Pablo

Can anyone tell me the story of Jaxon Joy? He's got like 24 matches in my database (and is 23-1!). Most of his matches list him as Spartan Combat RTC, but there are a couple of tournaments in Track where he is with Univ of Central Florida. His only loss is to Contrabone from Michigan (who only has 5 matches) Pablo has him like the 6th best wrestler at 149 this year. Is he redshirting for someone? Or is it something else?

As these things go, I'd say Mesenbrink and Stevenson are overwhelming favorites. I don't work in the gaming industry, but if this were going to odds, it would be something like 3 to 10 (remember that 1:1 odds mean 50/50)

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.

So if you see the other thread on Championship probabilities, I looked at the results for just the qualifiers. However, I just listed their probabilities and didn't show their ratings. You will have to give me until tomorrow, but I can edit those posts to list the ratings and rankings of all the wrestlers in the tournament. I will probably replace all the lists that are in that thread (if I am still allowed to edit), because I like your suggestion, and it is a better way to present it than what I have done.

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.

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.

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

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)

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

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

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

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

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

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

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

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

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

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

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.

197 285 1. 197:Penn St_Josh Barr 10358 1. 285:Minnesota_Gable Steveson 11353 2. 197:Iowa_Stephen Buchanan 10120 2. 285:Oklahoma St_Wyatt Hendrickson 10522 3. 197:Michigan_Jacob Cardenas 9848 3. 285:Penn St_Greg Kerkvliet 9967 4. 197:Penn St_Lucas Cochran 8768 4. 285:NC St_Isaac Trumble 9721 5. 197:CSU Bakersfield_AJ Ferrari 8758 5. 285:Ohio St_Nick Feldman 8690 6. 197:Illinois_Zac Braunagel 8712 6. 285:Michigan_Joshua Heindselman 8659 7. 197:Lehigh_Michael Beard 8546 7. 285:Lehigh_Owen Trephan 8645 8. 197:Little Rock_stephen little 8493 8. 285:Campbell_Taye Ghadiali 8623 9. 197:Nebraska_Camden McDanel 8425 9. 285:Arizona St_Cohlton Schultz 8503 10. 197:Minnesota_Isaiah Salazar 8348 10. 285:Virginia Tech_Jimmy Mullen 8310 11. 197:Oregon St_Trey Munoz 8343 11. 285:Iowa_Ben Kueter 8266 12. 197:Pittsburgh_Mac Stout 8336 12. 285:Illinois_Luke Luffman 8238 13. 197:Missouri_Aeoden Sinclair 8326 13. 285:Penn St_Cole Mirasola 8204 14. 197:Oklahoma St_Luke Surber 8244 14. 285:Rutgers_Yaraslau Slavikouski 8004 15. 197:Northern Iowa_Wyatt Voelker 8193 15. 285:Pittsburgh_Dayton Pitzer 7881 16. 197:Penn St_Connor Mirasola 8156 16. 285:Maryland_Seth Nevills 7833 17. 197:Oklahoma St_Cody Merrill 8080 17. 285:Virginia Tech_Hunter Catka 7721 18. 197:Princeton_Luke Stout 8069 18. 285:Cal Poly_Trevor Tinker 7621 19. 197:Northwestern_Evan Bates 8027 19. 285:Rider_David Szuba 7530 20. 197:Ohio St_Luke Geog 7809 20. 285:Army_Brady Colbert 7439 21. 197:South Dakota St_Zach Glazier 7661 21. 285:Indiana_Jacob Bullock 7437 22. 197:Wyoming_Joseph Novak 7459 22. 285:Morgan St_Xavier Doolin 7156 23. 197:West Virginia_Ian Bush 7431 23. 285:Missouri_Seth Nitzel 7100 24. 197:Minnesota_Gavin Nelson 7421 24. 285:South Dakota St_Luke Rasmussen 7024 25. 197:Stanford_Nikolas Stemmet 7314 25. 285:Oklahoma_Juan Mora 7015 26. 197:Ohio St_Seth Shumate 7223 26. 285:Binghamton_Cory Day 7014 27. 197:Indiana_Gabe Sollars 7197 27. 285:Lock Haven_Gavin Hoffman 6971 28. 197:Virginia Tech_Sonny Sasso 7196 28. 285:Stanford_Peter Ming 6908 29. 197:Iowa St_Christian Carroll 7180 29. 285:Army_Lucas Stoddard 6887 30. 197:The Citadel_Patrick Brophy 7165 30. 285:Iowa St_Daniel Herrera 6859 31. 197:Rutgers_John Poznanski 7083 31. 285:North Carolina_Nolan Neves 6813 32. 197:Virginia Tech_Andy Smith 7074 32. 285:Northern Iowa_Lance Runyon 6805 33. 197:Drexel_Mickey O'Malley 7015 33. 285:Cleveland St_Daniel Bucknavich 6805 34. 197:Michigan St_Remy Cotton 7008 34. 285:Purdue_Hayden Filipovich 6781 35. 197:West Virginia_Rune Lawrence 6953 35. 285:Ohio University_Jordan Greer 6761 36. 197:Campbell_Levi Hopkins 6946 36. 285:Navy_Spencer Lanosga 6634 37. 197:Lehigh_JT Davis 6945 37. 285:Cornell_Ashton Davis 6585 38. 197:Bucknell_Dillon Bechtold 6725 38. 285:Minnesota_Bennett Tabor 6571 39. 197:Iowa St_Sawyer Bartelt 6710 39. 285:Nebraska_Harley Andrews 6519 40. 197:Northern Iowa_Kalob Runyon 6660 40. 285:Duke_Connor Barket 6496

174 184 1. 174:Missouri_Keegan O`Toole 10087 1. 184:Northern Iowa_Parker Keckeisen 10350 2. 174:Penn St_Levi Haines 10031 2. 184:Penn St_Carter Starocci 10041 3. 174:Oklahoma St_Dean Hamiti Jr 9906 3. 184:Oklahoma St_Dustin Plott 8968 4. 174:Iowa_Patrick Kennedy 8926 4. 184:Minnesota_Max McEnelly 8895 5. 174:Nebraska_Lenny Pinto 8877 5. 184:Iowa_Angelo Ferrari 8482 6. 174:Ohio St_Carson Kharchla 8839 6. 184:South Dakota St_Bennett Berge 8437 7. 174:Illinois_Dan Braunagel 8507 7. 184:Ohio St_Rocco Welsh 8254 8. 174:Ohio University_Garrett Thompson 8458 8. 184:Cornell_Chris Foca 8076 9. 174:Binghamton_Brevin Cassella 8348 9. 184:Iowa St_Evan Bockman 7816 10. 174:North Carolina_Joshua Ogunsanya 8321 10. 184:Iowa_Gabe Arnold 7770 11. 174:South Dakota St_Cade DeVos 8304 11. 184:Maryland_Jaxon Smith 7762 12. 174:Stanford_Lorenzo Norman 8185 12. 184:Nebraska_Silas Allred 7703 13. 174:Pittsburgh_Luca Augustine 8173 13. 184:Oklahoma_Deanthony Parker Jr 7638 14. 174:Cornell_Simon Ruiz 8170 14. 184:NC St_Dylan Fishback 7560 15. 174:Navy_Danny Wask 8115 15. 184:Pittsburgh_Reece Heller 7518 16. 174:NC St_Matthew Singleton 8046 16. 184:Wyoming_Eddie Neitenbach 7502 17. 174:Iowa_Nelson Brands 7939 17. 184:Illinois_Edmond Ruth 7279 18. 174:Oklahoma_Gaven Sax 7913 18. 184:Indiana_Donnell Washington 7242 19. 174:Bucknell_Myles Takats 7899 19. 184:Rider_Isaac Dean 7216 20. 174:Iowa St_MJ Gaitan 7700 20. 184:Ohio St_Ryder Rogotzke 7216 21. 174:Northern Iowa_Jared Simma 7685 21. 184:West Virginia_Ian Bush 7188 22. 174:Virginia Tech_Lennox Wolak 7474 22. 184:Penn St_Zack Ryder 7123 23. 174:Pennsylvania_Nick Incontrera 7363 23. 184:Princeton_Kole Mulhauser 6980 24. 174:Minnesota_Clayton Whiting 7341 24. 184:Northern Iowa_CJ Walrath 6927 25. 174:Rutgers_Jackson Turley 7299 25. 184:Edinboro_Jared McGill 6908 26. 174:Little Rock_Tyler Brennan 7254 26. 184:North Carolina_Gavin Kane 6904 27. 174:Cornell_Christian Hansen 7244 27. 184:Indiana_Sam Goin 6796 28. 174:Appalachian St_Lucas Uliano 7213 28. 184:North Dakota St_Aidan Brenot 6781 29. 174:Oregon St_Sean Harman 7206 29. 184:Cornell_Colt Barley 6777 30. 174:Minnesota_Ethan Riddle 7198 30. 184:Oklahoma St_Jersey Robb 6692 31. 174:Central Michigan_Alex Cramer 7188 31. 184:Hofstra_Ross McFarland 6587 32. 174:West Virginia_Brody Conley 7169 32. 184:Missouri_Colton Hawks 6582 33. 174:Michigan_Joseph Walker 7108 33. 184:Rutgers_Shane Cartagena-Walsh 6525 34. 174:Army_Dalton Harkins 7097 34. 184:Purdue_James Rowley 6511 35. 174:Virginia_Rocco Contino 7053 35. 184:Columbia_Nick Fine 6502 36. 174:Nebraska_Leandro Araujo 7033 36. 184:George Mason_Malachi DuVall 6459 37. 174:Lock Haven_Avery Bassett 7008 37. 184:Utah Valley_Caleb Uhlenhopp 6407 38. 174:Drexel_Jasiah Queen 6994 38. 184:Unattached_James Conway 6385 39. 174:North Dakota St_Daniel Magayna 6979 39. 184:Pennsylvania_Maximus Hale 6370 40. 174:Chattanooga_Sergio Desiante 6964 40. 184:The Citadel_Billy Janzer 6309

157 165 1. 157:Cornell_Meyer Shapiro 9485 1. 165:Penn St_Mitchell Mesenbrink 11002 2. 157:Penn St_Tyler Kasak 9145 2. 165:Iowa_Mike Caliendo 9911 3. 157:Ohio St_Brandon Cannon 8320 3. 165:West Virginia_Peyton Hall 8930 4. 157:Nebraska_Antrell Taylor 8246 4. 165:Missouri_Cam Steed 8545 5. 157:Ohio St_Paddy Gallagher 8101 5. 165:Utah Valley_Terrell Barraclough 8466 6. 157:Virginia Tech_Rafael Hipolito Jr 8089 6. 165:Michigan_Brock Mantanona 8391 7. 157:Iowa_Jacori Teemer 8074 7. 165:Lehigh_Max Brignola 8372 8. 157:Purdue_Joey Blaze 8035 8. 165:Oklahoma St_Cameron Amine 8359 9. 157:Northern Iowa_Ryder Downey 8018 9. 165:Arizona St_Nicco Ruiz 8307 10. 157:Penn St_Alex Facundo 7997 10. 165:Cornell_Julian Ramirez 8167 11. 157:Northern Colorado_Vinny Zerban 7984 11. 165:Minnesota_Andrew Sparks 8071 12. 157:Minnesota_Charlie Millard 7971 12. 165:Michigan_Beau Mantanona 8041 13. 157:Little Rock_Matty Bianchi 7932 13. 165:Nebraska_Bubba Wilson 7912 14. 157:NC St_Ed Scott 7856 14. 165:South Dakota St_Drake Rhodes 7912 15. 157:Ohio St_Brock Herman 7770 15. 165:Stanford_Hunter Garvin 7749 16. 157:Northwestern_Trevor Chumbley 7666 16. 165:Nebraska_Christopher Minto 7716 17. 157:Ohio University_Peyten Kellar 7608 17. 165:Illinois_Braeden Scoles 7692 18. 157:Maryland_Ethen Miller 7585 18. 165:Army_Gunner Filipowicz 7571 19. 157:Minnesota_Tommy Askey 7580 19. 165:Ohio St_Paddy Gallagher 7488 20. 157:Central Michigan_Johnny Lovett 7454 20. 165:Northwestern_Maxx Mayfield 7411 21. 157:Pennsylvania_Jude Swisher 7449 21. 165:Iowa St_Aiden Riggins 7254 22. 157:South Dakota St_Cobe Siebrecht 7448 22. 165:Northern Iowa_Jack Thomsen 7227 23. 157:Oklahoma St_Caleb Fish 7397 23. 165:Little Rock_Joseph Bianchi 7203 24. 157:Iowa St_Cody Chittum 7285 24. 165:Ohio St_Sammy Sasso 7164 25. 157:Michigan_Chase Saldate 7232 25. 165:George Mason_Evan Maag 7113 26. 157:Pittsburgh_Dylan Evans 7168 26. 165:Appalachian St_Will Miller 6976 27. 157:Brown_Blake Saito 7104 27. 165:South Dakota St_Marcus Espinoza-Owens 6970 28. 157:Oregon St_CJ Hamblin 7077 28. 165:Columbia_Cesar Alvan 6934 29. 157:George Mason_DJ Mcgee 7043 29. 165:Minnesota_Blaine Brenner 6918 30. 157:North Carolina_Sonny Santiago 6953 30. 165:Virginia_Nick Hamilton 6900 31. 157:Missouri_James Conway 6924 31. 165:Bucknell_Noah Mulvaney 6818 32. 157:Wyoming_Jared Hill 6874 32. 165:NC St_Derek Fields 6719 33. 157:Stanford_Grigor Cholakyan 6849 33. 165:Pittsburgh_Jared Keslar 6707 34. 157:Lehigh_Logan Rozynski 6840 34. 165:Virginia Tech_Mac Church 6653 35. 157:Oregon St_Ethan Stiles 6830 35. 165:Indiana_Tyler Lillard 6609 36. 157:Columbia_Richard Fedalen 6784 36. 165:Navy_Dylan Elmore 6554 37. 157:North Dakota St_Maxwell Petersen 6739 37. 165:Binghamton_Carter Baer 6518 38. 157:Chattanooga_Noah Castillo 6718 38. 165:Indiana_Derek Gilcher 6504 39. 157:Cal Poly_Legend Lamer 6689 39. 165:Rutgers_Anthony White 6491 40. 157:Harvard_James Harrington 6601 40. 165:Hofstra_Kyle Mosher 6482

141 149 1. 141:Ohio St_Jesse Mendez 9273 1. 149:Nebraska_Ridge Lovett 9369 2. 141:Nebraska_Brock Hardy 9225 2. 149:Virginia Tech_Caleb Henson 9106 3. 141:Lehigh_Luke Stanich 8617 3. 149:Penn St_Shayne Van Ness 9090 4. 141:Penn St_Beau Bartlett 8613 4. 149:West Virginia_Ty Watters 8447 5. 141:Minnesota_Vance Vombaur 8466 5. 149:Iowa_Kyle Parco 8407 6. 141:Oklahoma St_Tagen Jamison 8462 6. 149:Spartan Combat RTC_Jaxon Joy 8298 7. 141:Northern Iowa_Cael Happel 8436 7. 149:Illinois_Kannon Webster 8263 8. 141:Northern Colorado_Andrew Alirez 8344 8. 149:Iowa St_Anthony Echemendia 8231 9. 141:Michigan_Sergio Lemley 8021 9. 149:North Carolina_Lachlan McNeil 8162 10. 141:Navy_Josh Koderhandt 7979 10. 149:Northern Iowa_Colin Realbuto 7986 11. 141:Pennsylvania_CJ Composto 7977 11. 149:Oregon St_Ethan Stiles 7847 12. 141:Iowa St_Jacob Frost 7876 12. 149:Rider_Sammy Alvarez 7828 13. 141:Rutgers_Joesph Oliveri 7742 13. 149:Pennsylvania_Cross Wasilewski 7808 14. 141:Pennsylvania_Evan Mougalian 7522 14. 149:Cal Poly_Chance Lamer 7784 15. 141:Virginia Tech_Sam Latona 7481 15. 149:Princeton_Ty Whalen 7742 16. 141:Lock Haven_Wyatt Henson 7370 16. 149:Little Rock_jordan williams 7729 17. 141:Rutgers_Joseph Olivieri 7353 17. 149:Stanford_Jaden Abas 7585 18. 141:South Dakota St_Tyson Peach 7352 18. 149:Ohio St_Dylan D`Emilio 7581 19. 141:Virginia_Dylan Cedeno 7227 19. 149:Pittsburgh_Kade Brown 7528 20. 141:Columbia_Lorenzo Frezza 7089 20. 149:Iowa St_Paniro Johnson 7479 21. 141:Princeton_Eligh Rivera 7087 21. 149:Oklahoma St_Carter Young 7185 22. 141:Stanford_Jason Miranda 7056 22. 149:George Mason_Kaden Cassidy 7105 23. 141:Missouri_Josh Edmond 7009 23. 149:Cornell_Ethan Fernandez 6972 24. 141:Purdue_Greyson Clark 7007 24. 149:Iowa_Caleb Rathjen 6960 25. 141:Nebraska_Blake Cushing 6962 25. 149:NC St_Koy Buesgens 6884 26. 141:Arizona St_Emilio Ysaguirre Jr 6943 26. 149:Edinboro_Ryan Michaels 6878 27. 141:Cornell_Joshua Saunders 6906 27. 149:Rutgers_Andrew Clark 6838 28. 141:South Dakota St_Julian Tagg 6842 28. 149:Arizona St_Jesse Vasquez 6823 29. 141:Gardner-Webb_Todd Carter 6767 29. 149:Lehigh_Malyke Hines 6815 30. 141:Illinois_Danny Pucino 6747 30. 149:Virginia_Jack Gioffre 6806 31. 141:Ohio St_Andre Gonzales 6726 31. 149:Central Michigan_Jimmy Nugent 6765 32. 141:Bucknell_Dylan Chappell 6717 32. 149:Wyoming_Gabe Willochell 6764 33. 141:Oklahoma_Mosha Schwartz 6716 33. 149:North Dakota St_Gavin Drexler 6758 34. 141:Drexel_Jordan Soriano 6687 34. 149:Central Michigan_Mason Shrader 6757 35. 141:Iowa_Cullan Schriever 6674 35. 149:Oklahoma_Willie McDougald 6755 36. 141:Pittsburgh_Briar Priest 6639 36. 149:Pittsburgh_Finn Solomon 6716 37. 141:Utah Valley_Haiden Drury 6602 37. 149:Army_Trae McDaniel 6631 38. 141:West Virginia_Jordan Titus 6571 38. 149:West Virginia_Sam Hillegas 6617 39. 141:Iowa_Jace Rhodes 6559 39. 149:Northwestern_August Hibler 6534 40. 141:North Carolina_Jayden Scott 6557 40. 149:Iowa St_Kane Naaktgeboren 6503

125 133 1 . 125:Purdue_Matt Ramos 9125 1. 133:Illinois_Lucas Byrd 8476 2 . 125:Penn St_Luke Lilledahl 8500 2. 133:Iowa_Drake Ayala 8098 3 . 125:Wisconsin_Nicolar Rivera 8353 3. 133:Little Rock_Nasir Bailey 8073 4 . 125:Oklahoma St_Troy Spratley 8322 4. 133:Ohio St_Ben Davino 7990 5 . 125:West Virginia_Jett Strickenberger 8242 5. 133:Northern Colorado_Dominick Serrano 7763 6 . 125:Virginia Tech_Eddie Ventresca 8210 6. 133:Virginia Tech_Connor McGonagle 7671 7 . 125:Arizona St_Richard Figueroa 8182 7. 133:Michigan_Dylan Ragusin 7577 8 . 125:Nebraska_Caleb Smith 7998 8. 133:Ohio St_Nic Bouzakis 7542 9 . 125:NC St_Vince Robinson 7931 9. 133:Maryland_Braxton Brown 7503 10 . 125:Northern Colorado_Stevo Poulin 7709 10. 133:Penn St_Braeden Davis 7471 11 . 125:Lehigh_Sheldon Seymour 7657 11. 133:Iowa St_Evan Frost 7467 12 . 125:Ohio St_Brendan McCrone 7516 12. 133:Cal Poly_Zeth Romney 7466 13 . 125:Rutgers_Dean Peterson 7496 13. 133:Stanford_Tyler Knox 7464 14 . 125:Princeton_Marc-Anthony McGowan 7354 14. 133:Nebraska_Jacob Van Dee 7416 15 . 125:South Dakota St_Brady Roark 7322 15. 133:Iowa St_Garrett Grice 7415 16 . 125:Pennsylvania_Max Gallagher 7295 16. 133:North Dakota St_Kyle Burwick 7269 17 . 125:Oregon St_Maximo Renteria 7214 17. 133:Indiana_Angelo Rini 7199 18 . 125:Indiana_Jacob Moran 7210 18. 133:Lock Haven_Anthony Noto 7091 19 . 125:Northern Illinois_Blake West 7201 19. 133:Wisconsin_Zan Fugitt 7091 20 . 125:Nebraska_Kael Lauridsen 7146 20. 133:Rutgers_Dylan Shawver 7082 21 . 125:North Carolina_Spencer Moore 7111 21. 133:Pennsylvania_Ryan Miller 7073 22 . 125:Oklahoma_Antonio Lorenzo 7071 22. 133:Northern Iowa_Julian Farber 7023 23 . 125:Penn St_Kurt McHenry 7002 23. 133:Northern Iowa_Cory Land 6976 24 . 125:Minnesota_Cooper Flynn 6975 24. 133:North Carolina_Ethan Oakley 6853 25 . 125:Nebraska_Alan Koehler 6962 25. 133:Minnesota_Tyler Wells 6845 26 . 125:Oklahoma_Beric Jordan 6919 26. 133:Minnesota_Jager Eisch 6725 27 . 125:West Virginia_Jace Schafer 6915 27. 133:Lehigh_Matty Lopes 6711 28 . 125:Ohio St_Vinny Kilkeary 6793 28. 133:Gardner-Webb_Takeo Davis 6707 29 . 125:Northern Iowa_Trever Anderson 6703 29. 133:Chattanooga_Blake Boarman 6693 30 . 125:Iowa St_Kysen Terukina 6693 30. 133:Oklahoma St_Cael Hughes 6656 31 . 125:Campbell_Anthony Molton 6683 31. 133:Bucknell_Kurt Phipps 6650 32 . 125:South Dakota St_Tanner Jordan 6677 32. 133:Army_Ethan Berginc 6625 33 . 125:Missouri_Gage Walker 6670 33. 133:Cornell_Tyler Ferrara 6596 34 . 125:Oklahoma St_Sam Smith 6629 34. 133:Cornell_Brett Ungar 6585 35 . 125:Army_Charlie Farmer 6528 35. 133:South Dakota St_Derrick Cardinal 6580 36 . 125:Cornell_Greg Diakomihalis 6514 36. 133:North Carolina_Derek Guanajuato 6537 37 . 125:North Dakota St_tristan daugherty 6483 37. 133:Oklahoma St_Reece Witcraft 6463 38 . 125:Indiana_Blaine Frazier 6459 38. 133:Rutgers_Mason Gibson 6461 39 . 125:Iowa St_Ethan Perryman 6435 39. 133:South Dakota St_Logan Swensen 6451 40 . 125:North Dakota St_Ezekiel Witt 6414 40. 133:Missouri_Kade Moore 6439

I've been working hard on getting Pablo rankings into shape. I have a lot more data now than I had 2 weeks ago, and so things are looking a lot better now. I'll drop the rankings below, but before doing that, a few things to note 1) I am now including the ratings for each wrestler, so I should talk a little bit about that. Recall the premise of the system, that an outcome of a match is a probability. The bigger the difference between the wrestlers, the higher the probability that the better wrestler will win. The closer they are, the closer the probability is to being 50% (remember, if a wrestler goes up against his duplicate, the it's a coin flip whether green or red is going to win). So this is how to interpret Pablo ratings. The bigger the ratings difference between two wrestlers, the higher the probability that the better wrestler wins. We can see this in action if we look at the outcomes from the conference tournaments. I calculated Pablo rankings before the conference tournaments and then looked at the outcomes of the matches that took place, taking into account the difference in Pablo ratings of the two wrestlers. After binning things up, I got the plot below, which shows the likelihood of winning as a function of the ratings difference (note it is symmetric around 0). So if the ratings difference is something like 150, the favored wrestler won about 55% of the time. When the difference was in the 2000 range, the favored wrestler won about 85% of the time. Notice that there are diminishing returns. When the difference gets very large, you don't improve the winning percentage as much as the difference gets bigger. In fact, in the conference tournaments, every wrestler who was at least 3000 Pablo points higher than their opponent won (something like 77-0), and it didn't matter if the difference was 3000 or 5000. This is exactly what you'd expect, that as the difference gets larger, the winning percentage will asymptote to 0 or 100%. The challenge here is that the winning percentage clearly has a relationship with ratings difference, but it's not simple. But, in fact, it is, if you know how to do it. You may remember from your introduction to stats class that this is a standard functional curve that is integrated normal distribution. As such, we can evaluated it that way. In particular, what I do is convert that winning percentage into a z-score, which is basically the number of standard deviations from the mean. This is done very easily in any math program (and I use Excel, where it is the NormSInv function). I just call it the "Pablo Transform" but in the end, it's just the z-score. To turn them into Pablo ratings, I basically use z-score*2000, where that 2000 value is just a matter to give convenient ratings. Here's why this is useful. If I take the data above and do the transform on the winning percentages, I get the graph below The thing that should jump out at you is the fact this is linear. And very linear. Now, that doesn't have to be the case (I've seen examples where it isn't), but that fact it is is a very good sign - it suggests that the underlying Pablo model is holding up. I will note that being linear is not merely enough, what also matters is the slope. In this type of plot, the higher the slope, the better. I mean, if it's a line but the slope is 0, that's worthless. Remember that a 0 difference indicates a 50/50 win probability, so if has a slope of 0, then that means it's always a 50/50 outcome. That isn't useful. On the other hand, if the slope is infinitely large, it means that the favorite always wins. By design, Pablo rankings are built on that concept of the rating difference = z-score*2000, and so that is what is plotted here. If Pablo is working as expected, the slope of this line should be 1. In fact, if you have a good eye, you will see that the slope is actually closer to 1.4, so higher than expected. That means, in fact, Pablo is even working a little better than designed. The TL; DR summary: Pablo has demonstrated predictive ability, and the difference in Pablo ratings can be used to predict a win probability. More on that in a separate post. 2) I've done a lot of analysis to get the best values I can for evaluating outcomes. This is an always evolving process that improves as I get more data. However, the results show that I'm getting close, and I think the underlying model is firm. In the current model, a pin is, on average, slightly better than an average outcome, but the data indicate a quick pin means more than a late pin, so this is programmed in. I've built in some subtleties in terms of the fitting. 3) One issue that I did include that is not as firm is the time dependence. The data I have is not great, but suggests that matches that took place 140 days ago are about half as informative as something recent. It's not a strong correlation, but that value is consistent with what I've found for other college sports. Therefore, I have put in a time dependence (it's an exponential decrease with a half-life of 140 days). 4) The rating scale is based on the median wrestler at each weight rated 5000. In order to be included in the ratings, a wrestler has to have at least 6 matches at a given weight in my database, but everyone with more than 5 matches is included. Doesn't matter if they are unattached or on non-D1. Non-D1 wrestlers must have at least 6 matches against D1 to be included, but D1 wrestlers just need to have 6 matches against anybody. There can be more than 1 ranked wrestler from a team at a given weight, as long as they have at least 6 matches. (FWIW, I include the outcomes for wrestlers who don't have 6 matches in the rankings calculation, I just don't include them in the rankings I show you all) Whew, that is long enough! Let's just get to the rankings! I think you will find them better than the last ones.