Thresholds:

TheBye Lockrefers to the most number of points that can be reached by 5th place and correspondingly, how many points a team would need to earn in order to guarantee themselves a 4th place finish. How I reached that scenario this time involves Yale, Dartmouth, Union, and Princeton winning every remaining game they don't have against each other, Princeton defeating Yale, and then ties for the remaining four games. That leaves all four of them sitting at 31 points and Quinnipiac is still capable of getting to (or above) that total, so to be guaranteed a weekend off, you need to finish with at least 31 points and win the appropriate tiebreakers.

Conversely,Bye Eligiblerefers to the least number of points that a team can earn and still have the first weekend of playoffs off. I was able to cause a large logjam at 18 points with Quinnipiac, Yale, and Dartmouth ahead of the pack and three teams just behind this logjam at 17 points. So, as long as you can get to 18 points, if you can win the right tiebreakers, you could potentially finish in 4th place.

Home Lockis similar to Bye Lock, except that it refers to boosting the points of 9th place, trying to determine the maximum number of points that a team would need in order to secure home-ice in the first round. By minimizing the points that I gave to Brown, Rensselaer, and Harvard (and then Quinnipiac, since they were clearly above this maximum after having hypothetically swept Brown and Harvard), I was able to cause the other eight teams to conglomerate around 25 or 26 points. Two teams ended up tied for eighth place at 25 points apiece, indicating that 25 points should be enough to guarantee yourself two extra home games.

That point merits some extra exploring, then. Let's say that Quinnipiac beats Brown on Friday night and somehow, that's the only game that gets played that night. Quinnipiac now has 25 points. Are they guaranteed an extra two home games after the conclusion of the regular season? Well, let's have the Bobcats lose out the rest of the regular season. And, we know that the Crimson can't catch them, so have Harvard lose out, too. Now, to have each of the ten remaining teams get to 25 points, 99 points would have to be distributed, but with both Quinnipiac's and Harvard's regular season finished, there are only eighty points remaining. So, clearly, not every team can catch and/or pass Quinnipiac. RPI, with nine hypothetical games remaining (and the least number of points accumulated so far), is next on the chopping block. We're still short. 67 points need to be accumulated, but there are only 31 games (and therefore 62 points) left. Good bye Brown. Finally, we're on the right side of the ledger. But, two teams will need to finish with 25 points while the remaining six can finish with 26. What two teams should finish with 25 points so that Quinnipiac would lose the tiebreakers and finish in 9th? Yale, who hasn't played Quinnipiac yet and would therefore have swept them in this hypothetical is an obvious choice. But, we need somebody else who could win the three-way tiebreaker to make sure that the head-to-head comes down to Yale and Quinnipiac. And, in the way that I generated this scenario, it falls to Colgate to become said third team. End result? Quinnipiac loses the relevant tiebreakers, finishes 9th, and is not guaranteed another weekend at home. So, don't forget, just because you've reached the relevant point plateau does not mean that you are guaranteed to have a bye or have earned home-ice. Tiebreakers matter, people.

And, finally,Home Eligible. The least number of points that can be had by the 8th place team at the end of the season. I was able to get a three-way tie for 8th place at 13 points. So, for now, if you can get to 13 points (and have the requisite tiebreakers), you can have home-ice in the playoffs.

I'm going to apologize in advance for the mathiness of the rest of this post (and the next one).

You all know what KRACH is, right? It's the application of the Bradley-Terry ranking system, but falls into the fatal flaw that it doesn't treat ties properly. It treats them like half-wins and half-losses. Now, there's a way to fix this. P. Rao and L. Kupper wrote a paper in 1967 which found a better way to treat ties. PDF paper with the details of the ranking system can be found here (Section 7.3). The problem is, I still don't like it. Luckily, Dr. Michael Rutter of Penn State Erie is awesome.He took the Mease College Football Rankings and adapted them for college hockey(slides 10-12 are the keys there). And then he allowed me to steal his spreadsheet and adapt it. The Mease Rankings are based on the idea that each team's abilities can be represented by a normal distribution centered at some value (THETA_i) with a variance of 0.5. Then, whenever two teams play each other, the likelihood of outcomes when Team i plays Team j is represented by a normal distribution centered at the difference of their THETA values with a variance of 1.0 (supporting webpage from Wolfram). We then try and maximize the log of these likelihoods by changing the thetas of each team and phi. This makes a lot of sense to me. Teams have good nights and they have bad ones. No team has a fixed ranking. It's a distribution of rankings centered around some number. And, a normal distribution sounds good to me.

Before we go any further, Mease suffers from many of the same flaws as B-T. It can only evaluate the games as they were played. It doesn't take into account referee screw-jobs, injuries, academic disqualifications, game misconducts or anything of the like. It doesn't matter if you win by one goal or fifteen, Mease treats them the same. It doesn't take into account hot streaks or home-ice advantage (at least, this version doesn't, it would be non-trivial to code, but it could be done). It is retrodictive, not predictive. It should not be used to predict games. With that out of the way, let's predict some games!

PS If someone knows how to codeCHODR, please let me know. It doesn't have a distribution, but it uses real scores instead of just game results and is actually a predictive model.