The Best Players Ever - a Statistical Evaluation

It’s as hard to compare chess grandmasters across time as it is to compare professional athletes from different eras. What if Fischer or Morphy were 25 years old today? They certainly would benefit from an expanded base of chess knowledge, as well as the assistance of sophisticated chess engines. And would Kasparov or Carlsen have been a match for Paul Morphy if they lived in the late 1850’s? Who can say, these are questions that remain open to speculation and conjecture.  

A couple years back, I created a spreadsheet to compare the statistics of the greatest chess masters that ever lived, both contemporary and historical. Though many factors have changed over the years, the one thing that remains constant is that a chess game will end in one of three ways – a win, a loss, or a draw. What has changed is the number of draws over time. Few if any modern masters draw less than 40% of their games. In contrast, Fischer drew 33% of his games, Lasker – 28%, and Alekhine – 27%. Paul Morphy drew less than 10% of his games, but that was another era.

It dawned on me that the best way to compare players from these different eras was to disregard draws all together and focus solely on their wins and losses. So I calculated the won/loss percentage as the number of WINS divided by the sum of their WINS + LOSSES.

Doing so provides us with some interesting results. It seems those players with the highest winning percentages are players who are not currently active. The highest ranking active player comes in at number 16!

For the spreadsheet below I have included 42 active players and 36 inactive players. The inactive players listed in RED were either world champions, or universally regarded as the strongest player of their era. Active players are listed in BLUE. Notice how the past world champions rise to the top of the this list. This may not tell us who the best player is in absolute terms, but it does tells us how well these masters fared against their contemporaries.

DISCLAIMER: all data is from CHESSGAMES.COM website, and was updated earlier this month. To update again after the Candidates Tournament.

[Updated listing 4-26-16]

Finally the neverending debate has been sorted out. But wait, who's Viktor kramnik?

All it tells us is, that there was a fewer number of strong players about, when Lasker was a lad.

How about (#wins + 0.5 × #draws) / #games ?

It does show what a strong player Keres was.

By this type of logic that would mean that a player who has just joined Chess.com & starts at a rating of 1200, then wins 6 games in a row with no draws has a 100% winning statisitc to his/her name. 

Which means by this formula he is better than say Kasparov for example? 

Who is at 87.04% statisitcally. 

The mathematical side of me is interested, but not very satisfied. It's very easy to make arbitary lists of things that don't actually reflect reality, but are just playing with numbers.

I am wondering where those draws went and how they could possibly be unimportant.

For example, why stop at draws? Why not a list of chess players in order of win percentage only, or loss percentage only? Both of these would create lists that impart some sort of meaning, but it's not clear what meaning.

I would argue that win/draw/loss is a meaningful statistic in the case of world champions only. The problem is, every club player in the world has the exact same win/draw/loss ratio because he is playing people around his level. This continues and it's not clear when it ends. 

For example, let's plug me into this equation. I am 53.94%. Woooot I am one of the 100 best chess players in the world!

Excpect all this measures is that I have been improving during my last few games, it says nothign about my strength. If my win percentage ever got low, my rating would drop enough to get it back up to 50% and if my win percentage started getting too high, chess.com would match me with higher rating players and it would drop down to 50%.

The win/loss of any chess player who has arbitarily strong opponents to face should always be 50%.

Of course, for super grandmasters, they only have the same few opponents and not a limitless tide of opponents of any given rating relative to them. But it's not clear when this stops. For example, if all chess games in the world were done chess.com match style with -200 +200 rating, then 2500 players should still have a 50% win ration because there are 2700s. However, chess games are not done this way and it's all about tournament practice. Win/loss alone is just meaningless and only works for a world champion who you are sure is the strongest player in the world and therefore can compare his win/loss to other world champions.

Has everyone on this list faced the best players of their times a comparable amount? If not, how can you say that their win/loss percentages are relevant? It would be like putting my win/loss against chess.com 1400s on this list. It's nothing meaningful and there's no way to tell exactly what it means. We will have to stick with mystery rather than try to solve the problem of comparing grandmasters throughout history this way.

That Viktor Kramnik guy looks pretty good.

Ooops! I mean Vladimir. Sorry Vlad. Correction made. Thanks.

Perhaps, but isn't it interesting that Kasparov, a near contemporary, sits near the top of this list.

You're 100% correct. That's why a sound statistical analysis requires a sample larger than 6 games! If you check the table, you'll find that all the active players have a sample size (wins and losses) of at least 200 games, not counting draws, which reduces the likelihood of statistical anomolies.

That's a valid point. If anything, the numbers are skewed in favor of the older players.

Let's take Carlsen for example, yes his numbers are lower than the older GM's. That's because the games he played on his way to GM status, say from 2000 to 2500, are factored in the equation. If we run the clock forward 20 years, the losess he incurred during those formative years will represent a much smaller percentage of his total games, so if he maintains his relative strength, over time, those numbers will rise.

It's best to think of these numbers as a snapshot for the active players (performance to date), and as a career summary for the retired players.

Fascinating, Lou. Fascinating.

Why does Carlsen's statistics look not so good?

Because the games listed on Chessgames.com for Carlsen go back to the year 2000, when Magnus was only 10 years old, thus they include a large number of games played as he was working his way up through the ranks to GM status. By contrast, the games listed for Emanuel Lasker begin when he was 20 years old, and already at GM or near GM strength.

A fairer comparison might be to include only those games after a player achieved an master or grandmaster rating.

Interesti. However, I think you could improve the table taking into account not only the average wins-loses, but also the strenght of the opponents. Modern players have to face better opponents than, for example, Morphy.

It's trivially true that your win percentage depends on how good the people you play chess against are relative to your ability. Or in other words if you play a lot of pazers even a poor player can have a win percentage better than Kasparov! If you postulate that generally grandmasters play similar levels of opposition in their career then the win % has more validity but there are always differences:

Eras - more strength in depth today

Stage of career - a young grandmaster such as Carlsen challenging himself more and earlier

Top grandmaster still play more top players. Eg World champs and the candidates for the world champs

Did you end up playing at the top in lesser tournaments or lower down in harder ones?

Any way you look at it though Kasparovs win % is impressive being in the more modern era and with all those long championship matches