#include <algorithm>
// 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;
double binomial_precompute = prodai(k, a) / fac(k-1);
winfac /= rating_constant;
- return simpson_integrate(ProbScoreEvaluator(k, a, binomial_precompute, r1, mu2, sigma2, winfac), 0.0, 3000.0, int_step_size);
+ 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
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<pair<double, double> > 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)));
+ }
+ }
+
+ double mu_est, sigma_est;
+ normalize(curve);
+ estimate_musigma(curve, mu_est, sigma_est);
+ least_squares(curve, mu_est, sigma_est, mu, sigma);
+}
+
int main(int argc, char **argv)
{
double mu1 = atof(argv[1]);
double mu2 = atof(argv[3]);
double sigma2 = atof(argv[4]);
- if (argc > 6) {
+ 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;