Switch to more accurate double score calculation.

[foosball] / foosrank.cpp

diff --git a/foosrank.cpp b/foosrank.cpp
index ba24d0254e69fc32a58f7deca9c08856dc5d6b39..6991061fae2973d063d9d879aef7abe70dcf3133 100644 (file)
--- a/foosrank.cpp
+++ b/foosrank.cpp
@@ -6,8 +6,8 @@
 #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;
@@ -15,7 +15,7 @@ static const double rating_constant = 455.0;
 using namespace std;
 
 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 prob_score_real(int k, double a, double binomial, double rd_norm);
 double prodai(int k, double a);
 double fac(int x);
 
@@ -56,16 +56,16 @@ double simpson_integrate(const T &evaluator, double from, double to, double step
 //
 double prob_score(int k, double a, double rd)
 {
-       return prob_score_real(k, a, prodai(k, a), fac(k-1), 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..k-1) and (k-1)! as an argument in
+// 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 prodai, double kfac, double rd_norm)
+double prob_score_real(int k, double a, double binomial, double rd_norm)
 {
-       double nom = prodai * pow(2.0, rd_norm * a); 
-       double denom = kfac * pow(1.0 + pow(2.0, rd_norm), k+a);
+       double nom = binomial * pow(2.0, rd_norm * a); 
+       double denom = pow(1.0 + pow(2.0, rd_norm), k+a);
        return nom/denom;
 }
 
@@ -109,14 +109,14 @@ class ProbScoreEvaluator {
 private:
        int k;
        double a;
-       double prodai_precompute, kfac_precompute, r1, mu2, sigma2, winfac;
+       double binomial_precompute, r1, mu2, sigma2, winfac;
 
 public:
-       ProbScoreEvaluator(int k, double a, double prodai_precompute, double kfac_precompute, double r1, double mu2, double sigma2, double winfac)
-               : k(k), a(a), prodai_precompute(prodai_precompute), kfac_precompute(kfac_precompute), r1(r1), mu2(mu2), sigma2(sigma2), winfac(winfac) {}
+       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, prodai_precompute, kfac_precompute, (x - r1)*winfac);
+               double probscore = prob_score_real(k, a, binomial_precompute, (x - r1)*winfac);
                double z = (x - mu2)/sigma2;
                double gaussian = exp(-(z*z/2.0));
                return probscore * gaussian;
@@ -125,11 +125,10 @@ public:
 
 double opponent_rating_pdf(int k, double a, double r1, double mu2, double sigma2, double winfac)
 {
-       double prodai_precompute = prodai(k, a);
-       double kfac_precompute = fac(k-1);
+       double binomial_precompute = prodai(k, a) / fac(k-1);
        winfac /= rating_constant;
 
-       return simpson_integrate(ProbScoreEvaluator(k, a, prodai_precompute, kfac_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
@@ -394,6 +393,50 @@ void compute_new_rating(double mu1, double sigma1, double mu2, double sigma2, in
        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]);
@@ -401,7 +444,17 @@ int main(int argc, char **argv)
        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;