Given star ratings and votes, calculate bayesian estimate ratings to sort by popularity (taking number of votes into consideration)

bayesian_ranking.js

/*
  bayesian rating = (v ÷ (v+m)) × R + (m ÷ (v+m)) × C
  where:
  R = stars for the entry
  v = number of votes for the entry
  m = minimum votes required to be listed (eg. 10)
  C = the mean stars across the whole list (eg. 4.1)

  This rating only includes entries that have at least 10 votes. 
  The bayesian estimate is a statistical technique used to reduce the noise 
  due to low sample counts. In effect, the less an entry has votes, the more 
  it is pulled towards the mean (e.g. 4.1). In other words, these are the entry 
  that many people agree are great.
  
  https://www.animenewsnetwork.com/encyclopedia/ratings-anime.php#best_bayesian
*/
const calculateBayesianEstimate = (R,v,m,C)=>{
  return (v / (v + m)) * R + (m / (v + m)) * C
}

// calculate mean (= average)
const mean = arr=>arr.reduce((p,c)=>p + c, 0) / arr.length;

const entries = [{
  id: 1,
  stars: 4.5,
  votes: 700
}, {
  id: 2,
  stars: 3.7,
  votes: 1000
}, {
  id: 3,
  stars: 5,
  votes: 10
}, {
  id: 4,
  stars: 4.8,
  votes: 169
}, {
  id: 5,
  stars: 2.3,
  votes: 8000
}, ]

const totalVotesMean = mean(entries.map(e=>e.votes))
const totalStarsMean = mean(entries.map(e=>e.stars))
const minVotes = totalVotesMean * 0.1 // 10 percent of mean votes is minimum

console.log({
  totalVotesMean,
  totalStarsMean,
  minVotes
})
// => {totalVotesMean: 1975.8, totalStarsMean: 4.0600000000000005, minVotes: 197.58}

for (const entry of entries) {
  const rank = calculateBayesianEstimate(entry.stars, entry.votes, minVotes, totalStarsMean)
  entry.rank = rank
}
console.log(entries.sort((a,b)=>a.rank - b.rank).reverse())
/* => 
[
  {
    "id": 1,
    "stars": 4.5,
    "votes": 700,
    "rank": 4.403144900733082
  },
  {
    "id": 4,
    "stars": 4.8,
    "votes": 169,
    "rank": 4.401153363522287
  },
  {
    "id": 3,
    "stars": 5,
    "votes": 10,
    "rank": 4.105283746025629
  },
  {
    "id": 2,
    "stars": 3.7,
    "votes": 1000,
    "rank": 3.759393777451194
  },
  {
    "id": 5,
    "stars": 2.3,
    "votes": 8000,
    "rank": 2.3424199336877467
  }
]
*/

This took way too long to figure out 😅