Chessmetrics

I found a fascinating website (http://www.chessmetrics.com/) that has developed a modified Elo rating system to rate historical players before the advent of the current FIDE rating system. These historical ratings, despite their obvious shortcomings, nevertheless provide a great deal of insight into the playing strength of the contenders in this historic match. One of the calculations ChessMetrics performs is the determination of all-time rating leaders across their peak 1, 3, 5, 9 and 15-year periods. Some of their results are reproduced below.

If you click on the names or dates in the following tables, you will link to the ChessMetrics website where more details are available.

One-year period
1 - Capablanca, José R - 2921 - 1921
2 - Fischer, Robert J - 2914 - 1971
3 - Kasparov, Garry K - 2895 - 1999
4 - Lasker, Emanuel - 2886 - 1919
5 - Morphy, Paul C - 2840 - 1864
6 - Anand, Viswanathan - 2836 - 1997
7 - Steinitz, Wilhelm - 2834 - 1877
8 - Kramnik, Vladimir - 2831 - 2000
9 - Botvinnik, Mikhail M - 2828 - 1949
10 - Alekhine, Alexander A - 2827 - 1930

Fifteen-year period
1 - Kasparov, Garry K - 2853 - 1986 to 2000
2 - Capablanca, José R - 2841 - 1914 to 1928
3 - Fischer, Robert J - 2794 - 1960 to 1974 (*)
4 - Karpov, Anatoly E - 2788 - 1976 to 1990
5 - Botvinnik, Mikhail M - 2770 - 1943 to 1957
6 - Alekhine, Alexander A - 2762 - 1921 to 1935
(*) Although Fischer was world champion in 1973 and 1974, he played no games in those years.