5. On ratings:
Elo ratings reflect relative and not absolute chess strength.
Chess players are naturally arranged in populations partitioned by geopolitical regions and time periods that have infrequent contacts with one another. Within such a population, players get to play each other more frequently, thus forming a quasi-equilibrium group wherein individual ratings would tend to equilibrate quickly; but not with outside groups.
With caveats and in the proper context, FIDE/Elo ratings are simply fallible descriptors and predictors of an active player’s near-past and near-future performances against other rated players, and only within the same quasi-equilibrium group.
As corollaries: the best way to evaluate a player’s strength is to analyze his games and not his ratings; one cannot use ratings to accurately compare the quality of play of players from the past and present, or even the same player a decade ago and today; and care should be taken in the use of ratings as a criterion in choosing which players to seed into the upper levels of the World Championship cycle.
All the above often entail comparisons between players from different quasi-equilibrium groups separated by space and/or time.
Regarding inflation deniers, they imply that Elo ratings reflect absolute and not relative chess strength. Professor Elo himself would condemn their view. If the top 20 players were to suffer a serious brain injury and begin playing like patzers, but play no one else for the next decade, they would more or less retain their 2700s ratings, although they would be playing terrible patzerish chess.
6. The Romance of the Chess World Championship Match and the World Champions that won them:
There can only be two.
The Champion to hold the title he beat all the masters for.
The Challenger on quest for same title of yore.
Chess is uniquely distinguished by an unbroken line of successive world champions since the 1800s. Challengers have to beat the Titleholder in a match to seize the World Championship Title. I do not recognize so-called solely FIDE world champions.
* Wilhelm Steinitz, 1886 to 1894
* Emanuel Lasker, 1894 to 1921 (beat Steinitz in a match in 1894)
* Jose Raul Capablanca, 1921 to 1927 (beat Lasker in a match in 1921)
* Alexander Alexandrovich Alekhine, 1927 to 1935 and 1937 to 1946 (beat Capablanca in a match in 1927 and beat Euwe in a return match in 1937)
* Max Euwe, 1935 to 1937 (beat Alekhine in a match in 1935, but lost to Alekhine in 1937 in a return match)
* Mikhail Moiseevich Botvinnik, 1948 to 1957, 1958 to 1960, and 1961 to 1963 (Alekhine died as Word Champion in 1946. Botvinnik won the World Championship Tournament of 1948)
* Vasily Vasiliyevich Smyslov, 1957 to 1958. (beat Botvinnik in 1957 in a match, but lost to Botvinnik in 1958 in a return match)
* Mikhail Nekhemievich Tal, 1960 to 1961 (beat Botvinnik in 1960 in a match, but lost to Botvinnik in 1961 in a return match)
* Tigran Vartanovich Petrosian, 1963 to 1969 (beat Botvinnik in 1963 in a match)
* Boris Vasilievich Spassky, 1969 to 1972 (beat Petrosian in 1969 in a match)
* Robert James Fischer, 1972 to 1975 (beat Spassky in 1972 in a match, but abdicated in 1975)
* Anatoly Yevgenyevich Karpov, 1975 to 1985 (won the Candidates Matches in 1974 and declared World Champion in 1975 by FIDE as Fischer had abdicated.)
* Garry Kimovich Kasparov, 1985 to 2000 (beat Karpov in 1985 in a match)
* Vladimir Borisovich Kramnik, 2000 to 2007 (beat Kasparov in 2000 in a match)
* Viswanathan Anand, 2007 to 2013 (beat Kramnik in 2007 in a match)
* Magnus Carlsen, 2013 to 2022 (beat Anand in 2013 in a match, but abdicated in 2022)
* Ding Liren, 2023 to 2024 (Ding finished second to Ian Nepomniachtchi in the World Championship Candidates of 2022. Later in 2023 he beat Nepomniachtchi in a World Championship match.)
* Dommaraju Gukesh, 2024 to present (beat Ding Liren 2024 in a match)/PN
