From f390fceb530a44d7571f29a5c4416f0004ba882c Mon Sep 17 00:00:00 2001 From: "Steinar H. Gunderson" Date: Mon, 8 Oct 2007 20:15:05 +0200 Subject: [PATCH] Support k != 10, ie. the new table. --- foosrank.cpp | 94 +++++++++++++++++++++++++------------------- www/assess-single.pl | 25 ++++++++++-- www/assess.xml | 21 +++++++++- 3 files changed, 95 insertions(+), 45 deletions(-) diff --git a/foosrank.cpp b/foosrank.cpp index 3ad0bb1..bfcea11 100644 --- 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 > 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 66480e6..e9ffee1 100755 --- 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: $!"; -my @results = (); +my @results10 = (); while () { my ($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: $!"; + +my @results7 = (); +while () { + my ($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 887acf0..f6a4a34 100644 --- a/www/assess.xml +++ b/www/assess.xml @@ -20,7 +20,26 @@ - + + + + + + + + + + + + + + + + + + + + -- 2.39.2
ScoreProbability