A fascinating study on Magnus Carlsen's probabilities of reaching 2900 has been published. Photo: Unibet
Magnus Carlsen announced he has played his last World Championship match, intending to shift focus and and try to reach the "impossible": a rating of 2900. But how likely or unlikely is the target exactly? A new scientific study gives some fascinating insight on that question.
The 31-year-old world #1 currently has a live rating of 2861, 21 points shy of his world record of 2882, which he first reached in 2014 and then tied in 2019.
When Carlsen last year hinted that he will not defend his World Championship title, he also said he now has a new goal and is "very motivated to reach 2900".
In his announcement in July, he said:
I hope to be able to edge closer to one of my other big goals, which is to make a 2900 rating. It’s going to be tough, obviously, but at the very least I’ve managed to keep my rating this year, which is at least something. It means that the goal is not further than it was earlier, although it’s tough.
Many of his rivals expressed doubts as to whether the target is realistic, including Hikaru Nakamura, who spoke about it on his stream.
With 39 points to go, it does seem like an almost impossible target for Carlsen, who has been stable around 2860 since the beginning of 2020.
But what are his chances exactly? That is the question a new scientific study tries to answer. In the 11-page "On the Probability of Magnus Carlsen reaching 2900" authors Sohan Bendre, Shiva Maharaj, Nick Polson and Vadim Sokolov use probabilistic methods to address the question.
The study used two different sets of data to predict the probability, with one including 110 classical games from 2020-2022 and the other including 78 games from his "hot streak" in 2019.
2019 was an incredible year for Carlsen, who won every tournament he took part in, scored 32 wins, 47 draws and not a single loss, with a rating performance of 2889. He gained 50 rating points on the way and made it to 2882 in August, just 18 points away from his current goal.
Magnus Carlsen has so far hit 2882 in 2014 and 2019, but can he go higher? | source: 2700chess
After simulating 200 of Carlsen's future games 2000 times and assuming his performance (likely outcome) and the mix of opponents are the same in the two periods, the result for the the 2020-2022 period is:
In this simulation. Magnus reached the rating in 90 simulated trajectories out of 2000. If Magnus Carlsen continues showing the same performance as he did during the 2020-2022 period, he has 4.5% chance of reaching 2900.
For 2019, the conclusion is:
In this simulation. Magnus reached the rating in 1600 simulated trajectories out of 2000. If Magnus Carlsen continues showing the same performance as he did during the 2019 period, he has 80% chance of reaching 2900.
The study also shows how important the K-factor is for Carlsen's chances. The K-factor is the weight each game has for a player. The higher the factor, the more the rating changes per game. A player rated above 2400 will have a K-factor of 10, which means that players of the same strength who face each other will gain 5 points for a win and lose 5 points for a loss.
As Carlsen is so much higher rated than his competitors, he has a higher expected score, which means he will gain less points from a win and drop more points for a loss, according to the Elo model. The authors note:
To a large extent, as Elo’s model makes clear, the larger values of K will allow for greater fluctuation in rating. Due to this, it is quite difficult for Carlsen’s rating to increase by a large amount, but it also does ensure that his rating won’t immensely decrease either. If the K factor was increased to allow greater rating changes, theoretically if Carlsen won all his games he may be able to reach the 2900 threshold. However, drawing or losing a game would have a negative impact on his rating, because he is so much more highly rated than all other players. For example, with the current K factor, if Carlsen drew against the 2nd-ranked player in the world, Ding Liren (rating 2806), his rating would decrease by about 0.83 points. If instead he lost to Ding Liren, his rating would drop by a dramatic 5.83 points. However, increasing K to 20 (too large in Carlsen’s view), a draw would cause his rating to drop about 1.65 points and a loss would mean a drop of about 11.65 points. Considering that draws at the grandmaster level are occurring 70 − 75% of the time nowadays, the situation seems tough for Carlsen any way you look at it due to the dramatic increase in competition. Reaching such a goal would be one of the greatest sporting achievements.
If the K-factor was increased from 10 to 15, Carlsen's chances of reaching the goal would greatly increase, the authors note.
If Magnus Carlsen continues showing the same performance as he did during the 2020-2022 period, and K-factor is 15, he has 18% chance of reaching 2900.
Using his 2019 performance and increasing the K-factor, he will almost certainly reach his goal, according to the study:
If Magnus Carlsen continues showing the same performance as he did during the 2019 period, and K-factor is 15, he has 95% chance of reaching 2900.
Carlsen's next chance of climbing closer to the target is the Sinquefield Cup, starting in St. Louis on September 2nd. Since he is rated more than 100 points ahead of most of the field, he needs to score at least 6 points just to avoid dropping rating points.
The Norwegian is also rumoured to be playing for his club Offerspill in the European Club Cup in Austria at the start of October. Regardless of how well he performs in those 16 games, reaching 2900 is essentially impossible in 2022. But can he do it in 2023?