This always bugged me cause it means every project estimate should be infinite in length.

Zeno's Paradox. The solution is that a series can converge.

But then you'd expect it to converge, and that would break the law.

Cost estimation is an NP problem. Perhaps it will become practical when we can use a quantum supercomputer to estimate the time needed to build a single page web app.

No, because you'll just ask it to build it in constant time. Software costs more to measure than to do.

That's why PERT has problems. Estimate times for "best case", "likely case" and "worst case"

Expected time = (best + 4 * likely + worst) / 6

For those reading at home, the meaning is that the "most likely" is multiplied by 4, giving a triangular distribution that (very very) roughly approximates a normal distribution.

I went hunting for the origins of that formula a few years ago. I couldn't find the original source, and certainly none of the sources I found had a justification for it.

Someone who works at RAND could probably pull the original internal work and tell us. But I suspect it was chosen for ease of calculation.

While it's been criticised for being normal-esque instead of pessimistically skewed, it still outperforms single-point estimations. I think it's because of the "unpacking effect" that a full PERT estimate causes you to undergo.

There's a literature of people tinkering with the formula, but I don't think it's anywhere near as important as the unpacking effect is.

No, there is no justification, they just picked that because it has finite limits. They say it's a Beta distribution.

PERT was invented by the US Navy but these days the DoD recommends not using it but just use normal Critical Path Analysis instead where you just estimate a single time - hard enough on it's on without having to do it three times.

Right, 3-points are tedious to do by hand. That's why I began working on a tool. I figured if it's easy enough, people would actually do it.

And it also assumes that the optimal is just as likely as the pessimistic. As anyone who has ever planned anything knows, more things can conspire to introduce delay than work out just right enough to make it take less than you excepted.

Right, and there's lots of literature jumping on that and trying to repair it. Yet the original formula outperforms single point estimates.

But as I said elsewhere in this thread, my suspicion is that the unpacking effect dominates the "improvement" that's observed and that the particular formula is largely secondary.

Oh yes, you did say that, sorry. I only responded to your first point and then remembered the second myself.

PERT is taught as a time based planning tool but it also has a earned value element. The tools for that have moved on too.

https://en.wikipedia.org/wiki/Earned_value_management

I suppose the unpacking effect does make more sense though, over CPA.

"How long will it take?"

"6-8 weeks"

So what do you put in CPA - 6, 7, 8 ? PERT says 7.

It reminds me of Simpson's Rule:

https://en.wikipedia.org/wiki/Simpson%27s_rule

haha that's beautifully recursive