Update elo to support multiplayer

snippets/elo.md

@@ -1,24 +1,65 @@
 ### elo
 
-Computes the new ratings between two opponents using the [Elo rating system](https://en.wikipedia.org/wiki/Elo_rating_system). It takes an array
-of two pre-ratings and returns an array containing two post-ratings.
-The winner's rating is the first element of the array.
+Computes the new ratings between two or more opponents using the [Elo rating system](https://en.wikipedia.org/wiki/Elo_rating_system). It takes an array
+of pre-ratings and returns an array containing post-ratings.
+The array should be ordered from best performer to worst performer (winner -> loser).
 
 Use the exponent `**` operator and math operators to compute the expected score (chance of winning)
-of each opponent and compute the new rating for each. Omit the second argument to use the default
-K-factor of 32, or supply a custom K-factor value.
+of each opponent and compute the new rating for each. Loop through the ratings, using each permutation to compute the post-Elo rating for each player in a pairwise fashion. Omit the second argument to use the default K-factor of 32, or supply a custom K-factor value. For details on the third argument, see the last example.
 
 ```js
-const elo = ([a, b], kFactor = 32) => {
+const elo = ([...ratings], kFactor = 32, selfRating) => {
+  const [a, b] = ratings;
   const expectedScore = (self, opponent) => 1 / (1 + 10 ** ((opponent - self) / 400));
-  const newRating = (rating, i) => rating + kFactor * (i - expectedScore(i ? a : b, i ? b : a));
-  return [newRating(a, 1), newRating(b, 0)];
+  const newRating = (rating, i) =>
+    (selfRating || rating) + kFactor * (i - expectedScore(i ? a : b, i ? b : a));
+  if (ratings.length === 2) {
+    return [newRating(a, 1), newRating(b, 0)];
+  } else {
+    for (let i = 0; i < ratings.length; i++) {
+      let j = i;
+      while (j < ratings.length - 1) {
+        [ratings[i], ratings[j + 1]] = elo([ratings[i], ratings[j + 1]], kFactor);
+        j++;
+      }
+    }
+  }
+  return ratings;
 };
 ```
 
 ```js
+// Standard 1v1s
 elo([1200, 1200]); // [1216, 1184]
 elo([1000, 2000]); // [1031.8991261061358, 1968.1008738938642]
 elo([1500, 1000]); // [1501.7036868864648, 998.2963131135352]
 elo([1200, 1200], 64); // [1232, 1168]
+
+// 4 player FFA, all same rank
+elo([1200, 1200, 1200, 1200]).map(Math.round); // [1246, 1215, 1185, 1154]
+
+// For teams, each rating can adjusted based on own team's average rating vs. 
+// average rating of opposing team, with the score being added to their
+// own individual rating
+
+// 2v2 teams
+// Ratings: [1324, 1275] and [1300, 1318]
+// Calculate the average ratings of each team and use that as
+// the basis of the "expected score" calculation. Supply the individual
+// rating as the third argument to compute own Elo rating.
+const ratings = [1324, 1275, 1300, 1318];
+const averages = [(1324 + 1275) / 2, (1300 + 1318) / 2];
+const results = ratings
+  .map(
+    (rating, index) =>
+      elo(
+        [index > 1 ? averages[0] : averages[1], index > 1 ? averages[0] : averages[1]],
+        32,
+        rating
+      )[index > 1 ? 1 : 0]
+  )
+  .map(Math.round); // [1340, 1291, 1284, 1302]
+
+// Individual rank in the match out of each player is also possible to take into account
+// Try out 50/50 balance between win/loss and individual performance
 ```