Support k != 10, ie. the new table.

diff --git a/foosrank.cpp b/foosrank.cpp
index 3ad0bb1ea725203b402c3ee8fd438e084c7bcb0e..bfcea1121f73745a61c36d6eed1bfc0b38dc6ba1 100644 (file)
--- a/foosrank.cpp
+++ b/foosrank.cpp
@@ -14,16 +14,17 @@ static const double rating_constant = 455.0;
 
 using namespace std;
 
-double prob_score(double a, double rd);
-double prob_score_real(double a, double prodai, double rd_norm);
-double prodai(double a);
+double prob_score(int k, double a, double rd);
+double prob_score_real(int k, double a, double prodai, double kfac, double rd_norm);
+double prodai(int k, double a);
+double fac(int x);
 
-// probability of match ending 10-a when winnerR - loserR = RD
+// probability of match ending k-a (k>a) when winnerR - loserR = RD
 //
 //   +inf  
 //     / 
 //    |
-//    | Poisson[lambda1, t](a) * Erlang[lambda2, 10](t) dt
+//    | Poisson[lambda1, t](a) * Erlang[lambda2, k](t) dt
 //    |
 //   /
 // -inf
@@ -34,26 +35,36 @@ double prodai(double a);
 // Glicko/Bradley-Terry assumption that a player rated 400 points over
 // his/her opponent will win with a probability of 10/11 =~ 0.90909. 
 //
-double prob_score(double a, double rd)
+double prob_score(int k, double a, double rd)
 {
-       return prob_score_real(a, prodai(a), rd/rating_constant);
+       return prob_score_real(k, a, prodai(k, a), fac(k-1), rd/rating_constant);
 }
 
-// Same, but takes in Product(a+i, i=1..9) as an argument in addition to a. Faster
-// if you already have that precomputed, and assumes rd is already divided by 455.
-double prob_score_real(double a, double prodai, double rd_norm)
+// Same, but takes in Product(a+i, i=1..k-1) and (k-1)! as an argument in
+// addition to a. Faster if you already have that precomputed, and assumes rd
+// is already divided by 455.
+double prob_score_real(int k, double a, double prodai, double kfac, double rd_norm)
 {
-       double nom =
-               pow(2.0, -a*rd_norm) * pow(2.0, 10.0*rd_norm) * pow(pow(2.0, -rd_norm) + 1.0, -a)
-               * prodai;
-       double denom = 362880 * pow(1.0 + pow(2.0, rd_norm), 10.0);
+       double nom = prodai * pow(2.0, -rd_norm * a); 
+       double denom = kfac * pow(1.0 + pow(2.0, -rd_norm), k+a);
        return nom/denom;
 }
 
-// Calculates Product(a+i, i=1..9) (see above).
-double prodai(double a)
+// Calculates Product(a+i, i=1..k-1) (see above).
+double prodai(int k, double a)
 {
-       return (a+1)*(a+2)*(a+3)*(a+4)*(a+5)*(a+6)*(a+7)*(a+8)*(a+9);
+       double prod = 1.0;
+       for (int i = 1; i < k; ++i)
+               prod *= (a+i);
+       return prod;
+}
+
+double fac(int x)
+{
+       double prod = 1.0;
+       for (int i = 2; i <= x; ++i)
+               prod *= i;
+       return prod;
 }
 
 // 
@@ -75,31 +86,32 @@ double prodai(double a)
 // Set the last parameter to 1.0 if player 1 won, or -1.0 if player 2 won.
 // In the latter case, ProbScore will be given (r1-r2) instead of (r2-r1).
 //
-static inline double evaluate_int_point(double a, double prodai_precompute, double r1, double mu2, double sigma2, double winfac, double x);
+static inline double evaluate_int_point(int k, double a, double prodai_precompute, double kfac_precompute, double r1, double mu2, double sigma2, double winfac, double x);
 
-double opponent_rating_pdf(double a, double r1, double mu2, double sigma2, double winfac)
+double opponent_rating_pdf(int k, double a, double r1, double mu2, double sigma2, double winfac)
 {
-       double prodai_precompute = prodai(a);
+       double prodai_precompute = prodai(k, a);
+       double kfac_precompute = fac(k-1);
        winfac /= rating_constant;
 
        int n = int(3000.0 / int_step_size + 0.5);
        double h = 3000.0 / double(n);
-       double sum = evaluate_int_point(a, prodai_precompute, r1, mu2, sigma2, winfac, 0.0);
+       double sum = evaluate_int_point(k, a, prodai_precompute, kfac_precompute, r1, mu2, sigma2, winfac, 0.0);
 
        for (int i = 1; i < n; i += 2) {
-               sum += 4.0 * evaluate_int_point(a, prodai_precompute, r1, mu2, sigma2, winfac, i * h);
+               sum += 4.0 * evaluate_int_point(k, a, prodai_precompute, kfac_precompute, r1, mu2, sigma2, winfac, i * h);
        }
        for (int i = 2; i < n; i += 2) {
-               sum += 2.0 * evaluate_int_point(a, prodai_precompute, r1, mu2, sigma2, winfac, i * h);
+               sum += 2.0 * evaluate_int_point(k, a, prodai_precompute, kfac_precompute, r1, mu2, sigma2, winfac, i * h);
        }
-       sum += evaluate_int_point(a, prodai_precompute, r1, mu2, sigma2, winfac, 3000.0);
+       sum += evaluate_int_point(k, a, prodai_precompute, kfac_precompute, r1, mu2, sigma2, winfac, 3000.0);
 
        return (h/3.0) * sum;
 }
 
-static inline double evaluate_int_point(double a, double prodai_precompute, double r1, double mu2, double sigma2, double winfac, double x)
+static inline double evaluate_int_point(int k, double a, double prodai_precompute, double kfac_precompute, double r1, double mu2, double sigma2, double winfac, double x)
 {
-       double probscore = prob_score_real(a, prodai_precompute, (r1 - x)*winfac);
+       double probscore = prob_score_real(k, a, prodai_precompute, kfac_precompute, (r1 - x)*winfac);
        double z = (x - mu2)/sigma2;
        double gaussian = exp(-(z*z/2.0));
        return  probscore * gaussian;
@@ -347,17 +359,17 @@ void compute_new_rating(double mu1, double sigma1, double mu2, double sigma2, in
 {
        vector<pair<double, double> > curve;
 
-       if (score1 == 10) {
+       if (score1 > score2) {
                for (double r1 = 0.0; r1 < 3000.0; r1 += pdf_step_size) {
                        double z = (r1 - mu1) / sigma1;
                        double gaussian = exp(-(z*z/2.0));
-                       curve.push_back(make_pair(r1, gaussian * opponent_rating_pdf(score2, r1, mu2, sigma2, 1.0)));
+                       curve.push_back(make_pair(r1, gaussian * opponent_rating_pdf(score1, score2, r1, mu2, sigma2, 1.0)));
                }
        } else {
                for (double r1 = 0.0; r1 < 3000.0; r1 += pdf_step_size) {
                        double z = (r1 - mu1) / sigma1;
                        double gaussian = exp(-(z*z/2.0));
-                       curve.push_back(make_pair(r1, gaussian * opponent_rating_pdf(score1, r1, mu2, sigma2, -1.0)));
+                       curve.push_back(make_pair(r1, gaussian * opponent_rating_pdf(score2, score1, r1, mu2, sigma2, -1.0)));
                }
        }
 
@@ -374,27 +386,29 @@ int main(int argc, char **argv)
        double mu2 = atof(argv[3]);
        double sigma2 = atof(argv[4]);
 
-       if (argc > 5) {
+       if (argc > 6) {
                int score1 = atoi(argv[5]);
                int score2 = atoi(argv[6]);
                double mu, sigma;
                compute_new_rating(mu1, sigma1, mu2, sigma2, score1, score2, mu, sigma);
                printf("%f %f\n", mu, sigma);
        } else {
+               int k = atoi(argv[5]);
+
                // assess all possible scores
-               for (int i = 0; i <= 9; ++i) {
+               for (int i = 0; i < k; ++i) {
                        double newmu1, newmu2, newsigma1, newsigma2;
-                       compute_new_rating(mu1, sigma1, mu2, sigma2, 10, i, newmu1, newsigma1);
-                       compute_new_rating(mu2, sigma2, mu1, sigma1, i, 10, newmu2, newsigma2);
-                       printf("10-%u,%f,%+f,%+f\n",
-                               i, prob_score(i, mu1-mu2), newmu1-mu1, newmu2-mu2);
+                       compute_new_rating(mu1, sigma1, mu2, sigma2, k, i, newmu1, newsigma1);
+                       compute_new_rating(mu2, sigma2, mu1, sigma1, i, k, newmu2, newsigma2);
+                       printf("%u-%u,%f,%+f,%+f\n",
+                               k, i, prob_score(k, i, mu1-mu2), newmu1-mu1, newmu2-mu2);
                }
-               for (int i = 10; i --> 0; ) {
+               for (int i = k; i --> 0; ) {
                        double newmu1, newmu2, newsigma1, newsigma2;
-                       compute_new_rating(mu1, sigma1, mu2, sigma2, i, 10, newmu1, newsigma1);
-                       compute_new_rating(mu2, sigma2, mu1, sigma1, 10, i, newmu2, newsigma2);
-                       printf("%u-10,%f,%+f,%+f\n",
-                               i, prob_score(i, mu2-mu1), newmu1-mu1, newmu2-mu2);
+                       compute_new_rating(mu1, sigma1, mu2, sigma2, i, k, newmu1, newsigma1);
+                       compute_new_rating(mu2, sigma2, mu1, sigma1, k, i, newmu2, newsigma2);
+                       printf("%u-%u,%f,%+f,%+f\n",
+                               i, k, prob_score(k, i, mu2-mu1), newmu1-mu1, newmu2-mu2);
                }
        }
 }

diff --git a/www/assess-single.pl b/www/assess-single.pl
index 66480e6dcc174ebd9a92c3a5e36dbe5569faf6e3..e9ffee198e27a1157d5e9713db79e2e32614a349 100755 (executable)
--- a/www/assess-single.pl
+++ b/www/assess-single.pl
@@ -24,13 +24,29 @@ my $dbh = foosball::db_connect();
 my ($rating1, $rd1) = foosball::find_single_rating($dbh, $username1);
 my ($rating2, $rd2) = foosball::find_single_rating($dbh, $username2);
 
-open ASSESS, "/srv/foosball.sesse.net/foosrank $rating1 $rd1 $rating2 $rd2 |"
+# 10-x table
+open ASSESS, "/srv/foosball.sesse.net/foosrank $rating1 $rd1 $rating2 $rd2 10 |"
        or die "foosrank: $!";
 
-my @results = ();
+my @results10 = ();
 while (<ASSESS>) {
        my ($score, $prob, $rdiff1, $rdiff2) = split /,/, $_;
-       push @results, {
+       push @results10, {
+               score => $score,
+               prob => (sprintf "%.3f", $prob),
+               rdiff1 => (sprintf "%+d", int($rdiff1+0.5)),
+               rdiff2 => (sprintf "%+d", int($rdiff2+0.5)),
+       };
+}
+
+# 7-x table
+open ASSESS, "/srv/foosball.sesse.net/foosrank $rating1 $rd1 $rating2 $rd2 7 |"
+       or die "foosrank: $!";
+
+my @results7 = ();
+while (<ASSESS>) {
+       my ($score, $prob, $rdiff1, $rdiff2) = split /,/, $_;
+       push @results7, {
                score => $score,
                prob => (sprintf "%.3f", $prob),
                rdiff1 => (sprintf "%+d", int($rdiff1+0.5)),
@@ -45,6 +61,7 @@ my $doc = XML::Template::process_file('assess.xml', {
        'username2' => $username2,
        'rating1' => int($rating1+0.5),
        'rating2' => int($rating2+0.5),
-       '#results' => \@results,
+       '#results10' => \@results10,
+       '#results7' => \@results7,
 });
 print $doc->toString;

diff --git a/www/assess.xml b/www/assess.xml
index 887acf01caa7bf33103332f07a21e16b4104ef4a..f6a4a3428991b099626a79f22c50f856661c9219 100644 (file)
--- a/www/assess.xml
+++ b/www/assess.xml
@@ -20,7 +20,26 @@
          <th><t:username2 /></th>
        </tr>
       </thead>
-      <tbody t:id="results">
+      <tbody t:id="results10">
+        <tr>
+         <td><t:score /></td>
+         <td><t:prob /></td>
+         <td><t:rdiff1 /></td>
+         <td><t:rdiff2 /></td>
+       </tr>
+      </tbody>
+    </table>
+    
+    <table>
+      <thead>
+        <tr>
+          <th>Score</th>
+         <th>Probability</th>
+         <th><t:username1 /></th>
+         <th><t:username2 /></th>
+       </tr>
+      </thead>
+      <tbody t:id="results7">
         <tr>
          <td><t:score /></td>
          <td><t:prob /></td>