X-Git-Url: https://git.sesse.net/?a=blobdiff_plain;f=foosrank.cpp;h=b8070846a14d944eba3ae856e13d1bdb5e618250;hb=2e8c3d2f5f162a8ab68c4e979c57295f21dd366f;hp=3ad0bb1ea725203b402c3ee8fd438e084c7bcb0e;hpb=6b71fbcb1949c150dcc8f50bd9f138f56454964c;p=foosball diff --git a/foosrank.cpp b/foosrank.cpp index 3ad0bb1..b807084 100644 --- a/foosrank.cpp +++ b/foosrank.cpp @@ -6,24 +6,44 @@ #include // step sizes -static const double int_step_size = 50.0; -static const double pdf_step_size = 10.0; +static const double int_step_size = 75.0; +static const double pdf_step_size = 15.0; // rating constant (see below) 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 binomial, double rd_norm); +double prodai(int k, double a); +double fac(int x); -// probability of match ending 10-a when winnerR - loserR = RD +// Numerical integration using Simpson's rule +template +double simpson_integrate(const T &evaluator, double from, double to, double step) +{ + int n = int((to - from) / step + 0.5); + double h = (to - from) / n; + double sum = evaluator(from); + + for (int i = 1; i < n; i += 2) { + sum += 4.0 * evaluator(from + i * h); + } + for (int i = 2; i < n; i += 2) { + sum += 2.0 * evaluator(from + i * h); + } + sum += evaluator(to); + + return (h/3.0) * sum; +} + +// 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 +54,36 @@ 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 binomial(a+k-1, 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 binomial, 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 = binomial * pow(2.0, rd_norm * a); + double denom = 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; } // @@ -62,7 +92,7 @@ double prodai(double a) // +inf // / // | -// | ProbScore[a] (r2-r1) Gaussian[mu2, sigma2] (dr2) dr2 +// | ProbScore[a] (r1-r2) Gaussian[mu2, sigma2] (r2) dr2 // | // / // -inf @@ -75,34 +105,30 @@ 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); +class ProbScoreEvaluator { +private: + int k; + double a; + double binomial_precompute, r1, mu2, sigma2, winfac; + +public: + ProbScoreEvaluator(int k, double a, double binomial_precompute, double r1, double mu2, double sigma2, double winfac) + : k(k), a(a), binomial_precompute(binomial_precompute), r1(r1), mu2(mu2), sigma2(sigma2), winfac(winfac) {} + inline double operator() (double x) const + { + double probscore = prob_score_real(k, a, binomial_precompute, (r1 - x)*winfac); + double z = (x - mu2)/sigma2; + double gaussian = exp(-(z*z/2.0)); + return probscore * gaussian; + } +}; -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 binomial_precompute = prodai(k, a) / 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); - - for (int i = 1; i < n; i += 2) { - sum += 4.0 * evaluate_int_point(a, prodai_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 += evaluate_int_point(a, prodai_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) -{ - double probscore = prob_score_real(a, prodai_precompute, (r1 - x)*winfac); - double z = (x - mu2)/sigma2; - double gaussian = exp(-(z*z/2.0)); - return probscore * gaussian; + return simpson_integrate(ProbScoreEvaluator(k, a, binomial_precompute, r1, mu2, sigma2, winfac), 0.0, 6000.0, int_step_size); } // normalize the curve so we know that A ~= 1 @@ -347,17 +373,61 @@ 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))); + } + } + + double mu_est, sigma_est; + normalize(curve); + estimate_musigma(curve, mu_est, sigma_est); + least_squares(curve, mu_est, sigma_est, mu, sigma); +} + +// int(normpdf[mu2, sigma2](t2) * ..., t2=0..3000); +class OuterIntegralEvaluator { +private: + double theta1, mu2, sigma2, mu_t, sigma_t; + int score1, score2; + double winfac; + +public: + OuterIntegralEvaluator(double theta1, double mu2, double sigma2, double mu3, double sigma3, double mu4, double sigma4, int score1, int score2, double winfac) + : theta1(theta1), mu2(mu2), sigma2(sigma2), mu_t(mu3 + mu4), sigma_t(sqrt(sigma3*sigma3 + sigma4*sigma4)), score1(score1), score2(score2), winfac(winfac) {} + + double operator() (double theta2) const + { + double z = (theta2 - mu2) / sigma2; + double gaussian = exp(-(z*z/2.0)); + double r1 = theta1 + theta2; + return gaussian * opponent_rating_pdf(score1, score2, r1, mu_t, sigma_t, winfac); + } +}; + +void compute_new_double_rating(double mu1, double sigma1, double mu2, double sigma2, double mu3, double sigma3, double mu4, double sigma4, int score1, int score2, double &mu, double &sigma) +{ + vector > curve; + + 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 * simpson_integrate(OuterIntegralEvaluator(r1,mu2,sigma2,mu3,sigma3,mu4,sigma4,score1,score2,-0.5), 0.0, 3000.0, int_step_size))); + } + } 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 * simpson_integrate(OuterIntegralEvaluator(r1,mu2,sigma2,mu3,sigma3,mu4,sigma4,score2,score1,0.5), 0.0, 3000.0, int_step_size))); } } @@ -374,27 +444,39 @@ int main(int argc, char **argv) double mu2 = atof(argv[3]); double sigma2 = atof(argv[4]); - if (argc > 5) { + if (argc > 8) { + double mu3 = atof(argv[5]); + double sigma3 = atof(argv[6]); + double mu4 = atof(argv[7]); + double sigma4 = atof(argv[8]); + int score1 = atoi(argv[9]); + int score2 = atoi(argv[10]); + double mu, sigma; + compute_new_double_rating(mu1, sigma1, mu2, sigma2, mu3, sigma3, mu4, sigma4, score1, score2, mu, sigma); + printf("%f %f\n", mu, sigma); + } else 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, mu2-mu1), 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, mu1-mu2), newmu1-mu1, newmu2-mu2); } } }