Perhaps the longest-raging debate in the chess community is who is, as they say, the GOAT, or Greatest Of All Time.  It rages back and forth everywhere from forum sites like Reddit, to Chess.com forums, to over the board.   Sometimes, people say 'best World Chess Champion' based on their own like/dislike for their games and characters.  For example, Paul Morphy, a young chess player from the early 1900s, is sometimes called the best, because he was an American who took the European's chess dominance away from them.  Others say Mikhail Tal of Russia was the best ever, because he was known for a wild, attacking type of chess.  
     Others prefer to nominate their choice for the greatest World Champion based on where he came from.  For example, Americans like the famous Bobby Fischer of the USA, Russians like Anatoly Karpov, World Champion between Fischer and Garry Kasparov, because he is from Russia and was high up in Russian politics.  Cubans like Jose Raul Capablance of Cuba, and Phillipinos like Wesley So, who never even became World Champion.
     These choices are all based on feelings and personal biases, but there are three evidence-based methods which are often used.  These are:
          I.  Dominance over contemporaries
          II. Length and staying power of career
          III.  Computer accuracy
    The first method is fairly popular, especially amongst Bobby Fischer fans.  The famous American is known for having suddenly burst onto the chess scene in the late fifties and sixties, going from an obscure club player to World Champion in 16 years.  He dominated the chess world from 1966 to 1976, at one point having a 150-point rating gap between him and Number Two, Boris Spassky.  He would win tournaments undefeated, with scores such as 21.5/22 in the Manhattan Chess Club Rapid Tournament, and would also have dominant score in supertournaments, for example winning 18.5/21 in the 1971 Candidates, and winning the 1971 World Championship against Boris Spassky 12.5/21.  In 1975, however, he refused to play against rising star Anatoly Karpov, after the International Chess Federation, FIDE, refused his unreasonable demands.  He then quit chess.  During his brilliant career, he had dominated chess like never before or since.  
    Dominance alone, though, may not be the best method of calculating the best player.  It is argued that just because you can do well against a certain, possibly weaker group of people who comprise the top players of your era does not mean that you are better than other players.  Some people have tougher competition.  Some say that Fischer's sort, brilliant career is not enough to make him best of all time.  If he had stayed in chess and played Karpov, he might have lost.  He would have to dominate chess for longer that that, and against new groups of people.  These people say that Garry Kasparov of Russia was the greatest chess player ever due to his staying power.  Kasparov was #1 in the ratings from 1984 to 2006, when he retired, and World Champion from 1985 to 2000, when he lost the Championship to Vladimir Kramnik in a surprising upset.  This long dominance, second only the Emanuel Lasker's 37 years (which happened during wartime, and so Championships were delayed), as well as the power of his play, leads many people to consider Kasparov the greatest World Champion of all time.
     This, however, is also not the best method in existence.  Almost everyone prefers Kasparov to Lasker, yet Lasker was World Champion longer.  You might say Russian Alexander Alekheine was the greatest ever, because he never lost the title (he died as World Champion).  I, and many others, argue that in order to decide who was the greatest World Champion, you must decide how they would do against each other at their career peaks.  There are two ways to compare this.  The first is rating, a value assigned to players which moves around as they win, lose, and draw games against opponents of different strengths.  Bobby Fischer's peak rating was 2790, far above Number 2 Boris Spassky.  However, seventeen players have been higher rated than Fischer, including some who few people would consider better than him, such as Anish Giri and Teymor Radjabov.  The top two on this list, however, probably the greatest players of all time.  One is Kasparov, and the other is current World Champion Magnus Carlsen.  Kasparov takes #2 due to peak rating, and also due to his long chess dominance and playing power.  Magnus takes first because of two factors: his rating, and also due to his CAPS score.  CAPS is Computer Aggregated Precision Score, or how close the players moves are to the Computer's suggestions.  This is an excellent way to compare players, as Computers are by far the strongest chess players out there.  Magnus gets the 'right move' 98.36% of the time, above Kramnik (98.15) and Kasparov (98.01).  (By the way, Kasparov is still likely a little better than Kramnik because of his long and powerful career).  So, if these great World Champions all played each other in a tournament, Magnus Carlsen would probably be the best choice to take first.  Some argue this is unfair, as Fischer didn't have computer learning in his day.  This doesn't really matter though.  They can only be evaluated on how strong they were and are, not how strong they could have been.

P.S.  Apologies for the length of this, it's an actual essay, not just a quick OP.  I wanted to go through this thoroughly.  For those of you with attention spans of over 10 seconds, feel free to debate!

I would also like to point out that Magnus is a far more active player than Fischer ever was, making it harder for him to achieve a large rating gap between him and #2, like Fischer did.  He doesn't just get a big gap and keep it by not playing.  When you are that high rated, it is hard to preserve your rating if you play a lot.

I too think that Magnus is the best ever, but Morphy, Kasparov and  Fischer comes very close. Magnus is the most complete player ever. Compare him to Morphy, who GM Ben Finegold says that his rating would have been whatever Magnus has +10 points.  Morphy never got to play Giri, Kramnik, Kasparov, Anand, karjakin, Nakamura.... Because of less strong opposition, he won the games early and did never get as much endgamepractice as Magnus, nor did he get so hard defensive tasks.   Morphy of course , if he timetravelled , would adapt fast to top ten-level, ans after three years he would have been a very interesting VM contender to Magnus. What makes Magnus  the best is the very strong competion, his memory, calculating, knowledge, physical fitness, competition instinct, computer assisted preparation and more.   Magnus lose games from time to time. This is not as bad as it seems. Compare him to Anand(close to the greatest of all time). On top ten level Anand often plays for victory with white and draw with black, while Magnus fights for victory with both colours. that means Magnus is taking more risks, which leads to both more victories and losses, and less draws. Daring to risk at that level is a way to get even better. The best of Magnus is still to come. Imagine how good he can become when he reaches the current age of Aronian.

I think the question isn't so much how strong Morphy could be, today, but how strong he actually was, because we know that.  We don't know what Morphy could have been today.  He was a fascinating player, especially for that early on. But I certainly agree with you on Magnus.

It was Polgar’s husband, a vet, who pointed out just how easy it would be to implant a computer chip into a person (as in a dog or cat). But it’s one of the great joys of chess that you are effectively naked and answerable only to yourself. Most chess players – a proud and fiercely independent breed – would not naturally be drawn by the lure of the cyborg – and that’s definitely a mercy.  There's a kind of cyborg at play with Carlsen ?

In order to find a definitive best, you first need to split the eras. The players up to the end of Kasparov only had a board and some books, which makes them even more impressive to think how great they were, where as now days the players have much more available t9 them for study and prep as well as many more tournaments available with only a short plane ride to get there. 

For me Fischer is the goat. Not because of his rating or his tenure as champion but simply how he blew away everyone in his path to get to the championship match. He won 18 games in a row to make it into the championship match! That is insane by itself. Nobody will ever dominate matches like that ever again.  

i think if you take into account that Kasparov did what he did without the assistance of computers one could argue that he and other previous grandmasters were just as good as Carlsen. Computers have increased the quality of chess players as a whole- one could argue even an 800 or a 1200 today is better than an 800 or 1200 from 30 years ago. why? because our playing volume has increased so drastically. You used to have to pack up your board and head to the cafe or library or park and hope a player who was a decent match for you was there to play against. now, 24/7 in a matter of seconds you are matched with an appropriate opponent. Even hobby players nowadays have probably played more games than gms of the past. If you have an hour to play 1 minute blitz against someone OTB you'd be lucky to get 15 games in. Why? you have to take time to set up the board after each game. Online you spend ALL 60 minutes playing. We all as a whole have way more practice than we used to. then there is the benefit and time savings of computers analyzing positions vs having to sit there for hours on end and calculate each variation of a given line. its easy to argue that if masters of the past had access to the tools of today they would be on par with Magnus too. An interesting allegory to this was a video on shoe technology and how if you calculate marathon times correcting for the inefficiency of old cork soled running shoes in the 1920s and 30s vs modern synthetic shoes, marathon times would be very simllar. We are all a product of the tools at our disposal.

In the knockout Candidate Matches of 1971 against the former world champion and the top players in the world besides Spassky, Fischer went 6-0, 6-0, and 5W-1L-3D in the final against former World Champ Petrosian where Fischer was ill during the match.  Fischer's one year performance rating is still the best of all time and it's not, as suggest by the OP, among a weak group of players because they did much better against Karpov and Kasparov than when slaughtered by Fischer and Karpov and Kasparov were not slaughtered by future champions when they were at their peaks.

Greatest, or Best?

Greatest?  Fischer. 

Best? Kasparov.

Who was the Greatest Chess Player of All Time?

Perhaps to be technically precise, and besides you quote and reference CAPS (Computer Aggregated Precision Score), you should add the adjective "Human" in front of the words "Chess Player."

Otherwise, one could make the argument that AlphaZero is the Greatest Player of All Time (at this point in time) based on CAPS, lol.

There is no reason to suppose.logically.that the pool of human talent in one era is inherently different in quality from another.So dominance over contemporaries would be a good measure-EXCEPT -that in any organised competitive activity strength in depth increases over time. Also.as in sport.it is not said often enough that 'The Best' are recognised only from those that have had the opportunity-someone who starts early..receives coaching advice.plays constantly.has access to books or the Internet,will consistently beat a player for whom none of this applies.but who is naturally,all things being equal, better.

Kasparov.

Unless the computer chip is connected directly to the brain, though, a cheater would have to do suspicious things to tell it his opponent's moves.

Eventually, though, we may all have computer chips implanted so that we can move our consciousness to them (well, to a larger box they connect to, more likely) to avoid dying of old age. Then it won't be possible to take Chess seriously any more.

To be perfectly honest, I see very little point in using the CAPS metric, because what's easy for a computer maybe exceedingly difficult for a human being and vice versa. Furthermore, given that Magnus Carlsen and his contemperarories are standing on the shoulders of giants, giants which previous generations didn't have access to (because they were the giants on whose shoulders later generations then planted their feet), any such comparisons will always come out unfavourably for earlier generations. Their knowledge was quite simply much less extensive.

In my view, much more important metrics are domination, such as Fischer, which regularly outclassed fields, and longevity. Take Lasker, who in 1935, aged 67, took 3rd place at the Moscow International, only half a point behind the winners, the young guns Flohr and Botvinnik. For me, this makes Lasker a greater player than Capablanca, who struggled quite a bit against the newer generation and found it hard to reinvent his game in the 1930s (he was still a formidable opponent, obviously). The same could arguably be said about Fischer: after a hiatus of 20 years, he came back and crushed Spassky a second time. Remember that Spassky had been a regular in the World Cup tournaments of the mid to late 80s. Rubinstein, Botvinnik, Keres and Korchnoi were other such players.

100% Agree.   The CAPS metric is a nice attempt to appeal to a supposedly objective 3rd party observer, but it really fails for the reasons Bon Cat lists.

Domination and longevity are more important factors.   

I do give huge credit to Magnus for winning world titles in all 3 time controls for chess.  But drawing the classical portions of his WC matches with Karjakin and Cauana does not show domination.  

In fairness to Carlsen, he's only got the system he's playing under. I wish the format could have been different or that they would change it to a better one, for him to 'rehabilitate' himself!

By the way, I see that FIDE has at least partly adopted 'my' (I'm sure I wasn't the only advocating this) idea of organizing large giant Swisses for places in the Candidates Tournament, or rather, one big Swiss with 100 players invited by rating with one place up for grabs. I would have preferred more places being awarded this way in order to reduce the arbitrariness in the Candidates selection, but at least it's a start.

I think Botvinnik was a great World Champion.  But not in the discussion of greatest of all time   He had Bronstein at a distinct disadvantage.  Also Tal was ill in the rematch WC.  Smyslov beat Botvinnik as well.

But I do give huge credit to Botvinnik for coming back all the time and longevity and building up the Soviet School as well as being a professional engineer.  That's very difficult.  

That being said, I'm so glad Kasparov did not drink the Communist Kool-Aid that Botvinnik adored.  

uhhh....u ?

I think that Magnus Carlsen is the best player of all time. He had Kasparov undoing his tie when he was a kid! I’m an American and I still find myself rooting for this talented Norwegian. He is a back-to-back chess world champion. He is a walking chess computer who totally crushed Viswanathan Anad, who at the time was the world chess champion. And last year, in a series of 12 draws, Carlsen beat Caruana to the trophy. He is in my eyes the definitive best chess player ever.