For the whole period, it is .663. There were 16 observations for 1901-02, 16 for 1902-3, and so on. A total of 944 observations.
I also broke it down by decades
1901-10) .668
1911-20) .521
1921-30) .725
1931-40) .711
1941-50) .642
1951-60) .727
Not sure what happened in the teens. One year Connie Mack sold his best players after losing the World Series (1914). So they did very poorly in 1915. It does not seem likely that one team in one year would make that much difference. The 1940s might be a bit low due to the war. With players coming and going, teams could be much different in consecutive years.
Here are the five highest years
1936-1937) 0.877
1922-1923) 0.879
1930-1931) 0.885
1910-1911) 0.890
1941-1942) 0.896
Here are the five lowest years
1914-1915) 0.127
1917-1918) 0.221
1913-1914) 0.224
1901-1902) 0.298
1944-1945) 0.370
This graph shows the yearly correlations.
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