% PAC 12 Stochastic Matrix before past weekend
%    AZ  AZS CAL CU  OR  OSU STA UCLA USC UT WA  WAS
SMa=[ 0,  0, 1/3.,0, 1/3,.25, 0,   0,  0,  0, 0,  0;    %AZ
      0,  0,  0,  0,  0, .25, 0,   0  1/3, 0, 0,  0;    %AZS
      0,  0,  0,  0,  0, .25, 0,   0,  0,  0,.5,  0;    %CAL
      0, 1/3 ,0,  0,  0,  0,  0,  1/3, 0,  0, 0,  0;    %CU
      0,  0, 1/3  0,  0,  0,  0,   0,  0,  0,.5,  0;    %OR
      0,  0,  0, 1/3, 0,  0,  0,   0,  0,  0, 0,  0;    %OSU
      0, 1/3, 0,  0, 1/3, 0,  0,   0, 1/3, 0, 0,  0;    %STA
     1/3, 0, 1/3, 0,  0,  0,  0,   0,  0,  0, 0,  0;    %UCLA
     1/3, 0,  0, 1/3, 0,  0,  0,   0,  0,  0, 0,  1;    %USC
     1/3, 0,  0,  0,  0,  0, .5,  1/3,1/3, 0, 0,  0;    %UT
     0,  1/3, 0, 1/3, 0,  0,  0,  1/3, 0, .5, 0,  0;    %WA
     0,   0,  0,  0, 1/3,.25,.5,   0,  0, .5, 0,  0;]   %WAS
 
 %create a regular stochastic matrix with google fudge factor:
SMb=.15/12*ones(12,12)+.85*SMa
 % the columns of a large power of SMb should be essentially identical,
 % and are the equilibrium solution.  The entries can be used to rank
 % the Pac 12 teams, based on current records.
SMb^20




