algo-social-engagement

# Engagement Rate Calculation

## Overview

Engagement rate measures audience interaction relative to reach or audience size. Formula: (reactions + comments + shares) / denominator × 100%. The denominator choice (reach, impressions, followers) significantly affects the result. Computes in O(n) per post set.

## When to Use

**Trigger conditions:**
- Computing engagement metrics for social media reporting
- Benchmarking account or post performance against industry averages
- Comparing content performance across posts or accounts

**When NOT to use:**
- When evaluating influence holistically (use influence measurement)
- When modeling content spread dynamics (use virality models)

## Algorithm

```
IRON LAW: Engagement Rate Denominator MATTERS
By reach, by impressions, and by followers produce DIFFERENT numbers:
- ER by Reach = engagements / reach × 100% (most accurate, requires analytics access)
- ER by Impressions = engagements / impressions × 100% (always lower than by reach)
- ER by Followers = engagements / followers × 100% (public data, but inflated by non-reaching followers)
ALWAYS specify which variant when reporting or comparing.
```

### Phase 1: Input Validation
Collect per post: likes, comments, shares/retweets, saves (platform-specific), reach or impressions or follower count.
**Gate:** Consistent denominator across all posts being compared.

### Phase 2: Core Algorithm
1. Sum engagements per post: likes + comments + shares (+ saves, clicks if available)
2. Weight engagements if desired: share=3×, comment=2×, like=1× (shares indicate higher commitment)
3. Divide by chosen denominator (reach preferred, followers as fallback)
4. Compute: per-post ER, average ER across posts, median ER, ER trend over time

### Phase 3: Verification
Compare against platform benchmarks. Flag anomalies (ER > 20% likely data error or viral outlier).
**Gate:** Results within plausible range for platform.

### Phase 4: Output
Return engagement metrics with benchmarking context.

## Output Format

```json
{
  "metrics": {"avg_er_by_reach": 3.2, "avg_er_by_followers": 1.8, "median_er": 2.9, "top_post_er": 8.5},
  "benchmark": {"platform": "instagram", "industry": "fashion", "benchmark_er": 2.5, "percentile": 72},
  "metadata": {"posts_analyzed": 30, "period": "2025-Q1", "denominator": "reach"}
}
```

## Examples

### Sample I/O
**Input:** Post: 150 likes, 20 comments, 5 shares, reach=5000
**Expected:** ER by reach = (150+20+5)/5000 × 100% = 3.5%

### Edge Cases
| Input | Expected | Why |
|-------|----------|-----|
| Reach = 0 | Undefined, skip post | Can't divide by zero |
| Boosted/paid post | Separate from organic | Paid reach inflates denominator, deflates ER |
| Viral outlier (10x avg) | Flag, analyze separately | Skews averages |

## Gotchas

- **Platform algorithm changes**: Instagram's algorithm shifts regularly. Historical ER benchmarks become outdated. Use rolling 90-day benchmarks.
- **Vanity metric trap**: High ER doesn't mean business impact. 1000 likes on a meme ≠ 10 link clicks on a product post. Track meaningful engagements.
- **Story/Reel metrics differ**: Story engagement (taps, replies) and Reel engagement (plays, shares) need different formulas than feed posts. Don't mix.
- **Follower-based ER is noisy**: Not all followers see each post (reach < followers). ER by followers underestimates true engagement among those who saw the post.
- **Comparing across account sizes**: Smaller accounts naturally have higher ER by followers. Normalize or segment by account size for fair comparison.

## References

- For platform-specific benchmark data, see `references/platform-benchmarks.md`
- For weighted engagement scoring models, see `references/weighted-engagement.md`