100k Simulations of All Texas Private Six-Man Brackets

It was just time to get down to it. I had been delaying the inevitable, running 100,000 simulations of each and every private school six-man state bracket. For details on how I did this, please read the earlier posts I have written about the public school brackets and other Monte Carlo simulations I have written. This was very similar….

First build the start bracket using this week’s ratings from my website (www.sixmanfootball.com). Then calculate the probability of each first round game and simulate the result. After each round I update the ratings (not 100% like my formula, but a close enough estimation) and continue…. do this 100,000 times and see what happened.

Well, here’s what happened.

TAPPS D1          
TEAM FIRST QUARTERS SEMIS FINAL CHAMPION
Boerne Geneva 0 16679 33496 12466 37359
Midland Trinity 0 13728 45784 12329 28159
Baytown Christian 0 38588 25904 24432 11076
Watauga Harvest 25725 17419 26487 20469 9900
Rockwall Heritage 35535 37235 13252 10377 3601
Sugar Land Logos Prep 24633 61253 8646 2274 3194
Houston Emery-Weiner 74275 9537 10169 4741 1278
Pasadena First Baptist 64465 24177 6168 3917 1273
Abilene Christian 45374 38952 10399 4169 1106
Round Rock Christian 49480 43205 5492 864 959
Katy Faith West 50520 43067 4867 711 835
Austin Hill Country 54626 34092 7621 2879 782
Waco Vanguard 75367 22068 1715 372 478
TAPPS D2          
TEAM FIRST QUARTERS SEMIS FINAL CHAMPION
Waco Live Oak 0 9711 16354 17471 56464
Austin Veritas 0 20885 34691 29735 14689
Orange Community Christian 0 46910 27849 18231 7010
Dallas Tyler Street 36085 17714 34388 5019 6794
SA Castle Hills 22194 38296 19682 14086 5742
Cedar Park Summit 25660 66166 3416 2406 2352
Denton Calvary 0 69007 26428 2318 2247
Kerrville Our Lady of the Hills 63915 13279 18663 1980 2163
Bulverde Bracken Christian 36088 49169 9136 4452 1155
Dallas Lakehill 77806 14794 4581 2204 615
Conroe Covenant Christian 63912 29946 4061 1649 432
Lubbock Christ The King 74340 24123 751 449 337
TAPPS D3          
TEAM FIRST QUARTERS SEMIS FINAL CHAMPION
Longview Trinity 0 25590 27022 16279 31109
Fredericksburg Heritage 0 29268 21774 25772 23186
WF Notre Dame 0 36128 35968 11996 15908
Fort Worth Covenant Classical 11814 54054 22060 5912 6160
Granbury North Central Texas Academy 43834 15878 24039 10298 5951
Seguin Lifegate 15010 58039 11590 10003 5358
Richardson Canyon Creek Christian 41133 42480 8406 3951 4030
San Marcos Hill Country Christian 56166 14491 19126 6837 3380
Alvin Living Stones 0 69631 22245 5739 2385
WF Wichita Christian 58867 31930 5010 2152 2041
Brenham Christian 84990 12693 1226 805 286
Selma River City Believers 88186 9818 1534 256 206
TCAF D1          
TEAM SEMIS FINAL CHAMPION
Fort Worth Nazarene 25645 32238 42117
Wylie Preparatory 26385 35665 37950
Dallas Inspired Vision 74355 15287 10358
Waco Methodist Childrens Home 73615 16810 9575
TCAF D2          
TEAM SEMIS FINAL CHAMPION
Azle Christian 20861 16452 62687
Granbury Cornerstone 32698 49507 17795
Weatherford Christian 79139 7600 13261
Arlington St. Paul Prep 67302 26441 6257
TCAL D1          
TEAM QUARTERS SEMIS FINAL CHAMPION  
Bryan Allen Academy 1340 2173 2839 93648
SA The Atonement 47104 23154 28492 1250
Tyler King’s Academy 48830 49877 289 1004
Greenville Phoenix 44302 28918 25840 940
EP Faith 52896 22695 23532 877
Bryan Christian Homeschool (BVCHEA) 51170 47717 255 858
Houston Mount Carmel 98660 233 266 841
Clear Lake Christian 55698 25233 18487 582
TCAL D2          
TEAM QUARTERS SEMIS FINAL CHAMPION
Stephenville Faith 2150 4906 24891 68053
Sugar Land HCYA Fort Bend 4188 21572 49549 24691
Corpus Christi Annapolis 12883 64578 18001 4538
Killeen Memorial 37562 58609 2464 1365
SA Sunnybrook 62438 35860 1165 537
Corpus Christi Abundant Life 97850 625 1092 433
Corpus Christi WINGS 87117 11393 1290 200
Lockhart Lighthouse Christian 95812 2457 1548 183
TAIAO D1          
TEAM QUARTERS SEMIS FINAL CHAMPION
Tyler HEAT 9493 28388 28029 34090
SA FEAST Homeschool 23317 29535 20494 26654
Capital City Christian Home School 34148 35468 15424 14960
Temple Centex Homeschool 39095 38257 12965 9683
Fort Worth THESA 65852 22050 7102 4996
Crosby Victory and Praise 60905 27484 7228 4383
Bryan Aggieland Home School (BCAL) 76683 12947 6135 4235
Plano CHANT 90507 5871 2623 999
TAIAO D2          
TEAM QUARTERS SEMIS FINAL CHAMPION
Austin NYOS 0 18228 29436 52336
Bastrop Tribe Consolidated 0 29389 40156 30455
Waco Parkview 19490 54627 17568 8315
San Marcos Homeschool 21741 62559 8584 7116
Weatherford Home School 78259 19213 1626 902
Victoria Home School 80510 15984 2630 876

Obviously for TCAF, I am moving straight into this week since the first round was played last weekend.

Another thing to notice is that teams like Austin NYOS do not lose in the first round. Why? They got a bye.

The biggest shocker at first glance – the fact that Bryan Allen Academy is such a huge favorite. I expected it to be high, but 93.6% to win it all is a little obscene.

So I hope everyone enjoys this… and remember, no wagering.

East and Throckmorton likely to rule UIL D2 Six-Man Playoffs

After 100,000 simulations, the Throckmorton Greyhounds appear to have a 29.8% chance to win the UIL D2 Six-Man State Championship. The biggest challenge it appears will be the dominance of the East bracket, which won a dominating 80.1% of the time in the simulation.

Yesterday I wrote about how the Crowell Wildcats are a somewhat dominant 33.1% to repeat as the D1 UIL State Six-Man Champions. If you would like to read more details on the methods, I have several posted below.

Basic note: The table represents how many times each team LOST in that round or became the champion (final column).

TEAM BI-DISTRICT AREA QUARTERS SEMIS FINALS CHAMPION
Throckmorton 2277 17879 26568 18537 4942 29797
Guthrie 7473 13276 45288 15376 3977 14610
Calvert 7171 26565 28201 20608 3668 13787
Richland Springs 16212 9781 33384 23044 3859 13720
Groom 14392 22605 26298 11473 18726 6506
Follett 20907 9637 30748 13218 19457 6033
Jonesboro 21822 51329 15095 7807 1096 2851
Motley County 36812 49576 7304 3538 821 1949
Buena Vista 24382 31007 18346 15296 9149 1820
Balmorhea 35900 17918 21475 14798 8314 1595
Blanket 26142 37455 17133 12373 5848 1049
Southland 16387 56498 15533 5156 5424 1002
Chillicothe 14573 70298 12063 1898 356 812
Oglesby 83788 4289 8126 2777 309 711
Lueders-Avoca 63188 31122 3323 1401 289 677
Mt. Calm 26113 62182 8582 2343 252 528
Sands 64100 13218 12862 6674 2706 440
McLean 79093 4955 10141 2791 2601 419
Blackwell 30030 45928 14678 6701 2320 343
Mullin 78178 17599 2828 1014 112 269
Sierra Blanca 75618 14193 5708 3167 1158 156
Whitharral 41417 49108 6784 1462 1082 147
Jayton 92527 2983 3809 455 90 136
Lefors 85608 7191 4864 1239 973 125
Trinidad 92829 4507 1933 566 61 104
Loraine 73858 17345 5047 2663 984 103
High Island 73887 23748 1851 406 26 82
Rising Star 69970 22936 4751 1763 507 73
Kress 58583 36300 3781 770 511 55
Lazbuddie 83613 13706 1851 456 333 41
Harrold 97723 1423 667 125 28 34
Forestburg 85427 13443 978 105 21 26

It is interesting to note that while Richland Springs and Calvert have higher ratings at the current time, Guthrie actually has the second-highest chance to win the tournament (14610 to 13720 and 13787, for RS and Calvert, respectively). This is due to the fact that Guthrie has it easier in the first two rounds.

Out West, Groom and Follett (6506 and 6033 wins) have a combined probability that’s less than any of the top-4 from the East. On the bright side, they reach the finals more than each of these, mostly due to the fact that Throckmorton is not in their half of the draw.

It certainly looks like the West is more competitive in the sense that the teams are more even and quite a few more have solid opportunities to reach the semis and finals.

Coming Next: All of the private school draws.

 

Crowell Favorite to Win Six-Man Title with 33.1% Win Probability

I have created several Monte Carlo simulations over the past year to try and determine probabilities for various sporting events. This week I decided to tackle the Texas Six-Man state tournament. (I will publish more bracket evaluations as the week goes on)

For the past 21 seasons, I have been producing rankings for six-man football. For those of you who do not know the history, I would fax my rankings to newspapers across the state and several would actually publish them. I eventually put together a newsletter, The Huntress Report, where I would add scores, game stories, stats and schedules to the rankings and mail (or fax) to subscribers. Eventually I moved to a website, where I would update the information a week behind, so that my subscribers would be getting the freshest information first. That all was scrapped in 1999 when I decided to go 100% to the website (www.sixmanfootball.com).

METHODOLOGY

You can read some of my earlier posts (see below here at sixmanguru.com) where I discuss Monte Carlo simulations if you are interested. In this case I played the UIL Division I tournament 100,000 times using probabilities calculated from the ratings on my website. To account for upsets and a more Bayesian methodology, I modified the teams ratings to also simulate my rating systems (generally) after each round. I also recorded each round a team lost and below are the results.

Crowell, the defending DI state champions, wins the title again a whopping 33.1% of the time and reached the finals over 41% of the time.

TEAM BI-DISTRICT AREA QUARTERS SEMIS FINALS CHAMP
Crowell 8686 12684 25264 11843 8426 33097
Ira 16846 9048 41178 9920 6573 16435
May 1911 8450 19585 28915 26882 14257
Blum 9396 2817 28089 27327 22565 9806
Borden County 16195 24064 21597 25036 4836 8272
Happy 9925 21253 34686 24447 4075 5614
Abbott 26692 4293 40184 16474 9330 3027
Water Valley 22717 63399 8220 2512 1390 1762
Valley 21460 50424 14276 10825 1381 1634
Gordon 30614 18265 35123 9414 5227 1357
Knox City 83154 4192 9627 1484 664 879
Grady 42027 41247 11329 4300 508 589
Highland 91314 3270 3476 935 478 527
Aquilla 73308 2813 17360 4297 1795 427
Sterling City 44824 47109 6529 782 373 383
Zephyr 17303 55678 21972 3477 1296 274
Anton 83805 8484 4666 2544 254 247
Newcastle 69386 11555 15094 2678 1046 241
Garden City 55176 39651 4328 411 224 210
Ropes 57973 32379 6938 2288 218 204
Marfa 77283 20647 1378 374 151 167
Nazareth 78540 17028 2724 1409 143 156
Milford 90604 972 5262 2335 697 130
Santa Anna 48258 46737 2667 1705 539 94
Rochelle 51742 44020 2323 1416 429 70
Spur 90075 5121 3784 890 64 66
Leverett’s Chapel 35599 59216 4515 531 121 18
Eden 82697 14502 2461 249 77 14
Chester 44796 52912 1717 462 99 14
Tioga 98089 793 775 280 50 13
Campbell 55204 43299 1154 281 51 11
Savoy 64401 33678 1719 159 38 5

The good news is every teams has a chance to win it all — even Savoy. The bad news — it appears they only an approximate 5 in 100,000 chance. I did run this a few times and they did get as high as 12 in one of the iterations. Tioga, a team that loses 98.1% of the time in the first round actually has a better chance than Savoy with 12 wins.

Another thing that stands out would be the fact that Ira, despite winning the title a theoretical 16.4% also seems to lose in the first round (16.8%) much more often than teams like Crowell (8.7%) or May (an amazing 1.9%). This goes to show that despite the 45-point expected spread on the Ira-Knox City game, it is still a much more difficult match-up for the Bulldogs than Highland or Tioga will be for Crowell and May, respectively.

Also interesting to note is that the East wins a dominant 70.2% of the time.

The most common final is a rematch of last year’s, May v. Crowell, with Blum v Crowell coming in next. The good news for May is they reach the final 41.1% of the time, which is a very good season. Blum is expected to reach the final about 32.4% of the time.

Wednesday I will release my UIL DII simulation results (they are already done, but it is my anniversary and we are going out for dinner). I will release the private school results either late Wednesday or early Thursday.

Quick Post on MLB Probabilities (100k Monte Carlo Simulations)

I just did a quick run of 100,000 playoff simulations and wanted to share the quick results. I will try to get some finer detail or maybe look into a few changes, but here are the raw World Series champion results.

Detroit — 4950
Baltimore — 18592
LA Angels — 31876
Kansas City — 9058
Washington — 19768
San Francisco — 4246
St. Louis — 1662
LA Dodgers — 9848

So the Angels win it all 31.8% of the time, with Washington and Baltimore in a tight race for second most.

NCAA Men’s DI Tennis Regionals Simulated 50,000 times

This is posted on my college tennis website so aptly named, texascollegetennis.com. I decided to post it here as well.. why not, right?

I’m sitting in the middle of exams and term projects looking for ways to relax. What better way than to run a Monte Carlo Simulation of each of the men’s regionals, based on my year-end ratings?

So I ran each regional 50,000 times and you can see the results. One of the more intriguing of course is the Nashville Regional, where I could not really account for the home court (and probably outdoor) advantage the Vanderbilt will have over Columbia. That probably sways things a little, I am guessing in the range of 5-15%.

The first number is how many times each team won the entire regional. The second is their probability of coming out of the regional.

BEST FIRST ROUND MATCH-UPS: The Vanderbilt-Virginia Tech match-up looks good, as do the Oklahoma State-Michigan, Memphis-Drake, South Florida-Florida State,  Northwestern-Mississippi, Wake Forest-Louisville, Boise State-USD and Auburn-Harvard. There are a few more, but that’s my quick take.

USC Regional

University of Southern California 45307 90.614%
University of Idaho 122 0.244%
Oklahoma State University 2283 4.566%
University of Michigan 2288 4.576%

.

Nashville Regional

Vanderbilt University 9815 19.630%
Virginia Tech 7818 15.636%
East Tennessee State University 1917 3.834%
Columbia University 30450 60.900%

.

Austin Regional

University of Texas 39580 79.160%
Marist College 224 0.448%
University of Louisiana at Lafayette 1140 2.280%
Mississippi State University 9056 18.112%

.

College Station Regional

California 11649 23.298%
Texas Tech University 5420 10.840%
Alcorn State University 42 0.084%
Texas A&M University 32889 65.778%

.

Waco Regional

Baylor University 43520 87.040%
Texas A&M-Corpus Christi 497 0.994%
Stanford University 3601 7.202%
University of Tulsa 2382 4.764%

.

Champaign Regional

University of Memphis 6515 13.030%
Drake University 5669 11.338%
Ball State University 374 0.748%
University of Illinois 37442 74.884%

.

South Bend Regional

University of Notre Dame 35693 71.386%
Univ. of Wisconsin-Green Bay 381 0.762%
Northwestern University 6925 13.850%
University of Mississippi 7001 14.002%

.

Charlottesville Regional

Penn State University 3489 6.978%
UNC Wilmington 636 1.272%
U.S. Military Academy 104 0.208%
University of Virginia 45771 91.542%

.

Columbus Regional

Ohio State University 45064 90.128%
Bryant University 72 0.144%
Wake Forest University 2384 4.768%
University of Louisville 2480 4.960%

.

Gainesville Regional

University of South Florida 7877 15.754%
Florida State University 7821 15.642%
St. John’s University 1541 3.082%
University of Florida 32761 65.522%

.

Durham Regional

Duke University 35589 71.178%
Winthrop University 606 1.212%
University of Tennessee 12034 24.068%
Elon University 1771 3.542%

.

UCLA Regional

University of San Diego 2321 4.642%
Boise State University 3591 7.182%
Cal Poly 375 0.750%
UCLA 43713 87.426%

.

Chapel Hill Regional

North Carolina 40147 80.294%
South Carolina State 233 0.466%
University of South Carolina 8986 17.972%
George Washington University 634 1.268%

.

Athens Regional

North Carolina State 7642 15.284%
University of Oregon 5472 10.944%
Jacksonville State University 161 0.322%
University of Georgia 36725 73.450%

.

Lexington Regional

University of Kentucky 32487 64.974%
University of Denver 948 1.896%
Clemson University 9801 19.602%
Purdue University 6764 13.528%

.

Norman Regional

Auburn University 2313 4.626%
Harvard University 2361 4.722%
Montana 88 0.176%
University of Oklahoma 45238 90.476%