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Bracketology: Odds of Deep Runs or Early Outs

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January 29th, 2013 at 4:56 PM
#1
dmonet
Joined: 09/17/2010
MGoPoints: 112
Bracketology: Odds of Deep Runs or Early Outs

With all the talk about seedings and potential national championship runs, I've been curious about what the odds look like for Michigan getting to the Final Four / Championship Game / Winning it all.

I decided to take ESPN's bracket and calculate the odds using KenPom's Pyth score to simulate the bracket.  The percentage in each column reflects the odds of the team reaching that round given the opponents they are likely to face along the way.

The percentages are calculated using a composite of a team's odds of winning against all possible opponents they might face in a given round rather than just against the team they are most likely to see.  I think this gives a better overall picture.

Here's what I have:

    Odds of making it to Round #:          
    Round of 32 Sweet 16 Elite 8 Final 4 Title Game Champion
  SOUTH (North Texas)            
1 Kansas 94.2% 49.6% 39.7% 23.8% 8.1% 3.9%
16 Southern 5.8% 0.4% 0.1% 0.0% 0.0% 0.0%
8 Wisconsin 38.3% 16.5% 12.1% 6.1% 1.6% 0.6%
9 Pittsburgh 61.7% 33.5% 27.3% 16.8% 6.0% 3.0%
               
5 North Carolina St. 56.8% 32.7% 7.8% 2.5% 0.4% 0.1%
12 La Salle 43.2% 22.1% 4.2% 1.1% 0.1% 0.0%
4 New Mexico 65.4% 33.1% 7.3% 2.2% 0.3% 0.1%
13 Louisiana Tech 34.6% 12.1% 1.6% 0.3% 0.0% 0.0%
               
6 Ucla 51.1% 20.3% 5.9% 1.7% 0.3% 0.1%
11 Iowa St. 48.9% 18.9% 5.3% 1.5% 0.2% 0.0%
3 Michigan St. 83.3% 56.0% 24.5% 10.7% 2.6% 0.9%
14 Harvard 16.7% 4.8% 0.7% 0.1% 0.0% 0.0%
               
7 Mississippi 65.1% 20.3% 10.1% 3.6% 0.7% 0.2%
10 Memphis 34.9% 7.2% 2.5% 0.6% 0.1% 0.0%
2 Syracuse 93.9% 71.4% 50.8% 29.1% 10.0% 4.8%
15 Northeastern 6.1% 1.1% 0.2% 0.0% 0.0% 0.0%
               
  WEST (Los Angeles)            
1 Florida 98.7% 91.2% 78.5% 67.0% 54.6% 41.7%
16 Montana 1.3% 0.2% 0.0% 0.0% 0.0% 0.0%
8 Georgetown 48.9% 4.1% 1.5% 0.5% 0.1% 0.0%
9 Colorado 51.1% 4.4% 1.6% 0.5% 0.2% 0.0%
               
5 Wichita St. 70.1% 29.4% 4.5% 1.9% 0.7% 0.2%
12 Maryland 29.9% 7.3% 0.6% 0.1% 0.0% 0.0%
4 Ohio St. 76.7% 53.5% 12.4% 7.1% 3.6% 1.6%
13 Akron 23.3% 9.8% 1.0% 0.3% 0.1% 0.0%
               
6 Nevada Las Vegas 64.1% 25.9% 10.4% 1.7% 0.6% 0.2%
11 Illinois 35.9% 10.3% 2.9% 0.3% 0.1% 0.0%
3 Miami Fl 87.6% 60.7% 33.4% 8.3% 4.0% 1.6%
14 Davidson 12.4% 3.1% 0.5% 0.0% 0.0% 0.0%
               
7 Kansas St. 37.9% 11.3% 3.9% 0.5% 0.1% 0.0%
10 Kentucky 62.1% 24.8% 11.4% 2.0% 0.7% 0.2%
2 Arizona 91.6% 62.5% 37.3% 9.7% 4.8% 2.0%
15 Niagara 8.4% 1.4% 0.2% 0.0% 0.0% 0.0%
               
  MIDWEST (Indianapolis)            
1 Michigan 97.0% 82.3% 61.1% 38.1% 22.3% 9.8%
16 Charleston Southern 3.0% 0.5% 0.0% 0.0% 0.0% 0.0%
8 Notre Dame 49.5% 8.5% 3.0% 0.7% 0.2% 0.0%
9 North Carolina 50.5% 8.8% 3.1% 0.8% 0.2% 0.0%
               
5 Creighton 68.3% 47.4% 19.2% 8.8% 3.7% 1.1%
12 Southern Mississippi 31.7% 16.3% 4.2% 1.2% 0.3% 0.1%
4 Oregon 66.1% 27.2% 7.7% 2.5% 0.7% 0.1%
13 Stephen F. Austin 33.9% 9.1% 1.6% 0.3% 0.1% 0.0%
               
6 San Diego St. 56.3% 17.1% 7.2% 2.4% 0.7% 0.2%
11 Belmont 43.7% 11.2% 4.1% 1.1% 0.3% 0.1%
3 Louisville 89.9% 68.9% 46.4% 26.5% 14.8% 6.2%
14 Stony Brook 10.1% 2.7% 0.6% 0.1% 0.0% 0.0%
               
7 Virginia Commonwealth 67.8% 28.6% 10.6% 3.7% 1.3% 0.3%
10 Oklahoma 32.2% 8.7% 2.0% 0.4% 0.1% 0.0%
2 Gonzaga 92.4% 61.5% 29.1% 13.3% 5.9% 1.9%
15 Long Beach St. 7.6% 1.1% 0.1% 0.0% 0.0% 0.0%
               
  EAST (Washington, D.C.)            
1 Duke 94.9% 70.7% 46.0% 26.9% 14.7% 6.0%
16 Western Illinois 5.1% 0.7% 0.1% 0.0% 0.0% 0.0%
8 Baylor 44.5% 11.7% 4.4% 1.4% 0.4% 0.1%
9 Colorado St. 55.5% 16.9% 7.1% 2.7% 0.9% 0.2%
               
5 Minnesota 85.4% 58.9% 29.2% 15.0% 7.0% 2.4%
12 Temple 14.6% 4.3% 0.7% 0.1% 0.0% 0.0%
4 Cincinnati 78.0% 32.6% 11.9% 4.6% 1.5% 0.4%
13 Lehigh 22.0% 4.1% 0.6% 0.1% 0.0% 0.0%
               
6 Marquette 55.9% 31.3% 8.2% 2.4% 0.6% 0.1%
11 Middle Tennessee 44.1% 22.2% 4.9% 1.2% 0.3% 0.0%
3 Butler 70.5% 37.1% 9.7% 2.8% 0.7% 0.1%
14 Valparaiso 29.5% 9.4% 1.3% 0.2% 0.0% 0.0%
               
7 Missouri 39.5% 7.9% 4.0% 1.1% 0.3% 0.0%
10 Oklahoma St. 60.5% 16.3% 9.9% 3.5% 1.1% 0.2%
2 Indiana 96.1% 75.2% 62.0% 38.1% 22.0% 9.6%
15 Florida Gulf Coast 3.9% 0.5% 0.1% 0.0% 0.0% 0.0%

Let me know what you think

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January 29th, 2013 at 5:03 PM
#2
orobs
Joined: 10/03/2010
MGoPoints: 3205
41% chance for florida to win

41% chance for florida to win it all?  the fuck?

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January 29th, 2013 at 5:07 PM
(Reply to #2) #3
anwonadell
Joined: 11/19/2009
MGoPoints: 386
High number...

But as Ace and Brian have mentioned, KenPom does have them far and away the best performing team, statistically speaking. Since the KenPom data was used to construct these percentages, it's not incredibly surprising.

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January 29th, 2013 at 5:26 PM
(Reply to #4) #4
orobs
Joined: 10/03/2010
MGoPoints: 3205
It is not only surprising, it

 In the last 4 years, 75% of #1 seeds haven't even made the final four.  And they are saying that florida would win it all nearly 1 in 2 times? 

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January 29th, 2013 at 6:47 PM
(Reply to #5) #5
Syyk
Syyk's picture
Joined: 01/26/2009
MGoPoints: 2023
Yeah, it's a ridiculous

Yeah, it's a ridiculous percentage, but no one is saying that Florida would win 41.7% of the time. It's based on a statistical methodology that's helpful as a guide, but can only be a guide, given the imperfection of the stats put into it.

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January 29th, 2013 at 8:46 PM
(Reply to #4) #6
MGoSteelers
MGoSteelers's picture
Joined: 06/19/2011
MGoPoints: 3561
LRMC has been my go-to

LRMC has been my go-to rankings the past couple years.  It's kind of mathy but it's shown to be more accurate than RPI/KenPom

 

http://www2.isye.gatech.edu/~jsokol/lrmc/

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January 29th, 2013 at 5:37 PM
(Reply to #2) #7
dmonet
Joined: 09/17/2010
MGoPoints: 112
I totally agree that

I totally agree that Florida's chances are pretty ridiculous and that they'll come down as the year goes on. I'll also have to check the math to make sure all the formulas are correct, but I'm pretty sure they are.

Just thought it would be interesting to look at how the odds broke down given this is the first time in a long time Michigan has been poised for a deep tourney run. This just emphasizes how much luck is involved.

Also, if there is any interest to see this regularly, it's pretty easy for to update.

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January 29th, 2013 at 5:07 PM
#8
mGrowOld
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Joined: 10/04/2010
MGoPoints: 111756
I think that's math-speak for

I think that's math-speak for "their bracket sucks".

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January 29th, 2013 at 5:26 PM
#9
notYOURmom
Joined: 03/13/2009
MGoPoints: 1406
Why

Do the "percent chance to be in title game" column adds up to Waaaaaaay more than 100% how can that be; I realize there are two teams in the title game but any given team can only be on one side of the bracket - they don't get a chance at the other side

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January 29th, 2013 at 5:32 PM
(Reply to #6) #10
Trebor
Trebor's picture
Joined: 06/30/2008
MGoPoints: 3707
Well, there's a 100% chance a

Well, there's a 100% chance a team emerges from the South/West half of the bracket and a 100% chance that a team emerges from the Midwest/East half of the bracket. So the total should be 200% (but only 100% for the top half and 100% for the bottom half, which by my quick excel math is the case).

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January 29th, 2013 at 5:34 PM
(Reply to #7) #11
Blue_MQT
Joined: 10/24/2011
MGoPoints: 219
Exactly. The total % for each

Exactly. The total % for each column adds up to the number of teams in that round x 100(%). That said, it looks like there are some rounding issues that make some columns add up to slightly more or less than their required amount, but nothing unusual.

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January 29th, 2013 at 6:15 PM
(Reply to #6) #12
oriental andrew
oriental andrew's picture
Joined: 06/30/2008
MGoPoints: 19793
because you're reading the table wrong

The column headings are a little misleading.  OP made titled it such that the header indicates the next round the winner would advance to.  For instance, Kansas vs. Southern is the first round, but would advance to the round of 32, per the column header.  So the Title Game column indicates that the winner in that column would advance to the title game.  The last column indicates that the winner would be the Champion. 

 

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January 29th, 2013 at 5:36 PM
#13
MichGoBlue858
MichGoBlue858's picture
Joined: 11/20/2010
MGoPoints: 1889
How are you posting with only

How are you posting with only 7 points?

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January 29th, 2013 at 5:38 PM
(Reply to #10) #14
dmonet
Joined: 09/17/2010
MGoPoints: 112
Justingoblue grabbed it from

Justingoblue grabbed it from another thread

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January 29th, 2013 at 5:42 PM
(Reply to #12) #15
ish
Joined: 06/30/2008
MGoPoints: 13990
you're obviously a valuable

you're obviously a valuable contributor.  i wish upvoting you would give you the points necessary to post.

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January 29th, 2013 at 6:01 PM
(Reply to #13) #16
justingoblue
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Joined: 11/16/2010
MGoPoints: 29685
He's getting them.

I held off at first because of a real lack of posting history (three posts before the OP contents, I think), but everything looks pretty good, and the interest in posting updates didn't hurt either.

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January 29th, 2013 at 6:13 PM
(Reply to #20) #17
Smash Lampjaw
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Joined: 11/10/2011
MGoPoints: 2025
off-thread topic

JGB: Where is MGoSoftball with the news that Michigan is preseason #13?

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January 29th, 2013 at 6:19 PM
(Reply to #24) #18
justingoblue
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Joined: 11/16/2010
MGoPoints: 29685
No idea.

I know I'm getting excited for softball season, though.

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January 29th, 2013 at 5:56 PM
(Reply to #12) #19
MichGoBlue858
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Joined: 11/20/2010
MGoPoints: 1889
Ah, didn't realize that.

Ah, didn't realize that.

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January 29th, 2013 at 5:44 PM
(Reply to #10) #20
eschaton811ydau
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Joined: 11/03/2011
MGoPoints: 419
That's the number you choose

That's the number you choose to question?

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January 29th, 2013 at 5:52 PM
#21
Nick
Nick's picture
Joined: 06/30/2008
MGoPoints: 1094
The problem with this analysis

Is that these probabilities of reaching each specific round are determined by the pairings in this bracket.

The problem with that is teams like Wisconsin and Pitt are underseeded compared to their rank on Kenpom.

So then Kansas gets matched up with the winner of Wisc/Pitt, a matchup that is unlikely to happen ( as is any specific matchup at this point).

The result is Kansas has under 50% chance of winning two games in this study, solely because of their tough matchup in this mock bracket.

It would be more representative to run a simulation with each teams pythagorean rating v. an average pyth rating for the opponent from each 'pod' in prior tournaments.

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January 29th, 2013 at 5:58 PM
(Reply to #15) #22
dmonet
Joined: 09/17/2010
MGoPoints: 112
Definitely. I don't have

Definitely. I don't have access to that data but I'd definitely be interested in seeing that. I started out just playing with the bracket and it ended up looking like something interesting so I threw it up here.

What you mention would do a much better job of answering the question that I was originally curios about. I could also look at what the odds would be using a snake setup based strictly on kenpom or based on the averages kenpom ranking for each seed per the espn bracket.

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January 29th, 2013 at 6:10 PM
(Reply to #19) #23
Nick
Nick's picture
Joined: 06/30/2008
MGoPoints: 1094
Yeah im not mad or anything that you did it

Just pointing out that with this methodology, the matchups can create some unintuitive results.

People should view these odds as a decent picture of how this specific bracket would play out, but not exactly take them as representative of how the average bracket out of a huge sample of unique brackets would play out.

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January 29th, 2013 at 5:53 PM
#24
ReadYourGuard
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Joined: 08/21/2008
MGoPoints: 33682
I only glanced at the

I only glanced at the brackets, but I'd give a handsome sum of money to Mott's if Harvard played and beat MSU in the first round.

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January 29th, 2013 at 6:03 PM
#25
StateSmells
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Joined: 08/23/2011
MGoPoints: 222
No Way

The 16 seeds have 1, 3, 5 and 6 percent chance of beating their respective 1 seeds. 

If that was at all realistic and roughly representative of probabilities for past years, we should have seen a 16 beat a 1 by now.

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January 29th, 2013 at 6:14 PM
(Reply to #21) #26
swan flu
swan flu's picture
Joined: 08/16/2010
MGoPoints: 8151
1) its based on specific

1) its based on specific Kenpom match-ups, not previous performance.

2) dont fall victim to the gambler's fallacy.  If you flip a coin 100 times and it lands 'heads' 60 times, the probability of the next coin flip being a 'heads' is 50%, not 60% as your point of view seems to indicate. 

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January 29th, 2013 at 7:34 PM
(Reply to #25) #27
LJ
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I don't think he was using

I don't think he was using the gambler's fallacy--he was just saying that if an average 16 would really beat an average 1 about 3% of the time, it would be very unlikely to have gone so many tournaments without a 16 ever beating a 1.  Thus, the numbers here are probably being too generous to the 16 seeds, likely for the reason explained by the comment below (the 16 seeds will actually be worse than these teams).

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January 29th, 2013 at 6:19 PM
(Reply to #21) #28
rdlwolverine
Joined: 09/28/2008
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In the actual tournament, the

In the actual tournament, the 16 seeds will not be as good as the 16 seeds in this bracket.  Some low major schools will win their conference tournaments and grab autobids from teams that are higher ranked on Kenpom.   Those teams will have much lower chances of pulling the upset than those used here.

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January 29th, 2013 at 6:09 PM
#29
swan flu
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The nit-picking geek in me is

The nit-picking geek in me is annoyed at so many 0.0% probabilities... they really should be <0.1% Since it is NOT mathematically impossible for a 16 seed to win three games.

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January 29th, 2013 at 6:37 PM
#30
LSAClassOf2000
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For Some Comparison...

If I read this correctly, this would project the following - per this table, the chances of the champion coming from the South bracket would be about 14% and the chances of the champion coming from the West bracket, by this figuring, to be about 48%. The Midwest and East brackets would sit around 19% each.

It is interesting that - in this projection - one bracket would be that much more imbalanced than the other three by appearances. Even though there are only 3-4 teams in each bracket which would have a >1% chance of being the champion, nobody has quite the easy run like Florida would in this scenario. The two that would come close, at least until later rounds, would be Syracuse and Lousiville..,perhaps Michigan and Indiana too. 

We can compare some of the results with TeamRanking's algorithm. They only discuss the projections for the Sweet Sixteen and the Final Four as well as the  Champion, but the ten most likely to win it all, in their view, are as follows:

 



Team Sweet 16 Final 4 Champ%
Florida 83% 50% 24.70%
Indiana 76% 38% 14.90%
Duke 67% 26% 7.20%
Kansas 68% 27% 7.00%
Louisville 65% 24% 6.80%
Syracuse 63% 21% 5.10%
Michigan 62% 20% 4.70%
Gonzaga 56% 15% 3.10%
Arizona 57% 16% 3.00%
Pittsburgh 42% 12% 2.70%

Interesting to think about this, however, and thanks to the OP for sharing this work.

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January 29th, 2013 at 6:37 PM
(Reply to #29) #31
Nick
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I have been looking at those TeamRankings projections lately

and I have no freaking clue what numbers they are using to conclude Indiana is 3 to 4 times more likely than Michigan to win the tournament.

It stems from them projecting Indiana to win the Big Ten and get a #1 seed much more often than Michigan, but given the performances of the two teams so far, I have no clue why they project Indiana get get a better seed than Michigan.

Michigan's advanced stats are about equal to Indiana and inferior to only Florida.  I would imagine they're over-weighting defensive efficiency or something, but regardless I think their formula is whack.

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January 29th, 2013 at 6:52 PM
(Reply to #30) #32
swan flu
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Joined: 08/16/2010
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I don't know what formula

I don't know what formula they used but your point about them projecting Indiana to win the big ten by a slight margin could be a culprit, it could be exponentiating the small difference between the two teams unfairly. In a sense they could be using the same data point multiple times which would result in falsely high confidence?

Or i could be monstrously mistaken, it has even a few years since I took stats.

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January 29th, 2013 at 6:45 PM
(Reply to #29) #33
Nothsa
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It is not due to bracket strength - it's due to Florida.

KenPom's numbers for Florida are ridiculous, though that's because Florida is absolutely blowing the doors off the SEC. The Gators played a pretty solid preseason slate and, aside from two pretty close non-home losses, have been crushing opponents. The last time they won by less than 15 was... well, last March. They've won 16 games by at least 15 (and often 20+) points.

Are they really that dominant? Hard to say until tournament time, given the quality of the SEC, but this guy is going by Pomeroy's numbers, and that's why they have the big numbers.

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January 30th, 2013 at 5:18 AM
(Reply to #29) #34
kevin holt
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I really hope Florida doesn't

I really hope Florida doesn't get an easy road, since they got one their entire conference schedule.

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January 29th, 2013 at 7:29 PM
#35
DH16
Joined: 11/19/2012
MGoPoints: 586
Past Statistics?

I wonder if there was any way to do this with past tournaments, with the probability all calculated before the tournament started, and then after the tournament see how well the predicitions held up. I think it would be interesting to see how well these TeamRanking predictions hold up, and other things like how improbable some of the cinderellas are or if some teams perpetually choke away good odds/make a habit of winning with bad odds.

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January 29th, 2013 at 7:39 PM
#36
snarling wolverine
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Given that no #16 seed has

Given that no #16 seed has ever beaten a #1 (and there have been over 100 of these 1-vs-16 matchups since 1985), shouldn't the #1 seeds each have like a 99.9% chance of winning the first round?  

 

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January 29th, 2013 at 8:05 PM
(Reply to #36) #37
eschaton811ydau
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Joined: 11/03/2011
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Depends on if you're in the

Depends on if you're in the Bayesian camp or the Frequentist

 

long live the Bayesian Conspiracy

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January 30th, 2013 at 6:31 AM
#38
Yeoman
Joined: 06/08/2011
MGoPoints: 13242
This seems to be KenPom specific.

KenPom has Florida 7 1/2 points better than the next best team (Michigan), which looks to be the biggest spread there's ever been between #1 and #2 in their eleven years of data.

At Massey, that difference is a little less than 2; Sagarin has it at about 2 1/2 (Sag has Indiana and Louisville ahead of Michigan). I'm using the Power and Predictor ratings here, not the versions with an ELO result built in, since those are the versions comparable to KenPom and they're the one's established as the best predictors.

To put it another way, KenPom doesn't think anyone in the country would be less than a 7-point underdog to Florida; Sagarin thinks there are 16 schools within seven points, Massey thinks there are four.

That seems to be a consistent trend through the years, as far as I can tell. KenPom consistently thinkis the strongest teams have distanced themselves by larger spreads from the teams below them.

Does anyone know enough about the systems to know why this would be? Or have any data on how the various systems have done with their predictions, historically?

 

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