Strength of schedule
The NCAA Division III playoff selection committee determines strength of schedule using opponents' winning percentage and opponents' opponents' winning percentage. A team's SOS is two-thirds opponents' winning percentage (OWP) and one-third opponents' opponents' winning percentage (OOWP).Those numbers follow, calculated by PrestoSports.
We've sorted these teams by their strength of schedule. This is only part of the process used to determine who will get selected to the NCAA playoffs.
Records and winning percentage are based on all games vs. full Division III opponents.
Only games which have been played so far are counted here.
OWP: Opponents' winning percentage. OOWP: Opponents' opponents' winning percentage. SOS: two-thirds OWP and one-third OOWP.These numbers are more of a guidepost for the committee. There is no established standard for what it takes to be chosen as an at-large team, and in fact, teams in conferences with 10 members will always have their SOS trend toward .500 because of the high number of conference games. However, it is still something that is used in the selection process, which is why we note it here.
| Team | D3 record |
D3 win % |
OWP (rank) | OOWP | NCAA SOS |
| 1 Huntingdon | 4-3 | .571 | .7308 (1) | .5000 | 0.654 |
| 2 Augustana | 2-8 | .200 | .6552 (2) | .5326 | 0.614 |
| 3 Millikin | 4-6 | .400 | .6517 (3) | .5364 | 0.613 |
| 4 Salisbury | 8-1 | .889 | .6316 (4) | .5326 | 0.599 |
| 5 Bridgewater | 5-4 | .556 | .6316 (5) | .5094 | 0.591 |
| 6 Olivet | 1-8 | .111 | .6133 (7) | .5273 | 0.585 |
| 7 UW-La Crosse | 2-7 | .222 | .6176 (6) | .5106 | 0.582 |
| 8 Washington and Lee | 7-2 | .778 | .6000 (8) | .5362 | 0.579 |
| 9 Salve Regina | 7-3 | .700 | .5889 (12) | .5336 | 0.570 |
| 10 North Central (Ill.) | 8-1 | .889 | .5696 (24) | .5709 | 0.570 |
| 11 Cal Lutheran | 8-1 | .889 | .5909 (11) | .5230 | 0.568 |
| 12 Howard Payne | 1-8 | .111 | .5946 (10) | .5155 | 0.568 |
| 13 Wheaton (Ill.) | 8-2 | .800 | .5698 (23) | .5631 | 0.568 |
| 14 La Verne | 4-4 | .500 | .5833 (13) | .5324 | 0.566 |
| 15 Centre | 8-1 | .889 | .5775 (15) | .5417 | 0.566 |
| 16 DePauw | 3-5 | .375 | .6000 (9) | .4931 | 0.564 |
| 17 St. John Fisher | 8-2 | .800 | .5765 (16) | .5402 | 0.564 |
| 18 Nichols | 0-10 | .000 | .5778 (14) | .5289 | 0.561 |
| 19 North Park | 3-7 | .300 | .5765 (17) | .5257 | 0.560 |
| 20 Framingham State | 7-4 | .636 | .5729 (20) | .5296 | 0.558 |
| 21 Ithaca | 4-6 | .400 | .5730 (19) | .5286 | 0.558 |
| 22 Gustavus Adolphus | 2-7 | .222 | .5750 (18) | .5212 | 0.557 |
| 23 Western New England | 10-1 | .909 | .5670 (26) | .5335 | 0.556 |
| 24 UW-River Falls | 1-8 | .111 | .5714 (21) | .5182 | 0.554 |
| 25 Delaware Valley | 10-0 | 1.000 | .5698 (22) | .5216 | 0.554 |
| 26 Mass-Dartmouth | 5-5 | .500 | .5632 (28) | .5346 | 0.554 |
| 27 Redlands | 8-1 | .889 | .5588 (31) | .5314 | 0.550 |
| 28 FDU-Florham | 1-8 | .111 | .5641 (27) | .5206 | 0.550 |
| 29 Austin | 0-8 | .000 | .5606 (30) | .5254 | 0.549 |
| 30 Westfield State | 5-5 | .500 | .5568 (33) | .5250 | 0.546 |
| 31 Albion | 6-2 | .750 | .5455 (41) | .5452 | 0.545 |
| 32 Hampden-Sydney | 8-2 | .800 | .5488 (39) | .5376 | 0.545 |
| 33 Plymouth State | 4-6 | .400 | .5568 (34) | .5193 | 0.544 |
| 34 Birmingham-Southern | 6-2 | .750 | .5410 (47) | .5495 | 0.544 |
| 35 Hope | 7-3 | .700 | .5476 (40) | .5347 | 0.543 |
| 36 John Carroll | 5-5 | .500 | .5632 (29) | .4980 | 0.541 |
| 37 Wilkes | 4-5 | .444 | .5513 (37) | .5213 | 0.541 |
| 38 Stevenson | 1-8 | .111 | .5513 (38) | .5194 | 0.541 |
| 39 St. John's | 6-4 | .600 | .5517 (36) | .5173 | 0.540 |
| 40 Illinois Wesleyan | 9-1 | .900 | .5341 (60) | .5522 | 0.540 |
| 41 Utica | 5-5 | .500 | .5402 (49) | .5366 | 0.539 |
| 42 Simpson | 5-5 | .500 | .5581 (32) | .4939 | 0.537 |
| 43 Massachusetts Maritime | 5-4 | .556 | .5443 (44) | .5174 | 0.535 |
| 44 Hartwick | 2-8 | .200 | .5393 (51) | .5270 | 0.535 |
| 45 Texas Lutheran | 5-5 | .500 | .5375 (54) | .5278 | 0.534 |
| 46 Catholic | 4-5 | .444 | .5417 (46) | .5164 | 0.533 |
| 47 Pomona-Pitzer | 0-9 | .000 | .5441 (45) | .5108 | 0.533 |
| 48 Linfield | 8-0 | 1.000 | .5517 (35) | .4948 | 0.533 |
| 49 Chicago | 5-5 | .500 | .5696 (25) | .4573 | 0.532 |
| 50 UW-Oshkosh | 7-2 | .778 | .5362 (55) | .5224 | 0.532 |
| 51 Lycoming | 8-2 | .800 | .5349 (57) | .5246 | 0.531 |
| 52 UW-Stout | 3-5 | .375 | .5323 (63) | .5297 | 0.531 |
| 53 McMurry | 7-1 | .875 | .5303 (65) | .5312 | 0.531 |
| 54 Sul Ross State | 1-7 | .125 | .5303 (67) | .5312 | 0.531 |
| 55 Rhodes | 3-6 | .333 | .5303 (66) | .5304 | 0.530 |
| 56 Alma | 2-7 | .222 | .5395 (50) | .5118 | 0.530 |
| 57 St. Norbert | 7-3 | .700 | .5444 (42) | .5012 | 0.530 |
| 58 Albright | 6-4 | .600 | .5349 (58) | .5192 | 0.530 |
| 59 Millsaps | 4-5 | .444 | .5286 (70) | .5316 | 0.530 |
| 60 Hardin-Simmons | 6-4 | .600 | .5316 (64) | .5218 | 0.528 |
| 61 Lawrence | 1-9 | .100 | .5444 (43) | .4938 | 0.528 |
| 62 Rochester | 3-5 | .375 | .5385 (53) | .5050 | 0.527 |
| 63 Alfred | 7-3 | .700 | .5176 (85) | .5442 | 0.526 |
| 64 King's | 1-8 | .111 | .5256 (72) | .5246 | 0.525 |
| 65 Randolph-Macon | 8-2 | .800 | .5294 (68) | .5165 | 0.525 |
| 66 Bethel | 8-2 | .800 | .5227 (79) | .5287 | 0.525 |
| 67 Hamline | 0-10 | .000 | .5357 (56) | .5014 | 0.524 |
| 68 Capital | 5-5 | .500 | .5349 (59) | .5027 | 0.524 |
| 69 Buffalo State | 5-5 | .500 | .5333 (61) | .5056 | 0.524 |
| 70 Lebanon Valley | 7-3 | .700 | .5233 (76) | .5235 | 0.523 |
| 71 Endicott | 9-1 | .900 | .5111 (94) | .5476 | 0.523 |
| 72 Rowan | 5-5 | .500 | .5333 (62) | .5017 | 0.523 |
| 73 St. Olaf | 8-2 | .800 | .5172 (87) | .5338 | 0.523 |
| 74 Sewanee | 4-5 | .444 | .5070 (97) | .5527 | 0.522 |
| 75 Carthage | 5-5 | .500 | .5056 (101) | .5530 | 0.521 |
| 76 Western Connecticut | 0-10 | .000 | .5393 (52) | .4835 | 0.521 |
| 77 LaGrange | 2-6 | .250 | .5238 (74) | .5090 | 0.519 |
| 78 Fitchburg State | 2-8 | .200 | .5233 (77) | .5089 | 0.518 |
| 79 Montclair State | 8-2 | .800 | .5222 (82) | .5084 | 0.518 |
| 80 Carleton | 2-8 | .200 | .5233 (78) | .5060 | 0.518 |
| 81 Monmouth | 9-1 | .900 | .5222 (81) | .5039 | 0.516 |
| 82 Chapman | 4-4 | .500 | .5082 (95) | .5320 | 0.516 |
| 83 Claremont-Mudd-Scripps | 4-5 | .444 | .5152 (89) | .5160 | 0.515 |
| 84 Luther | 3-6 | .333 | .5256 (71) | .4946 | 0.515 |
| 85 Kean | 9-1 | .900 | .5233 (75) | .4994 | 0.515 |
| 86 Lake Forest | 3-7 | .300 | .5222 (83) | .4983 | 0.514 |
| 87 Wilmington | 0-10 | .000 | .5227 (80) | .4961 | 0.514 |
| 88 Bridgewater State | 7-2 | .778 | .5063 (99) | .5292 | 0.514 |
| 89 East Texas Baptist | 5-5 | .500 | .5000 (108) | .5397 | 0.513 |
| 90 UW-Stevens Point | 3-6 | .333 | .5072 (96) | .5235 | 0.513 |
| 91 Kalamazoo | 4-6 | .400 | .5238 (73) | .4893 | 0.512 |
| 92 Wooster | 4-5 | .444 | .5405 (48) | .4538 | 0.512 |
| 93 Mary Hardin-Baylor | 9-0 | 1.000 | .4932 (117) | .5481 | 0.511 |
| 94 UW-Platteville | 7-3 | .700 | .5000 (104) | .5338 | 0.511 |
| 95 St. Lawrence | 3-6 | .333 | .5205 (84) | .4926 | 0.511 |
| 96 Adrian | 7-2 | .778 | .5000 (102) | .5333 | 0.511 |
| 97 Trinity (Texas) | 10-0 | 1.000 | .4868 (129) | .5593 | 0.511 |
| 98 Concordia-Moorhead | 5-4 | .556 | .5000 (107) | .5315 | 0.510 |
| 99 Mount Union | 9-0 | 1.000 | .5125 (91) | .5058 | 0.510 |
| 100 Otterbein | 2-7 | .222 | .5125 (92) | .5058 | 0.510 |
| 101 Buena Vista | 2-8 | .200 | .5176 (86) | .4938 | 0.510 |
| 102 Augsburg | 6-4 | .600 | .5116 (93) | .5053 | 0.510 |
| 103 Springfield | 6-4 | .600 | .4943 (114) | .5373 | 0.509 |
| 104 MIT | 2-7 | .222 | .4875 (127) | .5478 | 0.508 |
| 105 Elmhurst | 6-4 | .600 | .4773 (149) | .5682 | 0.508 |
| 106 Coast Guard | 2-7 | .222 | .5065 (98) | .5090 | 0.507 |
| 107 Muhlenberg | 7-3 | .700 | .5169 (88) | .4840 | 0.506 |
| 108 Wartburg | 8-2 | .800 | .5059 (100) | .5049 | 0.506 |
| 109 UW-Eau Claire | 5-4 | .556 | .4857 (131) | .5417 | 0.504 |
| 110 UW-Whitewater | 8-0 | 1.000 | .4839 (132) | .5451 | 0.504 |
| 111 Hanover | 5-5 | .500 | .5294 (69) | .4528 | 0.504 |
| 112 Wittenberg | 6-2 | .750 | .5000 (103) | .5094 | 0.503 |
| 113 Union | 6-4 | .600 | .4938 (116) | .5203 | 0.503 |
| 114 Ripon | 6-4 | .600 | .5000 (106) | .5034 | 0.501 |
| 115 Muskingum | 4-6 | .400 | .5000 (109) | .5020 | 0.501 |
| 116 Knox | 0-10 | .000 | .5000 (111) | .5018 | 0.501 |
| 117 Waynesburg | 5-4 | .556 | .5128 (90) | .4760 | 0.501 |
| 118 Coe | 6-3 | .667 | .5000 (105) | .4986 | 0.500 |
| 119 Hobart | 7-1 | .875 | .4923 (119) | .5067 | 0.497 |
| 120 Beloit | 2-8 | .200 | .4889 (124) | .5130 | 0.497 |
| 121 Cortland | 8-2 | .800 | .4889 (120) | .5101 | 0.496 |
| 122 Brockport | 3-7 | .300 | .4889 (123) | .5101 | 0.496 |
| 123 Central | 7-3 | .700 | .4824 (140) | .5173 | 0.494 |
| 124 Illinois College | 9-1 | .900 | .4778 (146) | .5230 | 0.493 |
| 125 Heidelberg | 8-2 | .800 | .4828 (137) | .5125 | 0.493 |
| 126 Curry | 5-4 | .556 | .4625 (166) | .5439 | 0.490 |
| 127 Guilford | 2-7 | .222 | .4737 (156) | .5204 | 0.489 |
| 128 Dickinson | 4-6 | .400 | .4943 (115) | .4784 | 0.489 |
| 129 Franklin and Marshall | 3-7 | .300 | .4886 (125) | .4884 | 0.489 |
| 130 Trine | 6-3 | .667 | .4730 (159) | .5187 | 0.488 |
| 131 Merchant Marine | 3-6 | .333 | .4930 (118) | .4781 | 0.488 |
| 132 Moravian | 2-8 | .200 | .4944 (113) | .4737 | 0.487 |
| 133 Oberlin | 3-6 | .333 | .5000 (110) | .4621 | 0.487 |
| 134 Carroll | 7-3 | .700 | .4778 (147) | .5067 | 0.487 |
| 135 Case Western Reserve | 9-0 | 1.000 | .4861 (130) | .4894 | 0.487 |
| 136 Grove City | 3-7 | .300 | .4881 (126) | .4835 | 0.487 |
| 137 Ohio Northern | 6-4 | .600 | .4773 (150) | .5046 | 0.486 |
| 138 Washington and Jefferson | 6-4 | .600 | .4828 (138) | .4887 | 0.485 |
| 139 Wabash | 9-0 | 1.000 | .4795 (144) | .4955 | 0.485 |
| 140 Willamette | 3-5 | .375 | .4833 (133) | .4871 | 0.485 |
| 141 Whitworth | 4-5 | .444 | .4769 (152) | .4973 | 0.484 |
| 142 RPI | 4-5 | .444 | .4795 (145) | .4919 | 0.484 |
| 143 Gettysburg | 6-4 | .600 | .4831 (134) | .4828 | 0.483 |
| 144 Allegheny | 5-5 | .500 | .4872 (128) | .4730 | 0.482 |
| 145 Grinnell | 5-5 | .500 | .4773 (151) | .4920 | 0.482 |
| 146 St. Vincent | 5-4 | .556 | .4744 (154) | .4977 | 0.482 |
| 147 Concordia (Wis.) | 4-6 | .400 | .4889 (121) | .4657 | 0.481 |
| 148 Morrisville State | 1-9 | .100 | .4667 (165) | .5090 | 0.481 |
| 149 Lakeland | 4-6 | .400 | .4889 (122) | .4644 | 0.481 |
| 150 Pacific | 1-6 | .143 | .4808 (142) | .4803 | 0.481 |
| 151 Ferrum | 7-3 | .700 | .4824 (141) | .4759 | 0.480 |
| 152 Whittier | 2-6 | .250 | .4500 (178) | .5404 | 0.480 |
| 153 Thiel | 0-10 | .000 | .4828 (139) | .4721 | 0.479 |
| 154 Carnegie Mellon | 3-4 | .429 | .4737 (155) | .4883 | 0.479 |
| 155 Eureka | 4-6 | .400 | .4944 (112) | .4460 | 0.478 |
| 156 Pacific Lutheran | 5-3 | .625 | .4667 (164) | .5010 | 0.478 |
| 157 Christopher Newport | 8-1 | .889 | .4805 (143) | .4720 | 0.478 |
| 158 TCNJ | 7-3 | .700 | .4607 (167) | .5113 | 0.478 |
| 159 Northwestern (Minn.) | 6-4 | .600 | .4831 (135) | .4662 | 0.477 |
| 160 Geneva | 4-6 | .400 | .4713 (162) | .4880 | 0.477 |
| 161 William Paterson | 4-6 | .400 | .4607 (169) | .5079 | 0.476 |
| 162 Ursinus | 6-4 | .600 | .4719 (160) | .4851 | 0.476 |
| 163 Cornell | 2-7 | .222 | .4737 (157) | .4788 | 0.475 |
| 164 Juniata | 1-9 | .100 | .4719 (161) | .4800 | 0.475 |
| 165 Minnesota-Morris | 5-5 | .500 | .4831 (136) | .4572 | 0.474 |
| 166 Wisconsin Lutheran | 6-4 | .600 | .4778 (148) | .4657 | 0.474 |
| 167 Averett | 3-7 | .300 | .4767 (153) | .4673 | 0.474 |
| 168 Puget Sound | 0-8 | .000 | .4737 (158) | .4714 | 0.473 |
| 169 Bethany | 4-5 | .444 | .4684 (163) | .4820 | 0.473 |
| 170 Marietta | 3-7 | .300 | .4545 (176) | .5097 | 0.473 |
| 171 Dubuque | 8-1 | .889 | .4487 (182) | .5188 | 0.472 |
| 172 Widener | 8-2 | .800 | .4419 (187) | .5325 | 0.472 |
| 173 Greenville | 7-3 | .700 | .4607 (168) | .4817 | 0.468 |
| 174 Westminster (Pa.) | 5-5 | .500 | .4598 (170) | .4799 | 0.466 |
| 175 Susquehanna | 6-4 | .600 | .4545 (175) | .4879 | 0.466 |
| 176 McDaniel | 2-8 | .200 | .4545 (177) | .4866 | 0.465 |
| 177 Johns Hopkins | 9-0 | 1.000 | .4568 (174) | .4812 | 0.465 |
| 178 N.C. Wesleyan | 2-8 | .200 | .4588 (173) | .4676 | 0.462 |
| 179 Washington U. | 4-2 | .667 | .4286 (196) | .5258 | 0.461 |
| 180 WPI | 2-6 | .250 | .4462 (186) | .4854 | 0.459 |
| 181 Defiance | 4-6 | .400 | .4588 (172) | .4595 | 0.459 |
| 182 Concordia-Chicago | 8-2 | .800 | .4494 (179) | .4745 | 0.458 |
| 183 Loras | 1-9 | .100 | .4419 (188) | .4891 | 0.458 |
| 184 Kenyon | 0-9 | .000 | .4400 (189) | .4786 | 0.453 |
| 185 Martin Luther | 2-8 | .200 | .4494 (180) | .4591 | 0.453 |
| 186 Crown | 0-10 | .000 | .4494 (181) | .4591 | 0.453 |
| 187 Shenandoah | 6-4 | .600 | .4353 (190) | .4864 | 0.452 |
| 188 Methodist | 3-7 | .300 | .4471 (185) | .4616 | 0.452 |
| 189 Bluffton | 5-5 | .500 | .4471 (183) | .4606 | 0.452 |
| 190 Manchester | 4-6 | .400 | .4471 (184) | .4606 | 0.452 |
| 191 Aurora | 3-7 | .300 | .4333 (192) | .4768 | 0.448 |
| 192 Ohio Wesleyan | 4-5 | .444 | .4247 (199) | .4910 | 0.447 |
| 193 Husson | 0-9 | .000 | .4595 (171) | .4165 | 0.445 |
| 194 St. Scholastica | 10-0 | 1.000 | .4270 (198) | .4727 | 0.442 |
| 195 Mount St. Joseph | 6-4 | .600 | .4302 (194) | .4617 | 0.441 |
| 196 Worcester State | 8-2 | .800 | .4000 (207) | .5222 | 0.441 |
| 197 Norwich | 7-3 | .700 | .4302 (193) | .4605 | 0.440 |
| 198 Denison | 5-5 | .500 | .4167 (200) | .4808 | 0.438 |
| 199 Franklin | 8-0 | 1.000 | .4286 (195) | .4517 | 0.436 |
| 200 Anderson | 1-7 | .125 | .4286 (197) | .4517 | 0.436 |
| 201 Rose-Hulman | 5-5 | .500 | .4167 (201) | .4755 | 0.436 |
| 202 Maryville (Tenn.) | 4-5 | .444 | .4054 (204) | .4820 | 0.431 |
| 203 Westminster (Mo.) | 8-2 | .800 | .4157 (202) | .4565 | 0.429 |
| 204 Benedictine | 7-3 | .700 | .4000 (209) | .4812 | 0.427 |
| 205 Lewis and Clark | 7-2 | .778 | .4000 (208) | .4748 | 0.425 |
| 206 Anna Maria | 2-8 | .200 | .4337 (191) | .4004 | 0.423 |
| 207 Rockford | 0-10 | .000 | .4045 (205) | .4582 | 0.422 |
| 208 Greensboro | 0-9 | .000 | .4026 (206) | .4579 | 0.421 |
| 209 Hiram | 1-9 | .100 | .4000 (210) | .4530 | 0.418 |
| 210 Gallaudet | 4-4 | .500 | .4058 (203) | .4295 | 0.414 |
| 211 Castleton | 4-6 | .400 | .3855 (211) | .4439 | 0.405 |
| 212 SUNY-Maritime | 8-1 | .889 | .3377 (212) | .4505 | 0.375 |
| 213 Macalester | 3-5 | .375 | .3000 (213) | .4779 | 0.359 |
| 214 Berry | 0-0 | .000 | .0000 (214) | .0000 | 0.000 |
| 215 Belhaven | 0-0 | .000 | .0000 (215) | .0000 | 0.000 |
| 216 Alfred State | 0-0 | .000 | .0000 (216) | .0000 | 0.000 |
| 217 Alvernia | 0-0 | .000 | .0000 (217) | .0000 | 0.000 |
| 218 Amherst | 0-0 | .000 | .0000 (218) | .0000 | 0.000 |
| 219 Baldwin Wallace | 0-0 | .000 | .0000 (219) | .0000 | 0.000 |
| 220 Bates | 0-0 | .000 | .0000 (220) | .0000 | 0.000 |
| 221 Bowdoin | 0-0 | .000 | .0000 (221) | .0000 | 0.000 |
| 222 Brevard | 0-0 | .000 | .0000 (222) | .0000 | 0.000 |
| 223 Colby | 0-0 | .000 | .0000 (223) | .0000 | 0.000 |
| 224 Dean | 0-0 | .000 | .0000 (224) | .0000 | 0.000 |
| 225 Eastern | 0-0 | .000 | .0000 (225) | .0000 | 0.000 |
| 226 George Fox | 0-0 | .000 | .0000 (226) | .0000 | 0.000 |
| 227 Hamilton | 0-0 | .000 | .0000 (227) | .0000 | 0.000 |
| 228 Hendrix | 0-0 | .000 | .0000 (228) | .0000 | 0.000 |
| 229 Hilbert | 0-0 | .000 | .0000 (229) | .0000 | 0.000 |
| 230 Keystone | 0-0 | .000 | .0000 (230) | .0000 | 0.000 |
| 231 Lyon | 0-0 | .000 | .0000 (231) | .0000 | 0.000 |
| 232 Middlebury | 0-0 | .000 | .0000 (232) | .0000 | 0.000 |
| 233 Misericordia | 0-0 | .000 | .0000 (233) | .0000 | 0.000 |
| 234 Nebraska Wesleyan | 0-0 | .000 | .0000 (234) | .0000 | 0.000 |
| 235 Southern Virginia | 0-0 | .000 | .0000 (235) | .0000 | 0.000 |
| 236 Southwestern | 0-0 | .000 | .0000 (236) | .0000 | 0.000 |
| 237 Trinity (Conn.) | 0-0 | .000 | .0000 (237) | .0000 | 0.000 |
| 238 Tufts | 0-0 | .000 | .0000 (238) | .0000 | 0.000 |
| 239 University of New England | 0-0 | .000 | .0000 (239) | .0000 | 0.000 |
| 240 Wesleyan | 0-0 | .000 | .0000 (240) | .0000 | 0.000 |
| 241 Williams | 0-0 | .000 | .0000 (241) | .0000 | 0.000 |
Note: Because the NESCAC does not permit teams to participate in the football playoffs, we do not include their games in these calculations.