Carlsen vs Caruana: Who Played Best By CAPS?'s advanced computer metrics confirm it was a close match. | Photo: Peter Doggers /

Carlsen vs Caruana: Who Played Best By CAPS?

| 134 | Amazing Games

[What is CAPS? Read the explanation here.]

All 12 classical games are in the books for the 2018 world chess championship match between Magnus Carlsen and Fabiano Caruana. Spectators are divided on their opinion of who deserves to be world champion. All draws, not many opportunities for victory, and a three rating point difference between the players... Should they be co-champions? 

To continue our Computer Aggregated Precision Score (CAPS) series, we will take a look at what CAPS says about the players' performance throughout the match. 

CAPS by year:

In the CAPS Predicts the 2018 World Championship article we took a look at the players' yearly CAPS performances. Consistently since 2012, both players have been incredibly accurate, in the 98-99 CAPS range.null

CAPS by game segment:

Another interesting chart from the prediction article showed how precise the players were by number of piece points remaining. Caruana appeared to have the advantage between 31-36 piece points on the board, and Carlsen was the more accurate player with 30 or fewer piece points remaining.


How did the players perform in the 2018 world championship according to CAPS? Based on the CAPS metric, I am going to assign the players extra credit for their efforts. Traditionally a draw is worth 0.5 points and a win is worth 1.0 points. The mid point of the two results is 0.75 points, and anything between 0.26 and 0.74 is closer to a draw than a decisive result. 

The difference in CAPS for the 12 games range from 0.01-3.51, with the median being 0.25. Ranking the CAPS differences smallest to largest (1-12), we will assign the following scores for each player:

  • Higher CAPS Player = 0.5 + 0.02 * (13 - CAPS Difference Rank)
  • Lower CAPS Player = 1 - Higher Caps Player

If it sounds confusing, it'll make sense as we go!

  • Game 1 [CAPS: Carlsen 98.769, Caruana 98.7038] [CAPS Game Score: Carlsen 0.56-0.44]

This was the game that most of the analysts believed Carlsen should have won during the middlegame. Carlsen had the higher CAPS, as one might expect. What's surprising though is how small the advantage was for Carlsen over Caruana based on the CAPS. Caruana was very solid in defense, which is why his CAPS stayed close to Carlsen's for the full game score. This is the 10th-highest CAPS difference, so we will award Carlsen 0.56 points based on the formula.  

Match score through one game: Carlsen 0.56, Caruana 0.44

  • Game 2 [CAPS: Carlsen 97.0605, Caruana 99.2221] [CAPS Game Score: Caruana 0.72-0.28]

Caruana pushed hard this game and kept increasing his advantage until things started to slip in the rook and pawn ending. His CAPS advantaged landed him an impressive 0.72 points for the game! Caruana pulls out to a CAPS lead after two games, 1.16-0.84.

Match score: Carlsen 0.84, Caruana 1.16

  • Game 3 [CAPS: Carlsen 99.1795, Caruana 98.0954] [CAPS Game Score: Carlsen 0.70-0.30]
The third game in a row with the black pieces receiving a higher CAPS score. I spoke with the statistics team and in general White should have a very slight edge in CAPS, on average, since it's easier to play with the eval advantage. The match is tightening up after the third game according to CAPS!
Match score: Carlsen 1.54, Caruana 1.46
Games 4-6 were all close draws based on CAPS, and instead of showing the games, let's just look at the CAPS scores.
  • Game 4 [CAPS: Carlsen 97.9047, Caruana 97.9187] [CAPS Game Score: Caruana 0.52-0.48]
  • Game 5 [CAPS: Carlsen 99.4706, Caruana 99.453] [CAPS Game Score: Carlsen 0.54-0.46]
  • Game 6 [CAPS: Carlsen 99.074, Caruana 99.1764] [CAPS Game Score: Caruana 0.58-0.42]
Match score through 6 games: Carlsen 2.98, Caruana 3.02
Through six games the CAPS battle is almost dead even! Each player has led in CAPS in three games, and the black pieces have led in CAPS in all six games! Based on computer eval, Caruana had a fairly large lead in game six, and he carried that into a large CAPS advantage in game seven.
  • Game 7 [CAPS: Carlsen 98.6548, Caruana 99.1467] [CAPS Game Score: Caruana 0.66-0.34]

The game went into a Queen's Gambit Declined for game seven, and just like game two Caruana had a large CAPS advantage. Future opponents should take note of just how accurately Caruana plays from the black side of the Queen's Gambit Declined. This pulls Caruana ahead in the CAPS match.

Match score: Carlsen 3.32, Caruana 3.68

  • Game 8 [CAPS: Carlsen 99.1181, Caruana 98.9133] [CAPS Game Score: Carlsen 0.60-0.40]
The eighth game was back to Caruana playing the white pieces after holding draws with a CAPS advantage in games six and seven. Similar to the previous three games when Caruana had the white pieces, we saw 1.e4 c5 2.Nf3 Nc6. In this encounter, Caruana decided to take the game into Open Sicilian territory. Carlsen was prepared for this using the Sveshnikov Defense, and he was able to play more precisely than Caruana based on CAPS.
Match score: Carlsen 3.92, Caruana 4.08
  • Game 9 [CAPS: Carlsen 98.4545, Caruana 98.6954] [CAPS Game Score: Caruana 0.62-0.38]

This game Carlsen employed 1.c4 and the players reached a Four Knights English opening. Carlsen had the better pawn structure and a better bishop around move 24, and Stockfish was even giving him over a half-pawn advantage. As we saw in past games when Carlsen gained a small advantage, Caruana started to play very accurate chess, with clutch moves like 25...gxh5 and 26...f5! This game was a turning point in the match in terms of CAPS, and we will see Caruana outplay Carlsen in terms of precision in the next two games as well.

Match score: Carlsen 4.30, Caruana 4.70

  • Game 10 [CAPS: Carlsen 98.1532, Caruana 98.8048] [CAPS Game Score: Caruana 0.68-0.32]

Another Sicilian Sveshnikov when Caruana had the white pieces. Many of the spectators and commentators felt that Carlsen missed some chances to play for a win in this game. When analyzed with Stockfish and CAPS, the story is that Caruana played extremely solid defense and even outplayed Carlsen to reach a rook and pawn endgame up a pawn.

Match score: Carlsen 4.62, Caruana 5.38

  • Game 11 [CAPS: Carlsen 98.6047, Caruana 98.863] [CAPS Game Score: Caruana 0.64-0.36]
Similar to game six, in game 11 we saw Carlsen challenge Caruana's Petroff Defense. Carlsen was able to go up a pawn in an opposite-colored bishop ending, but according to CAPS, Caruana was still the more accurate player! That's three games in a row with Caruana scoring around 0.65 points based on the CAPS differential, which gives him a match score of over a full game point!
Match score: Carlsen 4.98, Caruana 6.02
  • Game 12 [CAPS: Carlsen 92.9558, Caruana 89.4471] [CAPS Game Score: Carlsen 0.74-0.26]
Game 12 was the final classical game in the 2018 world chess championship. There were a couple questions heading into this game. Would Caruana push for a win with White? Would Carlsen try to reach the rapid tiebreaker even if he had a lead? 
It appeared the answer to both of these questions was yes. Caruana challenged Carlsen yet again in the Open Sicilian, one of their most exciting openings in the match. Carlsen was able to gain a nice advantage and was looking ready to play for a conversion when a draw was offered (and accepted) at move 31!  This was the sloppiest game of the match according to CAPS and perhaps the players were a bit tired by this point.
Match score: Carlsen 5.72, Caruana 6.28
Final thoughts:

The most striking aspect of the CAPS metrics was that the players played very precise chess with the exception of game 12. In seven out of 12 games Caruana had the higher CAPS score, and he also won out on the CAPS match score system that we used in this article (6.28-5.72 Caruana). 
We also took a look at the CAPS metric for all moves played in the total match and Caruana outpaced Carlsen slightly again, 98.7737-98.6327. A tied classical match was a fair result based on the CAPS metrics, but if CAPS had to pick one player deserving of the classical win it would have been Fabiano Caruana.
Who do you think played more accurately in the classical games?
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