From 7e37999d4327bd3e2a431709859e333720a27680 Mon Sep 17 00:00:00 2001
From: Timothy Armes <tim@timothyarmes.com>
Date: Fri, 15 Sep 2023 13:03:42 +0200
Subject: [PATCH] Fix elo calculations

---
 app/[locale]/elo/page.tsx | 30 ++++----------
 utils/eloCalculator.ts    | 86 +++++++++++++++++++++++++++++++++++++++
 2 files changed, 93 insertions(+), 23 deletions(-)
 create mode 100644 utils/eloCalculator.ts

diff --git a/app/[locale]/elo/page.tsx b/app/[locale]/elo/page.tsx
index 5c5ff9f..6d9d9e1 100644
--- a/app/[locale]/elo/page.tsx
+++ b/app/[locale]/elo/page.tsx
@@ -9,26 +9,10 @@ import { z } from "zod";
 
 import { SelectField } from "@/components/form/SelectField";
 import { TextField } from "@/components/form/TextField";
+import { getNewRating } from "@/utils/eloCalculator";
 
 import { FetchResultsForm } from "./FetchResultsForm";
 
-const getNewRating = (
-  rating: number,
-  opponentRating: number,
-  result: 1 | 0 | 0.5,
-  kFactor: number,
-) => {
-  const myChanceToWin = 1 / (1 + Math.pow(10, (opponentRating - rating) / 400));
-  const delta =
-    Math.round((kFactor * (result - myChanceToWin) + Number.EPSILON) * 100) /
-    100;
-
-  return {
-    delta,
-    newRating: Math.round((rating + delta + Number.EPSILON) * 100) / 100,
-  };
-};
-
 const resultsSchema = z.object({
   currentElo: z.number().int().positive(),
   kFactor: z.enum(["40", "30", "20", "15", "10"]),
@@ -88,16 +72,15 @@ export default function Elo() {
             const result =
               game?.result === "win" ? 1 : game?.result === "loss" ? 0 : 0.5;
 
-            const { delta, newRating } = getNewRating(
-              acc.rating,
+            const { delta } = getNewRating(
+              currentElo!,
               game.opponentElo!,
               result,
               parseInt(kFactor!, 10),
             );
-
             return {
-              rating: newRating,
-              deltas: [...acc.deltas, { rating: newRating, delta }],
+              rating: acc.rating + delta,
+              deltas: [...acc.deltas, { rating: acc.rating + delta, delta }],
             };
           }
 
@@ -216,7 +199,8 @@ export default function Elo() {
                             deltas[i].delta! < 0 && "text-error",
                           )}
                         >
-                          {deltas[i]!.delta! >= 0 ? "+" : ""} {deltas[i].delta!}
+                          {deltas[i]!.delta! >= 0 ? "+" : ""}
+                          {deltas[i].delta!}
                         </span>
                         )
                       </div>
diff --git a/utils/eloCalculator.ts b/utils/eloCalculator.ts
new file mode 100644
index 0000000..1ffac22
--- /dev/null
+++ b/utils/eloCalculator.ts
@@ -0,0 +1,86 @@
+import { clamp, last } from "lodash";
+
+// Fide uses teh following table to establish the chance of winning based on the difference in elo.
+// https://handbook.fide.com/chapter/B022017
+
+const differenceToProbability: [
+  start: number,
+  end: number,
+  winChance: number,
+][] = [
+  [0, 3, 0.5],
+  [4, 10, 0.51],
+  [11, 17, 0.52],
+  [18, 25, 0.53],
+  [26, 32, 0.54],
+  [33, 39, 0.55],
+  [40, 46, 0.56],
+  [47, 53, 0.57],
+  [54, 61, 0.58],
+  [62, 68, 0.59],
+  [69, 76, 0.6],
+  [77, 83, 0.61],
+  [84, 91, 0.62],
+  [92, 98, 0.63],
+  [99, 106, 0.64],
+  [107, 113, 0.65],
+  [114, 121, 0.66],
+  [122, 129, 0.67],
+  [130, 137, 0.68],
+  [138, 145, 0.69],
+  [146, 153, 0.7],
+  [154, 162, 0.71],
+  [163, 170, 0.72],
+  [171, 179, 0.73],
+  [180, 188, 0.74],
+  [189, 197, 0.75],
+  [198, 206, 0.76],
+  [207, 215, 0.77],
+  [216, 225, 0.78],
+  [226, 235, 0.79],
+  [236, 245, 0.8],
+  [246, 256, 0.81],
+  [257, 267, 0.82],
+  [268, 278, 0.83],
+  [279, 290, 0.84],
+  [291, 302, 0.85],
+  [303, 315, 0.86],
+  [316, 328, 0.87],
+  [329, 344, 0.88],
+  [345, 357, 0.89],
+  [358, 374, 0.9],
+  [375, 391, 0.91],
+  [392, 411, 0.92],
+  [412, 432, 0.93],
+  [433, 456, 0.94],
+  [457, 484, 0.95],
+  [485, 517, 0.96],
+  [518, 559, 0.97],
+  [560, 619, 0.98],
+  [620, 735, 0.99],
+  [736, 1000, 1],
+];
+
+export const getNewRating = (
+  rating: number,
+  opponentRating: number,
+  result: 1 | 0 | 0.5,
+  kFactor: number,
+) => {
+  const differenceInElo = clamp(opponentRating - rating, -400, 400);
+  const tableRow = (differenceToProbability.find(
+    ([start, end]) =>
+      Math.abs(differenceInElo) >= start && Math.abs(differenceInElo) <= end,
+  ) ?? last(differenceToProbability)!)[2];
+
+  const probabilityOfWinning = differenceInElo < 0 ? tableRow : 1 - tableRow;
+  const delta =
+    Math.round(
+      kFactor * (result - probabilityOfWinning + Number.EPSILON) * 100,
+    ) / 100;
+
+  return {
+    delta,
+    newRating: Math.round((rating + delta + Number.EPSILON) * 100) / 100,
+  };
+};