@JEinOKC

http://jameseng.land

• Ratings based on "Linear Regression"
• Turns results of games into matrices & solve using math

• b = resulting ranking score
• X = n x n matrix of teams
• y = n x 1 matrix of results

• created a LAMP web interface to display results *
• generated ratings locally
• FTP'd json files to web server

* Did at least get my feet wet with AngularJS

• Original Project - http://sylvester.jcoglan.com/
• Node.js Implementation - https://github.com/NaturalNode/node-sylvester

Remember:

          var matrix_X = myMatrices.gameMatrix;//an nxn matrix of games played
          var matrix_Y = myMatrices.diffMatrix;//an nx1 matrix of game results
          var matrix_xTrans = matrix_X.transpose();
          var xTx = matrix_xTrans.x(matrix_X);
          var xTy = matrix_xTrans.x(matrix_Y);


          var xTx_array = xTx.elements;
          var xTy_array = xTy.elements;

          /*
            Defining Full Rank:
            
            A matrix is said to have full rank if its rank equals the largest possible for a matrix of the same dimensions, which is the lesser of the number of rows and columns

            To Obtain 'full rank': 
            nth row of xTx is all 1s
            nth row of xTy are all 0s

            By setting row of xTy to 0, that means that 0 will be average. As values increase, ranking is improved
          */

          for(var i=0;i<xTx_array[xTx_array.length-1].length;i++){
            xTx_array[xTx_array.length-1][i] = 1;
          }
            

          xTx = Matrix.create(xTx_array);

          for(i=0;i<xTy_array[xTy_array.length-1].length;i++){
            xTy_array[xTy_array.length-1][i] = 0;
          }
            

          xTy = Matrix.create(xTy_array);
          
          var xTx_Inverse = xTx.inv();
          if(xTx_Inverse !== null){
            console.log('inverse was created. Things going well..');
            return xTx_Inverse.x(xTy);  //BOOM!!
          }
          

          console.log("matrix is singular. Cannot create a ranking");

          throw "matrix is singular. Cannot create a ranking";




















        

• complex situations where results aren't necessary transitive
• 'Best of' lists where popularity saturates actual value - like The Academy Awards, Favorite TV Shows, Greatest Song Ever

https://en.wikipedia.org/wiki/List_of_songs_considered_the_best

Toxic?

• England Ratings - http://jameseng.land/Rank
• Oscar Matchups - http://jameseng.land/Oscars
• GitHub Project - https://github.com/JEinOKC/generic-ranking-methods
• npm install generic-ranking-methods
• Massey College Football Ranking Composite - http://www.masseyratings.com/cf/compare.htm

@JEinOKC

http://jameseng.land