Ken Pomeroy has started his work on projectiong the D-I conference tournaments over at his blog, so I thought I’d do the same for the GSC in this space. The method is to use pythagorean winning percentages (ideal winning percentages based on points scored and allowed) to predict the winners of individual games and the tournament as a whole. The CAA is already up on his site as an example.
I use a different exponent to arrive at my pythagorean percentages for the GSC, but I do post those in the Excel stat file that I regularly put on the site. I use a schedule adjustment for the GSC West that I’m not using for this exercise, but the idea is the same.
I won’t go into an explanation of log5 win probabilities, but there’s a great one over at Diamond Mind Baseball. Basically, the win percentages of two teams are pitted against one another to come up with a single-game win probability for a matchup between the two teams. In order to get the probabilities for each level of the tournament, you just take the probability for each team that could play in that game (weighted by their probability of reaching that round) and multiply it by their winning percentage. Then you plug it into the formula listed at the link above, and voila, you have the numbers in the chart below.
The table below is sorted by probability of winning the tournament. From left to right, you’ll see: points for and against, pythagorean win%, the probability of reaching each round, the probability of winning the tournament, and (roughly) the team’s odds of winning the tournament in betting terms. The numbers in each column don’t perfectly add up to 8, 4, 2, and 1 because of rounding errors, but it’s pretty close. I also came up with a set of sparklines to show each team’s performance over the course of the season in general. It’s pretty easy to figure out: up bars are wins, down bars are losses, and the bigger bars are wins or losses by 10 or more points. That’s the last column.
| Seed | Team | PPGF | PPGA | Pct | Qtrs | Semis | Finals | Champ | Odds | Trend |
| E1 | Montevallo | 88.7 | 74.7 | 0.824 | 1.000 | 0.818 | 0.572 | 0.392 | 5:2 | [spark][type bar][size 15,3][series -1,2,2,2,2,1,-1,2,2,1,2,-1,-2,-1,2,2,2,2,2,1,2,2,1,1,2,2,2][/spark] |
| W1 | Henderson State | 65.9 | 57.5 | 0.773 | 1.000 | 0.734 | 0.520 | 0.272 | 7:2 | [spark][type bar][size 15,3][series 2,1,-2,2,-1,2,-2,-1,2,2,2,1,2,2,1,1,1,1,-1,1,2,2,1,2,-1,-2,2][/spark] |
| W2 | Christian Brothers | 66.7 | 61.2 | 0.684 | 1.000 | 0.541 | 0.215 | 0.108 | 9:1 | [spark][type bar][size 15,3][series 2,2,1,2,-1,2,1,2,-2,2,2,2,2,2,2,-1,1,1,-2,-2,2,1,-1,2,1,2,1][/spark] |
| W3 | Harding | 72.1 | 68.4 | 0.616 | 1.000 | 0.578 | 0.225 | 0.077 | 13:1 | [spark][type bar][size 15,3][series 1,-1,2,2,2,1,2,-2,-2,-1,-1,-1,2,2,-2,-1,1,-1,2,2,1,-1,1,2,1,1,-1][/spark] |
| E3 | North Alabama | 85.3 | 79.7 | 0.648 | 1.000 | 0.459 | 0.165 | 0.076 | 13:1 | [spark][type bar][size 15,3][series 2,2,-1,-1,-1,-1,-1,1,2,-2,1,1,-2,-1,2,1,-2,2,2,-1,1,1,-1,2,-1,-1,2][/spark] |
| E2 | Valdosta State | 73.7 | 72.4 | 0.540 | 1.000 | 0.422 | 0.134 | 0.037 | 27:1 | [spark][type bar][size 15,3][series 2,-2,2,1,-2,-1,1,2,1,2,2,2,2,2,1,-2,2,2,-2,1,2,1,-2,2,1,-2,1][/spark] |
| W5 | Delta State | 72.5 | 70.1 | 0.575 | 0.551 | 0.157 | 0.077 | 0.023 | 43:1 | [spark][type bar][size 15,3][series 2,-1,2,-2,1,2,1,1,2,1,1,2,2,2,2,1,-1,2,-1,-1,-2,1,1,-1,-1,1,-2][/spark] |
| E4 | Alabama-Huntsville | 75.1 | 74.3 | 0.524 | 0.449 | 0.109 | 0.048 | 0.013 | 80:1 | [spark][type bar][size 15,3][series 2,1,-2,2,1,-2,1,2,2,-1,2,2,1,2,-2,1,-2,2,1,-1,-2,2,-1,2,2,-1,-2][/spark] |
| W4 | Ouachita Baptist | 73.1 | 72.4 | 0.522 | 0.522 | 0.098 | 0.035 | 0.012 | 86:1 | [spark][type bar][size 15,3][series 2,2,-2,-2,-2,-1,2,-2,-1,2,-2,-2,2,-1,1,-1,1,1,1,1,1,2,-1,-2,-1,2,1][/spark] |
| E5 | West Georgia | 77.2 | 77.2 | 0.500 | 0.478 | 0.084 | 0.028 | 0.009 | 113:1 | [spark][type bar][size 15,3][series 1,-1,1,2,-1,-2,2,-1,2,-2,-1,1,-1,-1,-2,1,1,-1,1,-2,-2,-1,2,2,-2,1,2][/spark] |
I won’t be trying to predict the winners of each game or the tournament as a whole myself, but this should give you an idea of how I might go about doing that. If I could, I would probably include two other factors in this analysis: 1) something to weight recent games more heavily, 2) something to account for the relative strength of each division (because the East is probably slightly better, by my guess). Still, it’s a pretty good way of looking at things.
In reality, I would give Christian Brothers a better shot to win than 9:1, maybe even a better shot than Henderson State, which is limping into this week’s games. Plus, CBU might as well be playing at home (the tournament is held in Southaven, MS, a Memphis suburb). I’d put Henderson State at closer to 5:1, with CBU at about 6 or 7:1. The Bisons are also playing well, and given the other (weaker) teams on their side of the bracket, I might call them 10:1. I’d lower the odds on VSU and DSU given their recent poor play. As a whole, though, I’d say the log5 system isn’t bad.
jfwiii.net 
I used to think that the Log5 method (what’s 5 have to do with anything, anyway?) was just something that worked because, well, because it just happened to work, in the same way that things like Runs Created just “work” despite not really being grounded in any kind of theory.
It turns out that the “Log5” formula for win percentages can actually be derived theoretically if you just make the assumption that game outcomes follow a logistic distribution instead of a normal distribution. And even if they DO follow a normal distribution, the Log5 formula is still a very good approximation as long as the percentages don’t get too close to 0 or 1.
Anyhow, I thought that was interesting, but then again, my sense of what’s interesting might be a little off-base.
Yeah, I was reading some of the theory on that, and it’s pretty interesting. I guess I’m far enough removed from trig and calculus classes that I don’t really remember the math behind it anymore, but it seems to work. It’s good to know that it’s based theoretically, too.
The biggest problem with what I’ve done here is probably the small sample size from which I derived the Pythagorean win percentages. With only 12 conference games for the East teams, there’s probably a fair amount of noise in there. Ultimately, I guess anything could happen at the tournament.
You should do this kind of analysis for the SEC to see how Florida looks heading into the SEC tourney. After they lose to Kentucky, of course.