Last week’s post, Swept at the GLI — how harmful to PWR?, introduced the idea of simulating the remaining season to predict the PWR and led to a lot of speculation about exactly what it would take for the Sioux to reach the NCAA tournament.
I’ll start with that last point — in simulations that have UND reach the top 12 in PWR, UND wins about 75% of its 16 remaining regular season games. That winning 75% of remaining games could land UND in the tournament is notably less pessimistic than most of the non-data based speculation I’ve seen, so wanted to get that out there. Further, the WCHA tournament could add up to 6 additional games to UND’s pre-NCAA tournament schedule, giving UND additional opportunities to climb in the PWR. In short, it’s very possible for UND to make the NCAA tournament with a reasonable run of good performance.
This stuff is very new and I’m still trying to figure out how to make it more usable and accessible to non-stats geeks, so if that’s you, jump to “What’s next” for a preview of those efforts.
Now it gets a little denser…
In noting last week that each weekend’s pair of games would knock out 3/4 of the remaining possible outcomes, I was concerned that the potential outcomes eliminated would be so biased as to make this exercise somewhat useless. That is, I wondered if a sweep would remove 3/4 of the bad outcomes, increasing the probability of good outcomes by 4x. A tool that predicted a 10% chance of a certain PWR before playing Bemidji St and a 40% chance of that same PWR after a sweep would be useless indeed. Fortunately, that wasn’t the case.
The predicted PWR outcomes based on Bradley/Terry (KRACH)-determined game outcomes made only a minor shift, as intuitively follows UND’s predicted 60% chance of winning each game.
A quick note on how to use KRACH to predict game outcomes: going into the Gopher series, UND’s KRACH is 100 vs UMN’s 252 (other sites may have other numbers, but the ratio should be about 1:2.5). Therefore, UMN stands a 2.5x greater chance than UND of winning each game. Restated, if they perform as they have to date, UND is predicted to have about a 28% chance of winning each game. These games are the least likely remaining wins on UND’s schedule, so wins this weekend would definitely shift the remaining possibilities and give us some very useful insight into this tool. So, let’s see ’em boys 🙂
I already noted that in simulations in which UND reaches top 12 in PWR, UND wins about 75% of its 16 remaining regular season games. However, what I think people really want to know is: What is the likelihood of UND making the tournament if its wins 75% of its remaining games? (or 50%, or 90%?)
I think that will be the most useful way to look at these results — probability distributions of likely PWRs given a particular winning percentage. e.g. a graph that shows that if UND wins 75% of its remaining games, it stands a 10% chance of being ranked 11, an 11.3% chance of being ranked 12, etc…