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The World Chess Championship In 5 Charts

This article is part of our 2021 World Chess Championship series.

The 2021 World Chess Championship ended last week with Magnus Carlen of Norway, the world No. 1, defending his title against challenger Ian Nepomniachtchi of Russia. It was Carlsen’s fifth victory in the world championship, a title he has held since 2013, and the match went a long way toward cementing his status as the greatest chess player of all time.

The contest featured some of the best chess ever played by humans, nearly flawless even when examined by modern, superhuman machines. It also featured a few inexplicable blunders, and just three bad moves saw Nepomniachtchi’s chances slip quickly and irretrievably away. The match also generated a lot of data! We’ve charted some of it below.

The match was scheduled as a best-of-14-game contest, but Carlsen wrapped it up in 11 games, securing the 7.5 points needed to clinch the championship. Below is a snapshot of the match after each of the 572 moves in those 11 games, calculated by the computer chess engine Stockfish. Computer engines evaluate chess positions in equivalents of pawn margin — positive numbers here are good for Carlsen and negative numbers good for Nepomniachtchi. In many games, these numbers hovered around zero, representative of that sparkling, accurate and dead-level chess. But Nepomniachtchi’s blunders broke our chart again and again, skyrocketing the evaluations in Carlsen’s favor in Games 8, 9 and 11.

Small multiple grid showing area charts for each of the 11 games played in the 2021 World Chess Championship. Each area chart shows the advantage by player for Magnus Carlsen and Ian Nepomniachtchi after each move. The championship was marked by some of the most flawless play in history but also grave blunders. Games 3, 7 and 10 were the three most accurate games of all world chess championship games to date. However, Nepo's blunders in Game 6, 8, 9 and 11 led to wins for Carlsen, allowing him to retain his world chess champion title.
Small multiple grid showing area charts for each of the 11 games played in the 2021 World Chess Championship. Each area chart shows the advantage by player for Magnus Carlsen and Ian Nepomniachtchi after each move. The championship was marked by some of the most flawless play in history but also grave blunders. Games 3, 7 and 10 were the three most accurate games of all world chess championship games to date. However, Nepo's blunders in Game 6, 8, 9 and 11 led to wins for Carlsen, allowing him to retain his world chess champion title.

The most interesting seismic swings, though, came in the jewel of the 2021 match, the instant-classic Game 6, during which the computer twitched violently up and down — and up and down and up. Game 6 was the longest game in the history of the world championship at 136 moves over nearly eight hours. And time pressure saw both players make their first real mistakes, injecting some human fallibility into the proceedings and stirring up human drama.

Players in the world championship begin the game with two hours on their clocks. After the 40th move, they get an hour added on, and after the 60th move, they get 15 minutes added on plus a bonus 30 seconds for every move they make afterward. Here is how the sands ran through the players’ hourglasses in that classic game — high-dosage, buzzer-beater drama, time-released over hours.

Line chart showing minutes remaining after each move for Magnus Carlsen and Ian Nepomniachtchi in Game 6 of the 2021 World Chess Championship. Carlsen and Nepo both ran into a time crunch before the 40 move time control, finishing their last moves with 30 and 25 seconds left, respectively.
Line chart showing minutes remaining after each move for Magnus Carlsen and Ian Nepomniachtchi in Game 6 of the 2021 World Chess Championship. Carlsen and Nepo both ran into a time crunch before the 40 move time control, finishing their last moves with 30 and 25 seconds left, respectively.

At these rarefied levels of play, much of the match comes down to the players’ meticulous preparation, which they undertake in close concert with powerful machines. They carefully (and secretively) plan their opening moves, and their responses to their opponent’s opening moves, and so on, often as many as 20 moves into the gnarly branches of the impossibly complex tree that is a game of chess.

Their chosen openings are shown below. When Carlsen had the white pieces, the games featured the Petrov defense, the Catalan or, broadly, the Queen’s Pawn game. When Nepomniachtchi had the white pieces, the game was usually steered into the familiar Ruy Lopez, or, when he was in desperate need of a change in fortune, the English opening.

Alt: Sunburst chart showing the chess openings and subsequent move sequences used in the first six plies of each game in the 2021 World Chess Championship. In the five games when Carlsen had the white pieces, he used Petrov's defense as an opening in three and a Catalan opening and general Queen's Pawn game in the others. In the six games when Nepo had the white pieces, there was little variation: Four employed the Ruy Lopez opening, and one used an English opening, and one had an Italian opening.
Alt: Sunburst chart showing the chess openings and subsequent move sequences used in the first six plies of each game in the 2021 World Chess Championship. In the five games when Carlsen had the white pieces, he used Petrov's defense as an opening in three and a Catalan opening and general Queen's Pawn game in the others. In the six games when Nepo had the white pieces, there was little variation: Four employed the Ruy Lopez opening, and one used an English opening, and one had an Italian opening.

During the opening, after the opening and, heck, all throughout a game of chess, the pieces go to squares. Here are the squares the grandmasters moved their pieces to over the course of the 11 games. Carlsen relatively favored the a4 and b3 squares, while Nepomniachtchi was more focused on the center of the board, including squares e5 and d6.

Heatmap of chessboard showing number of movements to squares for Magnus Carlsen and Ian Nepominachtchi in each game of the 2021 World Chess Championship, by player. Nepo played on squares more centrally focused, especially squares e5 and d6. Carlsen showed a higher concentration of movements toward squares a4 and b3.
Heatmap of chessboard showing number of movements to squares for Magnus Carlsen and Ian Nepominachtchi in each game of the 2021 World Chess Championship, by player. Nepo played on squares more centrally focused, especially squares e5 and d6. Carlsen showed a higher concentration of movements toward squares a4 and b3.

So after all these pieces were moved to all their squares, and the trophy was handed over to the Norwegian, what comes next for the highest title in chess? Well, Carlsen needs another challenger  — if he defends his title at all. 

Sometime next year, eight of the best chess players in the world will meet for the elite Candidates Tournament. The winner will earn the right to challenge Carlsen for the world title. Six of these spots have already been claimed: The competitors will include Nepomniachtchi himself; Fabiano Caruana, the American No. 1 who fought Carlsen to 12 straight draws in 2018; Sergey Karjakin, the Russian who sent the championship to tiebreakers in 2016; Jan-Krzysztof Duda, the world No. 13 from Poland; Teimour Radjabov, the world No. 14 from Azerbaijan; and Alireza Firouzja, the 18-year-old world No. 2, who’s rated even higher than Carlsen was at his age.

Carlsen said Tuesday on the Løperekka podcast that he may not have enough motivation to defend his title again — though he left the door open. “If someone other than Firouzja wins the Candidates Tournament it’s unlikely I will play the next world championship match,” he said. 

Here are all of these grandmasters’ ratings over time — prominently including Firouzja’s recent atmospheric climb — along with simulations of their chances should they face Carlsen in the next world championship.

Line chart showing the International Chess Federation (FIDE) ratings for the past five years for confirmed participants in the 2022 Candidates Tournament and Magnus Carlsen, and a small multiple chart of histograms showing the points earned by Carlsen in 10,000 simulations of a world chess championship versus each candidate based on their current Elo ratings. Alireza Firouzja has quickly soared through the ranks to become the second-highest-rated chess player in the world, with a higher rating at 18 years old than Carlsen did at his age.
Line chart showing the International Chess Federation (FIDE) ratings for the past five years for confirmed participants in the 2022 Candidates Tournament and Magnus Carlsen, and a small multiple chart of histograms showing the points earned by Carlsen in 10,000 simulations of a world chess championship versus each candidate based on their current Elo ratings. Alireza Firouzja has quickly soared through the ranks to become the second-highest-rated chess player in the world, with a higher rating at 18 years old than Carlsen did at his age.

Carlsen, the GOAT apparent, will likely be a big favorite over whoever sits opposite him in the glass box. But if just a few moves go the other way — a piece or two to the wrong square while a clock winds down — the crown may find its way to a new head.


Seven Games by Oliver Roeder

For even more writing on chess and other games, check out Roeder’s new book, “Seven Games: A Human History,” available in January.


Can you solve this puzzle about an alien planet? | FiveThirtyEight

Simran Parwani is FiveThirtyEight’s data visualization intern.

Oliver Roeder was a senior writer for FiveThirtyEight. He holds a Ph.D. in economics from the University of Texas at Austin, where he studied game theory and political competition.

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