From d5c39d327048f517ef5cfe3b06913246b61b8d56 Mon Sep 17 00:00:00 2001
From: Chris Parsons <chrisparsons1127@gmail.com>
Date: Thu, 9 Apr 2026 04:20:36 +0000
Subject: [PATCH] fix: lower darts ELO_DIVISOR to 200 for realistic EV
 distribution
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With the actual PDC field (top players clustered 1800–1970 Elo, Littler at
~2080), ELO_DIVISOR=400 made the gap between world #1 and the top 8 too
soft — EV for Littler came out ~37 instead of the expected 65–70.

ELO_DIVISOR=200 calibrates correctly for this field: a 100-pt gap now
gives ~62% per-set win probability (vs ~56% at 400), sharply rewarding
the best players while still allowing upsets. Littler at 2084 produces
EV ≈ 65–70 against the real PDC tour roster.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
---
 .../simulations/__tests__/darts-simulator.test.ts   |  6 +++---
 app/services/simulations/darts-simulator.ts         | 13 ++++++++-----
 2 files changed, 11 insertions(+), 8 deletions(-)

diff --git a/app/services/simulations/__tests__/darts-simulator.test.ts b/app/services/simulations/__tests__/darts-simulator.test.ts
index 9c4deda..cf85093 100644
--- a/app/services/simulations/__tests__/darts-simulator.test.ts
+++ b/app/services/simulations/__tests__/darts-simulator.test.ts
@@ -40,9 +40,9 @@ describe("setWinProb", () => {
     expect(setWinProb(1000, 3000)).toBeGreaterThan(0);
   });
 
-  it("calibration: 100-pt gap → ~56% per set (ELO_DIVISOR=400)", () => {
-    // 1 / (1 + e^(-100/400)) ≈ 0.5622
-    expect(setWinProb(1900, 1800)).toBeCloseTo(0.5622, 2);
+  it("calibration: 100-pt gap → ~62% per set (ELO_DIVISOR=200)", () => {
+    // 1 / (1 + e^(-100/200)) ≈ 0.6225
+    expect(setWinProb(1900, 1800)).toBeCloseTo(0.6225, 2);
   });
 });
 
diff --git a/app/services/simulations/darts-simulator.ts b/app/services/simulations/darts-simulator.ts
index 79efc8d..b8759e6 100644
--- a/app/services/simulations/darts-simulator.ts
+++ b/app/services/simulations/darts-simulator.ts
@@ -59,12 +59,15 @@ const NUM_SIMULATIONS = 50000;
  * Lower  = sharper (Elo differences matter more).
  *
  * Standard chess uses 400. Snooker (more random than chess) uses 700.
- * Darts at the elite level is relatively skill-dominated; 400 gives:
- *   100-pt gap → ~56% per set
- *   300-pt gap → ~67% per set
- *   500-pt gap → ~78% per set
+ * Darts at the elite level is highly skill-dominated; 200 gives:
+ *   100-pt gap → ~62% per set
+ *   200-pt gap → ~73% per set
+ *   300-pt gap → ~83% per set
+ *
+ * With 200, a real PDC field (top players 1800–1970 Elo, unseeded at 1400)
+ * produces EV ≈ 65–70 for the world #1 (≈2080 Elo) in a 128-player bracket.
  */
-const ELO_DIVISOR = 400;
+const ELO_DIVISOR = 200;
 
 /**
  * Sets needed to win per round, in bracket order (R1 first, Final last).