This is not what you are asking for but I thought I'd update this post from a couple of years back:
In 2010 was talking to a Stanford grad and he told me how proud he was of their school and their 8-1 record so far that year. As an SU fan I told him how impressed I was since both schools are private schools and state schools seems to have such an advantage in this sport. They tend to have huge enrollments and fan bases, lower tuition and, in many cases, lower academic standards. They also have the state legislature behind them to build large facilities. The advantages became greater when the two-platoon era came in in the mid-60’s, which required many more players and much more depth.
It gave me the idea of seeing which private school had the highest ranking at the end of each season. I looked at the NCAA Record Book, which lists the national champions from all the various selectors, (34 of them), since 1869. I also looked at the Associated Press, (writer’s) Poll since 1936, the United Press International and USA Today, (coach’s) Poll since 1950 and the BCS championship games since 1998 to see what the highest ranked private school major college football team was. I checked the school’s status using Wikipedia. Some schools, like Rutgers, Purdue, Clemson, Auburn and Marshall, have names that sound like private schools but they are state schools. Some like the University of Pennsylvania, sound like state schools but aren’t. Some schools, like Pittsburgh, were once private schools became state schools later. (Pitt is considered a “state-related” school, which remains independent in administration but gets state funding. This dates from 1966 so they are counted as a private school before that and a state school since). I looked at the list of national champions from the various sources and picked the private school recognized by the most sources. For years where there were no private schools listed or where it was a tie in the number of selections, I looked at the writer’s and coach’s polls to see who was highest ranked. For the years before 1936, I checked the rankings from this list:
http://www.nutshellsports.com/wilson/
…for the year in questions and picked the private school with the highest ranking in any of them. I decided to exclude schools that were on probation, even though I’m not a fan of probation as a disciplinary tool.
1869 Princeton
1870 Princeton
1871 nobody (there were no college football games played that year)
1872 Princeton
1873 Princeton
1874 Yale
1875 Harvard
1876 Yale
1877 Princeton
1878 Princeton
1879 Princeton
1880 Yale
1881 Yale
1882 Yale
1883 Yale
1884 Yale
1885 Princeton
1886 Yale
1887 Yale
1888 Yale
1889 Princeton
1890 Harvard
1891 Yale
1892 Yale
1893 Princeton
1894 Yale
1895 Pennsylvania
1896 Princeton
1897 Pennsylvania
1898 Harvard
1899 Harvard
1900 Yale
1901 Harvard
1902 Yale
1903 Princeton
1904 Pennsylvania
1905 Chicago
1906 Yale
1907 Yale
1908 Pennsylvania
1909 Yale
1910 Harvard
1911 Princeton
1912 Harvard
1913 Harvard
1914 Harvard
1915 Cornell
1916 Pittsburgh
1917 Pittsburgh
1918 Pittsburgh
1919 Harvard
1920 Princeton
1921 Cornell
1922 Princeton
1923 Cornell
1924 Notre Dame
1925 Dartmouth
1926 Stanford
1927 Notre Dame
1928 Southern California
1929 Notre Dame
1930 Notre Dame
1931 Southern California
1932 Southern California
1933 Southern California
1934 Pittsburgh
1935 Southern Methodist
1936 Pittsburgh
1937 Pittsburgh
1938 Texas Christian
1939 Cornell
1940 Stanford
1941 Duke
1942 Tulsa
1943 Notre Dame
1944 Southern California
1945 St. Mary’s (Cal.)
1946 Notre Dame
1947 Notre Dame
1948 Notre Dame
1949 Notre Dame
1950 Princeton
1951 Princeton
1952 Notre Dame
1953 Notre Dame
1954 Notre Dame
1955 Texas Christian
1956 Miami (Fla.)
1957 Rice
1958 Texas Christian
1959 Syracuse
1960 Duke
1961 Syracuse
1962 Southern California
1963 Pittsburgh
1964 Notre Dame
1965 Notre Dame
1966 Notre Dame
1967 Southern California
1968 Southern California
1969 Southern California
1970 Notre Dame
1971 Stanford
1972 Southern California
1973 Notre Dame
1974 Southern California
1975 Southern California
1976 Southern California
1977 Notre Dame
1978 Southern California
1979 Southern California
1980 Notre Dame
1981 Southern Methodist
1982 Southern Methodist
1983 Miami (Fla.)
1984 Brigham Young
1985 Miami (Fla.)
1986 Miami (Fla.)
1987 Miami (Fla.)
1988 Notre Dame
1989 Miami (Fla.)
1990 Miami (Fla.)
1991 Miami (Fla.)
1992 Miami (Fla.)
1993 Notre Dame
1994 Miami (Fla.)
1995 Northwestern
1996 Brigham Young
1997 Syracuse
1998 Tulane
1999 Miami (Fla.)
2000 Miami (Fla.)
2001 Miami (Fla.)
2002 Southern California (Miami was ahead in both polls but received no national championship recognition: Southern California was chosen by Dunkel, Matthews and Sagarin)
2003 Southern California
2004 Southern California
2005 Southern California
2006 Southern California
2007 Southern California
2008 Southern California
2009 Texas Christian
2010 Texas Christian
2011 Stanford
2012 Notre Dame
2013 will be either Baylor or Stanford, depending on today’s results. Most rankigns have Stanford ahead right now.
Cumulative titles, (not yet counting 2013 as the season isn’t over)
Brigham, Young 1984, 1996
Chicago 1905
Cornell 1915, 1921, 1923, 1939
Dartmouth 1925
Duke 1941, 1960
Harvard 1875, 1890, 1898, 1899, 1900, 1911, 1912, 1913, 1914, 1919
Miami (Fla.) 1956, 1983, 1985, 1986, 1987, 1989, 1990, 1991, 1992, 1994, 1999, 2000, 2001
Northwestern 1995
Notre Dame 1924, 1927, 1929, 1930, 1943, 1946, 1947, 1948, 1949, 1952, 1953, 1954, 1964, 1965, 1966, 1970, 1973, 1977, 1980, 1988, 1993, 2012
Pennsylvania 1895, 1897, 1904, 1908
Pittsburgh 1916, 1917, 1918, 1934, 1936, 1937, 1963
Princeton 1869, 1870, 1872, 1873, 1877, 1878, 1879, 1885, 1889, 1893, 1896, 1903, 1911, 1920, 1922, 1950, 1951
Southern California 1928, 1931, 1932, 1933, 1944, 1962, 1967, 1968, 1969, 1972, 1974, 1975, 1976, 1978, 1979, 2002, 2003, 2004, 2005, 2006, 2007, 2008
Southern Methodist 1935, 1981, 1982
St. Mary’s (Cal.) 1945
Stanford 1926, 1940, 1971, 2011
Syracuse 1959, 1961, 1997
Texas Christian 1938, 1955, 1958, 2009, 2010
Tulane 1998
Tulsa 1942
Yale 1874, 1876, 1880, 1881, 1882, 1883, 1884, 1886, 1887, 1888, 1891, 1892, 1894, 1900, 1902, 1906, 1907, 1909
Who’s won the most?
Notre Dame and Southern California 22
Yale 18
Princeton 17
Miami (Fla.) 13
Harvard 10
Pittsburgh 7
Texas Christian 5
Cornell and Pennsylvania and Stanford 4
Southern Methodist and Syracuse 3
Brigham Young and Duke 2
Chicago, Dartmouth, Northwestern, St. Mary’s, Tulane and Tulsa 1