One of my previous employers was a big fan of the Pareto Principle. Whenever a task landed on my desk I was told they wanted an “80/20 job”. They wanted me to only spend 20% of the time on it that I’d have needed to produce a perfect piece of work but they were happy for the quality to be 20% short of perfection. 20% of the effort for 80% of the results if you like. And that was fine by me.

I’ve been wondering ever since, though, whether there’s a mathematical formula that could be fitted to the rule and whether the formula would have any hidden lessons within it. Because I’m a scientist. That’s what scientists do.

At first I tried out formulae that looked like

Quality% = 1-exp(-const * time spent)

And I didn’t like the results. I liked how spending zero time on a piece of work resulted in zero quality. That was good. And I also liked how you could only get to 100% quality by working to infinity. Maybe this formula would work in the arty world, where a good poem/painting/album is never completed – only abandoned.

But then I tried an experiment with my formula, looking at the impact of micromanagement. If there’s a six day project, does it make a difference whether you (i) tell someone they have six days to do it or (ii) tell them they have two days to do it, then on days 3 and 5 tell them they have another two days (so still six in total)? And the formula let me down. It told me that however much you break it all down, you get the same quality at the end of six days.

I was disappointed. I wanted to see Duckworth-Lewis type results. You know the sort of thing. There’s a one-day cricket match, 50 overs each. One side bats for 10 overs, the heavens come down, the umpires close the first innings and tell the other side they can bat for 10 overs in the evening. But the second side needs to score loads more runs than the first side did because they know all along that they only have ten overs, rather than playing as if they had fifty.

Anyway, I went back to the drawing board and I now have a better formula. And here it is:

Quality% = 100% – 100%*(1-proportion of time spent)^alpha

Alpha is the Pareto parameter. For the 80/20 rule, we need to set alpha to ln(0.2)/ln(0.8), which is about 7.2. So what properties does the formula have? Well, zero time results in zero quality again. Good. And 100% time results in 100% quality. Perfection is achievable. Mind you, that would mean spending five times as long on the work as that former employer was prepared to invest.

But it’s the results of dividing up tasks that are of most interest to me here. Imagine we have a job that would take 30 days to do properly. Spending two days on this job we could achieve 39% quality, four days would get us to 64% and six days to 80%. And being an employer that operates according to Pareto, we budget six days work, while setting our expectations to receive something that’s only 80% of perfection. If we leave someone alone for six days, then they’ll reach that 80%. But if we divide up the job into three two-day chunks, they’ll only complete 39% in the first two days, 39% of what’s left in the next two and 395 of the rest in the last two. That only comes to 77.5%! Go on, add it up! Breaking it down into 2+4 days gets us to 78.3%.

So what’s my conclusion? Well, if you believe in the Pareto Principle and want people to do 80/20 jobs for you, that will only happen if you leave them alone. Otherwise quality will end up under 80% or time will run over your 20% budget.