Ranges, not points

The point. 19.63 billion yen a year is the top-down chain with every constructed share at its middle. It reads as twice the threshold. Nothing on the slide says that two of its four links are assumptions, or how far they could move.

The top-down range. Carry both shares to their lows together and to their highs together and the same chain prints 10.90 to 31.72. The whole range sits above a line at about 10, but the low end clears it by less than one billion yen, and "about 10" was never precise to the billion.

The bottom-up range. Built from Kettle & Co's own pilot inputs, the bottom-up prints 13.06 at the middle and 7.11 to 21.55 as a range. That range crosses the threshold. If the true value sits in its lower part, the decision is no.

So the honest answer to "go or no-go?" is neither. It is "measure more, and here is the one input to measure first". A range wholly above or below the threshold decides; a range across it tells you where to spend the next week.

Leaders sometimes hear a range as an analyst refusing to commit. Turn it around: a point that sits on the wrong side of the truth commits the business to a decision the evidence never supported. "Measure more" is only a dodge when it comes without a target. Paired with the tornado in Part 3, it becomes specific: which input, how wide it is today, and what a cheaper or better source would be.

It also tells you when to stop. Once a range sits wholly on one side of the threshold, further precision changes nothing about the decision, and the analyst can say so.

Every constructed input gets three values, and each value gets a reason. For Kettle & Co's top-down: premium share of leaf spend 0.25 / 0.33 / 0.40, share bought online 0.22 / 0.30 / 0.40. For the bottom-up: households that buy the category online 3.5% / 4.5% / 5.5%, spend per order 2,100 / 2,400 / 2,700 yen, orders per buyer a year 2.8 / 3.5 / 4.2. All constructed.

The two real links, 34,553,907 households and 5,737 yen of leaf spend per household, keep their single value: they are measured, and the sampling error of the survey table is not published in the table used, so it is not quantified here. Carry the constructed lows together and the top-down prints 10.90; the highs together print 31.72; the middles print 19.63.

Wide on purpose. A corner is the case where every assumption missed the same way. That can happen, especially when one cause moves several inputs (a weak economy lowers premium share and orders together), but it is the edge of the possible, not the middle of the likely.

Silent on likelihood. A corner range says nothing about whether 12 is more plausible than 28. Do not draw a bell curve on top of it, and do not write "90 percent confident" next to it. Nobody measured a probability, so none goes on the page.

Scenarios. Instead of mechanical corners, write two or three named stories, a cautious one and a bold one, each with inputs that belong together. A scenario keeps inputs coherent (a world where few households buy online is probably also one where online orders are less frequent), and leaders find stories easier to argue with than corners. The cost: the stories are chosen, so a team can choose comfortable ones.

Sampling, often called Monte Carlo. Give each input a distribution, draw thousands of combinations, and read off the spread of results. It shows which part of the box is crowded, which corners cannot. The cost is that it needs a distribution for every input and a view on how inputs move together, and the output is only as real as those choices. A percentile computed from invented distributions is still invented.

Neither is wrong. Some teams start with corners because they are transparent, then move to sampling once they have real data behind the input distributions. Others refuse sampling until then. Pick the method your evidence can support, and say which you picked.

Why the gap, not the size. Each size on its own moves with every input. The gap between them is what tells you the two methods disagree, and an input that closes the gap is a candidate explanation for the disagreement. At the middle of every input the top-down is 1.50 times the bottom-up.

The order. Share bought online is widest: at its low the gap falls to 1.10, at its high it climbs to 2.00. Then premium share (1.14 to 1.82), households that buy online (1.93 at its low, 1.23 at its high), orders per buyer a year (1.88 to 1.25), and spend per order (1.72 to 1.34), the narrowest.

The direction. The two top-down inputs widen the gap as they rise, because they inflate the top-down. The three bottom-up inputs narrow it as they rise, because they inflate the bottom-up. Read the ends, not just the widths: a bar tells you which way the input would have to move to bring the methods together.

Measurement costs time and money. The widest bar is where a better number buys the most: narrow the online share and the gap's possible spread shrinks more than for any other input. Narrowing spend per order, the narrowest bar, would barely move the conversation even if it were cheap.

Width is not the only test. Ask also how cheaply the input can be narrowed. If two bars are close in width and one can be checked from Kettle & Co's own orders table in an afternoon, do that one first. The tornado ranks impact; you add cost.

A tornado holds every other input at its middle. Real inputs do not always sit still while one moves. If the households that buy online are fewer than assumed, the ones who do buy may also buy more often, so two bottom-up bars could partly cancel. Or one cause could push several inputs the same way and the joint effect would be larger than any single bar.

One-at-a-time sensitivity cannot see either case. Use it to rank where to look, not to state the combined uncertainty; the corners in Part 2 and, if your evidence supports it, scenarios or sampling cover the joint movement.