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Is that there are underlying geological & meteorological phenomena that cycle over very long periods of time.
Your analogy is equivalent to a situation in which James had measured the period 1904-1909 and then applied that to today.
In order for the meteorological historico-predictive models to be analogous to James', they'd have had to have gone back not 100-200, but a minimum of 25,000 years.
But then, you knew that.
.............
James' system obviously captures the "world" going back to the cooling of the oceans.  What is going to fundamentally change in baseball players' performance fluctuations, that is analogous to the cycling of ice ages and warming periods?!
Baseball isn't about to be hit by a comet, in the way that human beings have UP and DWN seasons.  You know that.