Average Rating โ Weighted Avg, Bayesian Avg, Wilson Score
Compute weighted average, Bayesian average, Wilson score for star ratings. Distribution, mode, median, standard deviation. Used by IMDb, Reddit, and product reviews.
Why This Statistical Analysis Matters
Why: Raw average is misleading with few reviews. A single 5-star review gives 100%. Bayesian average and Wilson score penalize low sample sizes for fair ranking.
How: Enter counts per rating. Weighted avg = ฮฃ(rรcount)/n. Bayesian = (Cรm + ฮฃ(rรcount))/(C+n). Wilson gives a conservative lower bound for ranking.
- โBayesian shrinks toward prior when few reviews
- โWilson used by Reddit for comment ranking
- โIMDb uses Cโ25,000, mโ7.0
Average Rating โ Weighted Avg, Bayesian Avg, Wilson Score for Star Ratings
Compute weighted average, Bayesian average, Wilson score. Distribution, mode, median, standard deviation.
Real-World Scenarios โ Click to Load
For educational and informational purposes only. Verify with a qualified professional.
Key Takeaways
- โข Weighted average: Rฬ = ฮฃ(rating ร count) / ฮฃ(count) โ the standard way to combine star ratings
- โข Bayesian average shrinks toward a prior mean when you have few reviews โ prevents new items from ranking too high
- โข Wilson score lower bound gives a conservative ranking that accounts for sample size โ used by Reddit, IMDb
- โข Standard deviation and variance measure spread of ratings; mode and median complement the mean
- โข Distribution percentages show how ratings are spread across star levels
Did You Know?
Expert Tips
Bayesian Prior
Set m to your scale midpoint (2.5 for 5-star, 5.5 for 10-point). C: higher = more weight on prior.
Wilson for Ranking
Use Wilson lower bound when ranking items. It penalizes low sample sizes and prevents gaming.
Scale Choice
5-star is universal; 10-point allows finer granularity (IMDb, games). Custom scales for specialized contexts.
Distribution Shape
J-shaped (many 5-stars) vs bimodal (polarized) โ distribution % reveals more than the average alone.
Why Use This Calculator vs Other Tools?
| Feature | This Calculator | Simple Avg | Excel |
|---|---|---|---|
| Weighted average | โ | โ | โ ๏ธ Manual |
| Bayesian average | โ | โ | โ |
| Wilson score | โ | โ | โ |
| Distribution % | โ | โ | โ ๏ธ Pivot |
| 5/10/custom scale | โ | โ | โ |
| Mode, median, SD | โ | โ | โ ๏ธ Multiple |
| Copy/share/AI | โ | โ | โ |
Frequently Asked Questions
What is the Bayesian average?
A prior-weighted average that shrinks toward a default (e.g., 3.0) when you have few reviews. Prevents new items from outranking established ones.
What is the Wilson score?
A confidence interval lower bound for a proportion. Used for ranking: conservative estimate that accounts for sample size.
Why not just use the simple average?
Simple average ignores sample size. 5.0 from 2 reviews is less reliable than 4.5 from 500. Bayesian and Wilson methods correct for this.
How do I choose C and m for Bayesian?
m = scale midpoint (2.5 for 5-star). C: start with 10โ25. Higher C = more shrinkage; lower = faster convergence to observed mean.
What counts as a positive rating for Wilson?
Typically ratings โฅ 60% of max (e.g., 4โ5 stars on 5-star scale, 7โ10 on 10-point).
Rating Systems by the Numbers
Official Data Sources
Disclaimer: Bayesian and Wilson parameters are configurable. Results depend on your choice of C, m, and positive threshold. Adjust for your use case.
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