The penultimate round failed to produce a decisive game, but five draws actually had a somewhat substantial impact on the odds. Namely, Aronian is now a much greater favorite to win the event than before. This should be intuitively odd, he held serve and noone gained ground on him, which is basically a win. Clearly a full point lead with just one round left to play is a lot safer than the same full point lead with two rounds left, and at least a share of first place has been clinched. Now he needs only to win or draw in the final round to guarantee sole victory and 13 points in the Grand Chess Tour standings. Of course he does have the black pieces against Topalov, so that’s not entirely sewn up yet. Our model gives Topalov roughly a one in three chance of winning the game, which would allow any of four players (Carlsen, Grischuk, Giri, or Vachier-Lagrave) opportunities to tie Aronian for the lead with a win.
Here is everyone’s updated odds of winning the event, keeping in mind that the model assumes all players have equal chances in tie-breaks for first place, so a two way tie is treated as “half a win” for each player, a three way tie as “a third of a win” etcetera:
Note that only five players are listed, because half of the field is mathematically eliminated. As for the Grand Chess Tour, today’s glut of draws changed the odds only minimally. Nakamura saw a slight gain from exceeding expectations (a draw is always a good result when you have black against the world champion), and Aronian saw a slight gain as his odds of winning this event outright increased, but we’re only talking a couple of percentage points. Mostly when the standings don’t change, we don’t see much meaningful change in the odds of winning the tour. Here’s everyone’s chances:
Since five draws is a relatively boring result, in terms of how it impacts the standings, let’s find something other than odds of victory to discuss. How likely are five draws? Much fuss was made in the first round of the fact that five decisive games were played. Is it similarly surprising that all five games were drawn? Not entirely. More than half of all games between elite players are drawn, so of course it’s more likely to get five draws than five decisive results, but it’s actually not as huge of a difference as you might suspect.
In the long run, about 56% of games at this level are drawn. If we use this number as gospel, and assume that every game is entirely independent (probabilistically) then here are the odds of a specific number of decisive results in a given 5-game round:
We can see that having NO decisive games in a round should be pretty rare too! Somewhere in the range of a 1/18 chance. As it works out, this should mean that in any given tournament with this format (a 10 player round robin, where nine rounds are played with five games per round), we should have about a 60% chance of making it the whole tournament without ever seeing five draws in a round.
Norway Chess saw five draws in round 7, so that’s two tournaments in a row where we’ve seen it happen. It’s not the most common format, but five draws in a single round did NOT occur at Shamkir Chess 2015 (the Gashimov Memorial), and there was also at least one decisive game in every round of Norway 2014. This is a very small sample, but at a glance it seems to support the table above. Maybe treating every game as an independent event (as our model does) isn’t so bad!
I do have plans to examine this idea in more detail at some point in the future though. Intuitively and anecdotally, without analyzing data, it “feels” like it’s more common for every game in a round to be drawn in later rounds. There is the logical explanation for this idea that in later rounds you’re more likely to find players who “want” a draw, based on their tournament position, and perhaps draw rates might increase. I feel this concept is worth studying closer in the future, to see if the data support or disprove the concept, but if it’s a real effect it’s probably not too strong, so for the meantime I will continue simulating tournaments on the assumption that all games are independent of each other.