Using Microsoft’s TrueSkill to Rank Texas Six-Man Football Teams

People have always compared six-man football to a computer game. With its wild scores and fast-paced style, six-man football can be just as exciting, if not more so.

So what if you played the entire six-man season on your Xbox?

That’s why I decided to use the TrueSkill Ranking System created by Microsoft Research for Xbox Live games and apply it to the season.

Microsoft uses this algorithm to track the skill of gamers in order to place them in competitive matches. On the Microsoft Research website it explains that the ranking system is characterized by two attributes: a players average skill level (ranking) and the degree of uncertainty in the gamer’s skill (this would be the variation in the players level). If you would like to read more, it can be found at the Microsoft Research website, http://research.microsoft.com/en-us/projects/trueskill/

Heck, gamers love this thing. If you want to really know more about the math behind it, a guy named Jeff Moser has written a bunch on the subject.

Very nerdy links—→
Here http://www.moserware.com/assets/computing-your-skill/The%20Math%20Behind%20TrueSkill.pdf

And here
http://www.moserware.com/2010/03/computing-your-skill.html

As with any algorithm, there are several ways you could implement it. I decided in the first trial I would start of with no priors. This means all teams started the season with the base ranking. Since I also program primarily in Python, I decided to use the Trueskill package developed by a South Korean game developer named Heungsub Lee. It seems to be well-written and moderately documented.

Let’s take a quick look at the top-10.

1 Richland Springs 432
2 Borden County 425
3 Buena Vista 409
4 Austin Veritas 408
5 Happy 403
6 Gorman 403
7 Jonesboro 396
8 SA FEAST Homeschool 388
9 Crowell 381
10 Houston Emery-Weiner 381

Not bad, but not stellar. Let’s see the next 20

11 Calvert 379
12 Midland Trinity 377
13 Garden City 374
14 Valley 373
15 Dallas Inspired Vision 372
16 Follett 370
17 Zephyr 370
18 Abbott 369
19 Pasadena First Baptist 368
20 Gordon 366
21 Balmorhea 366
22 San Marcos Hill Country Christian 366
23 Bryan Christian Homeschool (BVCHEA) 366
24 Rochelle 364
25 Baytown Christian 364
26 Mt. Calm 363
27 Hermleigh 360
28 Nazareth 357
29 Chester 357
30 Sterling City 352

OK, but again, you can see some flaws.

One of the really cool things TrueSkill brings is a pretty good ability to predict the winners of games. In the version I ran, I allowed TrueSkill to predict all of the games, but throwing out the really close ones where it determined the probabilities of a team were between 47%-53%. One of the reasons to do this would be that during all of week one games, with probabilities at 50-50, we can just throw those out.

For the season, TrueSkill predicted 832 of 1108 (75.1%) games, which isn’t bad. For the playoffs, it is even better at 82-20 (80.4%).

It will be interesting to see how it does this week.

Matchup: Zephyr (11-2-0) at Abbott (11-2-0)
Rating Before: 370~28 / 369~29
Match Quality: 0.82
Zephyr odds winning: 50.9%
Prediction: TOSS-UP –> Zephyr

Matchup: Crowell (9-3-0) at Borden County (13-0-0)
Rating Before: 381~28 / 425~33
Match Quality: 0.68
Crowell odds winning: 27.6%
Prediction: Borden County

Matchup: Follett (12-1-0) at Buena Vista (13-0-0)
Rating Before: 370~31 / 409~37
Match Quality: 0.68
Follett odds winning: 30.2%
Prediction: Buena Vista

Matchup: Midland Trinity (11-2-0) at Houston Emery-Weiner (11-2-0)
Rating Before: 377~28 / 381~28
Match Quality: 0.83
Midland Trinity odds winning: 47.4% [predict: TOSS-UP]
Prediction: TOSS-UP –> Houston Emery-Weiner

Matchup: Guthrie (11-2-0) at Richland Springs (13-0-0)
Rating Before: 351~29 / 432~35
Match Quality: 0.44
Guthrie odds winning: 13.8%
Prediction: Richland Springs

Matchup: San Marcos Hill Country Christian (11-1-0) at WF Notre Dame (9-2-0)
Rating Before: 366~35 / 341~30
Match Quality: 0.75
San Marcos Hill Country Christian odds winning: 63.3%
Prediction: San Marcos Hill Country Christian (this one was played this morning-correct)

Matchup: Austin Veritas (12-0-0) at Waco Live Oak (10-2-0)
Rating Before: 408~37 / 339~32
Match Quality: 0.51
Austin Veritas odds winning: 81.7%
Prediction: Austin Veritas (this one just finished-correct)

I plan on making some adjustments to this and seeing what comes up. Stay tuned.

Just for fun, here’s the entire list

1 Richland Springs 432
2 Borden County 425
3 Buena Vista 409
4 Austin Veritas 408
5 Happy 403
6 Gorman 403
7 Jonesboro 396
8 SA FEAST Homeschool 388
9 Crowell 381
10 Houston Emery-Weiner 381
11 Calvert 379
12 Midland Trinity 377
13 Garden City 374
14 Valley 373
15 Dallas Inspired Vision 372
16 Follett 370
17 Zephyr 370
18 Abbott 369
19 Pasadena First Baptist 368
20 Gordon 366
21 Balmorhea 366
22 San Marcos Hill Country Christian 366
23 Bryan Christian Homeschool (BVCHEA) 366
24 Rochelle 364
25 Baytown Christian 364
26 Mt. Calm 363
27 Hermleigh 360
28 Nazareth 357
29 Chester 357
30 Sterling City 352
31 Guthrie 351
32 Cedar Park Summit 351
33 Watauga Harvest 349
34 Milford 347
35 Waco Methodist Childrens Home 347
36 Southland 346
37 Austin Hill Country 344
38 Granbury North Central Texas Academy 344
39 Rockwall Heritage 341
40 WF Notre Dame 341
41 Ira 339
42 Waco Live Oak 339
43 Newcastle 335
44 Stephenville Faith 334
45 Bastrop Tribe Consolidated 333
46 Fort Worth THESA 331
47 Walnut Springs 330
48 Fort Worth Nazarene 329
49 Motley County 328
50 Willow Park Trinity 328
51 Aspermont 323
52 Tioga 315
53 Blum 314
54 Coolidge 314
55 Longview Trinity 314
56 Conroe Covenant Christian 313
57 Savoy 311
58 Bryson 311
59 Klondike 308
60 Sugar Land HCYA Fort Bend 308
61 Austin NYOS 308
62 Decatur Victory Christian 308
63 Meadow 307
64 Seguin Lifegate 303
65 Houston Texas Christian 302
66 Capital City Christian Home School 300
67 Knox City 299
68 Sands 298
69 Giddings State School 298
70 Miami 297
71 Katy Faith West 297
72 Red Oak Ovilla Christian 297
73 Robert Lee 296
74 Union Hill 296
75 EP Faith 296
76 Santa Anna 295
77 Bronte 294
78 Spur 293
79 Rising Star 292
80 Evant 292
81 Dallas Academy 292
82 Marfa 290
83 Irving Faustina 290
84 Loraine 289
85 Marshall Christian Academy 288
86 Dallas Tyler Street 286
87 Weatherford Christian 286
88 Oglesby 283
89 Forestburg 281
90 SA Castle Hills 281
91 Williamson County Home School 281
92 Temple Centex Homeschool 280
93 Oakwood 279
94 Sugar Land Logos Prep 279
95 Huntsville Alpha Omega 279
96 Arlington St. Paul Prep 279
97 EP Immanuel Christian 278
98 Groom 277
99 Anton 274
100 Rankin 274
101 McLean 273
102 Gholson 273
103 Eden 272
104 Denton Calvary 272
105 Lucas Christian 272
106 Waco Vanguard College Prep 271
107 Whitharral 270
108 Westlake Academy 270
109 Corpus Christi WINGS 270
110 Bulverde Bracken Christian 268
111 Petersburg 267
112 Lefors 264
113 Corpus Christi Annapolis 263
114 Plano CHANT 263
115 Rule 262
116 Kress 261
117 WF Wichita Christian 261
118 May 259
119 Iredell 259
120 Fort Davis 259
121 Paint Rock 258
122 Sierra Blanca 257
123 Cotton Center 257
124 Fredericksburg Heritage 256
125 Athens Christian Prep 252
126 Westbrook 251
127 O’Donnell 251
128 Avalon 251
129 Water Valley 249
130 Paducah 249
131 Hart 249
132 High Island 249
133 Sidney 249
134 Blanket 248
135 Lubbock Home School 248
136 Dallas Lutheran 248
137 Dallas Lakehill 248
138 Campbell 246
139 Tyler HEAT 245
140 Wylie Preparatory 242
141 Abilene Christian 242
142 Azle Christian 241
143 Bellville Faith 241
144 Corpus Christi Abundant Life 240
145 Austin Brentwood Christian 239
146 Hedley 237
147 Houston Mount Carmel 237
148 SA The Winston 237
149 Amherst 234
150 Wellman-Union 233
151 Richardson Canyon Creek Christian 232
152 SA Lutheran 232
153 Strawn 231
154 Cherokee 231
155 Chillicothe 230
156 Orange Community Christian 230
157 Grandfalls-Royalty 229
158 Fannindel 228
159 Lorenzo 224
160 White Deer 223
161 Wilson 222
162 Lewisville Lakeland 221
163 Aquilla 219
164 Haslet Heritage Christian 219
165 McKinney Cornerstone 218
166 Higgins 217
167 Blackwell 216
168 Dawson 215
169 Spring Providence Classical 215
170 Pflugerville Concordia 215
171 Woodson 214
172 SA Great Hearts Monte Vista 214
173 New Home 212
174 Lueders-Avoca 212
175 Lingleville 211
176 Medina 211
177 Morgan 211
178 Covington 210
179 Apple Springs 208
180 Arlington Newman 208
181 Plainview Christian 207
182 Trinidad 204
183 Kerrville Our Lady of the Hills 203
184 Lockhart Lighthouse Christian 202
185 Victoria Home School 199
186 Silverton 198
187 Saint Jo 198
188 Crosby Victory and Praise 197
189 Ropes 196
190 Lewisville Founders Classical 196
191 Mullin 194
192 Lake Jackson Brazosport Christian 194
193 EP Jesus Chapel 192
194 Brownwood Victory Life 189
195 Amarillo Holy Cross 189
196 Jayton 188
197 Benjamin 187
198 Canton EXEL 187
199 Dell City 187
200 Throckmorton 186
201 Rotan 186
202 SA The Atonement 186
203 Johnson County Sports Association 185
204 Cranfills Gap 182
205 Carrollton Christian 182
206 Spring Branch Living Rock Academy 182
207 Waco Parkview 181
208 Alvin Living Stones 181
209 Odessa Latter Rain 180
210 Granbury Cornerstone 178
211 Dallas Fairhill 178
212 Grady 175
213 Fort Hancock 175
214 SA Sunnybrook 175
215 Veribest 172
216 Greenville Christian 171
217 New Braunfels Christian 171
218 Moran 169
219 EP Home School 165
220 Highland 163
221 Bryan Allen Academy 163
222 Sanderson 160
223 Lometa 159
224 Temple Holy Trinity Catholic 157
225 Kopperl 156
226 Arlington Flint Academy 156
227 Paint Creek 155
228 Midessa Homeschool 151
229 Panther Creek 149
230 Tyler King’s Academy 148
231 Fruitvale 148
232 Houston Sanchez Charter 148
233 Leverett’s Chapel 146
234 Bynum 145
235 Buckholts 144
236 Whiteface 143
237 Prairie Lea 143
238 West Columbia Charter 141
239 Gustine 140
240 Lohn 140
241 East Texas Home School 140
242 Northside 139
243 Irving Universal Academy 137
244 Brookesmith 136
245 Lazbuddie 132
246 Fayette County Sports Association 125
247 Fort Worth Hill 123
248 Round Rock Christian 122
249 Trent 119
250 Fort Elliott 119
251 Loop 116
252 Clear Lake Christian 113
253 Patton Springs 111
254 Conroe Lifestyle Christian 111
255 Penelope 108
256 Selma River City Believers 107
257 Gold-Burg 105
258 Killeen Memorial 101
259 SA River City 100
260 Harrold 97

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.