Make a constant out of 455.

[foosball] / foorank.cpp

diff --git a/foorank.cpp b/foorank.cpp
index 659c6112877b439cadf3409afcf487db86691a69..096c185f3db0ad1ed8159e6f8ac70c3145c0c615 100644 (file)
--- a/foorank.cpp
+++ b/foorank.cpp
@@ -8,6 +8,9 @@
 // integration step size
 static const double step_size = 10.0;
 
+// rating constant (see below)
+static const double rating_constant = 455.0;
+
 using namespace std;
 
 double prob_score(double a, double rd);
@@ -32,7 +35,7 @@ double prodai(double a);
 //
 double prob_score(double a, double rd)
 {
-       return prob_score_real(a, prodai(a), rd/455.0);
+       return prob_score_real(a, prodai(a), rd/rating_constant);
 }
 
 // Same, but takes in Product(a+i, i=1..9) as an argument in addition to a. Faster
@@ -75,7 +78,7 @@ double opponent_rating_pdf(double a, double r1, double mu2, double sigma2, doubl
 {
        double sum = 0.0;
        double prodai_precompute = prodai(a);
-       winfac /= 455.0;
+       winfac /= rating_constant;
        for (double r2 = 0.0; r2 < 3000.0; r2 += step_size) {
                double x = r2 + step_size*0.5;
                double probscore = prob_score_real(a, prodai_precompute, (r1 - x)*winfac);
@@ -215,12 +218,12 @@ void solve3x3(double *A, double *x, double *B)
 }
 
 // Give an OK starting estimate for the least squares, by numerical integration
-// of x*f(x) and x^2 * f(x). Somehow seems to underestimate sigma, though.
+// of statistical moments.
 void estimate_musigma(vector<pair<double, double> > &curve, double &mu_result, double &sigma_result)
 {
-       double mu = 0.0;
-       double sigma = 0.0;
        double sum_area = 0.0;
+       double ex = 0.0;
+       double ex2 = 0.0;
 
        for (unsigned i = 1; i < curve.size(); ++i) {
                double x1 = curve[i].first;
@@ -230,17 +233,24 @@ void estimate_musigma(vector<pair<double, double> > &curve, double &mu_result, d
                double xm = 0.5 * (x0 + x1);
                double ym = 0.5 * (y0 + y1);
                sum_area += (x1-x0) * ym;
-               mu += (x1-x0) * xm * ym;
-               sigma += (x1-x0) * xm * xm * ym;
+               ex += (x1-x0) * xm * ym;
+               ex2 += (x1-x0) * xm * xm * ym;
        }
 
-       mu_result = mu / sum_area;
-       sigma_result = sqrt(sigma) / sum_area;
+       ex /= sum_area;
+       ex2 /= sum_area;
+
+       mu_result = ex;
+       sigma_result = sqrt(ex2 - ex * ex);
 }
        
 // Find best fit of the data in curves to a Gaussian pdf, based on the
 // given initial estimates. Works by nonlinear least squares, iterating
 // until we're below a certain threshold.
+//
+// Note that the algorithm blows up quite hard if the initial estimate is
+// not good enough. Use estimate_musigma to get a reasonable starting
+// estimate.
 void least_squares(vector<pair<double, double> > &curve, double mu1, double sigma1, double &mu_result, double &sigma_result)
 {
        double A = 1.0;