After Conference Tournament Pablo Rankings

[Pablo]

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.

[nhs67]

Let's see 'em, Boss.

[Pablo]

		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

[Pablo]

	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

[Pablo]

	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

[Pablo]

	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

[Pablo]

	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

[strange_daze]

Thanks for this work--I enjoyed reading through your rankings. It's going to be a fun week!

[ugarles]

First of all, this is great work. Thank you.

Second,* the rankings include redshirts, backups and injured wrestlers who are not in NCAAs. Any way to remove the guys ineligible for RPI/CR (to limit the field to starters eligible for the postseason) and possibly provide the rankings for NQs who aren't in the top 40? (As a Cornell fan, I see that Milani and Dellagatta are both outside this top-40.)

* Outside of work hours I might do some of this and anyone else is free to chip in!

[Pablo]

2 minutes ago, ugarles said:

First of all, this is great work. Thank you.

Second,* the rankings include redshirts, backups and injured wrestlers who are not in NCAAs. Any way to remove the guys ineligible for RPI/CR (to limit the field to starters eligible for the postseason) and possibly provide the rankings for NQs who aren't in the top 40? (As a Cornell fan, I see that Milani and Dellagatta are both outside this top-40.)

* Outside of work hours I might do some of this and anyone else is free to chip in!

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.

[Pablo]

If you want to see more of the rankings for those wrestlers competing in the NCAA championships, see my new posts in the Probability thread.  Includes rankings and ratings for the competing wrestlers outside of the top 40.

[Pablo]

The question came up the other day about bonus points, so I've taken a look at how we can predict bonus points based on Pablo ratings.  Using the predictions for conference tournaments, here is the distribution of outcomes for wins as a function of Pablo rating differences

So when the rating difference is below about 200, something like 84% of the matches won by the favorite are decided by a regular decision (when the rating difference is that low, the breakdown of losses is pretty similar).  9% are falls, 5% MDs and the very rare TF.  But when you get to other end, where the difference is greater than 3000, then it's only 14% regular decision, with something like 37% MD, 33% TF and 15% falls.  There is a pretty steady increase in the rate of MDs and TFs as you increase the rating difference, but there looks like there is a step of MD going to TF at about 2000.  Although there is a little bit of an increase in the pin rate, it's really not all that much, consistent with the idea that pins are not completely about difference in quality.  Yeah, when the difference is larger, it's more likely to be a pin, but not by much (maybe 50% greater than when they are even), unlike MDs and (especially) TFs which increase big time.

From these data, we can talk about expected returns in terms of bonus points.  If we take a dual approach, scoring 3,4,5,6, then we can talk about the average expected points for a ratings difference.  For example, if the difference is around 150, the average value of a win is 3.3 points.  List below

150 3.3

425 3.4

715 3.5

1125 3.6

1485 3.8

1945 3.9

2515 4.2

3300 4.5

So by the time the rating difference gets to 2000, then the average match outcome is a MD (and scoring-wise, a MD is a tad better than a fall (because falls are not strongly correlated with ratings difference)).  Out in the 3500 range, the average outcome is somewhere between a MD and TF.

What about tournament activity points?  We can do that as well. Using 1, 1.5, 2 as the bonus points, we have

150 .25

425 .34

715 .40

1125 .51

1485 .64

1945 .70

2515 .97

3300 1.18

Same conclusions, but different values.

The lesson here is, if you use Pablo ratings to predict points, assume chalk and count matches and advancements, you can add on the expected bonus points to get a more refined estimate.

 

[ugarles]

waiting for Flo to (re)post the session 1 upsets to compare Pablo to seeds...

Edited 20 hours ago by ugarles

[ugarles]

125:
#18 Moran over #15 Renteria (Pablo: Moran)

133:
#23 Spidle over #10 Shawver (Pablo: Shawver)
#21 Rini over #12 Oakley (Pablo: Rini)
#18 Farber over #15 Noto (Pablo: Noto*)

141:
#18 Tagg over #15 Olivieri (Pablo: Olivieri)
#20 Saunders over #13 Carter (Pablo: Saunders)
#21 Chappell over #12 Latona (Pablo: Latona)

149:
#33 Travis* over #32 Denkins (Pablo: Travis, but...)
#29 Gioffre over #4 Johnson (Pablo: Johnson*)
#19 Rutgers over #14 Lamer (Pablo: Lamer)
#17 Abas over #16 McDaniel (Pablo: Abas)

157:
#23 Saldate over #10 Miller (Pablo: Miller*)
#20 Chumbley over #13 Hill (Pablo: Chumbley)

165:
#33 Amaker over #32 Keslar (Pablo: Keslar)
#19 Thomsen over #14 Rhodes (Pablo: Rhodes)
#18 Mayfield over #15 Ruiz (Pablo: Ruiz)

174:
#33 Wilson over #32 McGill (??? - Pablo had the UALR guy)
#25 Harkins over #8 Pinto (Pablo: Pinto)
#24 Wolak over #9 Karchla (Pablo: Karchla)
#23 Gaitan over #10 Cramer (Pablo: Gaitan*)
#21 Ogunsanya over Takats (Pablo: Ogunsanya)
#18 Sax over #15 Augustine (Pablo: Augustine)

184:
#20 Fine over #13 Bockman (Pablo: Bockman)

197:
#26 Zurawski over #7 Voelker (Pablo: Voelker)
#25 Brophy over #8 Surber (Pablo: Surber)
#24 Sollars over #9 Braunagel (Pablo: Braunagel)
#23 Shumate over #10 Salazar (Pablo: Salazar)
#19 Smth over #14 Glazier (Pablo: Glazier)

285:
#33 Filipovich over #32 Monchery (Pablo: Filipovich)
#22 Colbert over #11 Mullen (Pablo: Colbert)

Obviously, this is one sided. Pablo picked 8 seed-upsets but I am not doing the work of looking for Pablo-upsets. I threw a few asterisks on matches where, whether Pablo got it right or wrong, it indicated that the higher seed that lost was seeded far too high.

[Pablo]

If you will be patient, I will do the analysis after the tournament.

[Pablo]

To follow up on that comment, one thing I've learned over the years of doing this is that it doesn't do much good to get hung up on individual outcomes where Pablo was right or Pablo was wrong.  The NCAA tournament is like 650 matches.  There are going to be places where seeds get it right and Pablo gets it wrong, places where Pablo gets it right and seeds get it wrong, and times when both are right or both are wrong.  Remember, the Fundamental Theorem of Pablo is that upsets happen.  They must happen, so Pablo must get matches wrong.  Similarly, seeds will get some matches wrong.  In the end, we'll see.

So again, patience.  Just enjoy the action.

Go Panthers.  Go Boilers.  Go everyone who is wrestling against an Iowa guy.