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Wizard
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April 5th, 2018 at 5:25:10 PM permalink
I have been meaning to do a proper analysis of this question for years. It was a slow day in the Emerald City so I analyzed all 2,142 March Madness games played since 1985 to answer the question. You can find my analysis of this question as well as some common props bet at my new page on Probability of a Perfect Bracket. For those who just want to jump to the answer, following my basic strategy, the probability is 1 in 42,743,890,552.

The question for the poll is what did you think of the page?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
darkoz
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April 5th, 2018 at 5:47:06 PM permalink
Arent these perfect brackets?

[ ]
For Whom the bus tolls; The bus tolls for thee
ThatDonGuy
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April 5th, 2018 at 5:51:27 PM permalink
Rules 20 and 21 are wrong. They should be:

20. The winner of the regional that had the #1 overall team as determined by the NCAA basketball committee when selecting the tournament teams plays the winner of the regional that had the #4 overall team; with the winner advancing.

21. The winners of the two regionals not mentioned in rule 20 play each other, with the winner advancing.

There was a time when the semi-final pairings were on a rotating basis, but this changed a few years ago, presumably because somebody was afraid the top two teams in the country could meet in a semi-final.
EDIT: 2004 was the first year the Final Four was paired based on the relative rankings of the #1 seeds.
Last edited by: ThatDonGuy on Apr 5, 2018
sodawater
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April 5th, 2018 at 5:54:10 PM permalink
I don't understand this paragraph:

Quote:

Warren Buffet has offered $1,000,000 per year, for life, to any employee of his who can fill out a perfect bracket. Warren has about 377,000 employees (source). Assuming each one followed the strategy above, and lived 60 more years, the expected cost to Mr. Buffet would be $529.20.



If everyone follows the strategy above (picking only the higher seeds), Buffett would only have to "sweat" eight possible brackets. So how is it relevant that he has 377,000 employees? Does the $530 expected cost for his promotion factor in that 377,000 employee number in any way? Are you assuming that if multiple employees won with the same bracket (377,000/8), they would each receive the full $60 million annuity?


Edit -- you're also missing the final t in Buffett.
TomG
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April 5th, 2018 at 6:18:41 PM permalink
If we take no-vig money lines to be the correct probabilities, it is almost always less than 10 billion to one, with some years under four billion to one. I'll try to find some online articles I've seen that verify me previous attempts at this

As always: if you disagree that the betting odds are the correct probabilities, why aren't you earning millions betting against the games that offer some of the highest maximums of the year?
TomG
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April 5th, 2018 at 6:21:48 PM permalink
Quote: TomG

If we take no-vig money lines to be the correct probabilities, it is almost always less than 10 billion to one, with some years under four billion to one. I'll try to find some online articles I've seen that verify me previous attempts at this

As always: if you disagree that the betting odds are the correct probabilities, why aren't you earning millions betting against the games that offer some of the highest maximums of the year?



For clarification: even before the first round, most sportsbooks have odds on winning two, three, four, five, or six games for each team
DrawingDead
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April 5th, 2018 at 6:51:00 PM permalink
Quote: darkoz

Arent these perfect brackets?

[ ]

[ x ] No.
Suck dope, watch TV, make up stuff, be somebody on the internet.
Wizard
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April 5th, 2018 at 7:01:48 PM permalink
Quote: ThatDonGuy

Rules 20 and 21 are wrong. They should be:

20. The winner of the regional that had the #1 overall team as determined by the NCAA basketball committee when selecting the tournament teams plays the winner of the regional that had the #4 overall team; with the winner advancing.

21. The winners of the two regionals not mentioned in rule 20 play each other, with the winner advancing.



Good correction, thank you. I copied and pasted your exact words onto the page. Again, thanks. Please add another beer to the number I already owe.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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April 5th, 2018 at 7:09:03 PM permalink
Quote: sodawater

If everyone follows the strategy above (picking only the higher seeds), Buffett would only have to "sweat" eight possible brackets. So how is it relevant that he has 377,000 employees? Does the $530 expected cost for his promotion factor in that 377,000 employee number in any way? Are you assuming that if multiple employees won with the same bracket (377,000/8), they would each receive the full $60 million annuity



First, thanks for the correction on the spelling. Being from the land of the best buffets in the world, I hope that counts as a little bit of an excuse.

What I'm trying to say is that if multiple people picked the same perfect bracket and won, maybe Warren would split the prize. I doubt he ever said what the sharing rule is one this, but if I worked for him, I would want to get all the publicity of the perfect bracket to myself and not share it. My suggestion is what you should do if you don't want to risk sharing a win, for whatever reason you don't want to. I think most people are selfish, including me, and wouldn't want to share in the glory of a perfect bracket.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
onenickelmiracle
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April 5th, 2018 at 7:15:53 PM permalink
Quote: darkoz

Arent these perfect brackets?

[ ]

Too small.
I am a robot.
sodawater
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April 5th, 2018 at 8:19:37 PM permalink
Quote: Wizard


What I'm trying to say is that if multiple people picked the same perfect bracket and won, maybe Warren would split the prize. I doubt he ever said what the sharing rule is one this, but if I worked for him, I would want to get all the publicity of the perfect bracket to myself and not share it. My suggestion is what you should do if you don't want to risk sharing a win, for whatever reason you don't want to. I think most people are selfish, including me, and wouldn't want to share in the glory of a perfect bracket.



Thanks.

So is it the same expected cost of $529, then, if Buffett had just eight employees and they all picked a unique bracket given your strategy?
smoothgrh
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April 5th, 2018 at 8:39:21 PM permalink
Quote:

The winners of steps 20 and 21 will play, the winner winning the tournament.



I'm confused妖oes this mean steps 22 and 23 should be deleted?


Quote:

The probability of the nine seed beating an eight seed is 47.8%



At one point容ither the late '90s or early 2000s葉he ninth seeds actually had a better record against eighth seeds.
Wizard
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April 5th, 2018 at 8:44:51 PM permalink
Quote: sodawater

Thanks.

So is it the same expected cost of $529, then, if Buffett had just eight employees and they all picked a unique bracket given your strategy?



My point with the $529 figure is that his offer gets quoted all over television in early March, when the reward compared to the probability of winning is minimal.

To address your question, let's say Warren had eight employees and they all make it to the Final Four with my strategy. If they really wanted to optimize their chances at money and fame, they should all pick one of the eight different combinations of the Final Four. Does that answer your question?
Last edited by: Wizard on Apr 9, 2018
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
djatc
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April 6th, 2018 at 4:55:07 AM permalink
I actually had an interesting conversation regarding this, and said that whoever can pick a perfect bracket will be extremely famous, if not get their 15 minutes of fame on news channels, etc.

I don't follow NCAA basketball too much, what's the closest someone has got to a perfect bracket?
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darkoz
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April 6th, 2018 at 8:12:50 AM permalink
Quote: onenickelmiracle

Quote: darkoz

Arent these perfect brackets?

[ ]

Too small.



Well I'm jewish

Its about the right size to me
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DJTeddyBear
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April 6th, 2018 at 8:12:53 AM permalink
Rules 22 & 23 seem unnecesssary.

Since they say the winners advance, but rule 24 says the winners of 20 & 21 play each other, gotta wonder where the winners of 22 & 23 advance to...
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
ThatDonGuy
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smoothgrh
April 6th, 2018 at 2:56:56 PM permalink
Quote: smoothgrh

I'm confused妖oes this mean steps 22 and 23 should be deleted?


22 and 23 should no longer be there, and 24 should be renumbered 22.
smoothgrh
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April 6th, 2018 at 3:54:56 PM permalink
Quote: DJTeddyBear


Since they say the winners advance, but rule 24 says the winners of 20 & 21 play each other, gotta wonder where the winners of 22 & 23 advance to...



They used to play a third place game!

I kinda liked that預 bronze medal! But I also see the simplicity and elegance of "lose and you're done."
TomG
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April 6th, 2018 at 4:53:51 PM permalink
http://fivethirtyeight.com/features/the-odds-youll-fill-out-a-perfect-bracket/

Says the odds of the favorites winning every game were close to one in two billion the year Kentucky was around a 35% favorite to win the championship. Most years the favorite is under 15% and the odds be higher.

(Of course this only applies if there is someone who implements the just pick the favorite in every game strategy -- if no one like that yet exists, then I next year I volunteer as tribute)
ThatDonGuy
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April 6th, 2018 at 7:31:24 PM permalink
Quote: smoothgrh

Quote: DJTeddyBear


Since they say the winners advance, but rule 24 says the winners of 20 & 21 play each other, gotta wonder where the winners of 22 & 23 advance to...



They used to play a third place game!

I kinda liked that預 bronze medal! But I also see the simplicity and elegance of "lose and you're done."


The last third place game was played the day President Reagan was shot in 1981.

Not only have they gotten rid of all third place games - baseball and softball had them at one point as well - but now, in sports like wrestling and swimming & diving that are points based, they give out fourth place team trophies (that are the same color as the third place ones), since they now give out four trophies in basketball.
smoothgrh
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April 7th, 2018 at 10:46:13 AM permalink
Quote: ThatDonGuy




Not only have they gotten rid of all third place games - baseball and softball had them at one point as well - but now, in sports like wrestling and swimming & diving that are points based, they give out fourth place team trophies (that are the same color as the third place ones), since they now give out four trophies in basketball.



World Cup Soccer still has the third place match, which shows the obvious superiority of American sports structures! USA! USA! USA!!!

Edit: We won't count the NIT.

Edit: Even the NIT dropped its third-place game!
Wizard
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April 9th, 2018 at 6:53:37 AM permalink
Quote: DJTeddyBear

Rules 22 & 23 seem unnecesssary.



You're right. Thank you for the correction.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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April 20th, 2018 at 10:13:08 PM permalink
I just bought a "creative pen tablet," if that is the right term, for the device that uses a pen instead of a mouse, to make whiteboard style videos. I then had to get two pieces of software to get from there to a video. That said, this video is pretty much a learning exercise in using the tablet and software.

Yes, I know it is a steaming pile of mule poop. So, please take it easy on me. With all the apologies out of the way, here is my first in what I'll my "Wizard Academy" videos, a respectful tribute to the Kahn Academy.


Direct link
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
TomG
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April 21st, 2018 at 11:07:45 AM permalink
Quote: Wizard

Yes, I know it is a steaming pile of mule poop.



It was close to being very good. Just very unpolished

It seemed like the introduction was trying to target laymen who are coming at this with very little background and need a lot of explaining, then jumped right into the formulas that would only make sense to someone with a well-developed understanding of how to solve these types of problems.

-----

Something this makes me think of is somehow creating random "quick-picks" to fill out a bracket, where each game is weighted. When the three seed plays the 14 seed, there is an 85% chance your bracket takes the three seed and 15% chance it gets the 14 seed. I'm sure there is already something like this, and should only take a few seconds to complete one. (The ones on ESPN take a few minutes to fill out and become tedious and humans can't come up with any degree of randomness on our own). If enough people kept producing random brackets using historical weights over four days would it be reasonable to think we could eventually see a perfect bracket?
Wizard
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April 21st, 2018 at 2:32:09 PM permalink
Thanks Tom for the comments. I am sure I'll do a better version after the 2019 season.

As to the first point, maybe I'm speaking over people's heads again, but it all seemed very simple to me. In my many hundreds of posts on the "two dice problem," I'm not sure that I converted anybody formerly in the 1/6 camp to the 1/11 camp. I'm not sure if I didn't explain it well or those in the 1/6 camp were just stubborn and refused to listen.

I probably should have made the point that if every higher seeded team won, a lot of people following this strategy would likely have a perfect bracket. For that reason, it would probably be good to pick some 9 and 10 seeds, just to deviate from the pack a bit. Sometimes these lower seeded teams are favored to win too. It is not difficult to look up the odds of every game in round 1. I'll emphasize that when I redo this in 2019.

I also thought of doing a method of applying a weight to each seed, where the probability of a team winning would be proportional to its weight. However, I thought it would muddy the waters and actually be less effective.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Keeneone
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April 21st, 2018 at 5:22:17 PM permalink
GlenG posted this video (with lots of numbers/charts etc.) in the WOV NCCA Challenge thread. You may have already seen it, but if not here it is:

TomG
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April 21st, 2018 at 5:26:57 PM permalink
Quote: Wizard

I also thought of doing a method of applying a weight to each seed, where the probability of a team winning would be proportional to its weight. However, I thought it would muddy the waters and actually be less effective.



Any one bracket filled out that way would be less effective. But lots of people fill out lots of them. If you did 10 per day from Sunday through Thursday, shouldn't that cut your odds against from roughly 50 billion to 1 billion?

-----

One thing about Khan, is that from what I've seen it's focused on educating people on math. Why not entertain people with math? This topic might be pretty cool with a minutephysics type video. Unfortunately, you'll be limited by skills in video production:

an impossible bet? https://www.youtube.com/watch?v=eivGlBKlK6M
7craps
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March 26th, 2019 at 4:35:16 PM permalink
Quote: Wizard

Thanks Tom for the comments. I am sure I'll do a better version after the 2019 season.

Man Picks Perfect NCAA Tourney Bracket Heading Into Sweet 16

https://www.nytimes.com/aponline/2019/03/26/us/ap-bkc-ncaa-perfect-bracket.html
Gregg Nigl of Columbus, Ohio
has made history with a March Madness bracket that's perfect through 48 games on the NCAA.com's "Bracket Challenge," according to the NCAA.

https://fivethirtyeight.com/features/the-odds-youll-fill-out-a-perfect-bracket/
"But even if you use a more sophisticated picking method like, say, FiveThirtyEight痴 March Madness predictions the chances of perfection are still in the neighborhood of 1 in 2 billion, depending on the year."

I lost the very 1st game played
and am going to be watching the final 15 games (resumes Thursday)
winsome johnny (not Win some johnny)
onenickelmiracle
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March 26th, 2019 at 6:00:54 PM permalink
What is the probability the entire tournament could be fixed, that lowers the odds of a perfect bracket. Only a few games have to be fixed based on the odds.
I am a robot.
Ayecarumba
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March 26th, 2019 at 9:19:43 PM permalink
The biggest problem I have each year is picking the 12 or 13 seed that will advance, busting the bracket of everybody who knows about college basketball and everybody who goes with the higher ranking.

I wonder how many perfect brackets were broken by UC Irvine this year?
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Wizard
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April 9th, 2019 at 2:54:23 PM permalink
I just updated my March Madness page with the 2019 data. With the new data, following the Wizard basic strategy, the probability of a perfect bracket has dropped to 1 in 55,380,246,801. It was 1 in 42,743,890,552 after the 2018 season.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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April 9th, 2019 at 4:06:52 PM permalink
Here are some comments on this 35th March Madness season:

  • After the first round, narrowing the field from 64 to 32, the average seed was exactly 6. As a basis of comparison, since the tournament started in 1985, the average is 5.81.
  • The biggest upset in the first round (based only on the seeds) was 13-seed U.C. Irvine (yay!) beating the 4-seed Kansas State.
  • In the second round, narrowing the file from 32 to 16, favorites did very well. In all 16 games, the higher seeded team won 15 times. The only upset was 5-seed Auburn beating 4-seed University of Kansas. Again, a favored Kansas school losing.
  • After the second round, the average seed was 3.06, compared to an average of 4.51. This ties a record with season 1 for the lowest average seed number after round 2. It also reverses a trend of lower seeded teams (or higher seed numbers) making it further in the tournament. From 2008 to 2018 the average seed after the second round was always 5 or more.
  • After the second round, 15 of the 16 surviving teams were a 1 to 5 seed. The only exception was 12-seed University of Oregon surviving.
  • After the third round, narrowing the field from 16 to 8, the average remaining seed was 2.25. On average it is 3.18. 12-seed Oregon got knocked out so all eight remaining teams were seeded 1 to 5. Three of the four number one seeds survived to this point.
  • The fourth round, narrowing the field from 8 to 4, saw three out of four upsets. A 2-seed beat a 1-seed, a 3-seed beat a 1-seed, and a 5-seed beat a 2-seed. Surviving to the Final Four were a 2, 1, 3, and 5 seeds. The average seed surviving to the Final Four was 2.75. The average at this point is 2.82, so the trend of favorites winning almost every game in rounds 2 and 3, finally ended. I usually root for the underdog, so I like to see this.
  • The fifth round, narrowing the field from 4 to 2, saw 1-seed Virginia beating 5-seed Auburn and 3-seed Texas Tech beating 2-seed Michigan State. The average seed remaining was obviously 2. The average at this point is 2.33.
  • As we know, the final game saw 1-seed University of Virginia beating 3-seed Texas Tech. This is the third year in a row a 1-seed has won the whole enchilada. Based on the 35 seasons played to date, a 1-seed wins 62.9% of the time.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Cheeks
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March 19th, 2021 at 7:25:27 AM permalink
I created an excel model to try and remove all human bias. It was my attempt at coming up with something based on the prior probabilities of an upset that would differentiate my picks from others'.
Press F9 and you get a new, printable bracket that is populated by seed #s for each matchup. So if a #1 is playing a #1 the user has to choose the team.

For each matchup, a random number is generated and if it falls in the probability of an upset then the underdog (based on seed) wins. For any matchup with minimal history, I use the average of an upset by the difference in seed #s. For example a 9 seed has played a 2 seed only twice. But if you sum all of the games with a difference of seven, the probability of an upset is .285.

For differences of 10 and 12, I interpolated since there are only 13 games total.

When I made picks myself I would always do horribly. I've improved substantially in pools that reward upsets.

Just thought i'd share this. I welcome any comments!
Cheers, Cheeks
gordonm888
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March 19th, 2021 at 7:55:42 AM permalink
The ESPN Tournament Bracket challenge allows you to autofill a bracket randomly according to one of several different ways:

Each matchup in the bracket you generate is given win/loss percentages according to:

1. Seed, or
2. BPI (ESPN's power rating index accounting for Win/Loss, opponents strength, win margin and injuries), or
3. Completely random (50/50)

However, the win/loss percentages are created, the autofill routine uses an RNG to pick a winner for each matchup.

ESPN allows each person to fill out up to 25 brackets. I filled out 50 brackets for my wife and I and about 35 of them were generated using autofill based on BPI.

When filling put large numbers of brackets my goal was not to place a lot of brackets in the top 10% - it was to maximize our chances of placing a bracket in the top 0.1%.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
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