Basic ELO sheets function

elo.js

const STARTING_ELO = 100
const K = 2

function normalized_win_probability(player_elo, total_game_elo, player_count) {
    const avg_opponent_elo = (total_game_elo - player_elo) / (player_count - 1)
    
    // Standard ELO algorithm with opponent ELO avged because we have more than one opponent
    const win_probability = 1 / (1 + Math.pow(10, (avg_opponent_elo - player_elo) / STARTING_ELO))
    
    // Normally ELO is calculated for 1 vs 1 games. We need to normalize the probability with the number of players. 
    const normalized_win_probability = 2 * win_probability / player_count

    return normalized_win_probability
}

function update_elo(players, winner, previous) {  
  const elos = previous || {}
  
  // Make sure any new players start with the default elo
  players.forEach(player => {
    elos[player] = elos[player] || STARTING_ELO
  })
  
   // We need the total game ELO and player count to calculate opponent avg elo
   let total_game_elo = 0
   let player_count = 0
   players.forEach(player => {
     total_game_elo += elos[player]
     player_count++
   })
   
   // Update all our player ELOs
   players.forEach(player => {
    const win_actual = player == winner ? 1 : 0
    const win_prob = normalized_win_probability(elos[player], total_game_elo, player_count)
    
    elos[player] += K * (win_actual - win_prob)
  })
  
  return elos
}

function player_elo(player, matchs, match_winners) {
  let elos = {}
  match_winners = match_winners.flat()
  for(let i = 0; i < matchs.length; i++) {
    const match = matchs[i]
    const winner = match_winners[i] // We assume match_winners only have one column
    
    elos = update_elo(match, winner, elos)
  }
 
  return elos[player]
}