WBF VP scale changes

[gnasher]

Then at which point do you establish an average?

Their final score for the bye is calculated at the end of the event. For assignment purposes and to show their running score, you recalculate it after each round, based on all their results to date.

[Gerben42]

So when do we switch to IMPs being scored in .01 steps? :) I mean it's unfair that a 20-point and 40-point swing are equal!

[kibitzert]

Are the scales in the USBF COC accurate?

Comparing my results to the scales in there gives me some off-by-1 errors.

 

I don't have the USBF COC scales. Are they different from what the WBF published?

 

I had some trouble understanding the way the WBF Scoring Panel dealt with the Concavity Rule (see the January 2013 report), but I think I get it now. I didn't follow their idea of using a vector of boolean and handled the problem by defining different array sizes for the scores array, the differences array and the second differences array.

I'm not much of a programmer (not even "Intermediate", I think), and I didn't bother with classes or even functions. The total code is way smaller than a hundred lines. I would politely ask to concentrate on correctness (does the code produce correct results?) rather than my odd programming style. :-)

The C++ code will compile with recent versions of g++, and probably with most C++ compilers. I checked the output against the 10, 14, 16, 20 and 32 tables on the WBF Continuous VP Scale that can be found on the Web (and which doesn't contain tables for 24, 28, 40, 48, 60, 64 boards).

 

/*
Reference: The New WBF IMP to VP Scales
Technical Report of WBF Scoring Panel (January 2013)
*/
#include <iostream>
#include <cmath>
using namespace std;

int main()
{
   const double R = 0.2360679775; /* == Tau^3 == sqrt(5) - 2 */
   const double V0 = 10.0; /* VP score in drawn match */
   double N, /* number of boards played */
          X, /* maximum win IMP margin, 15*sqrt(N) */
          VP,
          VPraw;

   cout << "number of boards played: ";
   cin >> N;

   // CALCULATION OF RAW VP SCORES
   X = 15 * sqrt(N);
   int blitz = ceil(X); // IMP margin for 20-0 score
   double * scores; // array of VP scores
   scores = new double[blitz+1]; // including zero margin
   for (int i=0; i!=blitz+1; ++i) // i is the IMP margin
   {
       // calculate VP scores
       VPraw = V0 + V0 * ((1 - pow(R, i/X)) / (1 - R));
       VP = min((round(100 * VPraw) /100), 2*V0); // rounding
       // add score to array
       scores[i] = VP;
   }

   // CORRECTION OF CONCAVITY RULE VIOLATIONS
   int * diff; // array of differences
   diff = new int[blitz];
   for (int i=0; i!=blitz; ++i)
       diff[i] = round(100*(scores[i+1] - scores[i]));

   int * diff2; // array of second differences
   diff2 = new int[blitz-1];
   for (int i=0; i!=blitz-1; ++i)
       diff2[i] = diff[i+1] - diff[i];

   bool violation = true;
   while (violation)
   {
       violation = false;
       for (int i=0; i!=blitz-1; ++i)
       {
           if (diff2[i] > 0)
           {
               scores[i+1] += 0.01;
               --diff2[i];
               violation = true;
           }
       }
       if (violation)
       { /* recalculate arrays diff and diff2 */
           for (int i=0; i!=blitz; ++i)
               diff[i] = round(100*(scores[i+1] - scores[i]));
           for (int i=0; i!=blitz-1; ++i)
               diff2[i] = diff[i+1] - diff[i];
       }
   }

   // SEND SCALE TO SCREEN
   cout << endl << endl;
   cout << "WBF CONTINUOUS VP SCALE for " << N << " boards" << endl
        << "(trailing zeros not shown)"
        << endl << endl << endl << "IMP margin and score" << endl;
   for (int i=0; i!=blitz+1; ++i)
       cout << i << "  " << scores[i] << " - " << 20 - scores[i] << endl;
   cout << endl << endl;

   delete [] scores; delete [] diff; delete [] diff2;
   char ch; cin >> ch;

   return 0;
}