Inspired by a discussion with Jan and Peter on what a chess generation is, I did some small statistics. I chose the following data set to decide who belongs to a generation:
I took the following years: 1951, 1953, 1956, 1959, 1962, 1965, 1968, 1971, 1975, 1977, 1981, 1984, 1987, 1990, 1993, 1995, 2002, 2005, 2007, 2012, 2013, 2014, 2016, 2018, i.e., 24 cycles.
By checking the overlap between all pairs of cycles, i.e., 276, I get the following graph. This gives me a a time constant (the time it takes to reduce the overlap from 100% to 37%, i.e., by a factor of e) of 8 years.
Another question you might ask is, how many years must pass before all players have been gone? That gives me about 14-34 years, with the mean at 23 years.
Finally, one can do some cluster analysis between these candidates tournaments. This would give a meaningful estimate of how many eras there have been.
I can define the distance matrix as 1-overlap and get the following tree: https://imgur.com/aSQ8iWZ (sorry about the format. the years are readable, the rest not.)
Depending on where we draw the line, we get either:
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