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Posted

In the other thread on Pablo rankings, I talked about how you can calculate the probability of a wrestler winning if you know the rating difference between them.  In the post, I just showed the plot and corresponding line, but ultimately, there is an analytical relationship that is easily calculated.  So let's calculate it.

Given the tournament brackets, it is possible to calculate the probability that a wrestler advances given their opponent.  So we can look at the 125 prelim match between Weiand and Milani.  Weiand has a Pablo rating of 5634 and Milani is rated 5968.  So according to Pablo ratings, Milani has a 59% chance of winning that match.

For the next round, the winner will face Lilledahl, who is rated 8500.  Therefore, Lilledahl has a 97% chance of beating Weiand and a 95% chance of beating Milani.  But there is only a 41% chance of wrestling Weiland and a 59% chance it is Milani.  It's possible to combine these all together, though, to come up with a probability of 96% for Lilledahl to advance out of the first round.  Then you can do that for the next round, taking into account the ratings of Gallagher and West and the probability they advance, and then the next round, and then next round, etc, to get the probability that a given wrestler advances.

Well, I've done that.  For all the wrestlers in all the rounds in all the weights in the NCAA championship.  So in this thread, I'm going to give you the probabilities that a given wrestler a) makes it to the Finals, and then b) wins the finals, according to Pablo rankings.

Again, these are calculated by using the probability of advancing through the championship bracket, and so the final probability is going to be based on 1) how good the wrestler is, and 2) the matchups he will face along the way.  There are plenty of examples where a higher ranked wrestler does not have a higher probability of winning the championship due to a tougher path.  With a lot more work, it's possible to isolate the wrestler quality from the path, but that takes a lot more work that I'm not going to do.

I'm listing the wrestlers in order of most likely to least likely to win.  You will have envision how that works in the brackets on your own.  So posts below are the probabilities of making the finals and winning it all.

  • Bob 1
Posted (edited)
125 Finals Winner
125:Purdue_Matt Ramos 0.486 0.362
125:Penn St_Luke Lilledahl 0.345 0.159
125:Arizona St_Richard Figueroa 0.207 0.079
125:Virginia Tech_Eddie Ventresca 0.132 0.070
125:Oklahoma St_Troy Spratley 0.122 0.068
125:Wisconsin_Nicolar Rivera 0.119 0.067
125:West Virginia_Jett Strickenberger 0.098 0.053
125:Nebraska_Caleb Smith 0.136 0.046
125:NC St_Vince Robinson 0.123 0.040
125:Lehigh_Sheldon Seymour 0.058 0.015
125:Northern Colorado_Stevo Poulin 0.025 0.010
125:Ohio St_Brendan McCrone 0.034 0.008
125:Rutgers_Dean Peterson 0.035 0.008
125:Princeton_Marc-Anthony McGowan 0.021 0.004
125:Pennsylvania_Max Gallagher 0.017 0.003
125:Northern Illinois_Blake West 0.012 0.002
125:Oklahoma_Antonio Lorenzo 0.009 0.001
125:Oregon St_Maximo Renteria 0.005 0.001
125:North Carolina_Spencer Moore 0.005 0.001
125:Indiana_Jacob Moran 0.004 0.001
125:Minnesota_Cooper Flynn 0.003 0.001
125:Army_Charlie Farmer 0.001 0.000
125:South Dakota St_Tanner Jordan 0.001 0.000
125:Northern Iowa_Trever Anderson 0.001 0.000
125:Iowa_Joey Cruz 0.001 0.000
125:North Dakota St_tristan daugherty 0.000 0.000
125:Cal Poly_Koda Holeman 0.000 0.000
125:Pittsburgh_Nick Babin 0.000 0.000
125:Virginia_Keyveon Roller 0.000 0.000
125:CSU Bakersfield_Richard Castro-Sandoval 0.000 0.000
125:Cornell_Marcello Milani 0.000 0.000
125:The Citadel_Gylon Sims 0.000 0.000
125:Michigan St_Caleb Weiand 0.000 0.000
Edited by Pablo
Posted (edited)
133 Finals Winner
133:Illinois_Lucas Byrd 0.433 0.293
133:Iowa_Drake Ayala 0.285 0.156
133:Little Rock_Nasir Bailey 0.264 0.143
133:Northern Colorado_Dominick Serrano 0.159 0.080
133:Virginia Tech_Connor McGonagle 0.118 0.052
133:Ohio St_Nic Bouzakis 0.093 0.038
133:Cal Poly_Zeth Romney 0.074 0.032
133:Stanford_Tyler Knox 0.072 0.031
133:Iowa St_Evan Frost 0.070 0.027
133:Penn St_Braeden Davis 0.060 0.026
133:Maryland_Braxton Brown 0.055 0.024
133:Nebraska_Jacob Van Dee 0.039 0.016
133:Indiana_Angelo Rini 0.035 0.013
133:Rutgers_Dylan Shawver 0.038 0.011
133:North Dakota St_Kyle Burwick 0.028 0.011
133:Wisconsin_Zan Fugitt 0.029 0.009
133:Lock Haven_Anthony Noto 0.027 0.008
133:Northern Iowa_Julian Farber 0.022 0.006
133:NC St_Kai Orine 0.019 0.005
133:Pennsylvania_Ryan Miller 0.014 0.005
133:North Carolina_Ethan Oakley 0.012 0.003
133:Minnesota_Tyler Wells 0.011 0.003
133:Gardner-Webb_Takeo Davis 0.009 0.002
133:Chattanooga_Blake Boarman 0.007 0.002
133:Cornell_Tyler Ferrara 0.005 0.001
133:Army_Ethan Berginc 0.006 0.001
133:Bucknell_Kurt Phipps 0.005 0.001
133:South Dakota St_Derrick Cardinal 0.005 0.001
133:Missouri_Kade Moore 0.003 0.001
133:Central Michigan_Sean Spidle 0.002 0.000
133:Edinboro_Colton Camacho 0.001 0.000
133:Cal Baptist_Hunter Leake 0.000 0.000
133:Michigan_Nolan Wertanen 0.000 0.000
       
Edited by Pablo
Posted
141 Finals Winner
141:Nebraska_Brock Hardy 0.506 0.308
141:Ohio St_Jesse Mendez 0.447 0.284
141:Penn St_Beau Bartlett 0.187 0.089
141:Northern Iowa_Cael Happel 0.191 0.079
141:Minnesota_Vance Vombaur 0.134 0.059
141:Oklahoma St_Tagen Jamison 0.120 0.052
141:Northern Colorado_Andrew Alirez 0.131 0.051
141:Navy_Josh Koderhandt 0.091 0.028
141:Pennsylvania_CJ Composto 0.039 0.013
141:Michigan_Sergio Lemley 0.038 0.013
141:Iowa St_Jacob Frost 0.033 0.009
141:Rutgers_Joesph Oliveri 0.022 0.006
141:Virginia Tech_Sam Latona 0.021 0.004
141:Lock Haven_Wyatt Henson 0.011 0.002
141:Virginia_Dylan Cedeno 0.005 0.001
141:Cornell_Joshua Saunders 0.004 0.001
141:Stanford_Jason Miranda 0.002 0.000
141:Princeton_Eligh Rivera 0.002 0.000
141:Gardner-Webb_Todd Carter 0.003 0.000
141:Columbia_Lorenzo Frezza 0.002 0.000
141:Purdue_Greyson Clark 0.002 0.000
141:Missouri_Josh Edmond 0.002 0.000
141:Illinois_Danny Pucino 0.001 0.000
141:Bucknell_Dylan Chappell 0.002 0.000
141:South Dakota St_Julian Tagg 0.001 0.000
141:North Carolina_Jayden Scott 0.001 0.000
141:Drexel_Jordan Soriano 0.001 0.000
141:Oklahoma_Mosha Schwartz 0.000 0.000
141:West Virginia_Jordan Titus 0.000 0.000
141:Pittsburgh_Briar Priest 0.000 0.000
141:Campbell_Shannon Hanna 0.000 0.000
141:Oregon St_Nash Singleton 0.000 0.000
141:Bellarmine_aj rallo 0.000 0.000
Posted
149 Finals Winner
149:Nebraska_Ridge Lovett 0.463 0.319
149:Virginia Tech_Caleb Henson 0.508 0.266
149:Penn St_Shayne Van Ness 0.326 0.205
149:Iowa_Kyle Parco 0.215 0.076
149:Illinois_Kannon Webster 0.064 0.027
149:North Carolina_Lachlan McNeil 0.052 0.021
149:Oregon St_Ethan Stiles 0.060 0.014
149:Pennsylvania_Cross Wasilewski 0.056 0.013
149:Northern Iowa_Colin Realbuto 0.035 0.013
149:Little Rock_jordan williams 0.045 0.010
149:Rider_Sammy Alvarez 0.024 0.008
149:Ohio St_Dylan D`Emilio 0.038 0.007
149:Cal Poly_Chance Lamer 0.018 0.006
149:Stanford_Jaden Abas 0.029 0.005
149:Iowa St_Paniro Johnson 0.029 0.005
149:Princeton_Ty Whalen 0.013 0.004
149:Oklahoma St_Teague Travis 0.005 0.001
149:NC St_Koy Buesgens 0.004 0.000
149:George Mason_Kaden Cassidy 0.002 0.000
149:Virginia_Jack Gioffre 0.003 0.000
149:Lehigh_Malyke Hines 0.002 0.000
149:Central Michigan_Mason Shrader 0.002 0.000
149:Oklahoma_Willie McDougald 0.002 0.000
149:Cornell_Ethan Fernandez 0.001 0.000
149:Rutgers_Andrew Clark 0.001 0.000
149:North Dakota St_Gavin Drexler 0.001 0.000
149:Army_Trae McDaniel 0.001 0.000
149:Wyoming_Gabe Willochell 0.000 0.000
149:Michigan_Dylan Gilcher 0.000 0.000
149:Maryland_Kal Miller 0.000 0.000
149:Northwestern_Sam Cartella 0.000 0.000
149:The Citadel_Carson DesRosier 0.000 0.000
149:Campbell_Wynton Denkins 0.000 0.000
Posted
157 Finals Winner
157:Cornell_Meyer Shapiro 0.615 0.430
157:Penn St_Tyler Kasak 0.550 0.304
157:Ohio St_Brandon Cannon 0.154 0.056
157:Nebraska_Antrell Taylor 0.106 0.043
157:Virginia Tech_Rafael Hipolito Jr 0.105 0.033
157:Purdue_Joey Blaze 0.078 0.023
157:Northern Iowa_Ryder Downey 0.060 0.021
157:Northern Colorado_Vinny Zerban 0.052 0.018
157:Iowa_Jacori Teemer 0.041 0.015
157:Little Rock_Matty Bianchi 0.037 0.012
157:NC St_Ed Scott 0.030 0.009
157:Northwestern_Trevor Chumbley 0.036 0.008
157:Minnesota_Tommy Askey 0.023 0.005
157:Maryland_Ethen Miller 0.017 0.005
157:Oklahoma St_Caleb Fish 0.018 0.003
157:Pennsylvania_Jude Swisher 0.012 0.003
157:South Dakota St_Cobe Siebrecht 0.012 0.003
157:Iowa St_Cody Chittum 0.010 0.002
157:Central Michigan_Johnny Lovett 0.006 0.001
157:Michigan_Chase Saldate 0.005 0.001
157:Pittsburgh_Dylan Evans 0.006 0.001
157:Oregon St_CJ Hamblin 0.005 0.001
157:George Mason_DJ Mcgee 0.004 0.001
157:Brown_Blake Saito 0.003 0.001
157:North Carolina_Sonny Santiago 0.003 0.000
157:Wyoming_Jared Hill 0.003 0.000
157:Lehigh_Logan Rozynski 0.003 0.000
157:Missouri_James Conway 0.002 0.000
157:Stanford_Grigor Cholakyan 0.001 0.000
157:Harvard_James Harrington 0.001 0.000
157:Columbia_Richard Fedalen 0.001 0.000
157:Chattanooga_Noah Castillo 0.000 0.000
157:Northern Illinois_Landen Johnson 0.000 0.000
Posted
165 Finals Winner
165:Penn St_Mitchell Mesenbrink 0.924 0.763
165:Iowa_Mike Caliendo 0.664 0.186
165:West Virginia_Peyton Hall 0.184 0.023
165:Utah Valley_Terrell Barraclough 0.029 0.008
165:Missouri_Cam Steed 0.017 0.005
165:Cornell_Julian Ramirez 0.014 0.003
165:Arizona St_Nicco Ruiz 0.036 0.003
165:Oklahoma St_Cameron Amine 0.010 0.003
165:Minnesota_Andrew Sparks 0.036 0.002
165:Michigan_Beau Mantanona 0.032 0.002
165:South Dakota St_Drake Rhodes 0.014 0.001
165:Illinois_Braeden Scoles 0.014 0.001
165:Nebraska_Christopher Minto 0.003 0.000
165:Stanford_Hunter Garvin 0.011 0.000
165:Army_Gunner Filipowicz 0.002 0.000
165:Ohio St_Paddy Gallagher 0.004 0.000
165:Northwestern_Maxx Mayfield 0.002 0.000
165:Little Rock_Joseph Bianchi 0.001 0.000
165:Northern Iowa_Jack Thomsen 0.001 0.000
165:Iowa St_Aiden Riggins 0.001 0.000
165:Appalachian St_Will Miller 0.000 0.000
165:NC St_Derek Fields 0.000 0.000
165:Bucknell_Noah Mulvaney 0.000 0.000
165:Virginia Tech_Mac Church 0.000 0.000
165:Columbia_Cesar Alvan 0.000 0.000
165:Indiana_Tyler Lillard 0.000 0.000
165:Virginia_Nick Hamilton 0.000 0.000
165:Pittsburgh_Jared Keslar 0.000 0.000
165:Hofstra_Kyle Mosher 0.000 0.000
165:Rider_Enrique Munguia 0.000 0.000
165:The Citadel_Thomas Snipes 0.000 0.000
165:Wisconsin_Cody Goebel 0.000 0.000
165:Central Michigan_Chandler Amaker 0.000 0.000
Posted
174 Finals Winner
174:Missouri_Keegan O`Toole 0.640 0.361
174:Penn St_Levi Haines 0.508 0.310
174:Oklahoma St_Dean Hamiti Jr 0.377 0.219
174:Nebraska_Lenny Pinto 0.083 0.023
174:Iowa_Patrick Kennedy 0.061 0.022
174:Ohio St_Carson Kharchla 0.070 0.018
174:Ohio University_Garrett Thompson 0.051 0.010
174:Illinois_Dan Braunagel 0.043 0.009
174:North Carolina_Joshua Ogunsanya 0.034 0.006
174:South Dakota St_Cade DeVos 0.024 0.004
174:Cornell_Simon Ruiz 0.027 0.004
174:Binghamton_Brevin Cassella 0.015 0.004
174:Navy_Danny Wask 0.015 0.003
174:Stanford_Lorenzo Norman 0.014 0.002
174:Pittsburgh_Luca Augustine 0.008 0.002
174:Bucknell_Myles Takats 0.009 0.001
174:NC St_Matthew Singleton 0.005 0.001
174:Oklahoma_Gaven Sax 0.003 0.001
174:Iowa St_MJ Gaitan 0.004 0.001
174:Northern Iowa_Jared Simma 0.001 0.000
174:Minnesota_Clayton Whiting 0.002 0.000
174:Virginia Tech_Lennox Wolak 0.001 0.000
174:Little Rock_Tyler Brennan 0.001 0.000
174:Central Michigan_Alex Cramer 0.001 0.000
174:Pennsylvania_Nick Incontrera 0.000 0.000
174:Rutgers_Jackson Turley 0.000 0.000
174:Purdue_Brody Baumann 0.000 0.000
174:Army_Dalton Harkins 0.000 0.000
174:Lock Haven_Avery Bassett 0.000 0.000
174:Drexel_Jasiah Queen 0.000 0.000
174:Chattanooga_Sergio Desiante 0.000 0.000
174:Maryland_Branson John 0.000 0.000
174:Columbia_Jack McGill 0.000 0.000
Posted
184 Finals Winner
184:Northern Iowa_Parker Keckeisen 0.839 0.542
184:Penn St_Carter Starocci 0.770 0.372
184:Minnesota_Max McEnelly 0.118 0.035
184:Oklahoma St_Dustin Plott 0.141 0.035
184:South Dakota St_Bennett Berge 0.055 0.009
184:Cornell_Chris Foca 0.018 0.003
184:Maryland_Jaxon Smith 0.010 0.001
184:Iowa St_Evan Bockman 0.009 0.001
184:Iowa_Gabe Arnold 0.006 0.001
184:Nebraska_Silas Allred 0.007 0.001
184:NC St_Dylan Fishback 0.005 0.000
184:Pittsburgh_Reece Heller 0.006 0.000
184:Oklahoma_Deanthony Parker Jr 0.003 0.000
184:Wyoming_Eddie Neitenbach 0.002 0.000
184:Illinois_Edmond Ruth 0.003 0.000
184:Rider_Isaac Dean 0.002 0.000
184:Ohio St_Ryder Rogotzke 0.002 0.000
184:Indiana_Donnell Washington 0.001 0.000
184:North Carolina_Gavin Kane 0.001 0.000
184:North Dakota St_Aidan Brenot 0.000 0.000
184:Edinboro_Jared McGill 0.000 0.000
184:Princeton_Kole Mulhauser 0.000 0.000
184:Hofstra_Ross McFarland 0.000 0.000
184:Missouri_Colton Hawks 0.000 0.000
184:Rutgers_Shane Cartagena-Walsh 0.000 0.000
184:Columbia_Nick Fine 0.000 0.000
184:George Mason_Malachi DuVall 0.000 0.000
184:Pennsylvania_Maximus Hale 0.000 0.000
184:Bellarmine_Devan Hendricks 0.000 0.000
184:Lock Haven_Colin Fegley 0.000 0.000
184:West Virginia_Dennis Robin 0.000 0.000
184:Lehigh_Caden Rogers 0.000 0.000
184:Oregon St_TJ McDonnell 0.000 0.000
Posted
197 Finals Winner
197:Iowa_Stephen Buchanan 0.744 0.390
197:Penn St_Josh Barr 0.565 0.366
197:Michigan_Jacob Cardenas 0.334 0.177
197:CSU Bakersfield_AJ Ferrari 0.107 0.023
197:Illinois_Zac Braunagel 0.034 0.010
197:Pittsburgh_Mac Stout 0.052 0.008
197:Lehigh_Michael Beard 0.023 0.006
197:Minnesota_Isaiah Salazar 0.033 0.005
197:Little Rock_stephen little 0.018 0.004
197:Northern Iowa_Wyatt Voelker 0.028 0.004
197:Princeton_Luke Stout 0.022 0.003
197:Oklahoma St_Luke Surber 0.009 0.002
197:Nebraska_Camden McDanel 0.007 0.002
197:Oregon St_Trey Munoz 0.005 0.001
197:Northwestern_Evan Bates 0.004 0.001
197:South Dakota St_Zach Glazier 0.007 0.001
197:Wyoming_Joseph Novak 0.003 0.000
197:West Virginia_Ian Bush 0.002 0.000
197:Ohio St_Seth Shumate 0.001 0.000
197:Virginia Tech_Andy Smith 0.001 0.000
197:Stanford_Nikolas Stemmet 0.000 0.000
197:Drexel_Mickey O'Malley 0.001 0.000
197:Indiana_Gabe Sollars 0.000 0.000
197:Michigan St_Remy Cotton 0.000 0.000
197:The Citadel_Patrick Brophy 0.000 0.000
197:Bucknell_Dillon Bechtold 0.000 0.000
197:Campbell_Levi Hopkins 0.000 0.000
197:Cornell_Michael Dellagatta 0.000 0.000
197:Navy_Payton Thomas 0.000 0.000
197:Army_Wolfgang Frable 0.000 0.000
197:Appalachian St_Carson Floyd 0.000 0.000
197:Rider_Brock Zurawski 0.000 0.000
197:Lock Haven_Tucker Hogan 0.000 0.000
Posted
285 Finals Winner
285:Minnesota_Gable Steveson 0.936 0.726
285:Oklahoma St_Wyatt Hendrickson 0.497 0.164
285:Penn St_Greg Kerkvliet 0.341 0.075
285:NC St_Isaac Trumble 0.137 0.025
285:Lehigh_Owen Trephan 0.021 0.003
285:Ohio St_Nick Feldman 0.018 0.003
285:Arizona St_Cohlton Schultz 0.010 0.001
285:Michigan_Joshua Heindselman 0.019 0.001
285:Iowa_Ben Kueter 0.006 0.001
285:Illinois_Luke Luffman 0.004 0.000
285:Virginia Tech_Jimmy Mullen 0.005 0.000
285:Rutgers_Yaraslau Slavikouski 0.002 0.000
285:Maryland_Seth Nevills 0.002 0.000
285:Pittsburgh_Dayton Pitzer 0.001 0.000
285:Indiana_Jacob Bullock 0.000 0.000
285:Cal Poly_Trevor Tinker 0.000 0.000
285:Army_Brady Colbert 0.000 0.000
285:South Dakota St_Luke Rasmussen 0.000 0.000
285:Iowa St_Daniel Herrera 0.000 0.000
285:Binghamton_Cory Day 0.000 0.000
285:Ohio University_Jordan Greer 0.000 0.000
285:Lock Haven_Gavin Hoffman 0.000 0.000
285:North Carolina_Nolan Neves 0.000 0.000
285:Cornell_Ashton Davis 0.000 0.000
285:Purdue_Hayden Filipovich 0.000 0.000
285:Stanford_Peter Ming 0.000 0.000
285:Northern Iowa_Lance Runyon 0.000 0.000
285:Cleveland St_Daniel Bucknavich 0.000 0.000
285:Duke_Connor Barket 0.000 0.000
285:Michigan St_Max Vanadia 0.000 0.000
285:CSU Bakersfield_Jake Andrews 0.000 0.000
285:Wyoming_Sam Mitchell 0.000 0.000
285:Appalachian St_Stephan Monchery 0.000 0.000
Posted (edited)

your getting closer! But I think the top 2 or 3 must come down and a minimum value distributed amongst anyone below .25 chance. To have 0 per cent chance is theoretical not practical. In a lot of cases it looks like the 3,4 seed are below our perceived expectations.

But one PSU Champ looks like it might upset a few stomachs.

Edited by Gene Mills Fan
Posted
3 minutes ago, Gene Mills Fan said:

your getting closer! But I think the top 2 or 3 must come down and a minimum value distributed amongst anyone below .25 chance. To have 0 per cent chance is theoretical not practical. In a lot of cases it looks like the 3,4 seed are below our perceived expectations.

I don't know.  Are you suggesting that a 22 seed has a greater than 0.1% chance of winning the championship at 125?

There are certainly some weight  classes that are more wide open than others, but in something like hwt, you can't be thinking there is anyone with any real chance outside of Stephenson and Hendrickson, would you? 

These are absolute probabilities, so it's not like "Well, if not Stephenson, then the others have an X% chance."

But we'll see.  We can revisit next week and see if any winners had a 0% chance.

(well, you can do that, I am out of town next week, sorry)

Posted
2 minutes ago, Pablo said:

I don't know.  Are you suggesting that a 22 seed has a greater than 0.1% chance of winning the championship at 125?

There are certainly some weight  classes that are more wide open than others, but in something like hwt, you can't be thinking there is anyone with any real chance outside of Stephenson and Hendrickson, would you? 

These are absolute probabilities, so it's not like "Well, if not Stephenson, then the others have an X% chance."

But we'll see.  We can revisit next week and see if any winners had a 0% chance.

(well, you can do that, I am out of town next week, sorry)

I think Kerk has equal chance as Wyatt but Wyatt is 16% and Kerk 7  I agree the bottoms can be so close to 0 it is 0

Posted (edited)
6 minutes ago, Gene Mills Fan said:

I think Kerk has equal chance as Wyatt but Wyatt is 16% and Kerk 7  

That's nice.  Do you actually have a basis for that probability (equal chance) or did you just make it up?

 

Edited by Pablo
Posted

One thing to be careful about when it comes to these probabilities is to wonder, how improbable does something need to be to be surprising if it occurs?

Over the years of doing this, my line is usually about 15%.  If something has a 15% probability of occurring, I generally say, I won't be surprised if it happens.  Kind of like, if I roll a 6 sided die and get a 1, then that's not a big surprise.  However, if a roll a d20 I'm not expecting a 1.  So that's kind of my line.

Let's see how I would apply that to these rankings above.  Let's go with 285, since that is where the discussion was.

From the probabilities, I would say, "I would be surprised" if Stevenson isn't in the finals.  93%, yeah, that's a pretty solid favorite.  But for the other guy in the finals, "I wouldn't be surprised" if it is either Hendrickson or Kerkvliet, and even Trumble wouldn't be a big shocker, but he's a taller order.

For winning it all, yeah, Stevenson is a huge favorite, but "I wouldn't be surprised" if it was Hendrickson.  From a Pablo standpoint, it's hard to point to anyone other than those two, BUT if you take the field, hey, that's a 1/8 chance (and if it is the field, then Kerk would be the best pick), so close to being not unexpected.  Hey, if you have 10 weight classes, there is something like a 75% chance that some "12% chance of happening" event ends up happening.  The question, though, is at what weight class will that happen?  Hard to predict (actually, not possible to predict).

In the end, although these types of probability calculations are fun to do and think about (for me, at least), it's really hard, in the end, to assess it or to say it was "wrong," even after the fact.

But it does give you fun things to think about and to put some hard values on.  For example, what is the most wide open weight class according to Pablo?  Well, if we draw a line and say that anyone with a 5% chance of winning is "in the mix" (see above - while there is a 75% chance that a 12% event happening for 10 weights, there is only a 40% chance of a 5% even happening), that means that for each weight we have

125 7 guys in the mix

133 5 guys in the mix

141 8 guys in the mix

149 4 guys in the mix

157 3 guys in the mix

165 2 guys in the mix

174 3 guys in the mix

184 2 guys in the mix

197 3 guys in the mix

285 3 guys in the mix

YMMV on where you draw the line of "in the mix" but basically, we see that 141 and 125 are the most wide open, while 165 and 184 the most dominated.

One thing I like about this exercise is that it is a way to evaluate those questions that people like to ask when the brackets come out.  The most fun one to do is the "who has the easiest path to the finals," which is what you always hear about the basketball brackets.  I've got a really good metric that I can use to do assessment, but it's a lot of work to program, and doing it for 10 weight classes is not something I feel like doing this year.  But I don't think that is as much a question for wrestling brackets.  More common questions are things like "Which is the low seed to look out for?"  I can do that, but need to think about it.

  • Brain 1
  • Fire 1
Posted
2 hours ago, Pablo said:

In the other thread on Pablo rankings, I talked about how you can calculate the probability of a wrestler winning if you know the rating difference between them.  In the post, I just showed the plot and corresponding line, but ultimately, there is an analytical relationship that is easily calculated.  So let's calculate it.

Given the tournament brackets, it is possible to calculate the probability that a wrestler advances given their opponent.  So we can look at the 125 prelim match between Weiand and Milani.  Weiand has a Pablo rating of 5634 and Milani is rated 5968.  So according to Pablo ratings, Milani has a 59% chance of winning that match.

For the next round, the winner will face Lilledahl, who is rated 8500.  Therefore, Lilledahl has a 97% chance of beating Weiand and a 95% chance of beating Milani.  But there is only a 41% chance of wrestling Weiland and a 59% chance it is Milani.  It's possible to combine these all together, though, to come up with a probability of 96% for Lilledahl to advance out of the first round.  Then you can do that for the next round, taking into account the ratings of Gallagher and West and the probability they advance, and then the next round, and then next round, etc, to get the probability that a given wrestler advances.

.

.

.

 

Thanks for pulling this together and for detailing your methodology. How many cycles did you simulate each round & combination in the bracket before landing on a final probability? Just wondering. It's pretty amazing that we have the ability to do this from our desktops in this day and age.

Posted
3 minutes ago, CHROMEBIRD said:

Thanks for pulling this together and for detailing your methodology. How many cycles did you simulate each round & combination in the bracket before landing on a final probability? Just wondering. It's pretty amazing that we have the ability to do this from our desktops in this day and age.

These are calculated analytically and not simulated.  That's why I stick with just the championship bracket and don't get into the consolations.  That would be a friggin mess and I would have to simulate it.  I have done a lot of work with optimizing tournament bracket construction, and in those cases, as soon as it gets to double elimination, I have always gone to simulation; btw, if anyone is interested, I've done an analysis of the NCAA national wrestling tournament setup

 Creating the Best Tournament. 5b. Application: The NCAA national wrestling tournament

The way I ended up doing (which was not perfectly efficient but I didn't know that going in) the calculation of the final probability in this case is something like a 25 term analytical expression. 

  • Bob 1
  • Fire 1
Posted
2 hours ago, Gene Mills Fan said:

your getting closer! But I think the top 2 or 3 must come down and a minimum value distributed amongst anyone below .25 chance. To have 0 per cent chance is theoretical not practical. In a lot of cases it looks like the 3,4 seed are below our perceived expectations.

But one PSU Champ looks like it might upset a few stomachs.

I actually think the 1 and 2 are a hair light, but certainly within the range of historical norms.

He has PSU predicted to win 2.7 titles. Seems about right to me.

  • Bob 1

Drowning in data, but thirsting for knowledge

Posted
12 minutes ago, Wrestleknownothing said:

I actually think the 1 and 2 are a hair light, but certainly within the range of historical norms.

He has PSU predicted to win 2.7 titles. Seems about right to me.

I guess I understand a bit more. I got 100 in three math regents but barely passed probability and statistics.   to get the 2.7 winners is that that sum of all the PSU wrestlers chances? I wasn't close to figuring that out.

Posted
9 minutes ago, Gene Mills Fan said:

I guess I understand a bit more. I got 100 in three math regents but barely passed probability and statistics.   to get the 2.7 winners is that that sum of all the PSU wrestlers chances? I wasn't close to figuring that out.

Note that if you sum up all the probabilities for all the wrestlers at a given weight, you get 1, and for all 10 weights, they sum up to 10, which is the total number of winners.

So yeah, then you realize, oh, if I sum up the Penn St probabilities, that is how many PSU winners it would be....

Sometimes, it can be that easy, amazingly.

Posted
1 minute ago, Gene Mills Fan said:

I guess I understand a bit more. I got 100 in three math regents but barely passed probability and statistics.   to get the 2.7 winners is that that sum of all the PSU wrestlers chances? I wasn't close to figuring that out.

Yes, for independent observations, like 10 individual weights, to get the expected total you just add the individual probabilities.

If you wanted to figure out the odds of all of them happening, you would multiple them all.

If you want to get the probability of each event from 0 wins to 10 wins you need to do an algebraic expansion of an equation that takes the form (Prob of event one +(1-Prob of event one)x)(prob of event two+(1-Prob of event two)...

The resulting factors in the expansion are the individual event odds.

  • Bob 1

Drowning in data, but thirsting for knowledge

Posted

Could you also say, based on these statistics, that Mesenbrink and Steveson are the only two wrestlers who are favorites against the field in their respective weights? And in the 70’s, that’s a big gap

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