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maligned

You asked for it; here it is...Analysis into 12 years of unbalanced brackets.

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the finals are 33 wrestlers vs 67 wrestlers. it's 1 wrestler vs. 1 wrestler. 50-50 should be expected, no?

 

maligned - thanks for the research.

 

is that the last 12 years of all world/oly wts or FS only? 

The point is that if the best wrestler wins the tournament, and the brackets are split 40:60 between the top and bottom, you would expect the wrestler from the bottom bracket to win 60% of the time.  In reality, this doesn't actually happen for a couple of reasons (one of which is your observation that a finals match is usually closer to a 50/50 situation).  

 

The takeaway though (if you want a point on your radio show) is that the unbalanced bracket not only affects the medal placements, but also has a significant impact on the identity of the champion.  From Maligned's data, being draw into the top is about 50% better than if you were drawn into the bottom (On top you win 53% percent of the time, despite only being 43% of the total pool, while on bottom you win 47% of the time despite being 57% of the pool.  (.53/.43)/(.47/.57)

 

If you want to be a world champion, being drawn to the top is on average a huge advantage.

Edited by Billyhoyle

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My calculations show a 5x10-38 chance of getting 700 or more heads with a thousand flips of an unbiased coin.

There is a one in million chance to get 571 or more heads in the same situation.

Sorry about nerdng out!

+1 from the nerd camp

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The point is that if the best wrestler wins the tournament, and the brackets are split 40:60 between the top and bottom, you would expect the wrestler from the bottom bracket to win 60% of the time.  In reality, this doesn't actually happen for a couple of reasons (one of which is your observation that a finals match is usually closer to a 50/50 situation).  

 

The takeaway though (if you want a point on your radio show) is that the unbalanced bracket not only affects the medal placements, but also has a significant impact on the identity of the champion.  From Maligned's data, being draw into the top is about 50% better than if you were drawn into the bottom (On top you win 53% percent of the time, despite only being 43% of the total pool, while on bottom you win 47% of the time despite being 57% of the pool.  (.53/.43)/(.47/.57)

 

If you want to be a world champion, being drawn to the top is on average a huge advantage.

 

Great analysis.

 

I don't understand people thinking this type of analysis is "crying".  It's pointing out flaws in the system.  Not that the entire system is bad, but that some things may be getting overlooked, like the advantage of being placed in the top bracket (which seems like common sense but apparently is not).

 

You must always be trying to build a bettter mousetrap.  Hopefully we learned this from the first time with FILA and their failures to adapt and change with the times.

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Isn't it obvious that having to wrestle less matches to get a gold or any other medal is easier than having to wrestle more matches.

All of the evidence and calculations don't necessarily show the unfairness of the current system versus the one where the pigtail matches are evenly split.

All the comparisons are between the current unbalanced system and the perfectly fair one.  There is no empirical data for one the that has pigtails evenly distributed.

 

Personally Old Dirty's reasoning that if you have a pigtail it is better to face another wrestler who just had a pigtail rather than one that got a bye  makes sense to me. 

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the finals are 33 wrestlers vs 67 wrestlers. it's 1 wrestler vs. 1 wrestler. 50-50 should be expected, no?

 

No.  

 

If the Mongol is the best guy on the top and Burroughs, Iran, and Russia are on the bottom, is it 50-50 that Burroughs wins?

 

Every time you have an unbalanced bracket, you stuff more top guys into the bottom than on the top.

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Isn't it obvious that having to wrestle less matches to get a gold or any other medal is easier than having to wrestle more matches.

All of the evidence and calculations don't necessarily show the unfairness of the current system versus the one where the pigtail matches are evenly split.

All the comparisons are between the current unbalanced system and the perfectly fair one.  There is no empirical data for one the that has pigtails evenly distributed.

 

Personally Old Dirty's reasoning that if you have a pigtail it is better to face another wrestler who just had a pigtail rather than one that got a bye  makes sense to me. 

 

Getting a pigtail is bad, but not nearly as bad as having them all on one side, like the current system. Tirrapel and I explained the reasoning for this in the previous thread, where the density of talent is more important than number of matches.  In other words, number of difficult matches is more important than simply number of matches.

 

The only point we are all trying to make is that the current bracketing system is one of the worst and most unfair ways to do it, outside of purposefully putting all the best wrestlers next to each other in the bracket.  

 

You say that it should be obvious that the side with more people is more difficult..We agree with this, and say it is obvious too.  However, many people come on and say things along the lines of "the cream rises to the top" or "the best wrestler will win the tournament no matter where he is in the bracket," or "Metcalf is the bad draw."  

 

We are trying to show that the current bracketing system directly impacts both the identity of the medalists and the identity of the champion in a negative manner, if the goal is to find the best wrestlers.  That is difficult for some people to accept, the fact that bracketing has a serious impact on results.  Obviously, UWW cares more about getting medals from obscure countries than finding the true world champion. 

 

Here is my solution:

 

1.  Seed the top 16 wrestlers based off of a point system that is published and publicly available (I think this is how the UWW rankings are done). Provide greater weight to the main tournaments:  previous year's WC, Golden Grand Prix, Continental championships, etc. Obviously this will not be ideal, because there will be injuries and people who don't peak best for these other tournaments...It will at least spread the talent better than the current system though and it will eliminate politics.  

 

2.  Balance the pigtail matches evenly on both sides.  Two seeded wrestlers will not meet in a pigtail match.  This will spread the density of talent, as I keep going on about.  

 

3.  Push the wrestlers who had to wrestle a pigtail match to the end of the 1/32 list of matches for the weight.  This will allow for a bit more rest time.  

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Getting a pigtail is bad, but not nearly as bad as having them all on one side, like the current system. Tirrapel and I explained the reasoning for this in the previous thread, where the density of talent is more important than number of matches.  In other words, number of difficult matches is more important than simply number of matches.

 

The only point we are all trying to make is that the current bracketing system is one of the worst and most unfair ways to do it, outside of purposefully putting all the best wrestlers next to each other in the bracket.  

 

You say that it should be obvious that the side with more people is more difficult..We agree with this, and say it is obvious too.  However, many people come on and say things along the lines of "the cream rises to the top" or "the best wrestler will win the tournament no matter where he is in the bracket," or "Metcalf is the bad draw."  

 

We are trying to show that the current bracketing system directly impacts both the identity of the medalists and the identity of the champion in a negative manner, if the goal is to find the best wrestlers.  That is difficult for some people to accept, the fact that bracketing has a serious impact on results.  Obviously, UWW cares more about getting medals from obscure countries than finding the true world champion. 

 

Here is my solution:

 

1.  Seed the top 16 wrestlers based off of a point system that is published and publicly available (I think this is how the UWW rankings are done). Provide greater weight to the main tournaments:  previous year's WC, Golden Grand Prix, Continental championships, etc. Obviously this will not be ideal, because there will be injuries and people who don't peak best for these other tournaments...It will at least spread the talent better than the current system though and it will eliminate politics.  

 

2.  Balance the pigtail matches evenly on both sides.  Two seeded wrestlers will not meet in a pigtail match.  This will spread the density of talent, as I keep going on about.  

 

3.  Push the wrestlers who had to wrestle a pigtail match to the end of the 1/32 list of matches for the weight.  This will allow for a bit more rest time.  

Your reasoning makes sense but there is no data to confirm this.

I like all of your suggestion for fixing the brackets.

I am pretty sure the Judo worlds are seeded based on rankings earned through the Grand Prix tournaments held that year and this seems to work, plus encourages the top guys to compete more.

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I think the point is that in a fair system, the bottom would win 2/3 of the time if it has 2/3 of the participants. Would you mind posting the exact average for participants instead of the range?

 

From your data, simply being in the top bracket makes you 20-30% more likely to win than you were going into the tournament, and about 50% more likely to win than if you had been placed in the bottom bracket.  

 

Think about that...the bracket system alone has that large of an effect on the overall outcome, not just the medal count.  

My most detailed post about why this idea of 2/3 of participants should equal 2/3 of wins will never, ever be true, no matter how fairly we distribute the talent or how much rest guys have... got buried as the last post on page 1 of this thread.  In it, I mention that the ratio of bottom bracket to top bracket participants is actually only about 1.38:1 (last 2 years...that's equivalent to 22:16 or 11:8).  In fact, it's even a little lower than that (1.36:1) if you take the average of the last 4 years (30 brackets).  With this ratio, and the fact that it's not reasonable to expect that the average randomly selected "favorite" from among the top 5 would beat a randomly selected "underdog" from the top 5 at this level of wrestling at any more than a 75% clip...I laid out why we will always have about a 50/50 distribution of top bracket rep vs. bottom bracket rep. gold medal results--even before consideration of "crowding out" and tiredness coming from the bottom.

Edited by maligned

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