# Ingale's Recursive Power Rankings

My ranking system is an iterative method that uses the results of games in any league to rank teams based on on-the-field performance. The system uses three pieces of data about each contest to compute this:
• The two participating teams
• The location
• The winner
This system was created with a few design constraints in mind. Specifically:
• The score is ignored. There is too much variability in scores to draw too many conclusions from the final score of a contest. Specifically, teams don't play to win by a certain amount but to just win. If a football team is beating its opponent late in the game and has the ball, the winning team is primarily interested in running out the clock rather than trying to score again.

• Teams aren't punished for beating weak teams. The big boys like their cupcakes. Many rankings systems are built such that a powerhouse beating a very week team sees their rating drop. While I chide the powerhouse for their choice of schedule, that doesn't mean that they are a worse team for it. In my ranking system, a team is never punished for beating a cupcake. The positive effect might be negligible (or even zero), but it won't drop. Likewise, teams aren't punished for losing to powerhouses. The fact that you lost to a powerhouse proves very little, so the effect is small.

My rankings systems is a recursive method. Teams are initially rated based on their winning percentage, and a general homefield advangate coefficient is calculated based on the percentage of games won by the home team. The algorithm iteratively updates each team's rating and the homefield coefficient as it factors the strengths of each team's opponents. As the process repeats, the team ratings and homefiel coefficient settle to their final numbers. Ties are treated as half-wins and half-losses for both participating teams. The homefield coefficient shown for each season reflects the strength of homefield advantage for that season and is to be used by multiplying by the home team's rating for that game. For instance if a team rated 0.640 is hosting a team rated 0.800 and the homefield advantage coefficient for that season is 1.250, the teams are basically equal, as 0.640*1.250 = 0.800.

I've computed rankings for each NCAA football season going back to 1869 and each NFL season going back to 1940.

As a sidenote (and before I get berated), the best way to crown a champion is on the field, and I do not dispute that in any way. In fact, one should be wary of anyone that claims anything different. At the same time, NCAA football currently has roughly 125 teams that each play only 12 games, so it must always rely on off-the-field analysis to crown its national champion. The place where these rankings excel is that they don't know the difference between an Alabama jersey and a Boise State jersey -- just who they beat.

## NCAA football

 1869 1870 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011  (as of 10/25/2011)

## National Football League

 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011  (as of 10/25/2011)

## National Hockey League

 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2009 2010

## Credits

I did *NOT* compile the game data myself and I want to give credit where credit is due.