I’m apparently a project manager this week, coordinating the installation of some gear that I can’t talk about. I have plenty to say on the topic of project management, but this isn’t that kind of post.
This post is about statistics and contingent probability. In fact, it’s about cumulative probability of multiple, coordinated events. Because my task this week is to attempt to achieve a successful outcome where any one of several different things could go wrong, and if any of them do, the whole thing won’t work. It’s quite common.
In the lift on my way out this evening, I got to wondering about the cumulative probability of my task (as one does). I thought about a specific case: What if, I thought, what if all these tasks are very likely to succeed indeed. What would that do to the likelihood of overall success?
I figured I had about 5 separate things that had to go well. Network cabling that has to be already available, because there isn’t enough time to buy or build any before the Christmas change freeze (1). The people doing the switch port allocation have to get it right (and there have to be enough spare switch ports in the right place in the datacentre) (2). The different team doing the IP allocation also have to get it right, and correctly configure the switch ports accordingly (3). The security people have to be right about the way IP routing works between different security zones (because I’m adding new IPs into new VLANs that may, or may not, be reachable from existing networks, I get to find out after it’s too late, don’t you just love this job) (4), and the people have to have their jobs done in the right order, or the cabling will be finished after the vendor’s engineers have left the datacentre for the weekend (5).
Let’s say each of them is quite likely to succeed, say 90% likely. What do you reckon the likelihood of all 5 succeeding is?
A few quick taps on the smartphone calculator later, and I had my answer: less than 60%.
Why Failure Is Assured
Because I’m a colossal nerd, here’s a chart showing why I’m doomed:
I had calculated the cumulative probability of 5 events, all with independent likelihood of 90% success. That’s equivalent to 0.9^5, which is just over 0.59, or slightly less than 60%. That’s not many events, and all of them quite likely to succeed. You can see from the chart how fast your likelihood for success drops off with the added number of events.
In reality, I have to have quite a few more things go well, and many of them are not 90% likely to succeed. 60% is, therefore, quite an optimistic estimate of my likelihood for success.
Left to my own devices, and starved of medicinal alcohol, I’m normally a realist (i.e. pessimist) about this sort of thing, and I didn’t really think my odds for success were this low. Not really. Not in my heart of hearts.
But mathematics is a harsh mistress, and now I know that if this actually succeeds, it’ll be nothing less than a Christmas miracle.
How are your projects going?