Published by Jim Dahl on 29 Dec 2008 at 07:16 pm
People who follow the PWR (PairWise Rankings) now know intuitively that getting swept at the GLI was particularly harmful to UND’s PWR (and NCAA tournament) chances, but for the first time ever anywhere, we can try to quantify how harmful.
The surprising bottom line — UND’s chances of getting a top 15 ranking in the PWR are now only about 1/3 to 1/4 what they would have been if UND had instead swept this tournament.
Without further ado, as simulated by the new PairWise Ranking Predictor, here are the distributions of UNDs PWR chances with the actual outcome of the Great Lakes Invitational vs if UND had swept.
Using KRACH to predict the outcomes of unfinished games, UND now stands under a 5% chance of ending the regular season in the top 15 of the PWR. Had UND swept the GLI, the Sioux would have instead stood over a 20% chance.
A few words about the chart — the horizontal axis is the desired PWR ranking (1 good, 25 bad), the vertical axis is the cumulative probability of achieving the corresponding PWR ranking, the green line represents UND’s actual chances as of today, the blue line what UND’s chances would have been with a sweep. Note that the KRACH probabilities used to predict the outcomes of remaining games are the same for both — the current KRACH ratings that incorporate being swept.
But wait, Jim, you say… using KRACH to predict the probabilities just extends how teams have performed to date through the end of the season. The mid-season KRACH last year would have also predicted doom and gloom for the Sioux. While that’s true, I’m using these predictions to point out how much the differential, how much the sweep hurt, not the actual levels (e.g. 5% chance of finishing top 15). Nonetheless, another interesting way to look at it is what proportion of the possible remaining outcomes land the Sioux in each PWR ranking. That can be somewhat answered with a similar simulation that makes the outcomes of each game random (50% win, 50% lose) rather than with probabilities determined by KRACH.
Though a random draw looks better for the Sioux than the KRACH predictions, UND’s chances of a top 15 PWR were harmed even more from comprising 50% of possible remaining scenarios to 15%. Note further that the number of potential outcomes that even land the Sioux as a TUC fell from nearly 80% to 50%.
A few extra notes for the geeks — the simulations were Monte Carlos with 1,000,000 trials per scenario. While I didn’t do formal sensitivity analysis, a few runs of one demonstrated that results for each potential ranking were generally within .001%, so I’m pretty happy with 1,000,000 trials.