The Unbalanced Bracket

The 2016 Olympic Games (Photo courtesy of Tony Rotundo;

The unbalanced bracket. Just reading that phrase raises blood pressures, starts rants, and makes folkstyle purists wear a smug smile. Ever since United World Wrestling (UWW) went to it for World Championship and Olympic competition, starting in 2005, questions have been asked and debates have raged. Today we'll take on one of those questions to see if it holds up to scrutiny. Does the unbalanced bracket often produce bottom-side bronze medalists that are stronger than their top-side counterparts?

One aspect of the unbalanced bracket that some have highlighted as a potential benefit is that it would seem to make a fluke bronze medalist more likely, expanding the number of countries that have a chance to medal, which could benefit struggling or emerging programs. Whether you see this as a good thing or not might depend on your role in the sport. A fan of pure competition might already think the double-bronze is a handout. Those who support a wrestler stuck on the bottom of the bracket with the three best in the weight might rage at a top side with half as many competitors. Wrestling leaders from a country that snagged an unexpected bronze and have seen their funding rise since might sing the praises of the system.

Regardless of where you fall, it seems obvious that the unbalanced bracket has the potential to skew competitions. For those that don't know, UWW uses a random draw system for most events. In the past, the Olympics and World Championships were a completely random draw as well, though some seeding has been introduced over the past five years. The unbalanced part comes into play with how the wrestlers are placed in the bracket after the draw. Effectively, the bottom of the bracket is filled first and it is filled from the bottom up. This means that in an unseeded bracket with 24 competitors, you end up with 8 wrestlers on the top side and 16 on the bottom. This is a worst-case scenario and seeding does help this a bit as the 2 and 3 seed now receive byes, pushing 2 more wrestlers to the top side of the bracket. Still, the bottom of the bracket is almost always larger, increasing the chances that the best wrestlers end up together down there.

To highlight the issue, here are the chances of the best wrestlers being drawn into the same side of an unseeded bracket of varying sizes.

24 wrestler bracket, 8 up, 16 down

48 wrestler bracket, 16 up, 32 down

These two are similar worst-case scenarios, but the numbers are slightly different. You won't see 48 wrestlers in any weight in Tokyo, but it does happen at the World Championships. With no seeding, we'd be looking at better than 1 in 4 of these brackets having the 3 best wrestlers on the bottom side and a greater than 30% chance of them being on the same side overall. There is greater than a 10% chance that the 5 best athletes will all be on the bottom. With the repechage system where any loss to a wrestler that fails to make the finals means no medal chance, having the 5 best on the same side is a disaster. 3 of the top 5 would fail to medal, even without any upsets, while the 6th and 7th best wrestlers might stand on the podium if they were bracketed up top.

That level of imbalance doesn't happen that often, though, so let's look at something between a perfect bracket and the worst-case.

20 wrestler bracket, 8 up, 12 down

40 wrestler bracket, 16 up, 24 down

In these two brackets, there are 50% more competitors in the bottom half compared to the top. All of the extra, in an unseeded scenario, would be in the same quarter, so we can again thank the addition of some seeding for avoiding that, at least. Still, though, we have a chance of the top 3 being on the same side that is around 1 in 4 brackets. The chance for the top 5 to all end up on the same side is higher than I'd like to see, but it is around half what it was in the worst-case brackets above. The 20 wrestler bracket is close to what we saw in Rio, with many weights featuring 19 competitors.

To be fair, any bracket that is randomly drawn could result in a doomsday scenario. So, we need to also look at perfect brackets to see what the chances would be.

16 wrestler bracket, 8 up, 8 down

32 wrestler bracket, 16 up, 16 down

As you can see, there is still a risk, especially of getting the top 3 on the same side. It is lower than with the other brackets we've looked at and both sides of the draw have the same chance, of course. The odds of the 4 or 5 toughest athletes showing up together is lower still, but it will never be zero without perfect seeding, which is likely impossible.

Now, you might be objecting to the fact that I've been using unseeded brackets for my numbers when seeding is now happening at the World Championship and Olympic level. However, most of the tournaments in the unbalanced bracket era, top-level events included, featured no seeding, so I wanted to explore those odds so that we'd have a good basis for exploring the question of whether bottom side bronze medalists are, overall, stronger than top-side. The other issue in play is that the seeding UWW uses does not guarantee that the strongest athletes in a weight are rewarded.

Comparing the men's freestyle initial seeds with Seth Petarra's June 4th MFS rankings, we find that just over half of the seeds will go to athletes ranked in the top 5 at their weights. At 57 kg, the top 2 in our rankings, Zavur Uguev (RUS) and Suleyman Atli (TUR), will be the 2 and 3 seeds, putting them on the same side of the bracket. Even worse, they'll be on the larger, bottom half. If Yuki Takahashi (JPN), 6th ranked, unseeded, and Bekhbayar Erdenebat (MGL), 8th ranked, unseeded, were to also get drawn into the lower half, it would have 4 of the top 5 ranked athletes who are eligible to compete.

This is not a unique situation either. Only 97 kg with Abdulrashid Sadulaev (RUS) and Kyle Snyder (USA) has the top two ranked wrestlers in the world guaranteed to be on opposite sides. Having one or two of the best on the top side does help, given the lower number of slots available on that side, but even that is hit or miss with this seeding system. Having a system set up to encourage competition and eliminating subjectivity is, on many levels, a good thing. However, it doesn't always help separate the best in the end.

While it is clear that the chances of a terrible draw increase with the unbalanced bracket and that the bottom side should see that happen more often than the top, we still need some hard data to investigate whether the bottom side bronze wrestlers are consistently tougher than their top side brothers and sisters. I've gathered data on the World and Olympic bronze medalists since the unbalanced brackets started. For each, I looked at how unbalanced the bracket was and what other World and Olympic medals the wrestlers won in their careers. I then compared medal totals, both weighted and unweighted, to see which side of the bracket prevailed.
Factoring in all brackets, I came up with the following results:

By pure medal count, the bottom bronze medal winners have an incredibly slim advantage, having won more than their top side competition in 134 cases, less 132 times, with 87 ties. Weighting the medals won in a couple of different manners increases the amount that the bottom side comes out on top, but it remains remarkably close.

The other metrics I looked at saw the same trend. 96 bottom-side bronze medalists won a gold medal at the world level at some point during their career. 89 top-side bronze medalists accomplished that. 113 bottom-side bronze medalists never won another medal compared to 114 topsiders.

While I would have expected a more pronounced difference, this data set does include many brackets which were either perfect or not unbalanced by much. So, I decided to look only at those brackets with at least 50% more competitors on the bottom side compared to the top. Here is what I found:

This, to me, is stunning. In the most unbalanced brackets, the top side bronze medalist has had a more decorated world-level career than the other bronze medalist more often than the other way around. The fact that the bottom side leads overall means that the bottom side is dominating those brackets with the smallest imbalances. This is completely counter-intuitive. We do, once again, see that the weighted medal counts shift the results towards the bottom siders, but it isn't enough to see them prevail.

In the other metrics, we see the same theme. Bottom-side bronze-medalists in the most unbalanced brackets count 34 gold medalists among their ranks while the top-side has 33. There have been 31 top-side bronze medalists in these brackets that never won another medal, while 37 bottom-side bronze medalists suffered that fate.

What happened here? What seemed to be an obvious theory hasn't been backed by the data at all. There are several possibilities. It could be that measuring the strength of a wrestler only by world-level medals isn't accurate enough. We could also be seeing that the system does a decent job of identifying the correct medalists even with the imbalance. Perhaps investigating the fifth-place finishers or those who lost to the bronze medalists would have revealed something different. It is also possible that the unbalanced bracket has such a small effect that we'd need a much larger sample size to see it. I would have thought 15 years of world-level championships across three styles would have been a large enough data set, but that gets cut down quite a bit when you filter for only the most unbalanced instances.

To be clear, this has to be a macro-level analysis. I would never want to besmirch those who won a bronze medal regardless of their path. To do so without investigating their bracket would be incredibly unfair. As we saw with the numbers, the top side can have the bad draw on occasion. It just happens less often than the bottom side, especially with certain numbers of competitors. That said, the theory that the unbalanced bracket can produce fluke bronze medalists isn't entirely debunked. It still stands to reason and the math doesn't lie. How often those flukes occur, though, should be in question. If we can't see a clear difference after 15 years, perhaps it isn't very likely. Add to that the Olympic brackets won't come close to the worst-case scenario sizing and it may not be worth worrying about in Tokyo at all. Until your favorite athlete gets the bad end, that is.


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