• Ding Liren vs Gukesh match is the most accurate one so far (least missed points)
• Excluding the ongoing match, Anand is the most accurate player
• Carlsen has the highest game intelligence score
• Figure illustrates a trend of decreasing missed points (increasing accuracy) over time.
• Initially, players averaged more than 1 missed points per game, meaning their mistakes added up to over one significant blunder per game. Over the years, average missed points have decreased significantly
• Increasing accuracy over the years is consistent with prior accuracy analyses and top GM opinion.
• However, this increase is not universal.
• José Raúl Capablanca, who is known as a generally accurate player, remained the most accurate player until Anatoly Karpov.
• Anand averaged 0.4 missed points per game. This is the highest accuracy in the dataset.
• However, Magnus Carlsen stands out with the highest game intelligence score of 161, which suggests that Carlsen’s playing style, while not always following the top engine move, tends to elicit more mistakes from his opponents compared to other players.

All details on Gukesh – Ding: Preview / Schedule / Venue / Live More: The game that did not happen / Record to chace / Video preview / Why is interest so high

Replay: Gukesh – Ding Liren game 1, 0-1, Ding Liren vs Gukesh game 2, 1/2-1/2 / Gukesh – Ding Liren game 3, 1-0 / Ding Liren – Gukesh game 4, 1/2-1/2 / Gukesh – Ding Liren game, 5 1/2-1/2 / All Gukesh – Ding Liren games live Parallel: Top Chess Engine Championship live

Dr. Mehmet Ismail concludes, “For each year, I calculated “average missed points” per game per player as in the picture. A value of 1.00 or 0.50 missed points corresponds to making a game-losing blunder in a winning or drawn position, respectively. 0 missed points mean perfect play. Missed points measures the points a player misses in a game according to Stockfish (depth 20). Each miss is calculated using the win-draw-loss probability of the top engine move and the actual move.”

Accurate performance ratings are essential in chess for awarding titles, prizes, and organizing tournaments, especially when tiebreaks matter. The Tournament Performance Rating (TPR) has been the standard for this purpose. However, TPR becomes undefined when a player wins all their games in a tournament. This was something that Elo himself acknowledged. To address these issues, I proposed the Complete Performance Rating (CPR), which I shared on Twitter/X

CPR is defined as the hypothetical rating R such that if the player were assigned this rating at the start of a tournament where the player scored m points in n games an additionally drew a game against an opponent with a rating R, the player’s initial rating would remain unchanged.

The main idea behind the CPR is that drawing a game against an opponent with the same rating does not change a player’s rating. Before computers were widely used, FIDE created a table for approximating TPR and included a rule that adds 800 points to the average Elo of a player’s opponents in case of a perfect score, while also acknowledging its limitation. While this worked when perfect scores were rare, it can lead to unexpected outcomes. For example:

• Winning one game against a 2000-rated player results in a TPR of 2800.
• Winning eleven games in a row against 2000-rated players also gives a TPR of 2800.

These two performances are very different, yet TPR treats them the same.

The Chess Olympiad 2024

GM Jacob Aagaard highlighted on Twitter/X an issue from the recent Women’s Olympiad. A player won a gold medal with a perfect score of 8/8 against opponents with an average Elo of 1876. Her TPR was 2676. In comparison, the silver medalist, who scored 7/8 against an average Elo of 2124, achieved a TPR of 2460. This shows that TPR may not accurately reflect differences in performance when one player has a perfect score.

Using the proposed CPR, the gold medalist’s performance is calculated as 2430, whereas the silver medalist’s CPR is 2439.

While this is certainly not a call for a revision of past awards—congratulations to all medal winners, who deservedly earned their medals—I believe implementing CPR for perfect scores will improve the accuracy and fairness of performance ratings moving forward.

For those interested in the details, I’ve shared a repository with the CPR calculations here, and you can find the paper here. Comments and critiques are welcome.

About the author: Dr. Mehmet Ismail is a lecturer in the Department of Political Economy at King’s College London. He earned his Ph.D. in Economics from Maastricht University. His research interests include game theory, political economy, sports, and topics at the intersection of economics and computer science. Beyond academia, he is a chess enthusiast and a former backgammon player. He has been a member of Norway Chess, doing stats for the past two years.