Define engagement metrics and analyze comment distribution

You are a Data Scientist for a video platform. A PM asks you to:

1. Define metrics for “engagement” (they want a clear metric framework they can use in experiments).
2. Analyze user comment distribution and propose how you would monitor it over time.

Part A — Engagement metric framework

Propose:

• Primary metric(s) (what you would optimize)
• Diagnostic metrics (to explain movement)
• Guardrail metrics (to prevent harmful changes)

Be explicit about:

• Unit of analysis (user-day, session, video-view, etc.)
• How you’d handle heavy users / skew (mean vs median, winsorization, log transforms)
• How you’d prevent gaming (spammy/low-quality engagement)

Part B — Comment distribution

Comments are known to be heavy-tailed (most users comment rarely; a small minority comment a lot).

Describe:

• What distributions you would compute (by user, by video, by cohort)
• What slices you would look at (new vs returning users, content categories, geos)
• How you would detect regressions or anomalies (e.g., bots, spam, ranking changes)
• What experiment you would run if the goal is to increase “healthy” commenting, including key confounders and how you’d interpret results