Recap

As you might well imagine, I take a fair amount of flak for my mathematical models. There are several reasons for this.

First of all, there is an interesting cultural effect. Although our civilization has untold millions of dollars in the total sunk cost of assembling our mathematical toolbox over the millennia, the average manager uses about 29 cents' worth of it. I have always found this puzzling. It's not like we don't teach any math at school. The reasons I usually hear have to do with "bad data," or "no data," but I think that is just an excuse.

Why do I like mathematical models? My response is simple. We all have rough ideas, even instincts, about how things work in the real world. What we don't have is a good grasp on how much, how severe, the effects are. So, when a project gets in trouble, and the manager uses good instinctsreduce scope instead of adding people, for examplewe are moving in the right direction. But to do even better, he or she should have an idea of by how much the scope needs to be reduced to make a difference. Absent this information, the manager is apt to cut too little. He then incurs the wrath of management for leaving something on the cutting-room floor and, at the same time, still being late because he didn't cut enough. This is the worst of both worlds.

The models I propose are all simple in concept. They usually don't involve any math more complicated than the notions of areas and volumes, and the idea that if things need to be conserved, something must go down when something else goes up. In this chapter I invoked some ideas about statistics, but I was careful to explain them as I went along. The lognormal distribution is somewhat obscure, but that does not undermine its validity. It is the correct distribution to use.

It is, of course, very difficult to compare the results of these models with experimental data. But I don't think that should keep you from inventing models. If you don't like mine, create some of your own. See how much your results differ from mine. What I have discovered over and over again is that when you finally get three or more competing models side by side, their predictions are remarkably similar. That is, if the models are at all faithful to reality in some regard, they will all get similar results, independent of their details.

What the model on trade-offs teaches us is that improving the probability of success is not easy. We have to modify parameters a lot to materially affect the outcome. In turn, this means that our estimating and scheduling activities need to be effective. I turn to these topics in more detail in the next two chapters. As you might expect, Roscoe Leroy has something to say about this. It will be interesting to compare some of his math models to mine.