Chess generations - how long?

Chess generations - how long?

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:

  1. World champions + the candidates
  2. The World Championships in 2005+2007 as well as Kramnik who refused to play.
  3. If the candidates were KO, I just took the quarter finals. If the candidates were a big round robin, I took the top 8.
  4. If there was no obvious candidates tournament I discarded that sample.
  5. Rematches obviously didn't count.

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. 

  1. The largest difference between two tournaments that still shared at least a player is 33 years: 1951-1984 (due to Smyslov).
  2. The smallest difference between two tournaments that shared no player is ‌14 years: 1981-1995.

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: (sorry about the format. the years are readable, the rest not.)

Depending on where we draw the line, we get either:

  1. Two eras: 1951-1990 and 1995-2018
  2. Five eras: 1951-1962, 1965-1981, 1984-1993, 1995-2005, and 2007-2018. Interestingly, all of these except 1965-1981 are roughly one decade.

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