nearly everyone -- except Venezuelans. On her final catwalk, the ranking Miss Universe, Stefania Fernandez, suddenly whipped out a Venezuelan flag in a patriotic but protocol-breaking gesture.

Fernandez waved her flag for the same reason Americans waved theirs after 9/11 -- to convey resolution amid distress. Her flag had seven stars, significant because Chavez had arbitrarily added an eighth, making any use of a difficult-to-find seven-star banner an act of defiance.

via The Killing Fields Of Caracas - IBD - Investors.com.