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klehner

What are the odds of these draws for one team?

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Cornell has seven wrestlers in the tournament.  One is the #1 seed, another is the #5 seed.  All five of the other guys are seeded such that
they have to face the #1 seed in the quarterfinals or earlier (assuming they get that far, of course).  Arujau #8, Tucker #9, Womack #16,
Honis #9, Sweany #24.

The same is true for Lehigh (5 out of 8 qualifiers), oddly enough.  Four teams have three such seedings.

The odds are about 1:1000 against five such seedings  happening to one team, but it did.

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1 hour ago, klehner said:

Cornell has seven wrestlers in the tournament.  One is the #1 seed, another is the #5 seed.  All five of the other guys are seeded such that
they have to face the #1 seed in the quarterfinals or earlier (assuming they get that far, of course).  Arujau #8, Tucker #9, Womack #16,
Honis #9, Sweany #24.

The same is true for Lehigh (5 out of 8 qualifiers), oddly enough.  Four teams have three such seedings.

The odds are about 1:1000 against five such seedings  happening to one team, but it did.

How do you figure these odds? Or did you just make up that number? 

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5 minutes ago, NJDan said:

How do you figure these odds? Or did you just make up that number? 

Eight of the 32 wrestlers in the bracket have a chance at meeting the #1 seed at or prior to the quarterfinals (two in the pigtail, two in the R16, four in the quarterfinals).  That's 1/(32/8), or 1/4.  Chances of that happening five times are 1/(4^5), or 1/1024.

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25 minutes ago, klehner said:

Eight of the 32 wrestlers in the bracket have a chance at meeting the #1 seed at or prior to the quarterfinals (two in the pigtail, two in the R16, four in the quarterfinals).  That's 1/(32/8), or 1/4.  Chances of that happening five times are 1/(4^5), or 1/1024.

I guess that's fair. But since these seeds are not expected to go past the quarters, I am not sure I see a beef.

 

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14 minutes ago, NJDan said:

I guess that's fair. But since these seeds are not expected to go past the quarters, I am not sure I see a beef.

 

It's about which half of the bracket you are on.  Dean, for example, would have been much better off as the 6 seed than the 5 seed.  Or a 10 seed for Vito may have been better than 8th.

It does seem odd that every Cornell wrestler ends up in the top half, and all but one the top 1/4 bracket.  No way you can rig that, IMO, but as Klehner notes - odd.

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Yes it is rare but if they're doing what they should do, the seeding committee is not looking back at where they seeded the previous people but are seeding the person that deserves to be there next. They shouldn't get to Max Dean if he's going to be the number 8 seed or 9 and say he's actually better off at 10 and move him down and move somebody else up.

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I only looked at the Lehigh draw last night and noticed that. I wonder how many other EIWA draws are similar. And further, are there other conferences that tend towards certain quadrants?

In response to Red Blades, there is a way to rig it but I'm fairly sure no one intentionally set up the computations to do that to Cornell and Lehigh. However, could it be that some of the calculations would have a tendency to put conferences at certain levels? I assume B1G tends towards the top seeds which would separate them from each other. Not saying it isn't earned but it could do that. Up until a few years ago there were one or two (depends if you call them separate) related conference separation rules in effect that have since been eliminated. They used to force conferences to not see each other until the round of 16. But at the same time they could all be on the same side of the bracket as long as they didn't meet too early. The rationale for the first was (as I heard it at my first assisting running of the NCAAs in 81) that PAC-10 teams should have to travel all the way to Princeton and then meet right away. The second I heard when I actually ran the computers starting in 87. Completely separating everyone beyond the seeding (12 at the time) would put up a kind of B1G wall. They wouldn't see each other usually until the quarters and everyone else could see them earlier. This happened by computer mistake/misunderstanding in 2007. It likely affected the team score that year.

Now (other than the last few) they fall where they are seeded.

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3 minutes ago, ConnorsDad said:

Yes it is rare but if they're doing what they should do, the seeding committee is not looking back at where they seeded the previous people but are seeding the person that deserves to be there next. They shouldn't get to Max Dean if he's going to be the number 8 seed or 9 and say he's actually better off at 10 and move him down and move somebody else up.

Sure, the seading committee won't do that... But as fans, WE do that!   We always grumble about what a bad draw our guys got (except on the rare occasion they actually get a lucky draw).  Doesn't change anything, but it is what we do. 

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2 minutes ago, ConnorsDad said:

Yes it is rare but if they're doing what they should do, the seeding committee is not looking back at where they seeded the previous people but are seeding the person that deserves to be there next. They shouldn't get to Max Dean if he's going to be the number 8 seed or 9 and say he's actually better off at 10 and move him down and move somebody else up.

I didn't say the fix is in, did I?  It's just an odd statistical occurrence, especially when you add the fact that it is Lehigh and Cornell (their respective arch-rivals) who have, by far, the most guys in the top 1/4 of their brackets.

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4 minutes ago, gimpeltf said:

I only looked at the Lehigh draw last night and noticed that. I wonder how many other EIWA draws are similar. And further, are there other conferences that tend towards certain quadrants?

In the EIWA, no team other than Lehigh and Cornell have more than one wrestling in the top 1/4; Princeton has none.

I suspect this has something to do with the fact that Lehigh and Cornell aren't the top-tier teams (meaning, not going for a team trophy), but are strong enough to have high-quality
guys in abundance.  So they end up in that 8-10 seeding range.  Most of the EIWA doesn't have that.  Unfortunately for Cornell, they got a bunch of those (near-) multiples of 8...

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14 minutes ago, klehner said:

In the EIWA, no team other than Lehigh and Cornell have more than one wrestling in the top 1/4; Princeton has none.

I suspect this has something to do with the fact that Lehigh and Cornell aren't the top-tier teams (meaning, not going for a team trophy), but are strong enough to have high-quality
guys in abundance.  So they end up in that 8-10 seeding range.  Most of the EIWA doesn't have that.  Unfortunately for Cornell, they got a bunch of those (near-) multiples of 8...

Thanks and that's pretty much what I was wondering.

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6 hours ago, klehner said:

I didn't say the fix is in, did I?  It's just an odd statistical occurrence, especially when you add the fact that it is Lehigh and Cornell (their respective arch-rivals) who have, by far, the most guys in the top 1/4 of their brackets.

No you didn't. Did I accuse you of saying the fix was in? I'll save everybody the time and no I didn't. It is an odd occurrence. I completely agree. I was just pointing out that if they were doing their job then it should happen from time to time. If the fix was in, then you would constantly see guys where they shouldn't be seeded both higher and lower. And nice catch by the way.

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9 hours ago, klehner said:

Eight of the 32 wrestlers in the bracket have a chance at meeting the #1 seed at or prior to the quarterfinals (two in the pigtail, two in the R16, four in the quarterfinals).  That's 1/(32/8), or 1/4.  Chances of that happening five times are 1/(4^5), or 1/1024.

Mind blowing you caught that and broke it down. A+ stuff

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Yep...Andy Noel definitely did his best to screw over Cornell. In fact, Andy Noel got himself onto the NCAA Wrestling Championships Committee for the sole, express purpose of screwing over Cornell.

If you believe a darned word of the above sentence, try doing a google search on who Andy Noel is.

(I know, Noel is only one of six members of the committee, and has to leave the room whenever a wrestler from his institution is discussed, but I think you know where I'm going with this)

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On 3/14/2019 at 7:50 AM, klehner said:

Eight of the 32 wrestlers in the bracket have a chance at meeting the #1 seed at or prior to the quarterfinals (two in the pigtail, two in the R16, four in the quarterfinals).  That's 1/(32/8), or 1/4.  Chances of that happening five times are 1/(4^5), or 1/1024.

Your math is off. First off, what you tried to do is only true in a random distribution. These are seeds and not random distribution (like the old international style brackets that were truly a draw, there is no draw in this NCAA bracket, just straight seeding). As a counter-example, take Duke in basketball, by your logic, their getting a 1 or 2 seed 10 years in a row would be (2/16)^10  or 1 in a trillion. But it is not because they have a good a basketball team that consistently earns the top seeds. For Cornell, they just happen to have several guys in the approximately 6-11 range who got 8 or 9 seeds. Not that surprising.

Secondly, your math only accounted for 5 guys who met the criteria. You did not include the 2 that did not fall in that same range. Even if this was a random draw, the odds of 5 of 7 people facing the "top ranked" guy in the first 3 rounds is: (7 choose 5)*(1/4)^5*(3/4)^2 = 1.1% which is still fairly rare, but not as bad 0.1%

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