private SkillGaussian CalculateTeamRating(IEnumerable <JamPlayerEffectiveness> side, IEnumerable <SkillGaussian> players)
{
if (side.Count() > 5)
{
throw new InvalidOperationException("too many players on team!");
}
// for each player, we need their mean and their playtime portion
double summedQuality = 0;
double summedVariance = 0;
foreach (JamPlayerEffectiveness player in side)
{
// we scale the jammer to be half of the total importance of the team
// we're adding in the beta variance here, rather than on the player,
// to make future updates to the player cleaner
SkillGaussian playerSkill = players.First(p => p.ID == player.PlayerID);
if (player.IsJammer)
{
summedQuality += player.JamPortion * playerSkill.Mean * 4;
summedVariance += player.JamPortion * (playerSkill.Variance + _betaSquared) * 4;
}
else
{
summedQuality += player.JamPortion * playerSkill.Mean;
summedVariance += player.JamPortion * (playerSkill.Variance + _betaSquared);
}
}
return(new SkillGaussian(0, summedQuality, summedVariance));
}
private void AnalyzeJam(IEnumerable <JamPlayerEffectiveness> players, DateTime dateOfJam)
{
var teams = players.GroupBy(p => p.TeamID);
var team1 = teams.First().ToList();
var team2 = teams.Last().ToList();
var skills1 = team1.Select(p => CreatePlayerSkill(p.PlayerID, p.IsJammer, dateOfJam));
var skills2 = team2.Select(p => CreatePlayerSkill(p.PlayerID, p.IsJammer, dateOfJam));
var team1Skill = CalculateTeamRating(team1, skills1);
var team2Skill = CalculateTeamRating(team2, skills2);
// the difference in team skills, adjusted by the beta, give us a sense of how we expected this matchup to go
// that can be compared to the actual result
double c = Math.Sqrt(team1Skill.Variance + team2Skill.Variance + 2 * _betaSquared);
// in normal TrueSkill, a Beta lead in rating is interpreted as having about an 80% chance of a win.
// in our implementation, it represents an 80% result; in the 0-penalty case,
// this is approximately equal to getting about a 3.5 point delta on a jam
// determine which team exceeded expectations
// basically, what in trueskill would be the main value becomes our "draw" value,
// and the actual result becomes our main value
double meanDiff = team1Skill.Mean - team2Skill.Mean;
double scaledMeanDiff = meanDiff / c;
double trueSkillDenominator = SkillGaussian.CumulativeTo(scaledMeanDiff, 0, 1);
double result = _pointDeltaCumulative[_jamTeamPointDeltaMap[players.First().JamID][team1.First().TeamID]];
// the denominator is effectively the percent result expected for team 1;
// if the actual result is greater, team 1 overperformed
double team1Multiplier = 1;
if (trueSkillDenominator > result)
{
meanDiff = team2Skill.Mean - team1Skill.Mean;
scaledMeanDiff = meanDiff / c;
trueSkillDenominator = SkillGaussian.CumulativeTo(scaledMeanDiff, 0, 1);
result = _pointDeltaCumulative[_jamTeamPointDeltaMap[players.First().JamID][team2.First().TeamID]];
team1Multiplier = -1;
}
double inverseResult = SkillGaussian.InverseCumulativeTo(result, 0, 1);
double newDenominator = SkillGaussian.CumulativeTo(scaledMeanDiff - inverseResult, 0, 1);
double v = (SkillGaussian.At(scaledMeanDiff - inverseResult, 0, 1)) / newDenominator;
double w = v * (v + scaledMeanDiff - inverseResult);
foreach (SkillGaussian player in skills1)
{
CalculateNewPlayerRating(c, team1Multiplier, v, w, player);
}
foreach (SkillGaussian player in skills2)
{
CalculateNewPlayerRating(c, -team1Multiplier, v, w, player);
}
}
// at some point, we'll need to take the current sigma of the player and increase it, probably based on time since last data
private double CalculateTimeEffect(SkillGaussian player, DateTime newTime)
{
// how much do we want to scale the player's std dev?
// it probably ought to be flat, not proportional
// one way to think of it: how long would a well-understood player have to disappear to be treated as new again?
// let's say two years-ish, and see what happens
TimeSpan timeSpan = newTime - player.LastUpdated;
if (timeSpan > _baseTimeSpan)
{
timeSpan = _baseTimeSpan;
}
double ratio = ((double)timeSpan.Ticks) / _baseTimeSpan.Ticks;
double range = _baseSigma - player.Sigma;
return(range * ratio);
}
private SkillGaussian CreatePlayerSkill(int playerID, bool isJammer, DateTime dateOfGame)
{
// variances, not std dev, are sum-able
// a^2 + b^2 != (a+b)^2
var dictionary = isJammer ? _jammerSkillDictionary : _blockerSkillDictionary;
if (!dictionary.ContainsKey(playerID))
{
SkillGaussian newPlayer = new SkillGaussian(playerID, 500, _baseVariance, isJammer, dateOfGame);
dictionary[playerID] = newPlayer;
return(newPlayer);
}
var startingPlayer = dictionary[playerID];
double tau = CalculateTimeEffect(startingPlayer, dateOfGame);
startingPlayer.AddVariance(Math.Pow(tau, 2));
startingPlayer.LastUpdated = dateOfGame;
return(startingPlayer);
}
private void CalculateNewPlayerRating(double c, double team1Multiplier, double v, double w, SkillGaussian player)
{
double meanMultiplier = player.Variance / c;
double stdDevMultiplier = meanMultiplier / c;
double playerMeanDelta = (team1Multiplier * meanMultiplier * v);
double newMean = player.Mean + playerMeanDelta;
double newVariance = player.Variance * (1 - (w * stdDevMultiplier));
SkillGaussian newValues = new SkillGaussian(player.ID, newMean, newVariance, player.IsJammer, player.LastUpdated);
if (player.IsJammer)
{
_jammerSkillDictionary[player.ID] = newValues;
}
else
{
_blockerSkillDictionary[player.ID] = newValues;
}
}
