[Bumped. Another tool for anyone who, like me, hasn't filled out their bracket yet. Dan, can you provide a little more technical information on how you calculate these ratings? Looks like a ton of work. -KJ]
(Alternate title: This Is Your Bracket on KRACH.)
Undoubtedly you have seen the log5 breakdowns of the bracket over at Basketball Prospectus, based on Ken Pomeroy's rankings. (If you haven't, what's stopping you? The link is to the Midwest preview, but the others are available as well.) You may also recall that back in December, I posted a short article on the Bradley-Terry ranking method (familiar to college hockey fans as KRACH) and applying it to college basketball as a potential RPI substitute. The main point in its favor is that exceptionally strong or weak opponents cannot have such a significant effect on strength of schedule that a loss raises your rating or a win lowers it; this is a significant flaw in the RPI (and some other record-only rating systems; it can happen in points-based rankings like Pomeroy's but that's because you won by less than his model predicted, so it's not really a flaw there). In fact, if you were to play the world's most awful team, a team that would never beat anyone, your rating would remain exactly unchanged (assuming you won). Likewise if you lost to a theoretically perfect team who had an infinite rating.
Another useful point about the Bradley-Terry method is that it, like Pomeroy's rankings, provides an easy method to calculate the odds of one team beating another: simply divide Team A's rating by the sum of (Team A's rating) and (Team B's rating), and you have Team A's probability of defeating Team B. (The formula for Pomeroy's rankings is only slightly more complex.) So I decided to do a similar bracket breakdown, giving odds of each and every team reaching each round.
Odds table after the jump.
| Team | Seed | B-T Rating |
2nd Round | Sweet 16 | Elite 8 | Final 4 | Title Game | Champ |
|---|---|---|---|---|---|---|---|---|
| Kansas | M1 | 95.3024 | 99.24% | 87.98% | 78.51% | 67.24% | 52.22% | 38.24% |
| Kentucky | E1 | 59.9940 | 98.36% | 82.45% | 63.84% | 44.67% | 32.60% | 17.42% |
| Syracuse | W1 | 43.7536 | 96.85% | 77.40% | 59.79% | 42.18% | 19.15% | 10.84% |
| West Virginia | E2 | 35.4880 | 95.98% | 75.83% | 50.67% | 24.29% | 15.01% | 6.30% |
| Duke | S1 | 29.6715 | 98.71% | 76.44% | 48.07% | 29.81% | 13.36% | 5.11% |
| Villanova | S2 | 24.3322 | 96.00% | 66.38% | 41.52% | 21.70% | 8.74% | 2.99% |
| Kansas St | W2 | 24.8326 | 93.90% | 61.30% | 40.01% | 19.26% | 6.59% | 2.86% |
| New Mexico | E3 | 23.2448 | 91.93% | 64.65% | 30.60% | 11.80% | 6.10% | 2.03% |
| Purdue | S4 | 23.8606 | 77.48% | 50.70% | 26.05% | 14.83% | 5.91% | 2.00% |
| Temple | E5 | 24.3970 | 71.62% | 49.37% | 17.60% | 8.74% | 4.62% | 1.59% |
| Georgetown | M3 | 20.1088 | 91.46% | 54.82% | 33.83% | 9.15% | 4.07% | 1.57% |
| Baylor | S3 | 19.3236 | 90.74% | 62.27% | 31.76% | 14.84% | 5.23% | 1.56% |
| PIttsburgh | W3 | 17.2214 | 82.78% | 52.88% | 24.71% | 9.87% | 2.74% | 0.96% |
| Ohio St | M2 | 16.2168 | 88.81% | 57.34% | 28.18% | 6.68% | 2.64% | 0.89% |
| Butler | W5 | 16.7066 | 65.70% | 40.92% | 14.37% | 6.96% | 1.89% | 0.65% |
| BYU | W7 | 16.4780 | 68.24% | 29.35% | 16.39% | 6.39% | 1.73% | 0.59% |
| Tennessee | M6 | 16.4854 | 64.64% | 31.59% | 18.03% | 4.32% | 1.72% | 0.59% |
| Texas A&M | S5 | 15.8677 | 70.84% | 33.02% | 13.84% | 6.52% | 2.03% | 0.54% |
| Maryland | M4 | 12.9482 | 86.71% | 50.72% | 8.46% | 3.86% | 1.34% | 0.39% |
| Vanderbilt | W4 | 12.8231 | 71.64% | 35.07% | 10.46% | 4.40% | 1.01% | 0.29% |
| Wisconsin | E4 | 13.6242 | 79.52% | 33.61% | 8.30% | 3.01% | 1.17% | 0.28% |
| Xavier | W6 | 12.1174 | 67.33% | 31.97% | 12.29% | 4.01% | 0.89% | 0.25% |
| Michigan St | M5 | 11.7461 | 76.19% | 40.09% | 6.22% | 2.69% | 0.88% | 0.24% |
| N Iowa | M9 | 14.0160 | 59.14% | 7.95% | 4.43% | 2.10% | 0.76% | 0.24% |
| Texas | E8 | 13.6891 | 62.03% | 12.28% | 5.56% | 2.02% | 0.79% | 0.19% |
| Gonzaga | W8 | 11.8179 | 54.00% | 12.64% | 6.14% | 2.47% | 0.54% | 0.15% |
| St Mary's | S10 | 11.2242 | 51.73% | 17.58% | 7.79% | 2.67% | 0.66% | 0.14% |
| Marquette | E6 | 11.5208 | 60.63% | 22.63% | 7.25% | 1.81% | 0.64% | 0.14% |
| Notre Dame | S6 | 10.3006 | 59.91% | 23.56% | 8.54% | 2.77% | 0.64% | 0.13% |
| Richmond | S7 | 10.4714 | 48.27% | 15.70% | 6.71% | 2.20% | 0.52% | 0.10% |
| Oklahoma St | M7 | 9.7051 | 54.87% | 23.32% | 8.61% | 1.45% | 0.42% | 0.10% |
| Florida St | W9 | 10.0687 | 46.00% | 9.60% | 4.29% | 1.57% | 0.31% | 0.08% |
| Missouri | E10 | 9.6902 | 51.40% | 12.37% | 4.57% | 1.01% | 0.32% | 0.06% |
| Louisville | S9 | 8.9170 | 51.61% | 12.41% | 4.34% | 1.47% | 0.31% | 0.05% |
| San Diego St | M11 | 9.0186 | 35.36% | 12.51% | 5.33% | 0.85% | 0.23% | 0.05% |
| UNLV | M8 | 9.6847 | 40.86% | 4.03% | 1.88% | 0.73% | 0.21% | 0.05% |
| UTEP | W12 | 8.7206 | 34.30% | 16.09% | 3.70% | 1.23% | 0.22% | 0.05% |
| Clemson | E7 | 9.1622 | 48.60% | 11.25% | 4.02% | 0.85% | 0.26% | 0.05% |
| Cornell | E12 | 9.6673 | 28.38% | 13.63% | 2.64% | 0.77% | 0.24% | 0.05% |
| Georgia Tech | M10 | 7.9837 | 45.13% | 17.25% | 5.63% | 0.82% | 0.21% | 0.04% |
| California | S8 | 8.3612 | 48.39% | 11.10% | 3.72% | 1.21% | 0.24% | 0.04% |
| Florida | W10 | 7.6704 | 31.76% | 8.64% | 3.27% | 0.79% | 0.13% | 0.03% |
| Wake Forest | E9 | 8.3804 | 37.97% | 5.13% | 1.75% | 0.46% | 0.13% | 0.02% |
| Old Dominion | S11 | 6.8942 | 40.09% | 12.45% | 3.47% | 0.86% | 0.15% | 0.02% |
| Washington | E11 | 7.4802 | 39.37% | 11.31% | 2.73% | 0.50% | 0.13% | 0.02% |
| Siena | S13 | 6.9356 | 22.52% | 8.23% | 2.06% | 0.59% | 0.10% | 0.01% |
| Utah St | S12 | 6.5318 | 29.16% | 8.04% | 1.93% | 0.53% | 0.09% | 0.01% |
| Minnesota | W11 | 5.8808 | 32.67% | 10.38% | 2.47% | 0.49% | 0.06% | 0.01% |
| Murray St | W13 | 5.0753 | 28.36% | 7.92% | 1.21% | 0.28% | 0.03% | 0.005% |
| New Mexico St | M12 | 3.6712 | 23.81% | 6.62% | 0.40% | 0.08% | 0.01% | 0.001% |
| Oakland | W14 | 3.5825 | 17.22% | 4.78% | 0.77% | 0.10% | 0.009% | 0.001% |
| Wofford | E13 | 3.5096 | 20.48% | 3.39% | 0.29% | 0.04% | 0.006% | 0.0005% |
| Santa Barbara | M15 | 2.0441 | 11.19% | 2.10% | 0.24% | 0.01% | 0.001% | 0.00006% |
| Houston | M13 | 1.9848 | 13.29% | 2.57% | 0.09% | 0.01% | 0.0009% | 0.00005% |
| Sam Houston St | S14 | 1.9723 | 9.26% | 1.72% | 0.18% | 0.02% | 0.0009% | 0.00005% |
| Montana | E14 | 2.0411 | 8.07% | 1.42% | 0.12% | 0.008% | 0.0007% | 0.00004% |
| Ohio | M14 | 1.8769 | 8.54% | 1.08% | 0.15% | 0.007% | 0.0005% | 0.00003% |
| North Texas | W15 | 1.6135 | 6.10% | 0.71% | 0.09% | 0.006% | 0.0003% | 0.00001% |
| Morgan St | E15 | 1.4848 | 4.02% | 0.55% | 0.05% | 0.002% | 0.0002% | 0.000006% |
| Vermont | W16 | 1.4211 | 3.15% | 0.36% | 0.04% | 0.003% | 0.0001% | 0.000006% |
| Robert Morris | S15 | 1.0140 | 4.00% | 0.34% | 0.03% | 0.001% | 0.00004% | 0.000001% |
| East Tenn St | E16 | 1.0015 | 1.64% | 0.14% | 0.009% | 0.0004% | 0.00002% | 0.0000005% |
| Lehigh | M16 | 0.7255 | 0.76% | 0.04% | 0.003% | 0.0001% | 0.000004% | 0.0000001% |
| Ark Pine Bluf | S16 | 0.3863 | 1.29% | 0.06% | 0.001% | 0.00003% | 0.0000004% | 0.000000004% |
Blue indicates a team that the Bradley-Terry method rates more highly than Pomeroy's (in terms of probability of beating an "average" team), red indicates the reverse. The darker the shade, the more significant the difference. The most extreme positive difference: New Mexico is expected to win 95.88% of the time against an average team by the Bradley-Terry method but just 88.21% by Pomeroy. Utah State, on the other extreme, is expected to win 86.72% by the Bradley-Terry method but 93.01% by Pomeroy. (Minnesota and Wisconsin, interestingly, are the two next most extreme in B-T pessimism. Oakland and Kentucky are second and third in B-T optimism.)
Some notable differences, bullet-style:
- Kansas is #1 by a mile in the Bradley-Terry rankings; only Kentucky and Syracuse even have a 30% chance of pulling the upset. This and the models' disagreement on Ohio State and Maryland (Pomeroy likes both considerably better) leads to a big jump in Kansas's title chances.
- Bradley-Terry gives Duke just over a 5% chance to win it all, compared to 24% by Pomeroy. Part of this is that Duke is more lightly regarded here, but the fact that all of the next six teams by seed in their region are rated at least as high here as by Pomeroy plays a role as well. West Virginia, despite having to get past Kentucky just to get to the Final Four, is considered to be more likely to win it all.
- Kentucky also sees a big jump in their chances of winning it all here, in large part due to difference of opinion on Wisconsin (who's actually the favorite, by a narrow margin, to escape the East according to Pomeroy's numbers).
- Both systems rate us about equally (24th Pomeroy, 26th Bradley-Terry). The main differences in our percentages are due to our opponents: New Mexico State is considered a much tougher opponent by this system (79th) than it is by Pomeroy's (115th), reporting a 23.8% chance of upset compared to 14.2%. But Maryland is not so highly regarded (10th Pomeroy, 22nd Bradley-Terry), so this model gives us a slightly better chance of reaching the Sweet 16. Then we meet the buzzsaw named Kansas, and Bradley-Terry considers them a much bigger busszaw, so our chances thereafter drop accordingly.
- Pomeroy's formula has Wisconsin tied for 3rd most likely to win it all (with Syracuse, behind Duke and Kansas). This one has them 21st.
- Just two 10 seeds (and no one lower) are favored in the first round by this method: St. Mary's and Missouri. Pomeroy favors Old Dominion, Utah State, Georgia Tech, and St. Mary's.
- Poor Arkansas-Pine Bluff. Pomeroy's model gives them a 1 in 2.5 billion chance of winning it all; this method isn't even that generous, at 1 in 25 billion. (That may be an artifact of their calculations simply being for the "play-in winner", which could have been Winthrop, who is rated slightly higher.)
I don't mean this to supplant Pomeroy's rankings and the analysis by the group over at Basketball Prospectus, of course; their data factors in scores and not just win-loss records. But by ignoring record entirely, their analysis also loses some information. Losing (or winning) close games isn't all luck, and a team that consistently failed in the clutch is more likely to do so again. Ideally some hybrid of the two could be used, perhaps by averaging the two rankings in some way before applying log5.
Finally, some major differences among the RPI and Bradley-Terry rankings:
- Teams the RPI overrates: San Diego State (19th vs. 38th), Cal (20th vs. 42nd), Siena (27th vs. 48th), Old Dominion (28th vs. 50th), Utah State (32nd vs. 54th), UAB (42nd vs. 58th), Wichita State (45th vs. 60th), Kent St. (47th vs. 74th), Oakland (51st vs. 80th), New Mexico State (52nd vs. 79th). Common thread, for most: Lots of games against the 100-200 range and/or low 200s, very few against the high 200s and 300s. Oakland seems to be the exception; theirs may be due to the opposite effect of playing teams way over their ranking and getting a huge SOS boost to offset the effect the loss has on RPI.
- Teams the RPI underrates: Gonzaga (37th vs. 25th), Missouri (46th vs. 33rd), Notre Dame (48th vs. 30th), Cornell (49th vs. 35th), Marquette (50th vs. 27th), Virginia Tech (58th vs. 36th), Ole Miss (62nd vs. 47th), Seton Hall (68th vs. 43rd). Again, there's a common theme: Tons of games against "RPI anchors" which aren't (for good teams) functionally that much different from playing teams in the 150-200 range but are punished far more severely in the RPI.
This seems to confirm what conventional wisdom has always said: RPI puts a big emphasis on choosing your cupcakes carefully. Choose poorly, and your RPI will suffer even if you win. Choose wisely, and you can get a bunch of near-guaranteed wins without making your strength of schedule look too embarrassing. This year, Virginia Tech chose ... poorly. And it is the reason they didn't make the tournament.
