So I went ahead and performed that wacky stat I was talking about over in this thread
. I used as my guinea pig the results from IS-96 that are currently complete and usable (15s/10s/-5s for each team in every game, BC for each team, no lightning rounds or other stuff like that). Well, okay, I didn't use all
the results, just results from teams that looked strong. I used IS-96 because it's a tournament that's been played in a lot of places nationwide and because naqt.com presents the data in a way very conducive to doing mental arithmetic on opponent data (note: take these rankings with a grain of salt, since my arithmetic may be off).
Anyway, I used a slightly modified version of the model in which expected values were converted to whole numbers (e.g. a value of 0.200 for a1,T was converted into 4 ten-point tossups) instead of doing everything in decimals and then rounding the final answer to the nearest 5 points. I did it the original way, too, with all the decimals. Anyway, you don't care about that. You care about this:
Top 10 performances on IS-96, that I can find, so far
1. Richard Montgomery (9-0, 375.56 ppg, 236.67 ppga)*
2. Bellarmine A (8-1, 323.33 ppg, 269.44 ppga)
3. St. Anselm's (7-2, 330.56 ppg, 258.88 ppga)**
4. Hunter A (6-3, 318.89 ppg, 266.67 ppga)
5. TJ A (5-4, 307.78 ppg, 290.56 ppga)
6. Georgetown Day (4-5, 278.88 ppg, 303.33 ppga)
7. MSJ A (3-6, 279.44 ppg, 315.56 ppga)
8. Walter Johnson (2-7, 269.44 ppg, 328.33 ppga)
9. La Jolla A (1-8, 250 ppg, 327.22 ppga)
10. St. Mark's (0-9, 230 ppg, 367.22 ppga)
*Note that all ten of these teams "defeated" all other teams I entered statistics for, so these are only the results of the games against each other. St. Mark's did tie Kellenberg when I tried it the original not-rounding-to-whole-numbers way.
**No, overall ppg didn't exactly correspond to finish order. Bellarmine ended up winning a lot of close games (many of the games in this hypothetical tournament were won by 5 or 10 points) - their absurd power percentage and bonus conversion appeared to help them more than their habit of negging against bad teams hurt them.
Things this does:
-It takes into account, perhaps even to a fault, strength of schedule - witness, for example, Georgetown Day finishing ahead of Walter Johnson, La Jolla, and St. Mark's, all of which had better numbers on paper.
-It penalizes teams for negging against poor teams (since a negged tossup that isn't converted just ends up as a dead tossup).
-It measures a team's tossup performance as well as can be measured given variable schedule strength. It doesn't take into account the actual results of games, however.
-For some reason, it appears to constrain games between the best teams to a range of about 550-650 total points (the max. combined score I can find anywhere on my spreadsheet in 640). I have a feeling this is due to bonus conversions being around 20. Then again, this is what we'd expect to see if these two teams played an infinite number of times, not just once (although we're counting it as one win/loss/tie).
At some point I will write a MATLAB script to efficiently compute a-values (and the resultant giant round robin) for each pair of teams, at which point I will compile the data and release full results instead of just this teaser.