#!/usr/bin/perl

# Make a pool of random players with known true ratings between 1000 to 2000
# Set the calculated ratings to be the same as the true ratings
# Play games between randomly selected players with the outcome
#     determined by the true ratings
# Calculate the system error

$MaxPlayers = 10;

print "# players = $MaxPlayers\n";

print "drift test: 100 trials, skip Px100 games, measure error for Px10 games\n";
$e = drift(100, $MaxPlayers*100, $MaxPlayers*10);
print "    drift error: $e rating points\n";

print "convergence test: 100 trials, stop when error gets below $e\n";
$c = convergence(100, $e);
print "    convergence rate: $c games per player\n";

print "disruption test: 100 trials, stop when error gets below $e\n";
($r, $c) = disruption(100, $e);
print "    disruption error: $r rating points\n";
print "    disruption rate: $c games per player\n";

exit;

sub disruption{
  local($trials, $conv) = @_;
  local($i, $j, $merr, $err, $c, $tc, $terr);

  $tc= 0;
  for($i=0;$i<$trials;$i++){
tryAgain:
    makePlayers();
    for($j=0;$j<$MaxPlayers;$j++){
      $Cr[$j] = 1500;
    }
    $MaxPlayers -= 1;

    $err = playGames($MaxPlayers-1);
    while($err>$conv){
      $err = playGames($MaxPlayers-1);
#print "  $err\n";
    }
    $MaxPlayers += 1;
#print "converged  $Cr[$MaxPlayers-1] $Tr[$MaxPlayers-1]\n";

    $merr = playGames($MaxPlayers);

    if (abs($merr-$err)<5){ goto tryAgain; }

    $err = $merr;
#print "  $err\n";
    $c = 1;
    while($merr>$conv){
      $merr = playGames($MaxPlayers);
#print "  $merr\n";
      $err += $merr;
      $c += 1;
    }

#print "  $c\n";
    $tc += $c;
    $terr += $err;
  }
# Normalize the result so that it gives the number of games each
#   player has to play
print "  terr is $terr   tc is $tc\n";
  $terr = $terr/$tc;
  $tc = $tc/$trials;
  $tc = $tc*2; # because if there are 10 players and 10 total games played
               #     then on average each player got to play 2 games
#print "$tc\n";
  return ($terr, $tc);

}


sub convergence{
  local($trials, $conv) = @_;
  local($i, $j, $err, $c, $tc);

  $tc= 0;
  for($i=0;$i<$trials;$i++){
    makePlayers();
    for($j=0;$j<$MaxPlayers;$j++){
      $Cr[$j] = 1500;
    }
    $err = playGames($MaxPlayers);
    $c = $MaxPlayers;
    while($err>$conv){
      $err = playGames($MaxPlayers);
#print "    $i $err\n";
      $c += $MaxPlayers;
    }
#print "  $c\n";
    $tc += $c;
  }
# Normalize the result so that it gives the number of games each
#   player has to play
  $tc = $tc/$MaxPlayers/$trials;
  $tc = $tc*2; # because if there are 10 players and 10 total games played
               #     then on average each player got to play 2 games
#print "$tc\n";
  return $tc;

}

sub drift{
  local($trials, $skip, $games) = @_;
  local($i, $err, $terr);

  $terr = 0;
  for($i=0;$i<$trials;$i++){
    makePlayers();
    @Cr = @Tr;

    $err = playGames($skip);
    $err = playGames($games);
    $terr += $err;
#print "  $err\n";
  }
  return $terr/$trials;
}

sub makePlayers{
  local($i);

  for($i=0;$i<$MaxPlayers;$i++){
    $Tr[$i] = int(rand(1000)) + 1000;
  }
}

sub playGames{
  local($ng) = @_;
  local($i, $p1, $p2, $outcome, $err, $terr);
  local($err2, $err3);

  $err = 0;
  for($i=0;$i<$ng;$i++){
selectPlayers:
    $p1 = int(rand($MaxPlayers));
    $p2 = int(rand($MaxPlayers));
#print "p1=$p1 p2=$p2\n";
    if ($p1==$p2){ goto selectPlayers; }
    $outcome = playGame($p1, $p2);
    updateRatings($p1, $p2, $outcome);
    $err = sysErr(\@Tr, \@Cr);
    $terr += $err;
#print "    $err\n";
  }
  return $terr/$ng;
}

sub playGame{
  local($p1, $p2) = @_;

  return outcome($Tr[$p1], $Tr[$p2]);
}

sub outcome{
  local($r1, $r2) = @_;
  local($rdiff, $wp, $ran);

  $rdiff = ($r2 - $r1)/400;
  $wp = 1.0/(1.0 + 10.0**$rdiff);
  $ran = rand(1);
  if ($ran<$wp){ return 1;}
  return 0;
}

sub updateRatings{
  local($p1, $p2, $w1) = @_;

  ($r1) = newRating($Cr[$p1], $Cr[$p2], $w1);
  ($r2) = newRating($Cr[$p2], $Cr[$p1], 1 - $w1);
  $Cr[$p1] = $r1;
  $Cr[$p2] = $r2;
}

sub newRating{
  local($mr, $or, $iwon) = @_;
  local($rdiff, $wp, $k, $nr);

  $rdiff = ($or - $mr)/400;
  $wp = 1.0/(1.0 + 10.0**$rdiff);

  $k = 24;
  $nr = int($mr + $k*($iwon - $wp) + 0.5);
  return $nr;
}

sub sysErr{
  local($t, $c) = @_;
  local(@tr) = @$t;
  local(@cr) = @$c;
  local($i, $j, $err);

  $err = 0;
  for($i=0;$i<$MaxPlayers;$i++){
    for($j=0;$j<$i;$j++){
      if ($i!=$j){
#print "  $i $j $err += abs(abs($tr[$i]-$tr[$j]) - abs($cr[$i]-$cr[$j])) \n";
        $err += abs(abs($tr[$i]-$tr[$j]) - abs($cr[$i]-$cr[$j]));
      }
    }
  }
#print " return $err/($MaxPlayers-1)/$MaxPlayers \n";
  return $err/($MaxPlayers-1)/$MaxPlayers;
}

# Dont use these error function; they dont give good results
sub sysErr2{
  local($t, $c) = @_;
  local(@tr) = @$t;
  local(@cr) = @$c;
  local($i, $j, $err);

  $err = 0;
  for($i=0;$i<$MaxPlayers;$i++){
    $err += abs($tr[$i]-$cr[$i]);
  }
  return $err/$MaxPlayers;
}

# Dont use these error function; they dont give good results
sub sysErr3{
  local($t, $c) = @_;
  local(@tr) = @$t;
  local(@cr) = @$c;
  local($i, $j, $err, $avtr, $avcr);

  $err = 0;
  for($i=0;$i<$MaxPlayers;$i++){
    $err += abs($tr[$i]-$cr[$i]);
    $avtr += $tr[$i];
    $avcr += $cr[$i];
  }
$j = $avtr - $avcr;
print "  $j $avtr $avcr\n";
  $err = abs($err - ($avtr - $avcr));
  return $err/$MaxPlayers;
}