Add user rating using Glicko rating system (#1498)

Mage.Server/src/main/java/mage/server/rating/GlickoRatingSystem.java

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+/*
+ *  Copyright 2011 BetaSteward_at_googlemail.com. All rights reserved.
+ *
+ *  Redistribution and use in source and binary forms, with or without modification, are
+ *  permitted provided that the following conditions are met:
+ *
+ *     1. Redistributions of source code must retain the above copyright notice, this list of
+ *        conditions and the following disclaimer.
+ *
+ *     2. Redistributions in binary form must reproduce the above copyright notice, this list
+ *        of conditions and the following disclaimer in the documentation and/or other materials
+ *        provided with the distribution.
+ *
+ *  THIS SOFTWARE IS PROVIDED BY BetaSteward_at_googlemail.com ``AS IS'' AND ANY EXPRESS OR IMPLIED
+ *  WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+ *  FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL BetaSteward_at_googlemail.com OR
+ *  CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+ *  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+ *  SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ *  ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ *  NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
+ *  ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ *  The views and conclusions contained in the software and documentation are those of the
+ *  authors and should not be interpreted as representing official policies, either expressed
+ *  or implied, of BetaSteward_at_googlemail.com.
+ */
+package mage.server.rating;
+
+import java.util.Date;
+
+/**
+ *
+ * @author Quercitron
+ */
+public class GlickoRatingSystem {
+
+    // rating deviation will grow back from 50 to max 350 in 2 years
+    public static final double C = 0.00137934314767061324980397708525;
+
+    public static final double BaseRating = 1500;
+    public static final double BaseRD = 350;
+    public static final double MinRD = 30;
+
+    private static final double Q = Math.log(10) / 400;
+
+    public static GlickoRating getInitialRating() {
+        return new GlickoRating(GlickoRatingSystem.BaseRating, GlickoRatingSystem.BaseRD, 0);
+    }
+
+    public static int getDisplayedRating(GlickoRating rating) {
+        long currentTime = new Date().getTime();
+        double updatedRatingDeviation = getUpdatedRD(rating, currentTime);
+        return (int) Math.max(rating.getRating() - 2 * updatedRatingDeviation, 0);
+    }
+
+    public static int getDefaultDisplayedRating() {
+        return getDisplayedRating(getInitialRating());
+    }
+
+    public void updateRating(GlickoRating playerRating, GlickoRating opponentRating, double outcome, long gameTimeMs) {
+        playerRating.setRatingDeviation(getUpdatedRD(playerRating, gameTimeMs));
+        opponentRating.setRatingDeviation(getUpdatedRD(opponentRating, gameTimeMs));
+
+        GlickoRating newPlayerRating = getNewRating(playerRating, opponentRating, outcome);
+        GlickoRating newOpponentRating = getNewRating(opponentRating, playerRating, 1 - outcome);
+
+        playerRating.setRating(newPlayerRating.getRating());
+        playerRating.setRatingDeviation(newPlayerRating.getRatingDeviation());
+        playerRating.setLastGameTimeMs(gameTimeMs);
+
+        opponentRating.setRating(newOpponentRating.getRating());
+        opponentRating.setRatingDeviation(newOpponentRating.getRatingDeviation());
+        opponentRating.setLastGameTimeMs(gameTimeMs);
+    }
+
+    private static double getUpdatedRD(GlickoRating rating, long gameTimeMs) {
+        double newRatingDeviation;
+        if (rating.getLastGameTimeMs() != 0)
+        {
+            double newRD = Math.sqrt(
+                    rating.getRatingDeviation() * rating.getRatingDeviation()
+                            + C * C * Math.max(gameTimeMs - rating.getLastGameTimeMs(), 0));
+            newRatingDeviation = Math.max(Math.min(BaseRD, newRD), MinRD);
+        }
+        else
+        {
+            newRatingDeviation = BaseRD;
+        }
+        return newRatingDeviation;
+    }
+
+    private GlickoRating getNewRating(GlickoRating playerRating, GlickoRating opponentRating, double outcome) {
+        double RD = playerRating.getRatingDeviation();
+
+        double g = gFunc(opponentRating.getRatingDeviation());
+        double p = -g * (playerRating.getRating() - opponentRating.getRating()) / 400;
+        double e = 1 / (1 + Math.pow(10, p));
+        double d2 = 1 / (Q * Q * g * g * e * (1 - e));
+
+        // todo: set minimum K?
+        double newRating = playerRating.getRating() + Q / (1 / RD / RD + 1 / d2) * g * (outcome - e);
+        double newRD = Math.sqrt(1 / (1 / RD / RD + 1 / d2));
+
+        return new GlickoRating(newRating, newRD);
+    }
+
+    private double gFunc(double rd) {
+        return 1 / Math.sqrt(1 + 3 * Q * Q * rd * rd / Math.PI / Math.PI);
+    }
+
+}