From 22f5b3ab638af0c4bad6e14f8cf40b7b52f3e23e Mon Sep 17 00:00:00 2001
From: Ant Zucaro <azucaro@gmail.com>
Date: Sun, 17 Dec 2017 10:33:29 -0500
Subject: [PATCH] Start work on Glicko in Python (for per-game calculations).

---
 xonstat/glicko.py | 69 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 69 insertions(+)
 create mode 100644 xonstat/glicko.py

diff --git a/xonstat/glicko.py b/xonstat/glicko.py
new file mode 100644
index 0000000..1f1ca9f
--- /dev/null
+++ b/xonstat/glicko.py
@@ -0,0 +1,69 @@
+import logging
+import math
+
+log = logging.getLogger(__name__)
+
+# the default initial rating value
+MU = 1500
+
+# the default ratings deviation value
+PHI = 350
+
+# the default volatility value
+SIGMA = 0.06
+
+# the default system volatility constant
+TAU = 0.3
+
+# the ratio to convert from/to glicko2
+GLICKO2_SCALE = 173.7178
+
+
+class PlayerGlicko(object):
+    def __init__(self, mu=MU, phi=PHI, sigma=SIGMA):
+        self.mu = mu
+        self.phi = phi
+        self.sigma = sigma
+
+    def to_glicko2(self):
+        """ Convert a rating to the Glicko2 scale. """
+        return PlayerGlicko(
+            mu=(self.mu - MU) / GLICKO2_SCALE,
+            phi=self.phi / GLICKO2_SCALE,
+            sigma=self.sigma
+        )
+
+    def from_glicko2(self):
+        """ Convert a rating to the original Glicko scale. """
+        return PlayerGlicko(
+            mu=self.mu * GLICKO2_SCALE + MU,
+            phi=self.phi * GLICKO2_SCALE,
+            sigma=self.sigma
+        )
+
+
+def g(phi):
+    return 1 / math.sqrt(1 + (3 * phi ** 2) / (math.pi ** 2))
+
+
+def e(mu, mu_j, phi_j):
+    return 1. / (1 + math.exp(-g(phi_j) * (mu - mu_j)))
+
+
+def v(gs, es):
+    """ Estimated variance of the team or player's ratings based only on game outcomes. """
+    total = 0.0
+    for i in range(len(gs)):
+        total += (gs[i] ** 2) * es[i] * (1-es[i])
+
+    return 1. / total
+
+
+def delta(v, gs, es, results):
+    """ Compute the estimated improvement in rating by comparing the pre-period rating to the
+    performance rating based only on game outcomes. """
+    total = 0.0
+    for i in range(len(gs)):
+        total += gs[i] * (results[i] - es[i])
+
+    return v * total
-- 
2.39.2