Pablo Posted 20 hours ago Posted 20 hours ago 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. 1
Pablo Posted 20 hours ago Author Posted 20 hours ago (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 20 hours ago by Pablo
Pablo Posted 20 hours ago Author Posted 20 hours ago (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 20 hours ago by Pablo
Pablo Posted 20 hours ago Author Posted 20 hours ago 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
Pablo Posted 20 hours ago Author Posted 20 hours ago 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
Pablo Posted 20 hours ago Author Posted 20 hours ago 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
Pablo Posted 20 hours ago Author Posted 20 hours ago 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
Pablo Posted 20 hours ago Author Posted 20 hours ago 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
Pablo Posted 20 hours ago Author Posted 20 hours ago 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
Pablo Posted 20 hours ago Author Posted 20 hours ago 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
Pablo Posted 20 hours ago Author Posted 20 hours ago 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
Gene Mills Fan Posted 20 hours ago Posted 20 hours ago (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 20 hours ago by Gene Mills Fan
Pablo Posted 20 hours ago Author Posted 20 hours ago 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)
Gene Mills Fan Posted 20 hours ago Posted 20 hours ago 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
Pablo Posted 20 hours ago Author Posted 20 hours ago (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 20 hours ago by Pablo
Pablo Posted 19 hours ago Author Posted 19 hours ago 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. 1 1
CHROMEBIRD Posted 18 hours ago Posted 18 hours ago 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.
Pablo Posted 18 hours ago Author Posted 18 hours ago 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. 1 1
Wrestleknownothing Posted 17 hours ago Posted 17 hours ago 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. 1 Drowning in data, but thirsting for knowledge
Gene Mills Fan Posted 17 hours ago Posted 17 hours ago 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.
Pablo Posted 16 hours ago Author Posted 16 hours ago 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.
Wrestleknownothing Posted 16 hours ago Posted 16 hours ago 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. 1 Drowning in data, but thirsting for knowledge
MLB9 Posted 16 hours ago Posted 16 hours ago 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
Co'ji Campbell St. Joseph Catholic Academy, Wisconsin Class of 2025 Committed to Illinois Projected Weight: 125, 133
Jackson Albert Saucon Valley, Pennsylvania Class of 2025 Committed to George Mason Projected Weight: 149, 157
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