Solution results for MinV and CLP for seven major American sports, using win counts; Opt = optimal objective function value; Secs = seconds of solution time; Gap = gap between solution and optimal solution_
| Non-Zeros | MinV | CLP | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Sport | Teams | Opt | Zeros | Mean | SD | Secs | Gap | Secs | Gap |
| CBB 2022 | 301 | 465 | 97.2% | 1.73 | 1.01 | 102.2 | - | 356% | |
| CBB 2023 | 305 | 488 | 97.0% | 1.70 | 0.98 | 252.2 | - | 345% | |
| CBB 2024 | 305 | 499 | 97.0% | 1.65 | 0.95 | 67.3 | - | 324% | |
| CFB 2021 | 130 | 72 | 96.2% | 1.01 | 0.07 | 0.7 | - | 226% | |
| CFB 2022 | 131 | 84 | 96.3% | 1.00 | 0.05 | 2.2 | - | 220% | |
| CFB 2023 | 133 | 74 | 96.3% | 1.00 | 0.05 | 2.0 | - | 238% | |
| MBB 2022 | 358 | 347 | 97.7% | 1.28 | 0.51 | 2,166 | - | 421% | |
| MBB 2023 | 363 | 417 | 97.6% | 1.27 | 0.50 | 31,453 | 5.76% | 346% | |
| MBB 2024 | 362 | 451 | 97.6% | 1.25 | 0.47 | 230,815 | 7.78% | 330% | |
| MLB 2021 | 30 | 91 | 74.3% | 3.00 | 2.48 | 1.0 | - | 0.1 | - |
| MLB 2022 | 30 | 95 | 71.0% | 2.84 | 2.34 | 0.8 | - | 0.1 | - |
| MLB 2023 | 30 | 149 | 57.6% | 2.17 | 1.60 | 1.1 | - | 0.1 | - |
| NBA 2022 | 30 | 63 | 70.1% | 2.20 | 0.91 | 0.6 | - | 0.1 | - |
| NBA 2023 | 30 | 78 | 71.7% | 2.20 | 0.92 | 0.8 | - | 0.1 | - |
| NBA 2024 | 30 | 61 | 71.7% | 2.25 | 0.99 | 0.6 | - | 0.1 | - |
| NFL 2021 | 32 | 37 | 82.1% | 1.17 | 0.38 | 0.7 | - | 0.1 | - |
| NFL 2022 | 32 | 28 | 82.9% | 1.13 | 0.36 | 0.5 | - | 0.1 | - |
| NFL 2023 | 32 | 38 | 82.6% | 1.14 | 0.34 | 0.6 | - | 0.1 | - |
| NHL 2022 | 32 | 105 | 65.9% | 1.97 | 0.82 | 1.0 | - | 0.1 | - |
| NHL 2023 | 32 | 99 | 67.5% | 1.93 | 0.83 | 1.1 | - | 0.1 | - |
| NHL 2024 | 32 | 114 | 69.0% | 1.97 | 0.84 | 1.2 | - | 0.2 | - |
Solution results for MinV and CLP for seven major American sports, using collective victory margins; Opt = optimal objective function value; Secs = seconds of solution time; Gap = gap between solution and optimal solution_
| Non-Zeros | MinV | CLP | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Sport | Teams | Opt | Zeros | Mean | SD | Secs | Gap | Secs | Gap |
| CBB 2022 | 301 | 1977 | 96.9% | 9.91 | 9.00 | 36.8 | - | 568% | |
| CBB 2023 | 305 | 2153 | 96.8% | 9.85 | 8.26 | 140.2 | - | 549% | |
| CBB 2024 | 305 | 2165 | 96.8% | 9.68 | 8.29 | 29.2 | - | 510% | |
| CFB 2021 | 130 | 483 | 96.2% | 16.75 | 13.12 | 0.6 | - | 14.7 | - |
| CFB 2022 | 131 | 584 | 96.2% | 15.65 | 12.99 | 0.8 | - | 13.6 | - |
| CFB 2023 | 133 | 526 | 96.3% | 16.23 | 12.71 | 0.9 | - | 15.2 | - |
| MBB 2022 | 358 | 3161 | 97.3% | 15.24 | 11.95 | 141.9 | - | 661% | |
| MBB 2023 | 363 | 3584 | 97.2% | 14.94 | 11.88 | 770.7 | 0.22% | 608% | |
| MBB 2024 | 362 | 3666 | 97.2% | 15.16 | 12.06 | 203.0 | - | 619% | |
| MLB 2021 | 30 | 366 | 71.7% | 12.95 | 12.88 | 1.0 | - | 0.1 | - |
| MLB 2022 | 30 | 304 | 70.9% | 12.22 | 11.21 | 0.7 | - | 0.1 | - |
| MLB 2023 | 30 | 561 | 55.7% | 9.61 | 8.54 | 1.3 | - | 0.1 | - |
| NBA 2022 | 30 | 1070 | 54.4% | 24.53 | 19.97 | 1.0 | - | 0.1 | - |
| NBA 2023 | 30 | 1212 | 54.6% | 21.15 | 17.88 | 1.4 | - | 0.1 | - |
| NBA 2024 | 30 | 904 | 54.1% | 25.28 | 20.63 | 1.2 | - | 0.1 | - |
| NFL 2021 | 32 | 349 | 80.7% | 14.38 | 12.82 | 0.8 | - | 0.1 | - |
| NFL 2022 | 32 | 229 | 80.5% | 10.81 | 9.68 | 0.6 | - | 0.1 | - |
| NFL 2023 | 32 | 279 | 80.0% | 12.49 | 11.46 | 0.6 | - | 0.1 | - |
| NHL 2022 | 32 | 260 | 57.9% | 4.26 | 2.88 | 1.2 | - | 0.1 | - |
| NHL 2023 | 32 | 259 | 58.2% | 4.24 | 2.75 | 1.8 | - | 0.2 | - |
| NHL 2024 | 32 | 290 | 59.5% | 4.16 | 2.81 | 1.6 | - | 0.1 | - |