Williamson System
The Williamson System was a mathematical system used to rank college football teams. The system was created by Paul B. Williamson, a geologist and member of the Sugar Bowl committee.
The NCAA college football records book includes the Williamson System as a "major selector" of national championships for the years 1932-1963.
Paul Williamson died in 1955. His son Mitch Williamson subsequently took up his father's syndicated column for the 1955–1963 seasons.
National champions
The following teams were ranked No. 1 by the Williamson System for the 1932–1963 college football seasons.The NCAA Football Bowl Subdivision Records book contains five apparent errors in its listing of Williamson System champions. The following table contains the contemporary champions syndicated by Paul Williamson. The NCAA record book's errors are documented in the Notes column.
| Season | Champion | Record | Coach | Notes |
| 1932 | USC | 10–0 | Howard Jones | |
| 1933 | USC | 10–1–1 | Howard Jones | |
| 1934 | Alabama | 10–0 | Frank Thomas | |
| 1935 | TCU | 12–1 | Dutch Meyer | |
| 1936 | Minnesota | 7–1 | Bernie Bierman | |
| 1937 | California | 10–0–1 | Stub Allison | |
| 1938 | TCU | 11–0 | Dutch Meyer | |
| 1938 | Tennessee | 11–0 | Robert Neyland | |
| 1939 | Texas A&M | 11–0 | Homer Norton | |
| 1940 | Stanford | 10–0 | Clark Shaughnessy | |
| 1941 | Texas | 8–1–1 | Dana X. Bible | |
| 1942 | Georgia | 10–1 | Wally Butts | |
| 1943 | Notre Dame | 9–1 | Frank Leahy | |
| 1944 | Army | 9–0 | Earl Blaik | |
| 1945 | Army | 9–0 | Earl Blaik | |
| 1946 | Georgia | 11–0 | Wally Butts | |
| 1947 | Notre Dame | 9–0 | Frank Leahy | |
| 1948 | Michigan | 9–0 | Bennie Oosterbaan | |
| 1949 | Notre Dame | 10–0 | Frank Leahy | |
| 1950 | Oklahoma | 10–1 | Bud Wilkinson | |
| 1951 | Tennessee | 10–1 | Robert Neyland | |
| 1952 | Michigan State | 9–0 | Biggie Munn | |
| 1953 | Notre Dame | 9–0–1 | Frank Leahy | |
| 1954 | Ohio State | 10–0 | Woody Hayes | |
| 1955 | Oklahoma | 11–0 | Bud Wilkinson | |
| 1956 | Oklahoma | 10–0 | Bud Wilkinson | |
| 1957 | Auburn | 10–0 | Ralph Jordan | |
| 1958 | LSU | 11–0 | Paul Dietzel | |
| 1959 | Syracuse | 11–0 | Ben Schwartzwalder | |
| 1960 | Ole Miss | 10–0–1 | Johnny Vaught | |
| 1961 | Alabama | 11–0 | Bear Bryant | |
| 1962 | USC | 11–0 | John McKay | |
| 1963 | Texas | 11–0 | Darrell Royal |