Magnus Carlsen vs. Hikaru Nakamura In Titled Tuesday

Credit for this article goes to Torsten Blass, a professional data analyst who runs The Data Digest, a YouTube channel. You can visit his channel at https://www.youtube.com/@TheDataDigest. 

The weekly Chess.com event Titled Tuesday has long been GM Hikaru Nakamura's domain. He has won dozens of them over several years, while no one else has gotten to within a couple of wins of 20.

After Chess.com merged with Play Magnus in December of 2022, however, Nakamura no longer had the tournament to himself—GM Magnus Carlsen instantly became a threat every time he played. Just since May of 2022, Carlsen has won on 16 occasions.

The first year of Titled Tuesday tournaments that regularly featured both of them was 2023. They are two of only three players to ever score a perfect 11/11; two of only six players to win twice in one day. Nakamura continued to play more often in 2023, but who came out on top after accounting for that difference in how often?

All stats for the 2023 calendar year unless otherwise indicated.

• Introduction
• Wins And Prizes Per Tournament
• Winning With White vs. Black
• Winning Streaks
• Winning both tournaments ("Sweeping the day")
• Direct Comparisons
• Strength of Opponents Faced
• Lowest-rated layer to lose against
• So, Who Was Better?

Introduction

In this article we are looking into the two dots of the top right corner of this scatter plot that shows players (in gray), international masters and grandmasters that participated in at least ten Titled Tuesday Tournaments with their average rating and average score (x out of 11). The top right corner is reserved for Hikaru Nakamura and Magnus Carlsen.

We can look at the total prize money earned throughout 2023 to find Hikaru ($28,700) winning almost twice as much as Magnus ($15,850). Hikaru also won the tournament twice as often as Magnus (18 wins versus nine), but this is mostly due to the fact that he participated almost twice as often (74 times versus 39). 

Wins and Prizes Per Tournament

To find out if one of the players was actually outperforming the other, we have to check their statistics on a per-tournament basis. It turns out that Hikaru won 18 out of 74 tournaments (24.3%), slightly ahead of Magnus, who won nine out of 39 tournaments (23.1%). Honorable mentions go to GM Liem Le, who won three out of 10 tournaments (30%), and GM Maxime Vachier-Lagrave, who won five out of 25 tournaments (20%).

See chart below for the top 10 players from Titled Tuesday 2023 tournaments with regards to their prize money won per event (minimum 10 events).

With regards to the average prize money per participation Magnus ($406) holds a slight edge over Hikaru ($388). Looked at this way, both averaged better than a third-place prize every time they played!

Winning With White vs. Black

When we look at players that participated in 10 or more Titled Tuesday tournaments (to have a somewhat solid foundation for winning percentages). We see that Magnus has the highest winning percentage of all players (80% with White and 72.7% with Black). Hikaru is ranked sixth for winning with the white pieces (77.4% of the time) and ranked third with the black pieces (70.1%).

However, Hikaru is really hard to beat. With the black pieces, he is slightly ahead of Magnus, only losing 13.4% of the games with Black compared to Carlsen's 13.9%. But Magnus only lost 6.3% of the games with White, a statistic that is far ahead of the competition.

Winning Streaks

The table below shows all players with a winning streak of 11 and higher in 2023:

Magnus won in rounds 10 and 11 in the late tournament on June 27, then won all his games in the late TT on July 4 and the first four games in the late TT on July 11 for a total of 17 (2+11+4). Hikaru won round 11 in the early tournament on August 22, then he won all games in the late TT the same day and the first three rounds in the early TT on September 5 for a total of 15 (1+11+3).

Winning streak distribution

The table above shows the longest winning streaks that were achieved by different players in 2023. How different are these maximums away from the average winning streaks Magnus and Hikaru manage to accomplish during their participations?

These charts that show the distribution of winning streaks are a bit misleading because a value of one is not actually a winning streak, but the result of winning a game and then not winning the next game. For Hikaru this “pseudo-streak” represents 25% (38/152) of his streak results. Which means that 75% of the time his wins led to an actual streak of 2-15 games. The “1-streak” result happened 18 times for Magnus which is 23.7% (18/76) of his results. Only the 15 games streak for Hikaru and the 17 streak for Magnus include their perfect days where they won 11 out of 11 games in a single tournament.

The charts above are based on all games, including skipped games. In other words, skipping a game would break a winning streak.

Winning Both Tournaments ("Sweeping The Day")

In 2023, there were six players who accomplished the feat of winning both events on the same day. Attempts refers to the times a player participated in both the early and late tournament on the same day.

Hikaru came close to a second sweep on three occasions.

• July 11: winning the early tournament but placing “only” second on the late event behind Magnus Carlsen
• October 3: again winning the early tournament but placing second behind Oleksandr Bortnyk on the late event.
• December 19: winning the late event but placing second on the early one behind Magnus Carlsen.

Magnus came close on two more occasions.

• August 1: winning the early event but placing second behind Alexander Grischuk.
• November 21: winning the early event but placing second behind Liem Le on the late event.

Direct Comparisons

In 2023 Hikaru Nakamura faced Magnus Carlsen 10 times, twice with the black pieces (drawing both games) and eight times playing with white (+3 =2 -3). Despite the even scores, we can give a slight advantage to Magnus here, because he played Black in eight out of 10 games.

Top matchups for Hikaru

As you can see Hikaru's best result is against Jose Martinez (10 wins in 12 games). He also did not lose against Maksim Chigaev, Jeffery Xiong, Vugar Rasulov and Bogdan Daniel Deac—all players that he faced seven or more times. But Hikaru could not beat Fabiano Caruana in any of the 9 encounters in 2023 Titled Tuesday Tournaments.

Other opponents that he faced 3 or more times and could not gain a point advantage on are:

Top match-ups for Magnus

Opponents that had a positive score against Magnus Carlsen:

Even though Hikaru and Magnus were the best Titled Tuesday players in 2023, GM Fabiano Caruana impressively won half his games against Magnus and five out of nine against Hikaru.

Strength of Opponents Faced

Hikaru played a total of 791 games in his 74 Titled Tuesday tournaments in 2023. He faced 394 different opponents. This figure below shows the rating of his opponents:

We can make a similar chart for Magnus, who participated in 39 tournaments, playing 399 games against 239 different opponents.

We see a similar pattern for both players. There are a few opponents with a rating below 2500, which come from the early stages of the tournament where players are matched with lower-rated players by design, instead of the tournament standings. As the score increases, which is usually the case for these super GMs, the players they face in later rounds also have higher scores and higher ratings.

We can compare the distribution of opponent ratings for both players with a density chart. It makes both players comparable, regardless of the fact that Hikaru played twice as many tournaments. The area under the red and blue line adds up to 100% respectively. We can see that on average Magnus had to play higher rated players a bit more often, by looking at how the blue line is shifted to the right.

However, a statistical test known as a t-test does not find this difference to be significant.

Lowest rated player to lose against

One last set of tables before we answer the big question of who was better in Titled Tuesday in 2023.

Here are the lowest-rated players Hikaru lost a game against:

And here are the lowest-rated players Magnus lost a game against:

So, Who Was Better?

Let’s conclude by seeing if we can decide which player was better throughout 2023. Using a linear model, we can try to predict the score (with the usual one point for a win, half-point for a draw, and zero for a loss) of each game, based on the rating of the opponent, and the pieces (black/white).

The line of best fit is above 0.5 for both players even on the right side of the chart where opponents have really high ratings. In other words, even against the absolute best opponents, both players should win more often than they lose. We could already have guessed this because both players have ~75% winning chance overall.

But the line for Magnus is above the line from Hikaru, which means that a linear model adds some points for the former player

If we look into the details based on the starting pieces, we see that both players have higher lines with white pieces, but that Magnus is still ahead of Hikaru, especially when playing with White.

In the chart below the overall effect of pieces is clearer. Against higher-rated players, having White is a bigger advantage. (blue line for white is above red). But as the opponents get weaker, this advantage is less important. Now even having black generally leads to a win.

In statistics this is called an interaction: The advantage of having White is different depending on the opponents rating. One factor interacts with another.

So, who was better in Titled Tuesday in 2023? The answer, based on how well they would score if they played the same number of Titled Tuesdays over a much longer period of time than one year, appears to be Magnus Carlsen. But Hikaru Nakamura still beats anyone else.