A Monte Carlo simulation, one random pick at a time
Sooner or later someone asks your team one of two questions. How many items will be done in the next month? Or: when will the next 20 items be done?
You could take the average and work it out on the back of an envelope. Or you could let your team's own history answer, by playing the future out many times over. This page does that for both questions, one at a time, and then puts them together in one picture at the end.
Open Simulation to play them out.
Given your team's history looks like this, one tile per day, how many items will be done in the month that follows?
Every bar is a number of items a month could end up with, and its height is how many of the simulated months landed there.
Now say you promised 15 items by the end of the month. How likely is that? Point at the bar for 15, or tap it. The line that appears runs over every month that finished 15 items or more, and its number is their share. Move left and the promise gets safer.
So the answer to "how many items next month?" isn't one number. It's a range with a chance attached. A promise that held in 85% of the months is something you can plan on.
Point at the busiest bars. The number on the line is close to 50%, and that total looks like the answer. It's a coin flip. Promise that number and you'll miss it every other month.
Now turn the question around. This time the number of items is fixed at 20, and what you don't know is how long they'll take.
It's the same history as above. A future doesn't stop at the end of a month anymore. It stops on the day the 20th item is done, and the answer is how many days that took. Weekends still count: the calendar doesn't stop for them, even when the work does.
Open Simulation to play it out.
Every bar is a number of days a run could take, and its height is how many of the runs took exactly that long.
Now say you promised all 20 within 35 days. How likely is that? Point at the bar for 35. This time the line runs to the left, over every run that had all 20 done in 35 days or fewer. Move right and the promise gets safer.
So "when?" gets a range with a chance attached too. Not "in 32 days", but "within 43 days, 85% of the time".
Point at the busiest bars: they play the same trick as before. Promise the number of days under them and it's a coin flip. A promise you can stand behind sits further to the right.
Both chapters played out futures and kept one number from each: a total, or a number of days. This time you keep the whole future.
Here's the same history again, drawn as one line that climbs every time an item gets done. Every future grows out of where that line ends today.
Open Simulation to draw them.
Every faint line is one future. Where they bunch up, most futures went. The thin edges are the rare ones. The three lines sum the cloud up: on every day ahead, each one marks where 50%, 85% or 95% of the futures got to, or further.
Turn on the three lines and point below the 50% line, say 28 days from now. The chart reads straight up from that day and tags where each line crosses, on a scale that counts from now. The 85% tag is how many items you can promise by then, 85% of the time. It's the first chapter's question.
Now point above the 50% line, at 20 on that scale. The chart reads across from that count and drops down from each line to the day it gets there. The 85% tag is how many days you need to promise all 20, 85% of the time. The second chapter's question.
While you point, the axis you're asking about changes color at each line, from red where it's a gamble to teal where 95% of the futures made it. Point high enough and the 95% reading disappears. Within ten weeks, the futures don't get there often enough to promise it that surely. Point at the past and the chart reads the history instead: what actually got done, no promise attached.
One line gives both answers, because every future you drew was both at once: a month, if you look at where it stood after four weeks, and a run, if you look at the day it reached 20 more.
The readings land close to what the chapters above found, but not exactly on them. Each chart played out its own futures. That's what a range with a chance attached looks like.
The first two chapters ran the same simulation. They just asked it from opposite ends. The fan above is that simulation in one picture.
Fix the duration and you get a range of counts. "How many in one month?" gives a range of totals, each with its chance.
Fix the count and you get a range of durations. "When will 20 be done?" gives a range of days, each with its chance.
Neither answer is one number, and both come from the same past days.