Naming tweak

Skills/TrueSkill/DrawMargin.php

@@ -0,0 +1,26 @@
+<?php
+namespace Moserware\Skills\TrueSkill;
+
+require_once(dirname(__FILE__) . "/../Numerics/GaussianDistribution.php");
+
+use Moserware\Numerics\GaussianDistribution;
+
+final class DrawMargin
+{
+    public static function getDrawMarginFromDrawProbability($drawProbability, $beta)
+    {
+        // Derived from TrueSkill technical report (MSR-TR-2006-80), page 6
+
+        // draw probability = 2 * CDF(margin/(sqrt(n1+n2)*beta)) -1
+
+        // implies
+        //
+        // margin = inversecdf((draw probability + 1)/2) * sqrt(n1+n2) * beta
+        // n1 and n2 are the number of players on each team
+        $margin = GaussianDistribution::inverseCumulativeTo(.5*($drawProbability + 1), 0, 1)*sqrt(1 + 1)*
+                        $beta;
+        return $margin;
+    }
+}
+
+?>

Skills/TrueSkill/FactorGraphTrueSkillCalculator.php

@@ -0,0 +1,207 @@
+<?php
+
+namespace Moserware\Skills\TrueSkill;
+
+require_once(dirname(__FILE__) . "/../GameInfo.php");
+require_once(dirname(__FILE__) . "/../Guard.php");
+require_once(dirname(__FILE__) . "/../ISupportPartialPlay.php");
+require_once(dirname(__FILE__) . "/../ISupportPartialUpdate.php");
+require_once(dirname(__FILE__) . "/../PartialPlay.php");
+require_once(dirname(__FILE__) . "/../PlayersRange.php");
+require_once(dirname(__FILE__) . "/../RankSorter.php");
+require_once(dirname(__FILE__) . "/../SkillCalculator.php");
+require_once(dirname(__FILE__) . "/../TeamsRange.php");
+require_once(dirname(__FILE__) . "/../Numerics/BasicMath.php");
+require_once(dirname(__FILE__) . "/../Numerics/Matrix.php");
+require_once(dirname(__FILE__) . "/TrueSkillFactorGraph.php");
+
+use Moserware\Numerics\DiagonalMatrix;
+use Moserware\Numerics\Matrix;
+use Moserware\Numerics\Vector;
+
+use Moserware\Skills\GameInfo;
+use Moserware\Skills\Guard;
+use Moserware\Skills\ISupportPartialPlay;
+use Moserware\Skills\ISupportPartialUpdate;
+use Moserware\Skills\PartialPlay;
+use Moserware\Skills\PlayersRange;
+use Moserware\Skills\RankSorter;
+use Moserware\Skills\SkillCalculator;
+use Moserware\Skills\SkillCalculatorSupportedOptions;
+use Moserware\Skills\TeamsRange;
+
+/**
+ * Calculates TrueSkill using a full factor graph.
+ */
+class FactorGraphTrueSkillCalculator extends SkillCalculator
+{
+    public function __construct()
+    {
+        parent::__construct(SkillCalculatorSupportedOptions::PARTIAL_PLAY | SkillCalculatorSupportedOptions::PARTIAL_UPDATE, TeamsRange::atLeast(2), PlayersRange::atLeast(1));
+    }
+
+    public function calculateNewRatings(GameInfo &$gameInfo,
+                                        array $teams,
+                                        array $teamRanks)
+    {
+        Guard::argumentNotNull($gameInfo, "gameInfo");
+        $this->validateTeamCountAndPlayersCountPerTeam($teams);
+
+        RankSorter::sort($teams, $teamRanks);
+
+        $factorGraph = new TrueSkillFactorGraph($gameInfo, $teams, $teamRanks);
+        $factorGraph->buildGraph();
+        $factorGraph->runSchedule();
+        
+        $probabilityOfOutcome = $factorGraph->getProbabilityOfRanking();
+
+        return $factorGraph->getUpdatedRatings();
+    }
+
+    public function calculateMatchQuality(GameInfo &$gameInfo,
+                                          array &$teams)
+    {
+        // We need to create the A matrix which is the player team assigments.
+        $teamAssignmentsList = $teams;
+        $skillsMatrix = $this->getPlayerCovarianceMatrix($teamAssignmentsList);
+        $meanVector = $this->getPlayerMeansVector($teamAssignmentsList);
+        $meanVectorTranspose = $meanVector->getTranspose();
+
+        $playerTeamAssignmentsMatrix = $this->createPlayerTeamAssignmentMatrix($teamAssignmentsList, $meanVector->getRowCount());
+        $playerTeamAssignmentsMatrixTranspose = $playerTeamAssignmentsMatrix->getTranspose();
+
+        $betaSquared = square($gameInfo->getBeta());
+
+        $start = Matrix::multiply($meanVectorTranspose, $playerTeamAssignmentsMatrix);
+        $aTa = Matrix::multiply(
+                        Matrix::scalarMultiply($betaSquared,
+                                               $playerTeamAssignmentsMatrixTranspose),
+                        $playerTeamAssignmentsMatrix);
+
+        $aTSA = Matrix::multiply(
+                    Matrix::multiply($playerTeamAssignmentsMatrixTranspose, $skillsMatrix),
+                    $playerTeamAssignmentsMatrix);
+
+        $middle = Matrix::add($aTa, $aTSA);
+
+        $middleInverse = $middle->getInverse();
+
+        $end = Matrix::multiply($playerTeamAssignmentsMatrixTranspose, $meanVector);
+
+        $expPartMatrix = Matrix::scalarMultiply(-0.5, (Matrix::multiply(Matrix::multiply($start, $middleInverse), $end)));
+        $expPart = $expPartMatrix->getDeterminant();
+
+        $sqrtPartNumerator = $aTa->getDeterminant();
+        $sqrtPartDenominator = $middle->getDeterminant();
+        $sqrtPart = $sqrtPartNumerator / $sqrtPartDenominator;
+
+        $result = exp($expPart) * sqrt($sqrtPart);
+
+        return $result;
+    }
+
+    private static function getPlayerMeansVector(array &$teamAssignmentsList)
+    {
+        // A simple vector of all the player means.
+        return new Vector(self::getPlayerRatingValues($teamAssignmentsList,
+                                                      function($rating) 
+                                                      { 
+                                                           return $rating->getMean();
+                                                      }));
+    }
+
+    private static function getPlayerCovarianceMatrix(array &$teamAssignmentsList)
+    {
+        // This is a square matrix whose diagonal values represent the variance (square of standard deviation) of all
+        // players.
+        return new DiagonalMatrix(
+                        self::getPlayerRatingValues($teamAssignmentsList,
+                                                    function($rating)
+                                                    {
+                                                       return square($rating->getStandardDeviation());
+                                                    }));
+    }
+
+    // Helper function that gets a list of values for all player ratings
+    private static function getPlayerRatingValues(array &$teamAssignmentsList,
+                                                  $playerRatingFunction)
+    {
+        $playerRatingValues = array();
+
+        foreach ($teamAssignmentsList as $currentTeam)
+        {
+            foreach ($currentTeam->getAllRatings() as $currentRating)
+            {
+                $playerRatingValues[] = $playerRatingFunction($currentRating);
+            }
+        }
+
+        return $playerRatingValues;
+    }
+
+    private static function createPlayerTeamAssignmentMatrix(&$teamAssignmentsList, $totalPlayers)
+    {
+        // The team assignment matrix is often referred to as the "A" matrix. It's a matrix whose rows represent the players
+        // and the columns represent teams. At Matrix[row, column] represents that player[row] is on team[col]
+        // Positive values represent an assignment and a negative value means that we subtract the value of the next
+        // team since we're dealing with pairs. This means that this matrix always has teams - 1 columns.
+        // The only other tricky thing is that values represent the play percentage.
+
+        // For example, consider a 3 team game where team1 is just player1, team 2 is player 2 and player 3, and
+        // team3 is just player 4. Furthermore, player 2 and player 3 on team 2 played 25% and 75% of the time
+        // (e.g. partial play), the A matrix would be:
+
+        // A = this 4x2 matrix:
+        // |  1.00  0.00 |
+        // | -0.25  0.25 |
+        // | -0.75  0.75 |
+        // |  0.00 -1.00 |
+
+        $playerAssignments = array();
+        $totalPreviousPlayers = 0;
+
+        $teamAssignmentsListCount = count($teamAssignmentsList);
+
+        $currentColumn = 0;
+
+        for ($i = 0; $i < $teamAssignmentsListCount - 1; $i++)
+        {
+            $currentTeam = $teamAssignmentsList[$i];
+
+            // Need to add in 0's for all the previous players, since they're not
+            // on this team
+            $playerAssignments[$currentColumn] = ($totalPreviousPlayers > 0) ? \array_fill(0, $totalPreviousPlayers, 0) : array();
+
+            foreach ($currentTeam->getAllPlayers() as $currentPlayer)
+            {
+                $playerAssignments[$currentColumn][] = PartialPlay::getPartialPlayPercentage($currentPlayer);
+                // indicates the player is on the team
+                $totalPreviousPlayers++;
+            }
+
+            $rowsRemaining = $totalPlayers - $totalPreviousPlayers;
+
+            $nextTeam = $teamAssignmentsList[$i + 1];
+            foreach ($nextTeam->getAllPlayers() as $nextTeamPlayer)
+            {
+                // Add a -1 * playing time to represent the difference
+                $playerAssignments[$currentColumn][] = -1 * PartialPlay::getPartialPlayPercentage($nextTeamPlayer);
+                $rowsRemaining--;
+            }
+
+            for ($ixAdditionalRow = 0; $ixAdditionalRow < $rowsRemaining; $ixAdditionalRow++)
+            {
+                // Pad with zeros
+                $playerAssignments[$currentColumn][] = 0;
+            }
+
+            $currentColumn++;
+        }
+
+        $playerTeamAssignmentsMatrix = Matrix::fromColumnValues($totalPlayers, $teamAssignmentsListCount - 1, $playerAssignments);
+
+        return $playerTeamAssignmentsMatrix;
+    }
+}
+
+?>

Skills/TrueSkill/Factors/GaussianFactor.php

@@ -0,0 +1,45 @@
+<?php
+
+namespace Moserware\Skills\TrueSkill\Factors;
+
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Factor.php");
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Message.php");
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Variable.php");
+require_once(dirname(__FILE__) . "/../../Numerics/GaussianDistribution.php");
+
+use Moserware\Numerics\GaussianDistribution;
+use Moserware\Skills\FactorGraphs\Factor;
+use Moserware\Skills\FactorGraphs\Message;
+use Moserware\Skills\FactorGraphs\Variable;
+
+abstract class GaussianFactor extends Factor
+{
+    protected function __construct($name)
+    {
+        parent::__construct($name);
+    }
+
+    /**
+     * Sends the factor-graph message with and returns the log-normalization constant.
+     */
+    protected function sendMessageVariable(Message &$message, Variable &$variable)
+    {
+        $marginal = &$variable->getValue();
+        $messageValue = &$message->getValue();
+        $logZ = GaussianDistribution::logProductNormalization($marginal, $messageValue);
+        $variable->setValue(GaussianDistribution::multiply($marginal, $messageValue));
+        return $logZ;
+    }
+
+    public function &createVariableToMessageBinding(Variable &$variable)
+    {
+        $newDistribution = GaussianDistribution::fromPrecisionMean(0, 0);
+        $binding = &parent::createVariableToMessageBindingWithMessage($variable,
+                                                      new Message(
+                                                          $newDistribution,
+                                                          sprintf("message from %s to %s", $this, $variable)));
+        return $binding;
+    }
+}
+
+?>

Skills/TrueSkill/Factors/GaussianGreaterThanFactor.php

@@ -0,0 +1,85 @@
+<?php
+namespace Moserware\Skills\TrueSkill\Factors;
+
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Message.php");
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Variable.php");
+require_once(dirname(__FILE__) . "/../../Numerics/GaussianDistribution.php");
+require_once(dirname(__FILE__) . "/../TruncatedGaussianCorrectionFunctions.php");
+require_once(dirname(__FILE__) . "/GaussianFactor.php");
+
+use Moserware\Numerics\GaussianDistribution;
+use Moserware\Skills\TrueSkill\TruncatedGaussianCorrectionFunctions;
+use Moserware\Skills\FactorGraphs\Message;
+use Moserware\Skills\FactorGraphs\Variable;
+
+/**
+ * Factor representing a team difference that has exceeded the draw margin.
+ *
+ * See the accompanying math paper for more details.
+ */
+class GaussianGreaterThanFactor extends GaussianFactor
+{
+    private $_epsilon;
+
+    public function __construct($epsilon, Variable &$variable)
+    {
+        parent::__construct(\sprintf("%s > %.2f", $variable, $epsilon));
+        $this->_epsilon = $epsilon;
+        $this->createVariableToMessageBinding($variable);
+    }
+
+    public function getLogNormalization()
+    {
+        $vars = &$this->getVariables();
+        $marginal = &$vars[0]->getValue();
+        $messages = &$this->getMessages();
+        $message = &$messages[0]->getValue();
+        $messageFromVariable = GaussianDistribution::divide($marginal, $message);
+        return -GaussianDistribution::logProductNormalization($messageFromVariable, $message)
+               +
+               log(
+                   GaussianDistribution::cumulativeTo(($messageFromVariable->getMean() - $this->_epsilon)/
+                                                     $messageFromVariable->getStandardDeviation()));
+
+    }
+
+    protected function updateMessageVariable(Message &$message, Variable &$variable)
+    {
+        $oldMarginal = clone $variable->getValue();
+        $oldMessage = clone $message->getValue();
+        $messageFromVar = GaussianDistribution::divide($oldMarginal, $oldMessage);
+
+        $c = $messageFromVar->getPrecision();
+        $d = $messageFromVar->getPrecisionMean();
+
+        $sqrtC = sqrt($c);
+
+        $dOnSqrtC = $d/$sqrtC;
+
+        $epsilsonTimesSqrtC = $this->_epsilon*$sqrtC;
+        $d = $messageFromVar->getPrecisionMean();
+
+        $denom = 1.0 - TruncatedGaussianCorrectionFunctions::wExceedsMargin($dOnSqrtC, $epsilsonTimesSqrtC);
+
+        $newPrecision = $c/$denom;
+        $newPrecisionMean = ($d +
+                             $sqrtC*
+                             TruncatedGaussianCorrectionFunctions::vExceedsMargin($dOnSqrtC, $epsilsonTimesSqrtC))/
+                             $denom;
+
+        $newMarginal = GaussianDistribution::fromPrecisionMean($newPrecisionMean, $newPrecision);
+
+        $newMessage = GaussianDistribution::divide(
+                              GaussianDistribution::multiply($oldMessage, $newMarginal),
+                              $oldMarginal);
+
+        // Update the message and marginal
+        $message->setValue($newMessage);
+
+        $variable->setValue($newMarginal);
+
+        // Return the difference in the new marginal
+        return GaussianDistribution::subtract($newMarginal, $oldMarginal);
+    }
+}
+?>

Skills/TrueSkill/Factors/GaussianLikelihoodFactor.php

@@ -0,0 +1,87 @@
+<?php
+namespace Moserware\Skills\TrueSkill\Factors;
+
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Message.php");
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Variable.php");
+require_once(dirname(__FILE__) . "/../../Numerics/GaussianDistribution.php");
+require_once(dirname(__FILE__) . "/GaussianFactor.php");
+
+use Moserware\Numerics\GaussianDistribution;
+use Moserware\Skills\FactorGraphs\Message;
+use Moserware\Skills\FactorGraphs\Variable;
+
+/**
+ * Connects two variables and adds uncertainty.
+ * 
+ * See the accompanying math paper for more details.
+ */
+class GaussianLikelihoodFactor extends GaussianFactor
+{
+    private $_precision;
+
+    public function __construct($betaSquared, Variable &$variable1, Variable &$variable2)
+    {
+        parent::__construct(sprintf("Likelihood of %s going to %s", $variable2, $variable1));
+        $this->_precision = 1.0/$betaSquared;
+        $this->createVariableToMessageBinding($variable1);
+        $this->createVariableToMessageBinding($variable2);
+    }
+
+    public function getLogNormalization()
+    {
+        $vars = &$this->getVariables();
+        $messages = &$this->getMessages();
+
+        return GaussianDistribution::logRatioNormalization(
+                $vars[0]->getValue(),
+                $messages[0]->getValue());
+    }
+
+    private function updateHelper(Message &$message1, Message &$message2,
+                                  Variable &$variable1, Variable &$variable2)
+    {        
+        $message1Value = clone $message1->getValue();
+        $message2Value = clone $message2->getValue();        
+        
+        $marginal1 = clone $variable1->getValue();
+        $marginal2 = clone $variable2->getValue();
+
+        $a = $this->_precision/($this->_precision + $marginal2->getPrecision() - $message2Value->getPrecision());
+
+        $newMessage = GaussianDistribution::fromPrecisionMean(
+            $a*($marginal2->getPrecisionMean() - $message2Value->getPrecisionMean()),
+            $a*($marginal2->getPrecision() - $message2Value->getPrecision()));
+
+        $oldMarginalWithoutMessage = GaussianDistribution::divide($marginal1, $message1Value);
+
+        $newMarginal = GaussianDistribution::multiply($oldMarginalWithoutMessage, $newMessage);
+
+        // Update the message and marginal
+
+        $message1->setValue($newMessage);
+        $variable1->setValue($newMarginal);
+
+        // Return the difference in the new marginal
+        return GaussianDistribution::subtract($newMarginal, $marginal1);
+    }
+
+    public function updateMessageIndex($messageIndex)
+    {
+        $messages = &$this->getMessages();
+        $vars = &$this->getVariables();       
+
+        switch ($messageIndex)
+        {
+            case 0:
+                return $this->updateHelper($messages[0], $messages[1],
+                                           $vars[0], $vars[1]);
+            case 1:
+                return $this->updateHelper($messages[1], $messages[0],
+                                           $vars[1], $vars[0]);
+            default:
+                throw new Exception();
+        }
+    }
+}
+
+?>

Skills/TrueSkill/Factors/GaussianPriorFactor.php

@@ -0,0 +1,48 @@
+<?php
+namespace Moserware\Skills\TrueSkill\Factors;
+
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Message.php");
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Variable.php");
+require_once(dirname(__FILE__) . "/../../Numerics/GaussianDistribution.php");
+require_once(dirname(__FILE__) . "/GaussianFactor.php");
+
+use Moserware\Numerics\GaussianDistribution;
+use Moserware\Skills\FactorGraphs\Message;
+use Moserware\Skills\FactorGraphs\Variable;
+
+/**
+ * Supplies the factor graph with prior information.
+ *
+ * See the accompanying math paper for more details.
+ */
+class GaussianPriorFactor extends GaussianFactor
+{
+    private $_newMessage;
+
+    public function __construct($mean, $variance, Variable &$variable)
+    {
+        parent::__construct(sprintf("Prior value going to %s", $variable));
+        $this->_newMessage = new GaussianDistribution($mean, sqrt($variance));
+        $newMessage = new Message(GaussianDistribution::fromPrecisionMean(0, 0),
+                                  sprintf("message from %s to %s", $this, $variable));
+
+        $this->createVariableToMessageBindingWithMessage($variable, $newMessage);
+    }
+
+    protected function updateMessageVariable(Message &$message, Variable &$variable)
+    {
+        $oldMarginal = clone $variable->getValue();
+        $oldMessage = $message;
+        $newMarginal =
+            GaussianDistribution::fromPrecisionMean(
+                $oldMarginal->getPrecisionMean() + $this->_newMessage->getPrecisionMean() - $oldMessage->getValue()->getPrecisionMean(),
+                $oldMarginal->getPrecision() + $this->_newMessage->getPrecision() - $oldMessage->getValue()->getPrecision());
+
+        $variable->setValue($newMarginal);
+        $newMessage = &$this->_newMessage;
+        $message->setValue($newMessage);
+        return GaussianDistribution::subtract($oldMarginal, $newMarginal);
+    }
+}
+
+?>

Skills/TrueSkill/Factors/GaussianWeightedSumFactor.php

@@ -0,0 +1,272 @@
+<?php
+namespace Moserware\Skills\TrueSkill\Factors;
+
+require_once(dirname(__FILE__) . "/../../Guard.php");
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Message.php");
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Variable.php");
+require_once(dirname(__FILE__) . "/../../Numerics/GaussianDistribution.php");
+require_once(dirname(__FILE__) . "/../../Numerics/BasicMath.php");
+require_once(dirname(__FILE__) . "/GaussianFactor.php");
+
+use Moserware\Numerics\GaussianDistribution;
+use Moserware\Skills\Guard;
+use Moserware\Skills\FactorGraphs\Message;
+use Moserware\Skills\FactorGraphs\Variable;
+
+/**
+ * Factor that sums together multiple Gaussians.
+ *  
+ * See the accompanying math paper for more details.s
+ */
+class GaussianWeightedSumFactor extends GaussianFactor
+{
+    private $_variableIndexOrdersForWeights = array();
+
+    // This following is used for convenience, for example, the first entry is [0, 1, 2]
+    // corresponding to v[0] = a1*v[1] + a2*v[2]
+    private $_weights;
+    private $_weightsSquared;
+
+    public function __construct(Variable &$sumVariable, array &$variablesToSum, array &$variableWeights = null)
+    {
+        parent::__construct(self::createName($sumVariable, $variablesToSum, $variableWeights));
+        $this->_weights = array();
+        $this->_weightsSquared = array();
+
+        // The first weights are a straightforward copy
+        // v_0 = a_1*v_1 + a_2*v_2 + ... + a_n * v_n
+        $variableWeightsLength = count($variableWeights);
+        $this->_weights[0] = \array_fill(0, count($variableWeights), 0);
+        
+        for($i = 0; $i < $variableWeightsLength; $i++)
+        {
+            $weight = &$variableWeights[$i];
+            $this->_weights[0][$i] = $weight;
+            $this->_weightsSquared[0][$i] = square($weight);
+        }
+
+        $variablesToSumLength = count($variablesToSum);
+
+        // 0..n-1
+        $this->_variableIndexOrdersForWeights[0] = array();
+        for($i = 0; $i < ($variablesToSumLength + 1); $i++)
+        {
+            $this->_variableIndexOrdersForWeights[0][] = $i;
+        }
+
+        $variableWeightsLength = count($variableWeights);
+
+        // The rest move the variables around and divide out the constant.
+        // For example:
+        // v_1 = (-a_2 / a_1) * v_2 + (-a3/a1) * v_3 + ... + (1.0 / a_1) * v_0
+        // By convention, we'll put the v_0 term at the end
+
+        $weightsLength = $variableWeightsLength + 1;
+        for ($weightsIndex = 1; $weightsIndex < $weightsLength; $weightsIndex++)
+        {
+            $currentWeights = \array_fill(0, $variableWeightsLength, 0);
+            
+            $variableIndices = \array_fill(0, $variableWeightsLength + 1, 0);
+            $variableIndices[0] = $weightsIndex;
+
+            $currentWeightsSquared = \array_fill(0, $variableWeightsLength, 0);
+
+            // keep a single variable to keep track of where we are in the array.
+            // This is helpful since we skip over one of the spots
+            $currentDestinationWeightIndex = 0;            
+
+            for ($currentWeightSourceIndex = 0;
+                 $currentWeightSourceIndex < $variableWeightsLength;
+                 $currentWeightSourceIndex++)
+            {
+                if ($currentWeightSourceIndex == ($weightsIndex - 1))
+                {
+                    continue;
+                }
+
+                $currentWeight = (-$variableWeights[$currentWeightSourceIndex]/$variableWeights[$weightsIndex - 1]);
+
+                if ($variableWeights[$weightsIndex - 1] == 0)
+                {
+                    // HACK: Getting around division by zero
+                    $currentWeight = 0;
+                }
+
+                $currentWeights[$currentDestinationWeightIndex] = $currentWeight;
+                $currentWeightsSquared[$currentDestinationWeightIndex] = $currentWeight*$currentWeight;
+
+                $variableIndices[$currentDestinationWeightIndex + 1] = $currentWeightSourceIndex + 1;
+                $currentDestinationWeightIndex++;
+            }
+
+            // And the final one
+            $finalWeight = 1.0/$variableWeights[$weightsIndex - 1];
+
+            if ($variableWeights[$weightsIndex - 1] == 0)
+            {
+                // HACK: Getting around division by zero
+                $finalWeight = 0;
+            }
+            $currentWeights[$currentDestinationWeightIndex] = $finalWeight;
+            $currentWeightsSquared[$currentDestinationWeightIndex] = square($finalWeight);
+            $variableIndices[count($variableWeights)] = 0;
+            $this->_variableIndexOrdersForWeights[] = $variableIndices;
+
+            $this->_weights[$weightsIndex] = $currentWeights;
+            $this->_weightsSquared[$weightsIndex] = $currentWeightsSquared;
+        }
+
+        $this->createVariableToMessageBinding($sumVariable);
+
+        foreach ($variablesToSum as &$currentVariable)
+        {
+            $localCurrentVariable = &$currentVariable;
+            $this->createVariableToMessageBinding($localCurrentVariable);
+        }        
+    }
+
+    public function getLogNormalization()
+    {
+        $vars = &$this->getVariables();
+        $messages = &$this->getMessages();
+
+        $result = 0.0;
+
+        // We start at 1 since offset 0 has the sum
+        $varCount = count($vars);
+        for ($i = 1; $i < $varCount; $i++)
+        {
+            $result += GaussianDistribution::logRatioNormalization($vars[$i]->getValue(), $messages[$i]->getValue());
+        }
+
+        return $result;
+    }
+
+    private function updateHelper(array &$weights, array &$weightsSquared,
+                                  array &$messages,
+                                  array &$variables)
+    {
+        // Potentially look at http://mathworld.wolfram.com/NormalSumDistribution.html for clues as
+        // to what it's doing
+
+        $message0 = clone $messages[0]->getValue();
+        $marginal0 = clone $variables[0]->getValue();
+
+        // The math works out so that 1/newPrecision = sum of a_i^2 /marginalsWithoutMessages[i]
+        $inverseOfNewPrecisionSum = 0.0;
+        $anotherInverseOfNewPrecisionSum = 0.0;
+        $weightedMeanSum = 0.0;
+        $anotherWeightedMeanSum = 0.0;
+
+        $weightsSquaredLength = count($weightsSquared);
+
+        for ($i = 0; $i < $weightsSquaredLength; $i++)
+        {
+            // These flow directly from the paper
+
+            $inverseOfNewPrecisionSum += $weightsSquared[$i]/
+                                         ($variables[$i + 1]->getValue()->getPrecision() - $messages[$i + 1]->getValue()->getPrecision());
+
+            $diff = GaussianDistribution::divide($variables[$i + 1]->getValue(), $messages[$i + 1]->getValue());
+            $anotherInverseOfNewPrecisionSum += $weightsSquared[$i]/$diff->getPrecision();
+
+            $weightedMeanSum += $weights[$i]
+                                *
+                                ($variables[$i + 1]->getValue()->getPrecisionMean() - $messages[$i + 1]->getValue()->getPrecisionMean())
+                                /
+                                ($variables[$i + 1]->getValue()->getPrecision() - $messages[$i + 1]->getValue()->getPrecision());
+
+            $anotherWeightedMeanSum += $weights[$i]*$diff->getPrecisionMean()/$diff->getPrecision();
+        }
+
+        $newPrecision = 1.0/$inverseOfNewPrecisionSum;
+        $anotherNewPrecision = 1.0/$anotherInverseOfNewPrecisionSum;
+
+        $newPrecisionMean = $newPrecision*$weightedMeanSum;
+        $anotherNewPrecisionMean = $anotherNewPrecision*$anotherWeightedMeanSum;
+
+        $newMessage = GaussianDistribution::fromPrecisionMean($newPrecisionMean, $newPrecision);
+        $oldMarginalWithoutMessage = GaussianDistribution::divide($marginal0, $message0);
+
+        $newMarginal = GaussianDistribution::multiply($oldMarginalWithoutMessage, $newMessage);
+
+        // Update the message and marginal
+
+        $messages[0]->setValue($newMessage);
+        $variables[0]->setValue($newMarginal);
+
+        // Return the difference in the new marginal
+        $finalDiff = GaussianDistribution::subtract($newMarginal, $marginal0);
+        return $finalDiff;
+    }
+
+    public function updateMessageIndex($messageIndex)
+    {        
+        $allMessages = &$this->getMessages();
+        $allVariables = &$this->getVariables();
+
+        Guard::argumentIsValidIndex($messageIndex, count($allMessages), "messageIndex");
+
+        $updatedMessages = array();
+        $updatedVariables = array();
+
+        $indicesToUse = &$this->_variableIndexOrdersForWeights[$messageIndex];
+
+        // The tricky part here is that we have to put the messages and variables in the same
+        // order as the weights. Thankfully, the weights and messages share the same index numbers,
+        // so we just need to make sure they're consistent
+        $allMessagesCount = count($allMessages);
+        for ($i = 0; $i < $allMessagesCount; $i++)
+        {
+            $updatedMessages[] = &$allMessages[$indicesToUse[$i]];
+            $updatedVariables[] = &$allVariables[$indicesToUse[$i]];
+        }
+        
+        return $this->updateHelper($this->_weights[$messageIndex],
+                                   $this->_weightsSquared[$messageIndex],
+                                   $updatedMessages,
+                                   $updatedVariables);
+    }
+
+    private static function createName($sumVariable, $variablesToSum, $weights)
+    {
+        // TODO: Perf? Use PHP equivalent of StringBuilder? implode on arrays?
+        $result = (string)$sumVariable;
+        $result .= ' = ';
+        
+        $totalVars = count($variablesToSum);
+        for($i = 0; $i < $totalVars; $i++)
+        {
+            $isFirst = ($i == 0);
+            
+            if($isFirst && ($weights[$i] < 0))
+            {
+                $result .= '-';
+            }
+
+            $absValue = sprintf("%.2f", \abs($weights[$i])); // 0.00?
+            $result .= $absValue;
+            $result .= "*[";
+            $result .= (string)$variablesToSum[$i];
+            $result .= ']';
+            
+            $isLast = ($i == ($totalVars - 1));
+            
+            if(!$isLast)
+            {
+                if($weights[$i + 1] >= 0)
+                {
+                    $result .= ' + ';
+                }
+                else
+                {
+                    $result .= ' - ';
+                }
+            }                
+        }
+        
+        return $result;
+    }
+}
+
+?>

Skills/TrueSkill/Factors/GaussianWithinFactor.php

@@ -0,0 +1,84 @@
+<?php
+namespace Moserware\Skills\TrueSkill\Factors;
+
+require_once(dirname(__FILE__) . "/../TruncatedGaussianCorrectionFunctions.php");
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Message.php");
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Variable.php");
+require_once(dirname(__FILE__) . "/../../Numerics/GaussianDistribution.php");
+require_once(dirname(__FILE__) . "/GaussianFactor.php");
+
+use Moserware\Numerics\GaussianDistribution;
+use Moserware\Skills\TrueSkill\TruncatedGaussianCorrectionFunctions;
+use Moserware\Skills\FactorGraphs\Message;
+use Moserware\Skills\FactorGraphs\Variable;
+
+/**
+ * Factor representing a team difference that has not exceeded the draw margin.
+ *
+ * See the accompanying math paper for more details.
+ */
+class GaussianWithinFactor extends GaussianFactor
+{
+    private $_epsilon;
+
+    public function __construct($epsilon, Variable &$variable)
+    {
+        parent::__construct(sprintf("%s <= %.2f", $variable, $epsilon));
+        $this->_epsilon = $epsilon;
+        $this->createVariableToMessageBinding($variable);
+    }
+
+    public function getLogNormalization()
+    {
+        $variables = &$this->getVariables();
+        $marginal = &$variables[0]->getValue();
+
+        $messages = &$this->getMessages();
+        $message = &$messages[0]->getValue();
+        $messageFromVariable = GaussianDistribution::divide($marginal, $message);
+        $mean = $messageFromVariable->getMean();
+        $std = $messageFromVariable->getStandardDeviation();
+        $z = GaussianDistribution::cumulativeTo(($this->_epsilon - $mean)/$std)
+             -
+             GaussianDistribution::cumulativeTo((-$this->_epsilon - $mean)/$std);
+
+        return -GaussianDistribution::logProductNormalization($messageFromVariable, $message) + log($z);
+    }
+
+    protected function updateMessageVariable(Message &$message, Variable &$variable)
+    {
+        $oldMarginal = clone $variable->getValue();
+        $oldMessage = clone $message->getValue();
+        $messageFromVariable = GaussianDistribution::divide($oldMarginal, $oldMessage);
+
+        $c = $messageFromVariable->getPrecision();
+        $d = $messageFromVariable->getPrecisionMean();
+
+        $sqrtC = sqrt($c);
+        $dOnSqrtC = $d/$sqrtC;
+
+        $epsilonTimesSqrtC = $this->_epsilon*$sqrtC;
+        $d = $messageFromVariable->getPrecisionMean();
+
+        $denominator = 1.0 - TruncatedGaussianCorrectionFunctions::wWithinMargin($dOnSqrtC, $epsilonTimesSqrtC);
+        $newPrecision = $c/$denominator;
+        $newPrecisionMean = ($d +
+                                   $sqrtC*
+                                   TruncatedGaussianCorrectionFunctions::vWithinMargin($dOnSqrtC, $epsilonTimesSqrtC))/
+                                  $denominator;
+
+        $newMarginal = GaussianDistribution::fromPrecisionMean($newPrecisionMean, $newPrecision);
+        $newMessage = GaussianDistribution::divide(
+                        GaussianDistribution::multiply($oldMessage, $newMarginal),
+                        $oldMarginal);
+
+        // Update the message and marginal
+        $message->setValue($newMessage);
+        $variable->setValue($newMarginal);
+
+        // Return the difference in the new marginal
+        return GaussianDistribution::subtract($newMarginal, $oldMarginal);
+    }
+}
+
+?>

Skills/TrueSkill/Layers/IteratedTeamDifferencesInnerLayer.php

@@ -0,0 +1,189 @@
+<?php
+namespace Moserware\Skills\TrueSkill\Layers;
+
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Schedule.php");
+require_once(dirname(__FILE__) . "/../TrueSkillFactorGraph.php");
+require_once(dirname(__FILE__) . "/TrueSkillFactorGraphLayer.php");
+require_once(dirname(__FILE__) . "/TeamPerformancesToTeamPerformanceDifferencesLayer.php");
+require_once(dirname(__FILE__) . "/TeamDifferencesComparisonLayer.php");
+
+use Moserware\Skills\FactorGraphs\ScheduleLoop;
+use Moserware\Skills\FactorGraphs\ScheduleSequence;
+use Moserware\Skills\FactorGraphs\ScheduleStep;
+use Moserware\Skills\TrueSkill\TrueSkillFactorGraph;
+
+// The whole purpose of this is to do a loop on the bottom
+class IteratedTeamDifferencesInnerLayer extends TrueSkillFactorGraphLayer
+{
+    private $_TeamDifferencesComparisonLayer;
+    private $_TeamPerformancesToTeamPerformanceDifferencesLayer;
+
+    public function __construct(TrueSkillFactorGraph &$parentGraph,
+                                TeamPerformancesToTeamPerformanceDifferencesLayer &$teamPerformancesToPerformanceDifferences,
+                                TeamDifferencesComparisonLayer &$teamDifferencesComparisonLayer)
+    {
+        parent::__construct($parentGraph);
+        $this->_TeamPerformancesToTeamPerformanceDifferencesLayer = $teamPerformancesToPerformanceDifferences;
+        $this->_TeamDifferencesComparisonLayer = $teamDifferencesComparisonLayer;
+    }
+
+    public function &getLocalFactors()
+    {
+        $localFactors =
+            \array_merge($this->_TeamPerformancesToTeamPerformanceDifferencesLayer->getLocalFactors(),
+                         $this->_TeamDifferencesComparisonLayer->getLocalFactors());
+        return $localFactors;
+    }
+
+    public function buildLayer()
+    {
+        $inputVariablesGroups = &$this->getInputVariablesGroups();
+        $this->_TeamPerformancesToTeamPerformanceDifferencesLayer->setInputVariablesGroups($inputVariablesGroups);
+        $this->_TeamPerformancesToTeamPerformanceDifferencesLayer->buildLayer();
+
+        $teamDifferencesOutputVariablesGroups = &$this->_TeamPerformancesToTeamPerformanceDifferencesLayer->getOutputVariablesGroups();
+        $this->_TeamDifferencesComparisonLayer->setInputVariablesGroups($teamDifferencesOutputVariablesGroups);
+        $this->_TeamDifferencesComparisonLayer->buildLayer();
+    }
+
+    public function createPriorSchedule()
+    {        
+        switch (count($this->getInputVariablesGroups()))
+        {
+            case 0:
+            case 1:
+                throw new InvalidOperationException();
+            case 2:
+                $loop = $this->createTwoTeamInnerPriorLoopSchedule();
+                break;
+            default:
+                $loop = $this->createMultipleTeamInnerPriorLoopSchedule();
+                break;
+        }
+
+        // When dealing with differences, there are always (n-1) differences, so add in the 1
+        $totalTeamDifferences = count($this->_TeamPerformancesToTeamPerformanceDifferencesLayer->getLocalFactors());
+        $totalTeams = $totalTeamDifferences + 1;
+
+        $localFactors = &$this->_TeamPerformancesToTeamPerformanceDifferencesLayer->getLocalFactors();
+
+        $firstDifferencesFactor = &$localFactors[0];
+        $lastDifferencesFactor = &$localFactors[$totalTeamDifferences - 1];
+        $innerSchedule = new ScheduleSequence(
+            "inner schedule",
+            array(
+                    $loop,
+                    new ScheduleStep(
+                        "teamPerformanceToPerformanceDifferenceFactors[0] @ 1",
+                        $firstDifferencesFactor, 1),
+                    new ScheduleStep(
+                        sprintf("teamPerformanceToPerformanceDifferenceFactors[teamTeamDifferences = %d - 1] @ 2", $totalTeamDifferences),
+                        $lastDifferencesFactor, 2)
+                )
+            );
+
+        return $innerSchedule;
+    }
+
+    private function createTwoTeamInnerPriorLoopSchedule()
+    {
+        $teamPerformancesToTeamPerformanceDifferencesLayerLocalFactors = &$this->_TeamPerformancesToTeamPerformanceDifferencesLayer->getLocalFactors();
+        $teamDifferencesComparisonLayerLocalFactors = &$this->_TeamDifferencesComparisonLayer->getLocalFactors();
+
+        $firstPerfToTeamDiff = &$teamPerformancesToTeamPerformanceDifferencesLayerLocalFactors[0];
+        $firstTeamDiffComparison = &$teamDifferencesComparisonLayerLocalFactors[0];
+        $itemsToSequence = array(
+                    new ScheduleStep(
+                        "send team perf to perf differences",
+                        $firstPerfToTeamDiff,
+                        0),
+                    new ScheduleStep(
+                        "send to greater than or within factor",
+                        $firstTeamDiffComparison,
+                        0)
+                );
+
+        return $this->scheduleSequence(
+            $itemsToSequence,
+            "loop of just two teams inner sequence");
+    }
+
+    private function createMultipleTeamInnerPriorLoopSchedule()
+    {
+        $totalTeamDifferences = count($this->_TeamPerformancesToTeamPerformanceDifferencesLayer->getLocalFactors());
+
+        $forwardScheduleList = array();
+
+        for ($i = 0; $i < $totalTeamDifferences - 1; $i++)
+        {
+            $teamPerformancesToTeamPerformanceDifferencesLayerLocalFactors = &$this->_TeamPerformancesToTeamPerformanceDifferencesLayer->getLocalFactors();
+            $teamDifferencesComparisonLayerLocalFactors = &$this->_TeamDifferencesComparisonLayer->getLocalFactors();
+
+            $currentTeamPerfToTeamPerfDiff = &$teamPerformancesToTeamPerformanceDifferencesLayerLocalFactors[$i];
+            $currentTeamDiffComparison = &$teamDifferencesComparisonLayerLocalFactors[$i];
+
+            $currentForwardSchedulePiece =
+                $this->scheduleSequence(
+                    array(
+                            new ScheduleStep(
+                                sprintf("team perf to perf diff %d", $i),
+                                $currentTeamPerfToTeamPerfDiff, 0),
+                            new ScheduleStep(
+                                sprintf("greater than or within result factor %d", $i),
+                                $currentTeamDiffComparison, 0),
+                            new ScheduleStep(
+                                sprintf("team perf to perf diff factors [%d], 2", $i),
+                                $currentTeamPerfToTeamPerfDiff, 2)
+                        ), sprintf("current forward schedule piece %d", $i));
+
+            $forwardScheduleList[] = $currentForwardSchedulePiece;
+        }
+
+        $forwardSchedule = new ScheduleSequence("forward schedule", $forwardScheduleList);
+
+        $backwardScheduleList = array();
+
+        for ($i = 0; $i < $totalTeamDifferences - 1; $i++)
+        {
+            $teamPerformancesToTeamPerformanceDifferencesLayerLocalFactors = &$this->_TeamPerformancesToTeamPerformanceDifferencesLayer->getLocalFactors();
+            $teamDifferencesComparisonLayerLocalFactors = &$this->_TeamDifferencesComparisonLayer->getLocalFactors();
+
+            $differencesFactor = &$teamPerformancesToTeamPerformanceDifferencesLayerLocalFactors[$totalTeamDifferences - 1 - $i];
+            $comparisonFactor = &$teamDifferencesComparisonLayerLocalFactors[$totalTeamDifferences - 1 - $i];
+            $performancesToDifferencesFactor = &$teamPerformancesToTeamPerformanceDifferencesLayerLocalFactors[$totalTeamDifferences - 1 - $i];
+
+            $currentBackwardSchedulePiece = new ScheduleSequence(
+                "current backward schedule piece",
+                array(
+                        new ScheduleStep(
+                            sprintf("teamPerformanceToPerformanceDifferenceFactors[totalTeamDifferences - 1 - %d] @ 0", $i),
+                            $differencesFactor, 0),
+                        new ScheduleStep(
+                            sprintf("greaterThanOrWithinResultFactors[totalTeamDifferences - 1 - %d] @ 0", $i),
+                            $comparisonFactor, 0),
+                        new ScheduleStep(
+                            sprintf("teamPerformanceToPerformanceDifferenceFactors[totalTeamDifferences - 1 - %d] @ 1", $i),
+                            $performancesToDifferencesFactor, 1)
+                ));
+            $backwardScheduleList[] = $currentBackwardSchedulePiece;
+        }
+
+        $backwardSchedule = new ScheduleSequence("backward schedule", $backwardScheduleList);
+
+        $forwardBackwardScheduleToLoop =
+            new ScheduleSequence(
+                "forward Backward Schedule To Loop",
+                array($forwardSchedule, $backwardSchedule));
+
+        $initialMaxDelta = 0.0001;
+
+        $loop = new ScheduleLoop(
+            sprintf("loop with max delta of %f", $initialMaxDelta),
+            $forwardBackwardScheduleToLoop,
+            $initialMaxDelta);
+
+        return $loop;
+    }
+}
+
+?>

Skills/TrueSkill/Layers/PlayerPerformancesToTeamPerformancesLayer.php

@@ -0,0 +1,106 @@
+<?php
+namespace Moserware\Skills\TrueSkill\Layers;
+
+require_once(dirname(__FILE__) . "/../../PartialPlay.php");
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Schedule.php");
+require_once(dirname(__FILE__) . "/../Factors/GaussianWeightedSumFactor.php");
+require_once(dirname(__FILE__) . "/../TrueSkillFactorGraph.php");
+require_once(dirname(__FILE__) . "/TrueSkillFactorGraphLayer.php");
+require_once(dirname(__FILE__) . "/TeamPerformancesToTeamPerformanceDifferencesLayer.php");
+require_once(dirname(__FILE__) . "/TeamDifferencesComparisonLayer.php");
+
+use Moserware\Skills\PartialPlay;
+use Moserware\Skills\FactorGraphs\ScheduleLoop;
+use Moserware\Skills\FactorGraphs\ScheduleSequence;
+use Moserware\Skills\FactorGraphs\ScheduleStep;
+use Moserware\Skills\TrueSkill\Factors\GaussianWeightedSumFactor;
+use Moserware\Skills\TrueSkill\TrueSkillFactorGraph;
+
+class PlayerPerformancesToTeamPerformancesLayer extends TrueSkillFactorGraphLayer
+{
+    public function __construct(TrueSkillFactorGraph &$parentGraph)
+    {
+        parent::__construct($parentGraph);
+    }
+
+    public function buildLayer()
+    {
+        $inputVariablesGroups = &$this->getInputVariablesGroups();
+        foreach ($inputVariablesGroups as &$currentTeam)
+        {
+            $localCurrentTeam = &$currentTeam;
+            $teamPerformance = &$this->createOutputVariable($localCurrentTeam);
+            $newSumFactor = $this->createPlayerToTeamSumFactor($localCurrentTeam, $teamPerformance);
+            
+            $this->addLayerFactor($newSumFactor);
+
+            // REVIEW: Does it make sense to have groups of one?
+            $outputVariablesGroups = &$this->getOutputVariablesGroups();
+            $outputVariablesGroups[] = array($teamPerformance);
+        }        
+    }
+
+    public function createPriorSchedule()
+    {
+        $localFactors = &$this->getLocalFactors();
+
+        $sequence = &$this->scheduleSequence(
+                                            array_map(
+                                                    function($weightedSumFactor)
+                                                    {
+                                                        return new ScheduleStep("Perf to Team Perf Step", $weightedSumFactor, 0);
+                                                    },
+                                                    $localFactors),
+                                            "all player perf to team perf schedule");
+        return $sequence;
+    }
+
+    protected function createPlayerToTeamSumFactor(&$teamMembers, &$sumVariable)
+    {
+        $weights = array_map(
+                        function($v)
+                        {
+                            $player = &$v->getKey();
+                            return PartialPlay::getPartialPlayPercentage($player);
+                        },
+                        $teamMembers);
+
+        return new GaussianWeightedSumFactor(
+                $sumVariable,
+                $teamMembers,
+                $weights);
+                                                 
+    }
+
+    public function createPosteriorSchedule()
+    {        
+        $allFactors = array();
+        $localFactors = &$this->getLocalFactors();
+        foreach($localFactors as &$currentFactor)
+        {
+            $localCurrentFactor = &$currentFactor;
+            $numberOfMessages = $localCurrentFactor->getNumberOfMessages();
+            for($currentIteration = 1; $currentIteration < $numberOfMessages; $currentIteration++)
+            {
+                $allFactors[] = new ScheduleStep("team sum perf @" . $currentIteration,
+                                                 $localCurrentFactor, $currentIteration);
+            }
+        }
+        return $this->scheduleSequence($allFactors, "all of the team's sum iterations");
+    }
+
+    private function &createOutputVariable(&$team)
+    {
+        $memberNames = \array_map(function ($currentPlayer)
+                                  {
+                                        return (string)($currentPlayer->getKey());
+                                  },
+                                  $team);
+
+        $teamMemberNames = \join(", ", $memberNames);
+        $outputVariable = &$this->getParentFactorGraph()->getVariableFactory()->createBasicVariable("Team[" . $teamMemberNames . "]'s performance");
+        return $outputVariable;
+    }
+}
+
+?>

Skills/TrueSkill/Layers/PlayerPriorValuesToSkillsLayer.php

@@ -0,0 +1,87 @@
+<?php
+namespace Moserware\Skills\TrueSkill\Layers;
+
+require_once(dirname(__FILE__) . "/../../Rating.php");
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Schedule.php");
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Variable.php");
+require_once(dirname(__FILE__) . "/../../Numerics/BasicMath.php");
+require_once(dirname(__FILE__) . "/../TrueSkillFactorGraph.php");
+require_once(dirname(__FILE__) . "/../Factors/GaussianPriorFactor.php");
+require_once(dirname(__FILE__) . "/TrueSkillFactorGraphLayer.php");
+
+use Moserware\Skills\Rating;
+use Moserware\Skills\FactorGraphs\ScheduleLoop;
+use Moserware\Skills\FactorGraphs\ScheduleSequence;
+use Moserware\Skills\FactorGraphs\ScheduleStep;
+use Moserware\Skills\FactorGraphs\Variable;
+use Moserware\Numerics\GaussianDistribution;
+use Moserware\Skills\TrueSkill\TrueSkillFactorGraph;
+use Moserware\Skills\TrueSkill\Factors\GaussianPriorFactor;
+
+// We intentionally have no Posterior schedule since the only purpose here is to
+// start the process.
+class PlayerPriorValuesToSkillsLayer extends TrueSkillFactorGraphLayer
+{
+    private $_teams;
+
+    public function __construct(TrueSkillFactorGraph &$parentGraph, array &$teams)
+    {
+        parent::__construct($parentGraph);
+        $this->_teams = $teams;
+    }
+
+    public function buildLayer()
+    {
+        $teams = &$this->_teams;
+        foreach ($teams as &$currentTeam)
+        {
+            $localCurrentTeam = &$currentTeam;
+            $currentTeamSkills = array();
+
+            $currentTeamAllPlayers = $localCurrentTeam->getAllPlayers();
+            foreach ($currentTeamAllPlayers as &$currentTeamPlayer)
+            {
+                $localCurrentTeamPlayer = &$currentTeamPlayer;
+                $currentTeamPlayerRating = $currentTeam->getRating($localCurrentTeamPlayer);
+                $playerSkill = &$this->createSkillOutputVariable($localCurrentTeamPlayer);
+                $priorFactor = &$this->createPriorFactor($localCurrentTeamPlayer, $currentTeamPlayerRating, $playerSkill);
+                $this->addLayerFactor($priorFactor);
+                $currentTeamSkills[] = $playerSkill;
+            }
+
+            $outputVariablesGroups = &$this->getOutputVariablesGroups();
+            $outputVariablesGroups[] = $currentTeamSkills;
+        }
+    }
+
+    public function createPriorSchedule()
+    {
+        $localFactors = &$this->getLocalFactors();
+        return $this->scheduleSequence(
+                array_map(
+                        function(&$prior)
+                        {
+                            return new ScheduleStep("Prior to Skill Step", $prior, 0);
+                        },
+                        $localFactors),
+                 "All priors");
+    }
+
+    private function createPriorFactor(&$player, Rating &$priorRating, Variable &$skillsVariable)
+    {
+        return new GaussianPriorFactor($priorRating->getMean(),
+                                       square($priorRating->getStandardDeviation()) +
+                                       square($this->getParentFactorGraph()->getGameInfo()->getDynamicsFactor()),
+                                       $skillsVariable);
+    }
+
+    private function &createSkillOutputVariable(&$key)
+    {
+        $parentFactorGraph = &$this->getParentFactorGraph();
+        $variableFactory = &$parentFactorGraph->getVariableFactory();
+        $skillOutputVariable = &$variableFactory->createKeyedVariable($key, $key . "'s skill");
+        return $skillOutputVariable;
+    }
+}
+
+?>

Skills/TrueSkill/Layers/PlayerSkillsToPerformancesLayer.php

@@ -0,0 +1,84 @@
+<?php
+namespace Moserware\Skills\TrueSkill\Layers;
+
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Schedule.php");
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Variable.php");
+require_once(dirname(__FILE__) . "/../../Numerics/BasicMath.php");
+require_once(dirname(__FILE__) . "/../TrueSkillFactorGraph.php");
+require_once(dirname(__FILE__) . "/../Factors/GaussianLikelihoodFactor.php");
+require_once(dirname(__FILE__) . "/TrueSkillFactorGraphLayer.php");
+
+use Moserware\Skills\FactorGraphs\ScheduleStep;
+use Moserware\Skills\FactorGraphs\KeyedVariable;
+use Moserware\Skills\TrueSkill\TrueSkillFactorGraph;
+use Moserware\Skills\TrueSkill\Factors\GaussianLikelihoodFactor;
+
+class PlayerSkillsToPerformancesLayer extends TrueSkillFactorGraphLayer
+{
+    public function __construct(TrueSkillFactorGraph &$parentGraph)
+    {
+        parent::__construct($parentGraph);
+    }
+
+    public function buildLayer()
+    {
+        $inputVariablesGroups = &$this->getInputVariablesGroups();
+        $outputVariablesGroups = &$this->getOutputVariablesGroups();
+
+        foreach ($inputVariablesGroups as &$currentTeam)
+        {
+            $currentTeamPlayerPerformances = array();
+
+            foreach ($currentTeam as &$playerSkillVariable)
+            {
+                $localPlayerSkillVariable = &$playerSkillVariable;
+                $currentPlayer = &$localPlayerSkillVariable->getKey();
+                $playerPerformance = &$this->createOutputVariable($currentPlayer);
+                $newLikelihoodFactor = $this->createLikelihood($localPlayerSkillVariable, $playerPerformance);
+                $this->addLayerFactor($newLikelihoodFactor);
+                $currentTeamPlayerPerformances[] = $playerPerformance;
+            }            
+            
+            $outputVariablesGroups[] = $currentTeamPlayerPerformances;
+        }
+    }
+
+    private function createLikelihood(KeyedVariable &$playerSkill, KeyedVariable &$playerPerformance)
+    {
+        return new GaussianLikelihoodFactor(square($this->getParentFactorGraph()->getGameInfo()->getBeta()), $playerPerformance, $playerSkill);
+    }
+
+    private function &createOutputVariable(&$key)
+    {
+        $outputVariable = &$this->getParentFactorGraph()->getVariableFactory()->createKeyedVariable($key, $key . "'s performance");
+        return $outputVariable;
+    }
+
+    public function createPriorSchedule()
+    {
+        $localFactors = &$this->getLocalFactors();
+        return $this->scheduleSequence(
+                array_map(
+                        function($likelihood)
+                        {
+                            return new ScheduleStep("Skill to Perf step", $likelihood, 0);
+                        },
+                        $localFactors),
+                "All skill to performance sending");
+    }
+
+    public function createPosteriorSchedule()
+    {
+        $localFactors = &$this->getLocalFactors();
+        return $this->scheduleSequence(
+                array_map(
+                        function($likelihood)
+                        {
+                            return new ScheduleStep("name", $likelihood, 1);                    
+                        },
+                        $localFactors),
+                "All skill to performance sending");
+    }
+}
+
+?>

Skills/TrueSkill/Layers/TeamDifferencesComparisonLayer.php

@@ -0,0 +1,48 @@
+<?php
+namespace Moserware\Skills\TrueSkill\Layers;
+
+require_once(dirname(__FILE__) . "/../DrawMargin.php");
+require_once(dirname(__FILE__) . "/../TrueSkillFactorGraph.php");
+require_once(dirname(__FILE__) . "/../Factors/GaussianGreaterThanFactor.php");
+require_once(dirname(__FILE__) . "/../Factors/GaussianWithinFactor.php");
+require_once(dirname(__FILE__) . "/TrueSkillFactorGraphLayer.php");
+
+use Moserware\Skills\TrueSkill\DrawMargin;
+use Moserware\Skills\TrueSkill\TrueSkillFactorGraph;
+use Moserware\Skills\TrueSkill\Factors\GaussianGreaterThanFactor;
+use Moserware\Skills\TrueSkill\Factors\GaussianWithinFactor;
+
+class TeamDifferencesComparisonLayer extends TrueSkillFactorGraphLayer
+{
+    private $_epsilon;
+    private $_teamRanks;
+
+    public function __construct(TrueSkillFactorGraph &$parentGraph, array &$teamRanks)
+    {
+        parent::__construct($parentGraph);
+        $this->_teamRanks = $teamRanks;
+        $gameInfo = &$this->getParentFactorGraph()->getGameInfo();
+        $this->_epsilon = DrawMargin::getDrawMarginFromDrawProbability($gameInfo->getDrawProbability(), $gameInfo->getBeta());
+    }
+
+    public function buildLayer()
+    {
+        $inputVarGroups = &$this->getInputVariablesGroups();
+        $inputVarGroupsCount = count($inputVarGroups);
+
+        for ($i = 0; $i < $inputVarGroupsCount; $i++)
+        {
+            $isDraw = ($this->_teamRanks[$i] == $this->_teamRanks[$i + 1]);
+            $teamDifference = &$inputVarGroups[$i][0];
+
+            $factor =
+                $isDraw
+                    ? new GaussianWithinFactor($this->_epsilon, $teamDifference)
+                    : new GaussianGreaterThanFactor($this->_epsilon, $teamDifference);
+
+            $this->addLayerFactor($factor);
+        }
+    }
+}
+
+?>

Skills/TrueSkill/Layers/TeamPerformancesToTeamPerformanceDifferencesLayer.php

@@ -0,0 +1,56 @@
+<?php
+namespace Moserware\Skills\TrueSkill\Layers;
+
+require_once(dirname(__FILE__) . "/../../FactorGraphs/Variable.php");
+require_once(dirname(__FILE__) . "/../TrueSkillFactorGraph.php");
+require_once(dirname(__FILE__) . "/../Factors/GaussianWeightedSumFactor.php");
+require_once(dirname(__FILE__) . "/TrueSkillFactorGraphLayer.php");
+
+use Moserware\Skills\FactorGraphs\Variable;
+use Moserware\Skills\TrueSkill\DrawMargin;
+use Moserware\Skills\TrueSkill\TrueSkillFactorGraph;
+use Moserware\Skills\TrueSkill\Factors\GaussianWeightedSumFactor;
+
+class TeamPerformancesToTeamPerformanceDifferencesLayer extends TrueSkillFactorGraphLayer
+{
+    public function __construct(TrueSkillFactorGraph &$parentGraph)
+    {
+        parent::__construct($parentGraph);
+    }
+
+    public function buildLayer()
+    {
+        $inputVariablesGroups = &$this->getInputVariablesGroups();
+        $inputVariablesGroupsCount = count($inputVariablesGroups);
+        $outputVariablesGroup = &$this->getOutputVariablesGroups();
+
+        for ($i = 0; $i < $inputVariablesGroupsCount - 1; $i++)
+        {
+            $strongerTeam = &$inputVariablesGroups[$i][0];
+            $weakerTeam = &$inputVariablesGroups[$i + 1][0];
+
+            $currentDifference = &$this->createOutputVariable();
+            $newDifferencesFactor = $this->createTeamPerformanceToDifferenceFactor($strongerTeam, $weakerTeam, $currentDifference);
+            $this->addLayerFactor($newDifferencesFactor);
+
+            // REVIEW: Does it make sense to have groups of one?            
+            $outputVariablesGroup[] = array($currentDifference);
+        }
+    }
+
+    private function createTeamPerformanceToDifferenceFactor(
+        Variable &$strongerTeam, Variable &$weakerTeam, Variable &$output)
+    {
+        $teams = array($strongerTeam, $weakerTeam);
+        $weights = array(1.0, -1.0);
+        return new GaussianWeightedSumFactor($output, $teams, $weights);
+    }
+
+    private function &createOutputVariable()
+    {
+        $outputVariable = &$this->getParentFactorGraph()->getVariableFactory()->createBasicVariable("Team performance difference");
+        return $outputVariable;
+    }
+}
+
+?>

Skills/TrueSkill/Layers/TrueSkillFactorGraphLayer.php

@@ -0,0 +1,18 @@
+<?php
+namespace Moserware\Skills\TrueSkill\Layers;
+
+require_once(dirname(__FILE__) . "/../../FactorGraphs/FactorGraphLayer.php");
+require_once(dirname(__FILE__) . "/../TrueSkillFactorGraph.php");
+
+use Moserware\Skills\FactorGraphs\FactorGraphLayer;
+use Moserware\Skills\TrueSkill\TrueSkillFactorGraph;
+
+abstract class TrueSkillFactorGraphLayer extends FactorGraphLayer
+{
+    public function __construct(TrueSkillFactorGraph &$parentGraph)
+    {
+        parent::__construct($parentGraph);
+    }
+}
+
+?>

Skills/TrueSkill/TrueSkillFactorGraph.php

@@ -0,0 +1,159 @@
+<?php
+namespace Moserware\Skills\TrueSkill;
+
+require_once(dirname(__FILE__) . '/../GameInfo.php');
+require_once(dirname(__FILE__) . '/../Rating.php');
+require_once(dirname(__FILE__) . '/../RatingContainer.php');
+require_once(dirname(__FILE__) . '/../FactorGraphs/FactorGraph.php');
+require_once(dirname(__FILE__) . '/../FactorGraphs/FactorList.php');
+require_once(dirname(__FILE__) . '/../FactorGraphs/Schedule.php');
+require_once(dirname(__FILE__) . '/../FactorGraphs/VariableFactory.php');
+require_once(dirname(__FILE__) . '/../Numerics/GaussianDistribution.php');
+require_once(dirname(__FILE__) . '/Layers/IteratedTeamDifferencesInnerLayer.php');
+require_once(dirname(__FILE__) . '/Layers/PlayerPerformancesToTeamPerformancesLayer.php');
+require_once(dirname(__FILE__) . '/Layers/PlayerPriorValuesToSkillsLayer.php');
+require_once(dirname(__FILE__) . '/Layers/PlayerSkillsToPerformancesLayer.php');
+require_once(dirname(__FILE__) . '/Layers/TeamDifferencesComparisonLayer.php');
+require_once(dirname(__FILE__) . '/Layers/TeamPerformancesToTeamPerformanceDifferencesLayer.php');
+
+use Moserware\Numerics\GaussianDistribution;
+use Moserware\Skills\GameInfo;
+use Moserware\Skills\Rating;
+use Moserware\Skills\RatingContainer;
+use Moserware\Skills\FactorGraphs\FactorGraph;
+use Moserware\Skills\FactorGraphs\FactorList;
+use Moserware\Skills\FactorGraphs\ScheduleSequence;
+use Moserware\Skills\FactorGraphs\VariableFactory;
+use Moserware\Skills\TrueSkill\Layers\IteratedTeamDifferencesInnerLayer;
+use Moserware\Skills\TrueSkill\Layers\PlayerPerformancesToTeamPerformancesLayer;
+use Moserware\Skills\TrueSkill\Layers\PlayerPriorValuesToSkillsLayer;
+use Moserware\Skills\TrueSkill\Layers\PlayerSkillsToPerformancesLayer;
+use Moserware\Skills\TrueSkill\Layers\TeamDifferencesComparisonLayer;
+use Moserware\Skills\TrueSkill\Layers\TeamPerformancesToTeamPerformanceDifferencesLayer;
+
+class TrueSkillFactorGraph extends FactorGraph
+{
+    private $_gameInfo;
+    private $_layers;
+    private $_priorLayer;    
+
+    public function __construct(GameInfo &$gameInfo, array &$teams, array $teamRanks)
+    {
+        $this->_priorLayer = new PlayerPriorValuesToSkillsLayer($this, $teams);
+        $this->_gameInfo = $gameInfo;
+        $newFactory = new VariableFactory(
+                                        function()
+                                        {
+                                            return GaussianDistribution::fromPrecisionMean(0, 0);
+                                        });
+                                        
+        $this->setVariableFactory($newFactory);
+        $this->_layers = array(
+                              $this->_priorLayer,
+                              new PlayerSkillsToPerformancesLayer($this),
+                              new PlayerPerformancesToTeamPerformancesLayer($this),
+                              new IteratedTeamDifferencesInnerLayer(
+                                  $this,
+                                  new TeamPerformancesToTeamPerformanceDifferencesLayer($this),
+                                  new TeamDifferencesComparisonLayer($this, $teamRanks))
+                              );
+    }
+
+    public function getGameInfo()
+    {
+        return $this->_gameInfo;
+    }
+
+    public function buildGraph()
+    {
+        $lastOutput = null;
+
+        $layers = &$this->_layers;
+        foreach ($layers as &$currentLayer)
+        {
+            if ($lastOutput != null)
+            {
+                $currentLayer->setInputVariablesGroups($lastOutput);
+            }
+
+            $currentLayer->buildLayer();
+
+            $lastOutput = &$currentLayer->getOutputVariablesGroups();       
+        }
+    }
+
+    public function runSchedule()
+    {
+        $fullSchedule = $this->createFullSchedule();
+        $fullScheduleDelta = $fullSchedule->visit();
+    }
+
+    public function getProbabilityOfRanking()
+    {
+        $factorList = new FactorList();
+
+        $layers = &$this->_layers;
+        foreach ($layers as &$currentLayer)
+        {
+            $localFactors = &$currentLayer->getLocalFactors();
+            foreach ($localFactors as &$currentFactor)
+            {
+                $localCurrentFactor = &$currentFactor;
+                $factorList->addFactor($localCurrentFactor);
+            }
+        }
+
+        $logZ = $factorList->getLogNormalization();
+        return exp($logZ);
+    }
+
+    private function createFullSchedule()
+    {
+        $fullSchedule = array();
+
+        $layers = &$this->_layers;
+        foreach ($layers as &$currentLayer)
+        {
+            $currentPriorSchedule = $currentLayer->createPriorSchedule();
+            if ($currentPriorSchedule != null)
+            {
+                $fullSchedule[] = $currentPriorSchedule;
+            }
+        }
+        
+        $allLayersReverse = \array_reverse($this->_layers);
+
+        foreach ($allLayersReverse as &$currentLayer)
+        {
+            $currentPosteriorSchedule = $currentLayer->createPosteriorSchedule();
+            if ($currentPosteriorSchedule != null)
+            {
+                $fullSchedule[] = $currentPosteriorSchedule;
+            }
+        }
+
+        return new ScheduleSequence("Full schedule", $fullSchedule);
+    }
+
+    public function getUpdatedRatings()
+    {
+        $result = new RatingContainer();
+
+        $priorLayerOutputVariablesGroups = &$this->_priorLayer->getOutputVariablesGroups();
+        foreach ($priorLayerOutputVariablesGroups as &$currentTeam)
+        {
+            foreach ($currentTeam as &$currentPlayer)
+            {
+                $localCurrentPlayer = &$currentPlayer->getKey();                
+                $newRating = new Rating($currentPlayer->getValue()->getMean(),
+                                        $currentPlayer->getValue()->getStandardDeviation());
+
+                $result->setRating($localCurrentPlayer, $newRating);
+            }
+        }
+
+        return $result;
+    }
+}
+
+?>

Skills/TrueSkill/TruncatedGaussianCorrectionFunctions.php

@@ -0,0 +1,133 @@
+<?php
+namespace Moserware\Skills\TrueSkill;
+
+require_once(dirname(__FILE__) . '/../Numerics/GaussianDistribution.php');
+
+use Moserware\Numerics\GaussianDistribution;
+
+class TruncatedGaussianCorrectionFunctions
+{
+    // These functions from the bottom of page 4 of the TrueSkill paper.
+
+    /**
+     * The "V" function where the team performance difference is greater than the draw margin.
+     * 
+     * In the reference F# implementation, this is referred to as "the additive
+     * correction of a single-sided truncated Gaussian with unit variance."
+     * 
+     * @param number $drawMargin In the paper, it's referred to as just "ε".
+     */
+    public static function vExceedsMarginScaled($teamPerformanceDifference, $drawMargin, $c)
+    {
+        return self::vExceedsMargin($teamPerformanceDifference/$c, $drawMargin/$c);
+    }
+
+    public static function vExceedsMargin($teamPerformanceDifference, $drawMargin)
+    {
+        $denominator = GaussianDistribution::cumulativeTo($teamPerformanceDifference - $drawMargin);
+
+        if ($denominator < 2.222758749e-162)
+        {
+            return -$teamPerformanceDifference + $drawMargin;
+        }
+
+        return GaussianDistribution::at($teamPerformanceDifference - $drawMargin)/$denominator;
+    }
+
+    /**
+     * The "W" function where the team performance difference is greater than the draw margin.
+     * 
+     * In the reference F# implementation, this is referred to as "the multiplicative
+     * correction of a single-sided truncated Gaussian with unit variance."
+     */
+    
+    public static function wExceedsMarginScaled($teamPerformanceDifference, $drawMargin, $c)
+    {
+        return self::wExceedsMargin($teamPerformanceDifference/$c, $drawMargin/$c);
+    }
+
+    public static function wExceedsMargin($teamPerformanceDifference, $drawMargin)
+    {
+        $denominator = GaussianDistribution::cumulativeTo($teamPerformanceDifference - $drawMargin);
+
+        if ($denominator < 2.222758749e-162)
+        {
+            if ($teamPerformanceDifference < 0.0)
+            {
+                return 1.0;
+            }
+            return 0.0;
+        }
+
+        $vWin = self::vExceedsMargin($teamPerformanceDifference, $drawMargin);
+        return $vWin*($vWin + $teamPerformanceDifference - $drawMargin);
+    }
+
+    // the additive correction of a double-sided truncated Gaussian with unit variance
+    public static function vWithinMarginScaled($teamPerformanceDifference, $drawMargin, $c)
+    {
+        return self::vWithinMargin($teamPerformanceDifference/$c, $drawMargin/$c);
+    }
+    
+    // from F#:
+    public static function vWithinMargin($teamPerformanceDifference, $drawMargin)
+    {
+        $teamPerformanceDifferenceAbsoluteValue = abs($teamPerformanceDifference);
+        $denominator =
+            GaussianDistribution::cumulativeTo($drawMargin - $teamPerformanceDifferenceAbsoluteValue) -
+            GaussianDistribution::cumulativeTo(-$drawMargin - $teamPerformanceDifferenceAbsoluteValue);
+
+        if ($denominator < 2.222758749e-162)
+        {
+            if ($teamPerformanceDifference < 0.0)
+            {
+                return -$teamPerformanceDifference - $drawMargin;
+            }
+
+            return -$teamPerformanceDifference + $drawMargin;
+        }
+
+        $numerator = GaussianDistribution::at(-$drawMargin - $teamPerformanceDifferenceAbsoluteValue) -
+                     GaussianDistribution::at($drawMargin - $teamPerformanceDifferenceAbsoluteValue);
+
+        if ($teamPerformanceDifference < 0.0)
+        {
+            return -$numerator/$denominator;
+        }
+
+        return $numerator/$denominator;
+    }
+
+    // the multiplicative correction of a double-sided truncated Gaussian with unit variance
+    public static function wWithinMarginScaled($teamPerformanceDifference, $drawMargin, $c)
+    {
+        return self::wWithinMargin($teamPerformanceDifference/$c, $drawMargin/$c);
+    }
+
+    // From F#:
+    public static function wWithinMargin($teamPerformanceDifference, $drawMargin)
+    {
+        $teamPerformanceDifferenceAbsoluteValue = abs($teamPerformanceDifference);
+        $denominator = GaussianDistribution::cumulativeTo($drawMargin - $teamPerformanceDifferenceAbsoluteValue)
+                       -
+                       GaussianDistribution::cumulativeTo(-$drawMargin - $teamPerformanceDifferenceAbsoluteValue);
+
+        if ($denominator < 2.222758749e-162)
+        {
+            return 1.0;
+        }
+
+        $vt = self::vWithinMargin($teamPerformanceDifferenceAbsoluteValue, $drawMargin);
+
+        return $vt*$vt +
+               (
+                   ($drawMargin - $teamPerformanceDifferenceAbsoluteValue)
+                   *
+                   GaussianDistribution::at(
+                       $drawMargin - $teamPerformanceDifferenceAbsoluteValue)
+                   - (-$drawMargin - $teamPerformanceDifferenceAbsoluteValue)
+                     *
+                     GaussianDistribution::at(-$drawMargin - $teamPerformanceDifferenceAbsoluteValue))/$denominator;
+    }
+}
+?>

Skills/TrueSkill/TwoPlayerTrueSkillCalculator.php

@@ -0,0 +1,181 @@
+<?php
+
+namespace Moserware\Skills\TrueSkill;
+
+require_once(dirname(__FILE__) . "/../GameInfo.php");
+require_once(dirname(__FILE__) . "/../Guard.php");
+require_once(dirname(__FILE__) . "/../PairwiseComparison.php");
+require_once(dirname(__FILE__) . "/../RankSorter.php");
+require_once(dirname(__FILE__) . "/../Rating.php");
+require_once(dirname(__FILE__) . "/../RatingContainer.php");
+require_once(dirname(__FILE__) . "/../SkillCalculator.php");
+
+require_once(dirname(__FILE__) . "/../PlayersRange.php");
+require_once(dirname(__FILE__) . "/../TeamsRange.php");
+
+require_once(dirname(__FILE__) . "/../Numerics/BasicMath.php");
+
+require_once(dirname(__FILE__) . "/DrawMargin.php");
+require_once(dirname(__FILE__) . "/TruncatedGaussianCorrectionFunctions.php");
+
+use Moserware\Skills\GameInfo;
+use Moserware\Skills\Guard;
+use Moserware\Skills\PairwiseComparison;
+use Moserware\Skills\RankSorter;
+use Moserware\Skills\Rating;
+use Moserware\Skills\RatingContainer;
+use Moserware\Skills\SkillCalculator;
+use Moserware\Skills\SkillCalculatorSupportedOptions;
+
+use Moserware\Skills\PlayersRange;
+use Moserware\Skills\TeamsRange;
+
+/**
+ * Calculates the new ratings for only two players.
+ * 
+ * When you only have two players, a lot of the math simplifies. The main purpose of this class
+ * is to show the bare minimum of what a TrueSkill implementation should have.
+ */
+
+class TwoPlayerTrueSkillCalculator extends SkillCalculator
+{
+    public function __construct()
+    {
+        parent::__construct(SkillCalculatorSupportedOptions::NONE, TeamsRange::exactly(2), PlayersRange::exactly(1));
+    }
+
+    public function calculateNewRatings(GameInfo &$gameInfo,
+                                        array $teams,
+                                        array $teamRanks)
+    {
+        // Basic argument checking
+        Guard::argumentNotNull($gameInfo, "gameInfo");
+        $this->validateTeamCountAndPlayersCountPerTeam($teams);
+
+        // Make sure things are in order
+        RankSorter::sort($teams, $teamRanks);
+        
+        // Since we verified that each team has one player, we know the player is the first one
+        $winningTeamPlayers = $teams[0]->getAllPlayers();
+        $winner = $winningTeamPlayers[0];
+        $winnerPreviousRating = $teams[0]->getRating($winner);
+        
+        $losingTeamPlayers = $teams[1]->getAllPlayers();
+        $loser = $losingTeamPlayers[0];
+        $loserPreviousRating = $teams[1]->getRating($loser);
+
+        $wasDraw = ($teamRanks[0] == $teamRanks[1]);
+
+        $results = new RatingContainer();
+
+        $results->setRating($winner, self::calculateNewRating($gameInfo,
+                                                              $winnerPreviousRating,
+                                                              $loserPreviousRating,
+                                                              $wasDraw ? PairwiseComparison::DRAW
+                                                                       : PairwiseComparison::WIN));
+
+        $results->setRating($loser, self::calculateNewRating($gameInfo,
+                                                             $loserPreviousRating,
+                                                             $winnerPreviousRating,
+                                                             $wasDraw ? PairwiseComparison::DRAW
+                                                                      : PairwiseComparison::LOSE));
+
+        // And we're done!
+        return $results;
+    }
+
+    private static function calculateNewRating(GameInfo $gameInfo, Rating $selfRating, Rating $opponentRating, $comparison)
+    {
+        $drawMargin = DrawMargin::getDrawMarginFromDrawProbability($gameInfo->getDrawProbability(),
+                                                                   $gameInfo->getBeta());
+
+        $c =
+            sqrt(
+                square($selfRating->getStandardDeviation())
+                +
+                square($opponentRating->getStandardDeviation())
+                +
+                2*square($gameInfo->getBeta()));
+
+        $winningMean = $selfRating->getMean();
+        $losingMean = $opponentRating->getMean();
+
+        switch ($comparison)
+        {
+            case PairwiseComparison::WIN:
+            case PairwiseComparison::DRAW:
+                // NOP
+                break;
+            case PairwiseComparison::LOSE:
+                $winningMean = $opponentRating->getMean();
+                $losingMean = $selfRating->getMean();
+                break;
+        }
+
+        $meanDelta = $winningMean - $losingMean;
+
+        if ($comparison != PairwiseComparison::DRAW)
+        {
+            // non-draw case
+            $v = TruncatedGaussianCorrectionFunctions::vExceedsMarginScaled($meanDelta, $drawMargin, $c);
+            $w = TruncatedGaussianCorrectionFunctions::wExceedsMarginScaled($meanDelta, $drawMargin, $c);
+            $rankMultiplier = (int) $comparison;
+        }
+        else
+        {
+            $v = TruncatedGaussianCorrectionFunctions::vWithinMarginScaled($meanDelta, $drawMargin, $c);
+            $w = TruncatedGaussianCorrectionFunctions::wWithinMarginScaled($meanDelta, $drawMargin, $c);
+            $rankMultiplier = 1;
+        }
+
+        $meanMultiplier = (square($selfRating->getStandardDeviation()) + square($gameInfo->getDynamicsFactor()))/$c;
+
+        $varianceWithDynamics = square($selfRating->getStandardDeviation()) + square($gameInfo->getDynamicsFactor());
+        $stdDevMultiplier = $varianceWithDynamics/square($c);
+
+        $newMean = $selfRating->getMean() + ($rankMultiplier*$meanMultiplier*$v);
+        $newStdDev = sqrt($varianceWithDynamics*(1 - $w*$stdDevMultiplier));
+
+        return new Rating($newMean, $newStdDev);
+    }
+
+    /**
+     * {@inheritdoc }
+     */
+    public function calculateMatchQuality(GameInfo &$gameInfo, array &$teams)
+    {
+        Guard::argumentNotNull($gameInfo, "gameInfo");
+        $this->validateTeamCountAndPlayersCountPerTeam($teams);
+
+        $team1 = $teams[0];
+        $team2 = $teams[1];
+
+        $team1Ratings = $team1->getAllRatings();
+        $team2Ratings = $team2->getAllRatings();
+
+        $player1Rating = $team1Ratings[0];
+        $player2Rating = $team2Ratings[0];
+
+        // We just use equation 4.1 found on page 8 of the TrueSkill 2006 paper:
+        $betaSquared = square($gameInfo->getBeta());
+        $player1SigmaSquared = square($player1Rating->getStandardDeviation());
+        $player2SigmaSquared = square($player2Rating->getStandardDeviation());
+
+        // This is the square root part of the equation:
+        $sqrtPart =
+            sqrt(
+                (2*$betaSquared)
+                /
+                (2*$betaSquared + $player1SigmaSquared + $player2SigmaSquared));
+
+        // This is the exponent part of the equation:
+        $expPart =
+            exp(
+                (-1*square($player1Rating->getMean() - $player2Rating->getMean()))
+                /
+                (2*(2*$betaSquared + $player1SigmaSquared + $player2SigmaSquared)));
+
+        return $sqrtPart*$expPart;
+    }
+}
+?>

Skills/TrueSkill/TwoTeamTrueSkillCalculator.php

@@ -0,0 +1,226 @@
+<?php
+
+namespace Moserware\Skills\TrueSkill;
+
+require_once(dirname(__FILE__) . "/../GameInfo.php");
+require_once(dirname(__FILE__) . "/../Guard.php");
+require_once(dirname(__FILE__) . "/../PairwiseComparison.php");
+require_once(dirname(__FILE__) . "/../RankSorter.php");
+require_once(dirname(__FILE__) . "/../Rating.php");
+require_once(dirname(__FILE__) . "/../RatingContainer.php");
+require_once(dirname(__FILE__) . "/../SkillCalculator.php");
+
+require_once(dirname(__FILE__) . "/../Team.php");
+
+require_once(dirname(__FILE__) . "/../PlayersRange.php");
+require_once(dirname(__FILE__) . "/../TeamsRange.php");
+
+require_once(dirname(__FILE__) . "/../Numerics/BasicMath.php");
+
+require_once(dirname(__FILE__) . "/DrawMargin.php");
+require_once(dirname(__FILE__) . "/TruncatedGaussianCorrectionFunctions.php");
+
+use Moserware\Skills\GameInfo;
+use Moserware\Skills\Guard;
+use Moserware\Skills\PairwiseComparison;
+use Moserware\Skills\RankSorter;
+use Moserware\Skills\Rating;
+use Moserware\Skills\RatingContainer;
+use Moserware\Skills\SkillCalculator;
+use Moserware\Skills\SkillCalculatorSupportedOptions;
+
+use Moserware\Skills\PlayersRange;
+use Moserware\Skills\TeamsRange;
+
+use Moserware\Skills\Team;
+
+/**
+ * Calculates new ratings for only two teams where each team has 1 or more players.
+ * 
+ * When you only have two teams, the math is still simple: no factor graphs are used yet.
+ */
+class TwoTeamTrueSkillCalculator extends SkillCalculator
+{
+    public function __construct()
+    {
+        parent::__construct(SkillCalculatorSupportedOptions::NONE, TeamsRange::exactly(2), PlayersRange::atLeast(1));
+    }
+
+    public function calculateNewRatings(GameInfo &$gameInfo,
+                                        array $teams,
+                                        array $teamRanks)
+    {
+        Guard::argumentNotNull($gameInfo, "gameInfo");
+        $this->validateTeamCountAndPlayersCountPerTeam($teams);
+
+        RankSorter::sort($teams, $teamRanks);
+
+        $team1 = $teams[0];
+        $team2 = $teams[1];
+
+        $wasDraw = ($teamRanks[0] == $teamRanks[1]);
+
+        $results = new RatingContainer();
+
+        self::updatePlayerRatings($gameInfo,
+                                  $results,
+                                  $team1,
+                                  $team2,
+                                  $wasDraw ? PairwiseComparison::DRAW : PairwiseComparison::WIN);
+
+        self::updatePlayerRatings($gameInfo,
+                                  $results,
+                                  $team2,
+                                  $team1,
+                                  $wasDraw ? PairwiseComparison::DRAW : PairwiseComparison::LOSE);
+
+        return $results;
+    }
+
+    private static function updatePlayerRatings(GameInfo $gameInfo,
+                                                RatingContainer &$newPlayerRatings,
+                                                Team $selfTeam,
+                                                Team $otherTeam,
+                                                $selfToOtherTeamComparison)
+    {
+        $drawMargin = DrawMargin::getDrawMarginFromDrawProbability($gameInfo->getDrawProbability(),
+                                                                   $gameInfo->getBeta());
+
+        $betaSquared = square($gameInfo->getBeta());
+        $tauSquared = square($gameInfo->getDynamicsFactor());
+
+        $totalPlayers = $selfTeam->count() + $otherTeam->count();
+
+        $meanGetter =
+            function($currentRating)
+            {
+                return $currentRating->getMean();
+            };
+
+        $selfMeanSum = sum($selfTeam->getAllRatings(), $meanGetter);
+        $otherTeamMeanSum = sum($otherTeam->getAllRatings(), $meanGetter);
+
+        $varianceGetter =
+            function($currentRating)
+            {
+                return square($currentRating->getStandardDeviation());
+            };
+
+        $c = sqrt(
+                  sum($selfTeam->getAllRatings(), $varianceGetter)
+                  +
+                  sum($otherTeam->getAllRatings(), $varianceGetter)
+                  +
+                  $totalPlayers*$betaSquared);
+
+        $winningMean = $selfMeanSum;
+        $losingMean = $otherTeamMeanSum;
+
+        switch ($selfToOtherTeamComparison)
+        {
+            case PairwiseComparison::WIN:
+            case PairwiseComparison::DRAW:
+                // NOP
+                break;
+            case PairwiseComparison::LOSE:
+                $winningMean = $otherTeamMeanSum;
+                $losingMean = $selfMeanSum;
+                break;
+        }
+
+        $meanDelta = $winningMean - $losingMean;
+
+        if ($selfToOtherTeamComparison != PairwiseComparison::DRAW)
+        {
+            // non-draw case
+            $v = TruncatedGaussianCorrectionFunctions::vExceedsMarginScaled($meanDelta, $drawMargin, $c);
+            $w = TruncatedGaussianCorrectionFunctions::wExceedsMarginScaled($meanDelta, $drawMargin, $c);
+            $rankMultiplier = (int) $selfToOtherTeamComparison;
+        }
+        else
+        {
+            // assume draw
+            $v = TruncatedGaussianCorrectionFunctions::vWithinMarginScaled($meanDelta, $drawMargin, $c);
+            $w = TruncatedGaussianCorrectionFunctions::wWithinMarginScaled($meanDelta, $drawMargin, $c);
+            $rankMultiplier = 1;
+        }
+
+        $selfTeamAllPlayers = &$selfTeam->getAllPlayers();
+        foreach ($selfTeamAllPlayers as &$selfTeamCurrentPlayer)
+        {
+            $localSelfTeamCurrentPlayer = &$selfTeamCurrentPlayer;
+            $previousPlayerRating = $selfTeam->getRating($localSelfTeamCurrentPlayer);
+
+            $meanMultiplier = (square($previousPlayerRating->getStandardDeviation()) + $tauSquared)/$c;
+            $stdDevMultiplier = (square($previousPlayerRating->getStandardDeviation()) + $tauSquared)/square($c);
+
+            $playerMeanDelta = ($rankMultiplier*$meanMultiplier*$v);
+            $newMean = $previousPlayerRating->getMean() + $playerMeanDelta;
+
+            $newStdDev =
+                sqrt((square($previousPlayerRating->getStandardDeviation()) + $tauSquared)*(1 - $w*$stdDevMultiplier));
+
+            $newPlayerRatings->setRating($localSelfTeamCurrentPlayer, new Rating($newMean, $newStdDev));
+        }
+    }
+
+    /**
+     * {@inheritdoc }
+     */
+    public function calculateMatchQuality(GameInfo &$gameInfo,
+                                          array &$teams)
+    {
+        Guard::argumentNotNull($gameInfo, "gameInfo");
+        $this->validateTeamCountAndPlayersCountPerTeam($teams);
+
+        // We've verified that there's just two teams
+        $team1Ratings = $teams[0]->getAllRatings();
+        $team1Count = count($team1Ratings);
+
+        $team2Ratings = $teams[1]->getAllRatings();
+        $team2Count = count($team2Ratings);
+
+        $totalPlayers = $team1Count + $team2Count;
+
+        $betaSquared = square($gameInfo->getBeta());
+
+        $meanGetter =
+            function($currentRating)
+            {
+                return $currentRating->getMean();
+            };
+
+        $varianceGetter =
+            function($currentRating)
+            {
+                return square($currentRating->getStandardDeviation());
+            };
+
+        $team1MeanSum = sum($team1Ratings, $meanGetter);
+        $team1StdDevSquared = sum($team1Ratings, $varianceGetter);
+
+        $team2MeanSum = sum($team2Ratings, $meanGetter);
+        $team2SigmaSquared = sum($team2Ratings, $varianceGetter);
+
+        // This comes from equation 4.1 in the TrueSkill paper on page 8
+        // The equation was broken up into the part under the square root sign and
+        // the exponential part to make the code easier to read.
+
+        $sqrtPart
+            = sqrt(
+                ($totalPlayers*$betaSquared)
+                /
+                ($totalPlayers*$betaSquared + $team1StdDevSquared + $team2SigmaSquared)
+                );
+
+        $expPart
+            = exp(
+                (-1*square($team1MeanSum - $team2MeanSum))
+                /
+                (2*($totalPlayers*$betaSquared + $team1StdDevSquared + $team2SigmaSquared))
+                );
+
+        return $expPart*$sqrtPart;
+    }
+}
+?>