Who will win the candidates 2016?
I have seen many people betting on who will win the candidate tournament and become Magnus Carlsen’s next challenger. In a previous post, I analyzed the rating progress of several top players to see if I could find statistical evidence that Carlsen’s performance is superior to the other players. And I did. This time around, I thought I’d take a similar approach to a different question: Who will win the candidate tournament?
My idea is that I look at the rating numbers from the past two years and try to predict the upcoming performance of the players in the tournament. The graph below shows the rating progress from January 2014 to March 2016 for the World champion and his potential challengers.
Based on this data, I have done two analyses. First, I compared the rating averages and expected variation for the ‘stable’ periods, which has resulted in one estimated rank. Secondly, I compared the rating levels for each of the candidate players to that of the world champion. This resulted in a second estimated rank. Finally, I have weighed these ranks together to indicate who is most likely to win the candidates tournament.
In the first graph (below), we see the rating progress for the candidates and the reigning world champion. It is not the easiest graph to read, since a lot of the values are close to one another. We will look more closely at the individual players later on. What is interesting about this graph is that the variation seems to be somewhat smaller during 2015 compared to 2014.
Looking at the rating progress for individual players, we can confirm that the variation has decreased for several players (but not all) during 2015. We can take Anish Giri as an example. In the graph below, the green line represents Giri’s average rating during the past two years. The red lines indicate the expected variation based on his performance during the same period.
In the graph, we see quite clearly that the level of Giri’s rating during 2015 is higher than during 2014. This suggests that his performance during 2015 should be a better predictor of his upcoming performance. A few other players have shown a change (positive or negative) of their performance during the past two years.
Other players have had their ups and downs, but it seems that their rating numbers are centered around approximately the same average. In the graph below, we see how Anand’s rating has varied over the same period.
So what I did was to first identify what I consider to be a stable rating level for all of the players in question. For Anand, Karjakin, Svidler and Topalov, I used the average for the entire period. For the remaining players (Aronian, Caruana, Giri and Nakamura), I considered the rating periods from May 2015 to March 2016, resulting in the graphs below.
Player |
Rating rank |
Expected (average) Rating |
Nakamura |
1 |
2800 |
Caruana |
2 |
2796 |
Topalov |
3 |
2792 |
Anand |
4 |
2791 |
Giri |
5 |
2788 |
Aronian |
6 |
2779 |
Karjakin |
7 |
2765 |
Svidler |
8 |
2744 |
From this first breakdown, we see that Nakamura tops the list closely followed by Caruana. It is important to note that each player has an interval within which their historical rating levels have varied, and this interval gives their estimated future performance a certain uncertainty. Therefore, there will be overlap in the expected rating intervals for several players, indicating that there is not necessarily a statistically significant difference in the rating levels. The intervals for each individual player can be seen in their respective graph (red lines).
In the second part of my analysis, I have used Carlsen’s rating as a benchmark and calculated the rating difference between Carlsen and each of the candidate players. Based on this, I have done a similar analysis as before. Whoever has the smallest difference in rating compared to the world champion will have the best chance to win.
Based on these graphs, we can compare the average difference from Carlsen’s rating. This gives us the following result.
Difference rank |
Player |
Avg difference to Carlsen |
1 |
Nakamura |
52 |
2 |
Topalov |
53 |
3 |
Anand |
54 |
4 |
Caruana |
57 |
5 |
Giri |
65 |
6 |
Aronian |
74 |
7 |
Karjakin |
93 |
8 |
Svidler |
111 |
Once again, we see that Nakamura is at the top of the list. This time, Topalov and Anand are close behind. And as before, there is an interval of uncertainty connected to each of the number, as represented by the red lines in the charts for each individual player.
Finally, we can weigh our two ranks together and get a qualified guess of who will be the victor of the candidates tournament and face off against Magnus Carlsen in November.
Estimated (average) rank |
Player |
Avg difference to Carlsen |
Avg R |
Difference rank |
Rating rank |
1 |
Nakamura |
52 |
2800 |
1 |
1 |
2,5 |
Topalov |
53 |
2792 |
2 |
3 |
3 |
Caruana |
57 |
2796 |
4 |
2 |
3,5 |
Anand |
54 |
2791 |
3 |
4 |
5 |
Giri |
65 |
2788 |
5 |
5 |
6 |
Aronian |
74 |
2779 |
6 |
6 |
7 |
Karjakin |
93 |
2765 |
7 |
7 |
8 |
Svidler |
111 |
2744 |
8 |
8 |
Based on this analysis, Carlsen’s most likely challenger will be Nakamura. He is at the top of both lists, and is thereby an undeniable number one on this final list.
So perhaps Nakamura will get his chance to stop the ‘Sauron of chess’. In a few weeks, we will find out.