% This program runs a simulation to determine each team's probability of making the
% playoffs, or of winning the Super Bowl. The program reads an ASCII file, here named 
% gameprobsfile.txt. If seedweighttype=1, the program estimates each team's probability
% of making the playoffs. If seedweighttype=2, the program estimates the teams' probabilities
% of winning the SB, using the default formulation. If seedweighttype=3, the user overrides some
% or all of the default probabilities by creating an appropriate input file weightoverrides.txt.

% Index of teams:

%   1 Buf       5 Balt      9 Hou      13 Den
%   2 Mia       6 Cin      10 Ind      14 KC
%   3 NE        7 Cle      11 Jax      15 Oak
%   4 Jets      8 Pitt     12 TN       16 SD

%  17 Dal      21 Chi      25 Atl      29 Ari
%  18 NYG      22 Det      26 Car      30 StL
%  19 Phil     23 GB       27 NO       31 SF
%  20 Wash     24 MN       28 TB       32 Sea

% Copyright 2006 by William S. Krasker

numtrials=1000;        % number of trials of simulation.

% seedweighttype=1 to compute probability of making the playoffs.
% seedweighttype=2 to compute probability of winning SB using default probabilities.
% seedweighttype=3 to compute probability of winning SB using overrides to default probabilities.
seedweighttype=2;

load gameprobs.txt -ascii

seedweights=ones(6,2);    % weights equal 1 to estimate prob of making playoffs.
if seedweighttype > 1
   p=0.6;                 % default prob that home team wins.
   Pmatrix=p*ones(32,32);
   Qmatrix=0.5*ones(32,32);
   if seedweighttype==3    % use overrides to default probabilities.
      load weightoverrides.txt -ascii      % read array containing overrides to defaults.
      for i=1:size(weightoverrides,1)
         Pmatrix(weightoverrides(i,1),weightoverrides(i,2))=weightoverrides(i,3);
         Pmatrix(weightoverrides(i,2),weightoverrides(i,1))=1-weightoverrides(i,4);
         Qmatrix(weightoverrides(i,1),weightoverrides(i,2))=weightoverrides(i,5);
         Qmatrix(weightoverrides(i,2),weightoverrides(i,1))=1-weightoverrides(i,5);
      end
   end
end

rand('state',0);
probofplayoffs=zeros(32,1);

for trial=1:numtrials

   a=gameprobs;

   u=rand(256,1);
   for j=1:256
      if gameprobs(j,3)==-1       % tie game.
         a(j,3)=-1;
      else
         if u(j) <= gameprobs(j,3)
            a(j,3)=1;
         else
            a(j,3)=0;
         end
      end
   end

   setup
   standings
   seeddivwinners
   getwcteams
   
   if seedweighttype > 1
      seedweights=getsbwinprobs(seeds,Pmatrix,Qmatrix);
   end

   for i=1:6
      probofplayoffs(seeds(i,1))=probofplayoffs(seeds(i,1))+seedweights(i,1);
      probofplayoffs(seeds(i,2))=probofplayoffs(seeds(i,2))+seedweights(i,2);
   end

end

probofplayoffs=probofplayoffs/numtrials;
format long
[(1:32)' probofplayoffs]
format short