Volume vs quality metrics, and mix shift in ratios

Maya

Board meeting on Thursday. I want to show which of my six dashboard tiles prove the product is improving. And Theo wants to double the ad budget for September.

Theo

Which will push every tile up. You're welcome.

Alex Tutor

Not every tile. Put one question to each number: would it still move if the product didn't change at all? Say Theo doubles ad spend, or a holiday sends half the country on trips.

If the answer is yes, it's a volume metric: how much. Users, groups, expenses, revenue totals. A quality metric says how well Halves works per user or per group: week-4 retention, the share of new groups that get a second member, expenses per active group.

You

So volume can be bought, and quality has to be built?

Alex Tutor

Mostly. The board needs both; they answer different questions. More ad money brings more people, not an easier way to split a bill.

Alex Tutor

Question 1

Theo doubles ad spend in September and the product doesn't change. Which of Maya's tiles would you expect to rise from the extra spend alone? Select all that apply.

Choose all that applyNew sign-ups per weekShare of new groups that get a second member within 3 daysTotal expenses added this monthShare of new users still active in week 4Plus revenue this monthExpenses added per active group

You

Our north star, weekly active groups, is a count. Does that make it a volume metric?

Alex Tutor

It's a count built from both kinds. One branch of the tree: newly active groups = new groups × share that get a second member × share that add a shared expense in week 1.

The first factor is volume, Theo's territory. The other two are quality, the product team's. Last week that was 1,000 × 40% × 47.5% = 190.

Theo

So if I double the first factor, the branch doubles.

Alex Tutor

Only if the newcomers behave like today's users. Cheaper audiences rarely do.

Alex Tutor

Question 2

Theo doubles new groups from 1,000 to 2,000 a week. The extra groups are less committed, so the share that gets a second member falls from 40% to 30%; the share that adds a shared expense in week 1 stays at 47.5%. How many newly active groups does the branch give?

Your answer

Units: groups (e.g. 150)

Maya

Fine, but I do have a quality number for the board: expenses per active group, 11.0 in May and 12.6 in July. The new expense screen shipped in June.

Alex Tutor

Then check it with the test. Something besides the product changed between May and July: summer. Here's the ratio split by group type.

Alex Tutor

Dataset · 6 rows

Halves active groups and expenses, May and July 2026

Expenses added by people (no recurring bills, no staff), by group type.

Download CSV

Columns
month: Calendar month
group_type: flat, couple or trip
active_groups: Groups with at least one expense added by a person that month
expenses: Expenses added by people that month

Data

month	group_type	active_groups	expenses
2026-05	flat	400	3200
2026-05	couple	300	3600
2026-05	trip	100	2000
2026-07	flat	380	2888
2026-07	couple	280	3248

Show 1 more row

2026-07

trip

340

6460

You

I'll rebuild July first: all July expenses over all July active groups.

Alex Tutor

Yes: sum expenses for July, sum active_groups, divide. If you land on Maya's number, we open the types.

Alex Tutor

Question 3

Using the table, compute expenses per active group for July, all group types together. Round to one decimal.

Your answer

Units: expenses per group (e.g. 9.9)

You

12.6, same as Maya. Now per type. Flats: 3,200 ÷ 400 = 8.0 in May, 2,888 ÷ 380 = 7.6 in July. Couples: 12.0, then 11.6. Trips: 20.0, then 19.0. Hold on.

Maya

Every type went down and the total went up? The export must be broken.

Theo

Don't look at me. My budget was flat all summer.

Alex Tutor

The export is fine, and so is Theo's budget. Before I explain, pick the reason yourself.

Alex Tutor

Question 4

Flats, couples and trips each added fewer expenses per group in July than in May, yet the overall figure rose from 11.0 to 12.6. What explains it?

Choose one answerThe export double-counted some July expensesTrip groups, the busiest type, became a much bigger share of active groupsThe quietest groups stopped being active, so the denominator shrankThe new expense screen helped groups add more expenses

It's who is inside the average. In May trip groups were 100 of 800, 12.5%. In July, 340 of 1,000: 34%. A trip group adds about 20 expenses a month, a flat about 8.

The overall ratio weights each type by its number of groups. Summer moved weight onto the busiest type, so the average climbed while every type slipped. That's mix shift: a quality metric passing on a change in volume.

You

So how do I show what the product did, with summer taken out?

Alex Tutor

Freeze the weights. Take July's rate for each type and apply it to May's number of groups of that type. Same people-mix, new behavior.

Alex Tutor

\text{July at May's mix} = \frac{\sum_{t} \text{rate}_{\text{Jul}}(t) \times \text{groups}_{\text{May}}(t)}{\sum_{t} \text{groups}_{\text{May}}(t)}

For each group type t: July's expenses per group, weighted by May's number of groups of that type.

Alex Tutor

Question 5

Freeze the mix: apply July's expenses per group for each type to May's number of groups of that type. What is expenses per active group at May's mix? Round to two decimals.

Your answer

Units: expenses per group (e.g. 9.99)

10.53 against May's 11.0, about −4.3%. With the mix frozen, groups added slightly fewer expenses, not more.

Maya

So which chart goes to the board?

Alex Tutor

The overall line, 11.0 → 12.6, would fool them: it invites credit for the expense screen. Show expenses per group by type instead, with 10.53 at May's mix next to it.

Keep the volume story too, because it's true: total expenses grew from 8,800 to 12,596. Summer brought more groups. What isn't true is that each group uses Halves more.

A ratio also lies when its denominator shrinks: if the quietest groups drop out, expenses per group rises while the total falls. Put the counts next to every ratio.

Maya

Then write me the note that goes under the by-type chart.

Alex Tutor

Question 6Short answer · AI-checked task

Write the 3–5 sentence note under Maya's by-type chart for the board: did Halves get better at its job between May and July? Use numbers from the table, and keep the volume claim and the quality claim apart.

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Alex Tutor

Key ideas

Volume metrics say how much (users, groups, expenses, revenue totals); quality metrics say how well the product works per user or per group (retention, second-member share, expenses per group).
The test: would the number still move if the product didn't change, say with doubled ad spend or a holiday? Volume metrics do; a quality metric that does is telling you about the mix.
Many counts combine both: newly active groups = new groups (volume) × second-member share × week-1 expense share (quality). Doubling the first factor doesn't double the branch if the quality factors drop.
An overall ratio is a weighted average of its segments. When the weights change it moves even if no segment does: mix shift. Check by segment, or freeze the mix (July's rates at May's mix: 10.53 vs 11.0).
A ratio can also rise because its denominator shrank. Show the counts next to it, and keep the volume claim and the quality claim apart.

Summer grew the volume and dressed it up as quality. The product's own answer sits inside each group type, and there it was a small dip.

Alex Tutor

That’s the lesson. You answered every task — nicely done.

Next lesson: DAU, WAU, MAU and stickiness