Sports fans are notoriously fond of underdog stories. Outside of games or matches involving our personally beloved teams or individuals, we almost always tend to root against the favorite. We love to see upsets! Knockout tournaments are excellent for this, especially in the early rounds. They set up lots of matches simultaneously, and even if each underdog has, individually, less than a 50% chance of winning (by the definition of “underdog”), probability dictates that several of them will likely still win. This is why basketball fans look forward to “March Madness” (the NCAA Tournament) all year, and it’s why chess fans should love watching the World Cup.
In the 2013 World Cup, out of 64 first round matchups, the lower seeded player advanced in 13 of those. The lowest seeded player to advance was some kid you’ve probably never heard of, just 14 years old, rated only 2557. What was his name again? Oh yeah, Wei Yi, and come to think of it maybe you have heard of him after all. We do enjoy writing about him here! Not only did he upset Nepomniachti in round one, he went on to knock of Shirov in round two, before finally falling to Mamedyarov in rapid tie breaks in round three. Elsewhere in the bracket we saw the #102 seed (Adhiban) and the #91 seed (Fier) face each other in round two, after both achieving upset victories over their first round foes. Adhiban won the privilege of advancing to the third round, where he was promptly dispatched by Nakamura. #75 seed Daniil Dubov and #89 seed Jon Ludvig Hammer also both reached the third round, scoring two upset victories to get there. And the #50 seed, Julio Granda, scored upsets over Leko and Giri in rounds two and three to reach the round of 16!
The point here is that upsets will inevitably occur this time around as well. We can’t predict any specific upset as likely, every underdog (by rating) is by definition expected to win less than 50% of the time, as we said before. We’re not going to highlight any individuals as more likely to overperform than any other underdogs. However we can estimate how MANY upsets are likely to occur, and what the biggest upset might be.
We used our model’s odds on each round 1 matchup to simulate the first round 10,000 times, counting how many upsets occurred each time. For these purposes we defined an upset as “the higher rated player loses”, so in a few cases this means the higher seeded player winning is considered an upset, as ratings did shift a little after seeds were determined.
Overall we saw an average of 15 first round upsets (median and mode of 14) across our simulations, and one crazy run through gave us as many as 27! We also saw one boring first round with only 3 upsets, but don’t worry, 95% of the time we saw at least 10 upsets in the round, with a 26% chance of 17 or more upsets occurring!
Now yes, some of these are less interesting than others. When the 64 and 65 seed play, it hardly matters if Zhigalko (2656) beats Bukavshin (2657), even though that counts in our simulation as an “upset”. Don’t fear, though, we also saw an average of 6 upsets where the weaker player was outrated by at least 50 ELO, with an 18% chance of 9 or more of these “real” upsets coming to pass.
We have a 95% chance of at least one 100+ rating point upset (and a 14% chance of five or more, with 10 occurring in a single simulation once out of the 10,000 run throughs).
Can we go higher? Sure! There is a 65% chance that we’ll see at least one upset of 150 rating points or more (remember that our largest upset in 2013 was 160 points, and fell in this category). There’s even a 34% chance that we might see someone advance ahead of an opponent rated 200 or more ELO higher, and a 250+ point upset comes in as a 20% likelihood.
The latter (a 250+ point upset) would mean one of the top 12 seeds losing in round 1. Parham Maghsoodloo, an untitled player from Iran, only has a 2% chance of knocking of Wesley So (his superior by 313 rating points), and GM Ziaur Rahman of Bangladesh gets a 4% shot at beating Tomashevsky (overcoming a 258 point rating gap), and these are more likely than some of the others in this group of 12. Individually they’re extraordinarily unlikely, but the chance that just one of the 12 might succeed aggregates to 20%! Still unlikely, but certainly not implausible!
Overall, the largest upset averages out to be 187 rating points (median 182). The mode (single most common value) for our biggest upset comes out at 124 rating points, which is probably because there are two chances for this to happen: #28 seed Vitiugov and #24 seed Wei Yi both outrate their first round opponents by exactly that amount. How ironic would it be if the biggest upset of the tournament this time around were Wei Yi losing to GM Saleh Salem? Salem has a 17% chance of winning, according to our model, although most of the time he does so it isn’t the biggest upset of the tournament!