Course · 3. Menu-based choice (MBC)

The menu simulator

The simulator plays out a menu for 20,000 simulated customers, each with a lasting taste and a fresh occasion on every visit. Change prices or take items off the menu, and every result is compared with the base menu on the same customers, so differences are not simulation noise.

What you can ask

Buy rates and revenue per visit, item by item, and the share of visits with no purchase.
Items per visit: the size of the average order.
Visits per customer (1 to 8): how many customers buy each item at least once over that many visits, and how many come back for it on the second.
Reach: tick a set of items to see how many visits include at least one of them, and how many customers buy from the set at least once over their visits. This is the audience for a range, a promotion or a loyalty card.
Units per item, bought separately plus inside bundles.
Bundles: each bundle's buy rate, and what its buyers also buy separately on the same visit.
Price sweep: one item's price (a bundle's, say) across the range tested in the survey, with its buy rate, revenue per visit and, for a bundle, its items bought separately and in units.
Compare with the standard model, which treats every visit as a new person.
95% ranges under each number (small print): the survey's uncertainty, from 100 sets of model parameters drawn around the fit, each played on the same customers. Changes against the base menu get their own ranges.

Example: the tutorial's healthy range

How many café customers buy Salad, Soup or Juice? With the default settings, about 50% of visits include one of them, and over 4 visits about 84% of customers buy from the range at least once (95% range 81% to 87%). The standard model agrees per visit but says 94% (92% to 95%) over 4 visits. It assumes someone who skipped the range today is as likely as anyone to buy it next time, when in fact the same customers keep coming back for it. Cutting Salad from $5.00 to $4.00 lifts its per-visit buy rate from about 26% to 37%, but adds only about 5 points to the customers the range reaches over 4 visits (4 to 6.5): mostly the same people buying more often.

The data was simulated, so the truth is known: 85% over 4 visits, +3.7 points, 25% to 34%. Our ranges contain 85% and the Salad rate; the +3.7 is just below the 4 to 6.5 range. Ranges miss sometimes: on 20 simulated surveys, the simulator's 95% ranges contained the truth 90 times in 100 checks, a little less often than they should. The standard model's 92% to 95% misses the 85% by far more. One simulated study, an illustration rather than a guarantee.

Example: pricing the meal deal

The tutorial's meal deal (Sandwich + Crisps + Juice, usually $6.50 against $8.20 bought separately) was tested from $5.20 to $8.12. Sweeping its price: at $5.20 about 20% of visits take the deal, against 10% at $8.12, and every item sells more units. But revenue per visit does not rise: $7.32 at $8.12 against $7.08 at $5.20, because a cheaper deal mostly moves people who would buy the items separately at full price. The difference, +$0.24 per visit, has a 95% range of -$0.11 to +$0.56, so the survey cannot say which end earns more; it can say a deeper discount does not pay for itself in revenue. The truth: 22% and 10%, $7.32 and $7.17 (+$0.15). Costs are not in the simulator, so check margins before reading this as a price recommendation.

Limits

Ranges cover the survey's uncertainty, not the model being wrong. In our checks they contained the truth a little less often than 95% (90 in 100 for the simulator, 92-94% for the results screens).
Taking an item off the menu moves no one to other items. The survey measures switching through prices only, so to ask what dropping an item does, raise its price to the top of the tested range instead.
Keep prices within the range tested in the survey.
"Visits" are a modelling device: the survey's menus stand in for real visits, and how often people actually come is not in the survey.

Try it in the tutorial: how many customers buy from the range

Next: When the menu model helps

Tutorial links open the example project in the app; it is free and needs a free account.