Present pirated-usage findings to a PM

You computed (1) monthly % of shops using pirated themes and (2) monthly and cumulative estimated revenue loss from pirated themes.

Explain how you would present these results to a Product Manager in a short readout (5–10 minutes).

Include:

• What the headline is and what decision you want to enable.
• Which metrics and visualizations you would show first vs. as diagnostics.
• Key assumptions behind the revenue-loss estimate.
• Data-quality checks and how you’d interpret extreme patterns (e.g., % jumping from ~0% to ~100%, or cumulative loss growing very fast).
• Concrete next steps / recommendations (product, enforcement, measurement).

Solution

1) Start with the decision and a 1-slide headline

Goal: enable a PM decision on whether to (a) investigate instrumentation/data issues, (b) prioritize anti-piracy enforcement, (c) adjust product flows/pricing, and/or (d) run an experiment.

Headline example (what I’d say first):

• “Pirated-theme usage appears to have increased materially in the last X months, and the implied revenue at risk is ~$Y per month (cumulative ~$Z). Before actioning, we should validate this isn’t an artifact of tracking/definition changes.”

2) Show the minimum set of primary + diagnostic + guardrail metrics

Primary metrics

1. Pirated shop rate (monthly): % of active shops with at least one pirated theme active in the month.
2. Monthly revenue loss estimate and cumulative (rolling) revenue loss.

Diagnostics (to explain “why”)

• Counts in numerator/denominator: pirated_shops and total_shops alongside the rate.
• New vs. existing pirated adopters: first month a shop appears pirated.
• Top pirated themes and concentration (is one theme driving the spike?).
• Country/segment splits (Simpson’s paradox risk): SMB vs. enterprise, geography, acquisition channel.

Guardrails (to avoid wrong conclusions)

• Overall theme installs volume, active shops trend, and marketplace revenue trend.
• Customer support tickets or fraud reports trend (if available).

3) Use 2–3 clear visuals (ordered)

1. Line chart: pirated shop % by month with numerator/denominator annotated.
2. Bar/line combo: monthly revenue-loss estimate (bars) + cumulative loss (line).
3. Pareto chart: revenue loss by theme (top 10) to show concentration.

Keep it interpretable: the PM should be able to answer “how big, how fast, what’s driving it?” in <2 minutes.

4) Make assumptions explicit (especially for revenue loss)

Revenue-loss estimates are often the most contestable part, so I would state:

• Counterfactual assumption: “If a shop uses a pirated theme, they would otherwise pay for the official theme at list price.” (This may overestimate if many would churn or choose a cheaper theme.)
• Pricing assumption: price_usd_per_month is stable and correctly mapped to the pirated theme.
• Time assumption: a theme is counted as active for the month if its validity range overlaps the month; NULL valid_to means still active.
• Double-counting risk: shops can have multiple active installs; clarify whether we count multiple themes per shop per month, and why.

I would offer a sensitivity range:

• Conservative: apply a “would-have-paid” factor (e.g., 30–70%).
• Conservative: cap at 1 theme per shop-month if that matches business reality.

5) Address extreme patterns as either data bugs or real incidents

If pirated % jumps from ~0% to ~100%

I would immediately propose checks before treating it as a real behavior shift:

• Definition/logic check: did total_shops change (e.g., accidentally filtering to only shops that appear in pirated table)?
• Join explosion: duplicated rows from many-to-many joins inflating counts.
• Tracking change: new detection pipeline turned on; pirated_themes table backfilled.
• Validity logic: incorrect month overlap condition; mishandled valid_to IS NULL.

If cumulative loss looks “exponential”

Cumulative curves naturally accelerate if monthly loss is increasing, but it can also signal:

• counting the same install multiple times,
• missing deduplication by (shop_id, theme_id, month),
• calendar expansion issues.

I’d show the PM monthly loss first to highlight true trend; cumulative second for “total exposure so far.”

6) Conclude with recommended next steps (actionable)

Measurement/validation (1–3 days)

• Validate numerator/denominator with spot checks: sample shops and verify theme state.
• Recompute with alternative definitions: “any pirated activity” vs. “majority of days in month.”
• Segment analysis to localize the spike.

Product + enforcement (1–4 weeks)

• Prioritize the top pirated themes/segments driving loss.
• Interventions: warnings, takedowns, improved license verification, friction in installation flow.

Causal evaluation

If proposing an intervention, recommend an experiment or quasi-experiment:

• A/B test or phased rollout to estimate impact on: marketplace revenue, theme installs, churn, support tickets.
• Guardrails: shop activation, churn, NPS/support load.

7) Close with what you need from the PM

• Confirm business definition of “active shop” and “theme revenue.”
• Align on acceptable assumptions for revenue-at-risk.
• Decide whether to treat this as (a) data quality incident, (b) enforcement priority, or (c) product opportunity—and set owners/timeline.