Tuesday, July 12, 2005
Another Question of Sport
My post on Garry Kasparov's retirement prompted a few comments about who the greatest chess player of all time was. Subjective opinions always make for a fun discussion, but it's also worthwhile to do some rigorous statistical analysis, and this is precisely what Jeff Sonas of Chessmetrics has done. Jeff has written a fascinating series of four articles for Chessbase, in which he looks at various measures of dominance:
Longest period as world champion: Emanuel Lasker was world champion for 27 years, though that span was artificially extended by WWI. Alexander Alekhine reigned for 16 years, but his stay was similarly extended by WWII. Kasparov was at the top for 15 years (and retired when he was still demonstrably the best player in the world). Finally, depending on when you consider his reign to have started, Wilhelm Steinitz was world champion for either 8, 22 or 28 years.
Largest ratings gap between first and second: Steinitz in 1876, Fischer in 1971, and Morphy in 1859 are the top three in this category. Fischer's 1971 achievement is especially striking when you reflect that the overall strength and depth of the chess world has (almost certainly) increased considerably since the 19th century. Steinitz's dominance of the 1870s was equally total: he won 25 straight games between 1873 and 1882 (no draws, all wins).
Longest period (non-consecutive) at top of ratings list: Lasker, 24 years, closely followed Kasparov, 22 years. Again, Kasparov could well have overtaken Lasker had he stayed in the game a bit longer.
Longest period (consecutive) at top of ratings list: Kasparov, 20 years, is streets ahead of Lasker, 13 years, and Karpov, 8 years. And for 19 of those 20 years, no other player came within 10 points of Kasparov's rating.
Highest peak rating (adjusted for comparisons across eras): The Chessmetrics ratings list for Oct 1st, 1971 had Fischer at 2895, after he won 19 straight games against strong opposition (including identical 6-0 annihilations of world #9 Mark Taimonov and #3 Bent Larsen). The second highest peak rating of 2886 belongs to Kasparov, after he took Linares 1993 (one of the two strongest tournaments of all time) with a stunning +7 score.
Highest match rating: Not surprisingly, Fischer's 6-0 demolition of Larsen was the strongest match performance of all time. Lasker's +8 win in 1896 over Steinitz (no slouch himself) gives him 2nd place on this list.
Highest tournament rating: Karpov's 11/13, +8, 2899 performance at Linares 1994, against a field including 9 of the top 11 players in the world, was simply astounding. It was the strongest performance by any player in any event in the history of chess.
Best tournament performances: Karpov may have had the single best tournament performance ever (at Linares 1994), but Kasparov was by far the best tournament player of all time. He had 5 of the top 10 tournament performances ever, and no less than 17 tournaments with performance ratings above 2820 (next best on this list is Lasker with 6). Kasparov also won 3 clear 1sts in category 20/21 tournaments (nobody else has won even 1). And he won more tournaments involving each of the top 5 players in the world (6) than everybody else combined.
Best annual performances (aka the Chess Oscar method): wherein we award gold, silver and bronze medals to the best three ratings performers each year, starting every year from zero. Kasparov has 16 golds and 5 silvers; Karpov has 11 golds and 12 silvers. Between them they won all 15 golds and 14 of 15 silvers in the period from 1981 through 1995. The duopoly also won 27 of 30 golds between 1973 and 2002.
This raises an interesting fantasy question. What would have happened if Garry Kasparov had never become a serious chessplayer? Jeff Sonas answers:
If Anatoly Karpov had still maintained his same ability and same overall results that he did in real life, then I think it would be a foregone conclusion by now that Karpov was the most dominant chess player of all time. He would have far surpassed almost all of the accomplishments of Emanuel Lasker, except those that were artificially extended due to the infrequency of play during Lasker's time. In fact, had Karpov defeated Kasparov in their first world championship match, it would almost certainly have eclipsed Fischer's main claim to all-time fame, which was his 6-0 match scores against Mark Taimanov and Bent Larsen ... I don't think it seems right to penalize Karpov for happening to be a contemporary of Kasparov. So I would actually place Karpov above both Lasker and Fischer in the all-time annals of who was most dominant.
And of course, once we stop the pretending, and acknowledge that Kasparov did in fact compete, and dominated even the mighty Karpov, then I think it's a no-brainer to answer the overriding question of these articles. If I had to hand out medals for who were the most dominant players of all time, I would give the gold medal to Garry Kasparov, and the silver medal (fittingly) to Anatoly Karpov. And then the bronze medal goes to either Emanuel Lasker or Bobby Fischer, depending on the fine print about whether the most important timeframe is their whole career or their peak year.
And there you have it.
Post Script 1: Kasparov, Karpov, Fischer, Lasker, Steinitz. Could 2005 be the year in which these names are finally superseded on the "strongest ever" list by the name of a computer chess program? Hydra's recent demolition of top-10 player Mickey Adams would certainly seem to imply so.
Post Script 2: How does Hydra work? Like most computer chess programs, it has a position evaluation function (Q=+9, R=+5, P=+1; control of centre is positive, doubled pawns are negative, and so on), and it does extensive (brute force) tree searches to calculate the "expected value" of any candidate move, averaged across all possible paths (with minimax pruning of course). This is somewhat similar to what most human GMs do, except that humans are much better at seeing which lines are important and which can be ignored (ie, their pruning is much more efficient). With one exception: Jose Raul Capablanca was once asked how many moves ahead he looked. He replied, "One move, the best one". In other words, his position evaluation function was so good that he didn't need to do a tree search to simplify the calculation. Amazing.
Longest period as world champion: Emanuel Lasker was world champion for 27 years, though that span was artificially extended by WWI. Alexander Alekhine reigned for 16 years, but his stay was similarly extended by WWII. Kasparov was at the top for 15 years (and retired when he was still demonstrably the best player in the world). Finally, depending on when you consider his reign to have started, Wilhelm Steinitz was world champion for either 8, 22 or 28 years.
Largest ratings gap between first and second: Steinitz in 1876, Fischer in 1971, and Morphy in 1859 are the top three in this category. Fischer's 1971 achievement is especially striking when you reflect that the overall strength and depth of the chess world has (almost certainly) increased considerably since the 19th century. Steinitz's dominance of the 1870s was equally total: he won 25 straight games between 1873 and 1882 (no draws, all wins).
Longest period (non-consecutive) at top of ratings list: Lasker, 24 years, closely followed Kasparov, 22 years. Again, Kasparov could well have overtaken Lasker had he stayed in the game a bit longer.
Longest period (consecutive) at top of ratings list: Kasparov, 20 years, is streets ahead of Lasker, 13 years, and Karpov, 8 years. And for 19 of those 20 years, no other player came within 10 points of Kasparov's rating.
Highest peak rating (adjusted for comparisons across eras): The Chessmetrics ratings list for Oct 1st, 1971 had Fischer at 2895, after he won 19 straight games against strong opposition (including identical 6-0 annihilations of world #9 Mark Taimonov and #3 Bent Larsen). The second highest peak rating of 2886 belongs to Kasparov, after he took Linares 1993 (one of the two strongest tournaments of all time) with a stunning +7 score.
Highest match rating: Not surprisingly, Fischer's 6-0 demolition of Larsen was the strongest match performance of all time. Lasker's +8 win in 1896 over Steinitz (no slouch himself) gives him 2nd place on this list.
Highest tournament rating: Karpov's 11/13, +8, 2899 performance at Linares 1994, against a field including 9 of the top 11 players in the world, was simply astounding. It was the strongest performance by any player in any event in the history of chess.
Best tournament performances: Karpov may have had the single best tournament performance ever (at Linares 1994), but Kasparov was by far the best tournament player of all time. He had 5 of the top 10 tournament performances ever, and no less than 17 tournaments with performance ratings above 2820 (next best on this list is Lasker with 6). Kasparov also won 3 clear 1sts in category 20/21 tournaments (nobody else has won even 1). And he won more tournaments involving each of the top 5 players in the world (6) than everybody else combined.
Best annual performances (aka the Chess Oscar method): wherein we award gold, silver and bronze medals to the best three ratings performers each year, starting every year from zero. Kasparov has 16 golds and 5 silvers; Karpov has 11 golds and 12 silvers. Between them they won all 15 golds and 14 of 15 silvers in the period from 1981 through 1995. The duopoly also won 27 of 30 golds between 1973 and 2002.
This raises an interesting fantasy question. What would have happened if Garry Kasparov had never become a serious chessplayer? Jeff Sonas answers:
If Anatoly Karpov had still maintained his same ability and same overall results that he did in real life, then I think it would be a foregone conclusion by now that Karpov was the most dominant chess player of all time. He would have far surpassed almost all of the accomplishments of Emanuel Lasker, except those that were artificially extended due to the infrequency of play during Lasker's time. In fact, had Karpov defeated Kasparov in their first world championship match, it would almost certainly have eclipsed Fischer's main claim to all-time fame, which was his 6-0 match scores against Mark Taimanov and Bent Larsen ... I don't think it seems right to penalize Karpov for happening to be a contemporary of Kasparov. So I would actually place Karpov above both Lasker and Fischer in the all-time annals of who was most dominant.
And of course, once we stop the pretending, and acknowledge that Kasparov did in fact compete, and dominated even the mighty Karpov, then I think it's a no-brainer to answer the overriding question of these articles. If I had to hand out medals for who were the most dominant players of all time, I would give the gold medal to Garry Kasparov, and the silver medal (fittingly) to Anatoly Karpov. And then the bronze medal goes to either Emanuel Lasker or Bobby Fischer, depending on the fine print about whether the most important timeframe is their whole career or their peak year.
And there you have it.
Post Script 1: Kasparov, Karpov, Fischer, Lasker, Steinitz. Could 2005 be the year in which these names are finally superseded on the "strongest ever" list by the name of a computer chess program? Hydra's recent demolition of top-10 player Mickey Adams would certainly seem to imply so.
Post Script 2: How does Hydra work? Like most computer chess programs, it has a position evaluation function (Q=+9, R=+5, P=+1; control of centre is positive, doubled pawns are negative, and so on), and it does extensive (brute force) tree searches to calculate the "expected value" of any candidate move, averaged across all possible paths (with minimax pruning of course). This is somewhat similar to what most human GMs do, except that humans are much better at seeing which lines are important and which can be ignored (ie, their pruning is much more efficient). With one exception: Jose Raul Capablanca was once asked how many moves ahead he looked. He replied, "One move, the best one". In other words, his position evaluation function was so good that he didn't need to do a tree search to simplify the calculation. Amazing.
