Grenke Chess Classic – Analysis of Win Chances

The model simulation of the Grenke Chess Classic showed that a 2-player tie-break was the most likely outcome. In this post I’m going to dig a bit deeper into the simulation and the numbers we get from them.

The initial distribution of likely winners of the Grenke Chess Classic 2015.

Underlying numbers

The pairings for the tournament does affect the model quite a bit. Having more games with white is always preferable, and especially against higher rated players. As stated, Magnus Carlsen is playing 4 games with black, and three of those against the highest rated players (he also has 3 of the first 4 games with black, and while that does not influence the model, it is probably not what he hoped for to start the tournament). Levon Aronian on the other hand has not only 4 games with white, but they are against the top 4 rated players in the field. Fabiano Caruana also has 4 games with white, and they are mostly against the top rated players. Viswanathan Anand is in the same boat as Carlsen, playing 4 games with black, and his white games are against the lowest rated players except the game against Carlsen. All of this influence how the model scores each individual game, thus influencing the overall outcome. Carlsen and Anand are expected to do worse than if everyone played each other twice, while Aronian and Caruana somewhat better.

Averages

Each game was simulated 10,000 times, which gives us some ideas about the central tendencies of points scored. Each players mean, median and mode is as follows:

Player	Mean	Median	Mode
Carlsen	4,03	4	4
Caruana	3,81	4	4
Anand	3,50	3,5	3,5
Aronian	3,53	3,5	3,5
Adams	3,48	3,5	3,5
Bacrot	3,40	3,5	3,5
Naiditsch	3,39	3,5	3,5
Baramidze	2,85	3	3

As seen, Carlsen and Caruana are slightly ahead of everyone else, while Baramidze is far below. Anand, Aronian and Adams are all performing similarly, while Bacrot and Naiditsch are grouped just below. The biggest discrepancy here is that Naiditsch has the second lowest average, yet he was rated the 4th most likely player to win. The reason for this is that he doesn’t draw a lot, so in some simulations he wins enough games to win the tournament, while in others he loses a lot.

Point distribution

This leads us to the distribution of expected points for each player. In the graph below I have plotted the number of points scored on the x-axis and how often it occurs on the y-axis.

Each player’s distribution of expected points.

As seen, Magnus Carlsen leads the pack, ahead of Fabiano Caruana. Then there are a bunch of players in the middle with David Baramidze expected to not score quite as many points. Arkadij Naiditsch has a very wide distribution compared to many of the other players, which explains some of the reason the model expects him to win about 7% of the time.

Carlsen’s Supertournament Record

In the last 16 tournaments Magnus Carlsen has played, he has either won or placed second. That is a very impressive record and statistic, so it is worth looking at his chances of continuing that streak. So I looked at all the simulations to see how often he placed either first or second in the tournament. And that happens about 53% of the time. He is expected to win outright 19% of the time, place second 20% of the time, and he will be one of the players in the tie-break 14% of the time.

How many points to win?

Last, let’s take a look at how many points a player needs to score in order to win the tournament. One way to do this would be to simply see how many points the winner scored; however, as Fabiano Caruana showed in the 2014 Sinquefield Cup, the winning margin may be large. So instead I chose to look at how many points the second best player scored to get a feel for what score you need to beat in order to win.

The number of points scored by the second best player

As can be seen, scoring more than 4.5 points will win the tournament about 85% of the time. Scoring more than 5 points will will win over 98% of the time, with most of the remaining 2% is ending in a tie-break.

Regardless, in the end it is the players that decide the outcome. Let’s see what they come up with.

Update:
Here are the expected outcomes for Day 1 according to the model:

White	Black	White wins	Draw	Black wins
Caruana	Anand	28.3%	54.3%	17.4%
Bacrot	Baramidze	37.7%	46.9%	15.4%
Aronian	Carlsen	19.5%	54.2%	26.3%
Adams	Naiditsch	30.3%	47.4%	22.2%