/// <summary>
/// Record a new result from a match between two players.
/// </summary>
/// <param name="winner"></param>
/// <param name="loser"></param>
/// <param name="isDraw"></param>
public Result(Rating winner, Rating loser, bool isDraw = false)
{
if (!ValidPlayers(winner, loser))
{
throw new ArgumentException("Players winner and loser are the same player");
}
_winner = winner;
_loser = loser;
_isDraw = isDraw;
}
/// <summary>
/// Given a particular player, returns the opponent.
/// </summary>
/// <param name="player"></param>
/// <returns></returns>
public Rating GetOpponent(Rating player)
{
Rating opponent;
if (_winner == player)
{
opponent = _loser;
}
else if (_loser == player)
{
opponent = _winner;
}
else
{
throw new ArgumentException("Player did not participate in match", "player");
}
return opponent;
}
/// <summary>
/// Returns the "score" for a match.
/// </summary>
/// <param name="player"></param>
/// <returns></returns>
public double GetScore(Rating player)
{
double score;
if (_winner == player)
{
score = PointsForWin;
}
else if (_loser == player)
{
score = PointsForLoss;
}
else
{
throw new ArgumentException("Player did not participate in match", "player");
}
if (_isDraw)
{
score = PointsForDraw;
}
return score;
}
/// <summary>
/// Check that we're not doing anything silly like recording a match with only one player.
/// </summary>
/// <param name="player1"></param>
/// <param name="player2"></param>
/// <returns></returns>
private static bool ValidPlayers(Rating player1, Rating player2)
{
return player1 != player2;
}
/// <summary>
/// This is a formula as per step 4 of Glickman's paper.
/// </summary>
/// <param name="player"></param>
/// <param name="results"></param>
/// <returns></returns>
private double Delta(Rating player, IList<Result> results)
{
return V(player, results)*OutcomeBasedRating(player, results);
}
/// <summary>
/// Test whether a particular player participated in the match represented by this result.
/// </summary>
/// <param name="player"></param>
/// <returns></returns>
public bool Participated(Rating player)
{
return player == _winner || player == _loser;
}
/// <summary>
/// This is the main function in step 3 of Glickman's paper.
/// </summary>
/// <param name="player"></param>
/// <param name="results"></param>
/// <returns></returns>
private static double V(Rating player, IEnumerable<Result> results)
{
var v = 0.0;
foreach (var result in results)
{
v = v + (
(Math.Pow(G(result.GetOpponent(player).GetGlicko2RatingDeviation()), 2))
*E(player.GetGlicko2Rating(),
result.GetOpponent(player).GetGlicko2Rating(),
result.GetOpponent(player).GetGlicko2RatingDeviation())
*(1.0 - E(player.GetGlicko2Rating(),
result.GetOpponent(player).GetGlicko2Rating(),
result.GetOpponent(player).GetGlicko2RatingDeviation())
));
}
return Math.Pow(v, -1);
}
/// <summary>
/// This is the function processing described in step 5 of Glickman's paper.
/// </summary>
/// <param name="player"></param>
/// <param name="results"></param>
private void CalculateNewRating(Rating player, IList<Result> results)
{
var phi = player.GetGlicko2RatingDeviation();
var sigma = player.GetVolatility();
var a = Math.Log(Math.Pow(sigma, 2));
var delta = Delta(player, results);
var v = V(player, results);
// step 5.2 - set the initial values of the iterative algorithm to come in step 5.4
var A = a;
double B;
if (Math.Pow(delta, 2) > Math.Pow(phi, 2) + v)
{
B = Math.Log(Math.Pow(delta, 2) - Math.Pow(phi, 2) - v);
}
else
{
double k = 1;
B = a - (k*Math.Abs(_tau));
while (F(B, delta, phi, v, a, _tau) < 0)
{
k++;
B = a - (k*Math.Abs(_tau));
}
}
// step 5.3
var fA = F(A, delta, phi, v, a, _tau);
var fB = F(B, delta, phi, v, a, _tau);
// step 5.4
while (Math.Abs(B - A) > ConvergenceTolerance)
{
var C = A + (((A - B)*fA)/(fB - fA));
var fC = F(C, delta, phi, v, a, _tau);
if (fC*fB < 0)
{
A = B;
fA = fB;
}
else
{
fA = fA/2.0;
}
B = C;
fB = fC;
}
var newSigma = Math.Exp(A/2.0);
player.SetWorkingVolatility(newSigma);
// Step 6
var phiStar = CalculateNewRatingDeviation(phi, newSigma);
// Step 7
var newPhi = 1.0/Math.Sqrt((1.0/Math.Pow(phiStar, 2)) + (1.0/v));
// note that the newly calculated rating values are stored in a "working" area in the Rating object
// this avoids us attempting to calculate subsequent participants' ratings against a moving target
player.SetWorkingRating(
player.GetGlicko2Rating()
+ (Math.Pow(newPhi, 2)*OutcomeBasedRating(player, results)));
player.SetWorkingRatingDeviation(newPhi);
player.IncrementNumberOfResults(results.Count);
}
/// <summary>
/// Add a result to the set.
/// </summary>
/// <param name="winner"></param>
/// <param name="loser"></param>
public void AddResult(Rating winner, Rating loser)
{
var result = new Result(winner, loser);
_results.Add(result);
}
/// <summary>
/// This is a formula as per step 4 of Glickman's paper.
/// </summary>
/// <param name="player"></param>
/// <param name="results"></param>
/// <returns>Expected rating based on outcomes.</returns>
private static double OutcomeBasedRating(Rating player, IEnumerable<Result> results)
{
double outcomeBasedRating = 0;
foreach (var result in results)
{
outcomeBasedRating = outcomeBasedRating
+ (G(result.GetOpponent(player).GetGlicko2RatingDeviation())
*(result.GetScore(player) - E(
player.GetGlicko2Rating(),
result.GetOpponent(player).GetGlicko2Rating(),
result.GetOpponent(player).GetGlicko2RatingDeviation()))
);
}
return outcomeBasedRating;
}
/// <summary>
/// Add a participant to the rating period, e.g. so that their rating will
/// still be calculated even if they don't actually compete.
/// </summary>
/// <param name="rating"></param>
public void AddParticipant(Rating rating)
{
_participants.Add(rating);
}
/// <summary>
/// Record a draw between two players and add to the set.
/// </summary>
/// <param name="player1"></param>
/// <param name="player2"></param>
public void AddDraw(Rating player1, Rating player2)
{
var result = new Result(player1, player2, true);
_results.Add(result);
}
/// <summary>
/// Get a list of the results for a given player.
/// </summary>
/// <param name="player"></param>
/// <returns></returns>
public IList<Result> GetResults(Rating player)
{
var filteredResults = new List<Result>();
foreach (var result in _results)
{
if (result.Participated(player))
{
filteredResults.Add(result);
}
}
return filteredResults;
}
/// <summary>
/// Test whether a particular player participated in the match represented by this result.
/// </summary>
/// <param name="player"></param>
/// <returns></returns>
public bool Participated(Rating player)
{
return(player == _winner || player == _loser);
}
/// <summary>
/// Check that we're not doing anything silly like recording a match with only one player.
/// </summary>
/// <param name="player1"></param>
/// <param name="player2"></param>
/// <returns></returns>
private static bool ValidPlayers(Rating player1, Rating player2)
{
return(player1 != player2);
}