Notice that the Krach trend line drops off dramatically within the first several teams, then flattens out which seems to indicate that the talent pool among the bottom 100 MN HS girls team is relatively homogenous. I'm not sure that this is the best of assumptions knowing the various levels of the girl's teams around the region. The Krach distribution can be modeled using the following exponential function
Y = AX^B where A = 1466.5, B = -1.0123 and X = Team ordinal rank
To make the Krach rating profile useful for the purposes of predicting actual future game score between teams, you will need to transform its rating profile using the following transformation equation:
Y = A*10^(Bx) where A = 0.00012417, B = 0.34586 and X = Krach Score
Here is a graph of the three distributions
Here is the game result comparison for Tue Jan 02, 2018
Code: Select all
[<--------- LSQRANK ------------>]
[ RAW ] [ Corrected ] [<-------- Jan 01 Profile ------>]
YYYY MM DD AWAY_TEAM HOME_TEAM ATS HTS ATS HTS [ PIM ] AWAY HOME PREDICT ACTUAL Residual
---- -- -- ----------------------- ---------------------- --- --- --- --- -------- -------- -------- ------- ------ -------
2018 01 02 ChisagoLakes Minneapolis 3 2 3.0 2.0 14 4 989.8354 991.8468 -2.0114 +1.00 -3.0114
2018 01 02 MankatoEast NewUlm 0 6 0.0 5.2 10 4 987.7293 992.6719 +4.9426 +5.20 -0.2574
2018 01 02 Blake Breck 3 1 2.8 1.0 4 6 999.6263 996.6429 +2.9834 +1.80 +1.1834
2018 01 02 MinnehahaUnited St.PaulUnited 1 10 0.8 11.75 6 6 989.8041 994.6318 +4.8277 +10.95 -6.1223
2018 01 02 Moorhead Bemidji 4 0 4.0 0.0 6 2 991.1780 987.9631 +3.2149 +4.0 -0.7851
2018 01 02 Wayzata EdenPrairie 1 4 1.0 4.0 6 8 996.7271 996.9053 +0.1782 +3.0 -2.8218
2018 01 02 Hopkins/St.LouisPark Minnetonka 1 6 1.0 5.4 6 4 994.8999 997.2163 +2.3164 +4.4 -2.0836
2018 01 02 Centennial ChamplinPark/CoonRapids 6 3 5.6 3.25 8 8 999.6040 994.1359 +5.4681 +2.35 +3.1181
2018 01 02 Owatonna Austin 7 1 7.0 1.0 2 8 991.1823 986.8917 +4.2906 +6.0 -1.7094
2018 01 02 Osseo/ParkCenter MoundWestonka 0 2 0.0 2.0 2 0 990.2798 992.1155 +1.8357 +2.0 -0.1643
2018 01 02 RiverLakes St.Cloud 0 3 0.0 3.0 0 4 991.8692 993.6653 +1.7961 +3.0 -1.2039
2018 01 02 NorthernLakes DetroitLakes 6 2 5.8 2.0 6 8 986.7534 987.4946 -0.7412 +3.8 -4.5412
2018 01 02 Hastings Stillwater 1 1 1.0 1.0 4 6 990.1077 992.9745 -2.8668 0.0 -2.8668
2018 01 02 Litchfield/Dassel-Cokato HenrySibley 2 3 2.0 2.8 10 8 987.1747 990.2014 +3.0267 +0.8 +2.2267
2018 01 02 WhiteBearLake Hill-Murray 0 3 0.0 2.8 6 6 995.7203 998.7587 +3.0384 +2.8 +0.2384
2018 01 02 RochesterMayo RochesterCentury - - -.- -.- - - 991.6283 984.4581 +7.1702 ____ _______
2018 01 02 Eveleth-Gilbert DuluthMarshall 1 6 0.8 6.05 4 12 988.5497 993.4131 +4.8634 +5.25 -0.3866
2018 01 02 EastGrandForks FargoNorth/South 5 4 4.8 3.8 6 4 993.6224 994.0375 -0.4151 +1.00 -1.4151
2018 01 02 Viroqua RockCounty 0 3 0.0 3.0 - - 987.9052 991.8922 +3.9870 +3.00 +0.9870
2018 01 02 AppletonUnited USMWildcats - - -.- -.- - - 987.3229 991.1075 +3.7846 _____ _______
2018 01 02 CapCityCougars Icebergs - - -.- -.- - - 990.2725 985.2761 +4.9964 _____ _______
2018 01 02 GrandForks DevilsLake 3 0 3.0 0.0 - - 986.6668 984.4254 +2.2414 +3.00 -0.7586
2018 01 02 Mandan Jamestown 4 0 4.0 0.0 - - 984.9303 983.1570 +1.7733 +4.00 -2.2267
=======
RMSE = 2.42
LSQRANK Predicted winner proportion 16 of 20 games = 80.00%
QRF Predicted winner proportion 15 of 19 games = 78.95%
KRACH Predicted winner proportion 13 of 16 games = 81.25%
MN Girls Rankings: January 2, 2018
[<------------------------------ LSQRANK ] [<------------------------------------------ QRF ] [<--------------------------------- KRACH ]
==============================================================================================================================================
1 Edina 1000.0000 1 Blake (14-0-1) 120.3 1 Blake 1321.266
2 Blake 999.6263 2 Centennial (13-1-1) 113.7 2 Centennial 1111.892
3 Centennial 999.6040 3 Eagan (14-2) 110.7 3 Edina 523.657
4 Hill-Murray 998.7587 4 Edina (11-1-1) 106.5 4 Eagan 298.647
5 Farmington 997.6146 5 Farmington (11-3) 100.7 5 Maple Grove 234.991
6 Andover 997.6012 6 Andover (10-3-1) 95.5 6 Andover 220.735
7 Blaine 997.5359 7 Minnetonka (9-3-3) 90.4 7 Blaine 183.136
8 Warroad 997.4886 8 Forest Lake (10-2-2) 89.7 8 Hill-Murray 180.47
9 MapleGrove 997.2404 9 Blaine (10-3-1) 87.0 9 Brainerd/Little Falls 136.332
10 Minnetonka 997.2163 10 Hill-Murray (12-3) 86.4 10 Minnetonka 132.482
11 Eagan 997.2013 11 Brainerd/Little Falls (13-3) 83.9 11 Forest Lake 130.817
12 EdenPrairie 996.9053 T-12 Lakeville South (9-6) 83.8 12 Farmington 129.695
13 Wayzata 996.7271 T-12 Roseau (11-4) 83.8 13 Roseau 94.565
14 LakevilleSouth 996.6654 14 Red Wing (12-4) 81.6 14 Eden Prairie 93.244
15 Breck 996.6429 15 Eden Prairie (10-6-1) 79.8 15 Warroad 76.718
16 Roseau 996.0683 16 White Bear Lake (12-4-1) 79.7 16 Lakeville South 76.204
17 ForestLake 996.0018 17 Maple Grove (9-4-3) 77.6 17 White Bear Lake 72.79
18 ElkRiver/Zimmerman 995.8557 18 Lakeville North (9-6) 77.1 18 Thief River Falls 68.295
19 LakevilleNorth 995.7372 19 Rochester Mayo (11-3) 76.4 19 Breck 67.37
20 WhiteBearLake 995.7203 20 Wayzata (8-5-1) 76.1 20 Lakeville North 58.784
21 Shakopee 995.7012 21 South St. Paul (12-3-1) 76.0 21 South St Paul 53.969
22 Cretin-DerhamHall 995.6613 22 Duluth Marshall (9-5) 73.1 22 Grand Rapids/Greenway 52.928
23 Brainerd/LittleFalls 995.6452 23 North Wright County (10-5-1) 72.4 23 Wayzata 51.68
24 SouthStPaul 995.2755 24 St. Cloud (10-4-1) 72.3 24 Shakopee 47.057
25 Anoka 995.2191 25 Holy Family Catholic/Waconia (11-5) 71.1 25 Elk River/Zimmerman 44.945
26 HolyFamily/Waconia 995.0869 26 St. Paul United (9-6) 70.7 26 Red Wing 43.933
27 AppleValley 995.0032 27 Thief River Falls (11-1-2) 70.6 27 Cretin-Derham Hall 39.365
28 GrandRapids/Greenway 994.9490 28 Warroad (11-2-2) 69.8 28 Holy Family/Waconia 38.661
30 Hopkins/St.LouisPark 994.8999 29 Hopkins/Park (10-5) 69.7 29 St. Cloud 37.307
31 Eastview 994.8671 30 Grand Rapids/Greenway (11-4-1) 69.5 30 Hopkins/St. Louis Park 36.434
32 Rogers 994.8450 31 CambridgeIsanti/Mora/Pine C (12-4) 69.3 31 St. Paul United 36.372
33 St.PaulUnited 994.6318 32 Shakopee (8-7-1) 69.2 32 Anoka 33.93
34 Burnsville 994.5434 33 Cretin-Derham Hall (8-6-1) 69.0 33 Alexandria 33.369
35 RedWing 994.5353 34 Breck (6-7-1) 67.5 34 Prior Lake 30.86
36 NorthWrightCounty 994.4183 35 Burnsville (7-7-2) 65.9 35 Duluth Marshall 29.034
37 Alexandria 994.2573 36 Alexandria (9-6) 65.8 36 North Wright County 27.165
39 MoundsView 994.2224 37 Champlin Park/Coon Rapids (9-4-1) 65.1 37 Rogers 25.746
40 ChamplinPark/CoonRapids 994.1359 38 Elk River/Zimmerman (6-6-2) 65.0 38 Cambridge-Isanti/Mora/PC 25.715
42 Chaska/Chanhassen 993.8835 39 Rogers (7-5-3) 64.9 39 East Grand Forks 25.388
43 Proctor/Hermantown 993.8751 40 Northfield (9-6-1) 64.5 40 Mounds View 25.036
44 Benilde-St.Margaret's 993.8239 41 St. Francis/North Branch (9-5) 64.3 41 Rochester Mayo 22.94
45 PriorLake 993.8149 42 Prior Lake (7-7-1) 64.0 42 Burnsville 22.729
46 ThiefRiverFalls 993.7694 43 Anoka (6-7-1) 63.9 43 Proctor/Hermantown 20.466
47 St.Cloud 993.6653 44 Mounds View (7-7-1) 61.4 44 Sartell/Sauk Rapids 19.252
48 EastGrandForks 993.6224 45 Sartell/Sauk Rapids (7-7-2) 60.7 45 Eastview 18.931
49 DodgeCounty 993.4684 46 New Ulm (12-3) 60.3 46 Champlin Park/Coon Rapids 17.072
50 DuluthMarshall 993.4131 47 Owatonna (9-4) 59.9 47 Apple Valley 16.858
51 NewPrague 993.2875 48 East Grand Forks (9-3-1) 59.0 48 St. Francis/North Branch 16.11
52 Cambridge-Isanti/Mora/PC 993.2645 49 Delano/Rockford (9-7) 58.2 49 Northfield 15.994
53 Delano/Rockford 993.1977 50 Apple Valley (6-9-1) 57.9 50 Rochester Lourdes 15.217
54 Roseville 993.0962 51 Proctor/Hermantown (8-8) 56.9 51 New Ulm 15.16
55 ParkofCottageGrove 993.0781 52 Dodge County (10-5) 56.7 52 Chaska/Chanhassen 14.527
56 EastRidge 992.9781 53 Eastview (4-9-2) 55.5 53 Benilde-St. Margaret's 14.025
58 Stillwater 992.9745 54 Mahtomedi (8-6-1) 54.2 54 Dodge County 13.998
59 Orono 992.9730 55 Hutchinson (7-7-1) 53.4 55 Delano/Rockford 13.953
60 RochesterLourdes 992.8905 56 Princeton/Big Lake/Becker (9-7-2) 53.2 56 Park of Cottage Grove 13.523
61 St.Francis/NorthBranch 992.8862 57 Faribault (9-6) 52.7 57 Mahtomedi 12.941
63 Hibbing/Chisholm 992.8453 58 C-E-C (5-7-1) 52.1 58 New Prague 11.3
65 Mahtomedi 992.7326 59 Rochester Lourdes/Dover-E (10-8) 51.8 59 Princeton 10.723
66 Cloquet-Esko-Carlton 992.6720 60 Park of Cottage Grove (6-8-1) 51.5 60 East Ridge 10.175
67 NewUlm 992.6719 61 Buffalo/Maple Lake (6-11) 50.7 61 Cloquet-Esko-Carlton 9.315
68 Sartell/SaukRapids 992.5963 62 Mankato East/Loyola (7-6) 50.1 62 Fergus Falls 9.243
70 FergusFalls 992.4310 63 East Ridge (6-10) 49.8 63 Orono 9.022
72 Princeton 992.3541 64 Mankato West (10-7) 48.8 64 Hutchinson 8.37
73 Duluth 992.3305 65 New Prague (6-8-1) 48.3 65 Buffalo 8.357
75 BloomingtonJefferson 992.2670 T-66 Chaska/Chanhassen (5-9-1) 47.1 66 Owatonna 8.354
76 SpringLakePark 992.2527 T-66 Spring Lake Park (7-9) 47.1 67 Bloomington Jefferson 7.113
77 Northfield 992.1600 68 Orono (6-10) 46.6 68 Duluth 7.044
78 Buffalo 992.1525 69 Bloomington Jefferson (6-9) 46.3 69 Stillwater 7.034
79 MoundWestonka 992.1155 70 Fergus Falls (9-8) 45.7 70 River Lakes 6.982
80 Hutchinson 991.9263 71 Benilde-St. Margaret's (5-9-1) 45.5 71 Moorhead 6.901
82 RiverLakes 991.8692 72 River Lakes (6-9) 45.4 72 Faribault 6.826
83 Minneapolis 991.8468 73 Henry Sibley (5-8) 43.3 73 Hibbing/Chisholm 6.667
86 RochesterMayo 991.6283 74 Hibbing/Chisholm (6-9-2) 43.2 74 Roseville 6.307
88 Willmar 991.2216 75 Totino-Grace (6-8-1) 43.0 75 Spring Lake Park 5.779
89 Owatonna 991.1823 76 Roseville (4-10-1) 42.9 76 Moose Lake Area 5.606
90 Moorhead 991.1780 77 Mound Westonka (5-7-2) 42.2 77 Willmar 5.544
95 InternationalFalls 990.8837 T-78 Willmar (6-9) 42.0 78 Mound Westonka 5.238
96 Totino-Grace 990.8821 T-78 Luverne (11-5-2) 42.0 79 International Falls 5.053
97 MooseLakeArea 990.8022 80 Minnehaha (8-6) 41.0 80 Minneapolis 4.972
98 HolyAngels 990.7048 81 International Falls (5-8-1) 40.7 81 Totino-Grace 4.398
104 Simley 990.3408 82 Moose Lake Area (5-7-1) 40.5 82 Osseo/Park Center 3.109
105 NorthSt.Paul/Tartan 990.3246 83 Stillwater Area (3-9-2) 40.1 83 Mankato East 3.037
106 Osseo/ParkCenter 990.2798 84 Minneapolis (6-9) 39.8 84 Mankato West 2.67
109 HenrySibley 990.2014 85 Austin (5-8) 39.5 85 Henry Sibley 2.389
110 Faribault 990.2005 86 Duluth (4-11-2) 39.2 86 Holy Angels 2.346
113 Hastings 990.1077 87 Marshall (7-8) 38.8 87 Chisago Lakes 2.024
121 ChisagoLakes 989.8354 88 Moorhead (3-9) 38.5 88 Rosemount 1.956
122 MinnehahaUnited 989.8041 89 Osseo/Park Center (5-8-1) 38.4 89 Simley 1.934
134 Rosemount 989.2863 90 Simley (4-9-1) 37.0 90 Eveleth-Gilbert 1.784
136 RobbinsdaleArmstrong/Cooper 989.1184 91 Rosemount (5-9-1) 36.3 91 Luverne 1.776
137 Irondale 989.0724 92 Prairie Centre (7-7) 34.6 92 North St. Paul/Tartan 1.727
140 PrairieCentre 988.9120 93 Chisago Lakes Area (4-11) 33.3 93 Prairie Centre 1.692
142 NorthShore 988.8156 94 Windom Area (6-6-1) 33.2 94 Minnehaha United 1.633
147 Eveleth-Gilbert 988.5497 T-95 Holy Angels/Richfield (4-9-1) 32.2 95 Marshall 1.526
150 MankatoWest 988.4001 T-95 Rochester John Marshall (5-11) 32.2 96 Irondale 1.509
151 Marshall 988.3303 97 North Shore (5-10) 30.9 97 Hastings 1.434
153 Woodbury 988.2157 98 Detroit Lakes (6-9) 30.6 98 Rochester John Marshall 1.353
160 Bemidji 987.9631 99 Eveleth-Gilbert (6-7-1) 30.4 99 Detroit Lakes 1.335
166 MankatoEast 987.7293 T-100 Minnesota River (5-9) 30.2 100 Austin 1.234
171 DetroitLakes 987.4946 T-100 North/Tartan (4-9-3) 30.2 101 Northern Lakes 1.119
174 Luverne 987.3180 102 Northern Lakes (5-7) 29.7 102 North Shore 1.019
175 Litchfield/Dassel-Cokato 987.1747 103 Hastings (2-13) 29.4 103 Bemidji 1.001
180 Austin 986.8917 104 Waseca (4-10) 28.8 104 Minnesota River 0.899
188 NorthernLakes 986.7534 105 Irondale/St. Anthony (3-13) 27.6 105 Windom 0.771
190 RochesterJohnMarshall 986.5773 106 Albert Lea (3-11) 24.5 106 Litchfield/Dassel-Cokato 0.722
194 MinnesotaRiver 986.3115 107 Litchfield/Dassel-Cokato (2-12) 24.3 107 Woodbury 0.668
198 Waseca 986.2136 108 Rochester Century (3-11) 23.9 108 Robbinsdale Armstrong/Cooper 0.53
203 Windom 985.6212 109 Bemidji (2-13) 23.7 109 Waseca 0.44
209 St.PaulBlades 985.1118 110 Worthington/Fulda (3-9) 23.5 110 Albert Lea 0.416
211 AlbertLea 985.0718 111 Robbinsdale Armstrong/Cooper (1-13) 21.9 111 Rochester Century 0.362
224 RochesterCentury 984.4581 112 Woodbury Area (2-13) 21.5 112 Worthington 0.312
232 ParkRapids 984.1031 113 St. Paul Blades (1-15) 17.0 113 St. Paul Blades 0.218
243 Crookston 983.1534 114 Park Rapids Area (2-13) 16.5 114 Park Rapids 0.143
251 Worthington 982.1207 115 Crookston (2-12) 15.6 115 Crookston 0.129
272 MorrisArea/BensonArea 980.2654 116 Fairmont (1-14) 13.9 116 Fairmont 0.071
274 Fairmont 979.8558 117 Morris/Benson Area (1-9) 11.8 117 Morris Area/Benson Area 0.053
QRF ND Girls Rankings: January 1, 2018 LSQRANK
====================================== ================================
1 Bismarck (7-3) 79.4 41 FargoNorth/South 994.0375
2 West Fargo (8-3-1) 77.5 64 Bismarck 992.7816
3 Fargo North/South (9-2) 73.5 92 WestFargoUnited 990.9773
T-4 Fargo Davies (6-4) 57.1 103 FargoDavies 990.3419
T-4 Minot (5-5) 57.1 158 Minot 988.0195
6 Grand Forks (5-4) 37.6 189 GrandForks 986.6668
7 Devils Lake (3-6) 32.9 212 Dickinson 984.9304
8 Dickinson (2-4) 25.4 213 Mandan 984.9303
9 Mandan (2-9) 25.3 225 DevilsLake 984.4254
10 Williston (3-6) 21.9 240 Williston 983.2816
11 Jamestown (2-8) 9.8 242 Jamestown 983.1570
247 Richland19U 982.9304
277 WatfordCity19U 979.2816