Re: RPI 2012-2013 Season Thread
Current Standings (by Points %):
--- Home Lock -
32
Harvard 29-
41 [1-5]
Cornell 28-
40 [1-6]
Clarkson 26-
38 [1-7]
St. Lawrence 21-
33 [1-8]
--- In -
21
Quinnipiac 20-
32 [1-9]
Dartmouth 17-
29 [2-11]
Rensselaer 15-
27 [3-11]
Princeton 10-
22 [4-12]
--- Home Eligible -
22
Colgate 9-
21 [5-12]
Yale 8-
20 [5-12]
Brown 6-
18 [6-12]
Union 3-
15 [8-12]
--- Out -
11
Remaining League Schedules:
Code:
----------------------------------------------------------
| | ||F2/08|S2/09|F2/15|S2/16|F2/22|S2/23|
----------------------------------------------------------
| Harvard | HA || YA | BN | @CR | @CG | SL | CK |
| Cornell | CR || @QN | @PN | HA | DA | @RP | @UC |
| Clarkson | CK || @RP | @UC | PN | QN | @DA | @HA |
| St. Lawrence | SL || @UC | @RP | QN | PN | @HA | @DA |
| Quinnipiac | QN || CR | CG | @SL | @CK | @YA | @BN |
| Dartmouth | DA || BN | YA | @CG | @CR | CK | SL |
| Rensselaer | RP || CK | SL | @YA | @BN | CR | CG |
| Princeton | PN || CG | CR | @CK | @SL | @BN | @YA |
| Colgate | CG || @PN | @QN | DA | HA | @UC | @RP |
| Yale | YA || @HA | @DA | RP | UC | QN | PN |
| Brown | BN || @DA | @HA | UC | RP | PN | QN |
| Union | UC || SL | CK | @BN | @YA | CG | CR |
----------------------------------------------------------
Individual Team Limits:
Teams Losing Out (Floors)
Harvard can be caught by Dartmouth, but I can't find a way for the Big Green to win a tiebreaker against the Crimson, so Harvard can't fall below 5th place.
Dartmouth can actually pass Cornell, so the Big Red's floor is 6th place.
Clarkson can also be caught by RPI, so they can drop all the way to 7th.
SLU is guaranteed to finish in the Top 8 (either Colgate or Princeton can catch them, but not both and SLU already has the head-to-head tiebreaker over Colgate, so it's better to let Princeton beat them), so they are guaranteed a spot in the playoffs.
Quinnipiac can fall all the way to a tie with Yale for 8th with Colgate sneaking past at 21 and Princeton falling just short, so they can drop to 9th.
There's enough of a gap between Quinnipiac and
Dartmouth that the Big Green can drop all the way until the only team that hasn't passed them is the Dutchwomen.
Rensselaer has swept Union and would be guaranteed at least a split against every other team that hasn't already passed them, so they also cannot finish in the basement.
Any team that is currently in the bottom five does not yet have enough separation from Union to be guaranteed finishing anywhere above twelfth.
Teams Winning Out (Ceilings)
Union can barely still climb into a playoff position. They could theoretically end up a full four points ahead of Colgate in 9th place.
Brown can hypothetically climb all the way past Dartmouth into 6th place. Don't bet on it, though.
Yale can finish tied for 5th with Quinnipiac and since they tied just this past Saturday, they would win the season series 3-1 and claim the #5 seed.
Colgate has to be passed by either SLU or Quinnipiac (or both) and since the Lady Raiders have already lost the season series to the Lady Saints, it's better to have St. Lawrence pass them outright and keep Quinnipiac sequestered behind them. Colgate's ceiling is also 5th place.
Princeton has enough points built up where SLU or Quinnipiac only has to tie the Tigers instead of outright passing them. And, if it ends up being a St. Lawrence-Princeton tie for 4th place, then they hypothetically split the season series (Tigers would win the Feb 16th game at Appleton) and each finish with 10-10-2 records. It would then come down to Record vs Top 4, which Princeton would win because they also would have had to claw out wins against Clarkson and Cornell in their quest for 4th place.
RPI can finish in 3rd place by themselves, behind just Harvard and Cornell.
Dartmouth has to be passed by at least one of Harvard and Cornell, so they can't finish with the #1 seed. They can finish by themselves in 2nd, though.
Any of the top 5 teams are close enough to the Cornell / Harvard pair that they can finish by themselves in 1st place.
Thresholds:
Home Lock - The maximum number of points necessary for 4th place to have to finish ahead of 5th, so the goal is to bump up the point totals of the Top 5 teams. I can get Cornell, Clarkson, and Harvard with at least 35 and St. Lawrence and Quinnipiac with 32 and 31 points in some order. So, 32 points lands you a home-ice position.
Home Eligible - The minimum number of points that a team can gather and still finish in 4th place. With St. Lawrence and Quinnipiac at 21 and 20 points with a game to play against each other, still, the minimum is 22 points. And, it is possible to keep them still in 4th and 5th place with 22 and 21 points, so... 22 it is. If you can get to 22 points, you can still play an extra pair of home games.
In - The maximum number of points necessary for 8th place to have to finish ahead of 9th. If Princeton and Colgate win out their five remaining games against everyone but themselves, they end up sitting at 20 and 19 points with one game remaining. And, there are enough remaining games that RPI, Dartmouth, Quinnipiac, and St. Lawrence can all stay ahead of the Tigers and Raiders. And, with that knowledge, we can get 9th place up to 20 points, meaning that 8th would need 21. So, 21 points is a guarantee that you are in the playoffs.
Out - The minimum number of points that a team can gather and still finish in 8th place. If each of the Top 7 win all of their games against the Bottom 5, then there are 6 games remaining. But, now Union can't catch 8th place Princeton, so we let them win out. Now Brown only has the opportunity to get to 8 points, so they can win out, too. Now we're left with Princeton at 10 points who has one game remaining with both Colgate (9) and Yale (8). We can let Yale win their game against the Tigers and then a non-Princeton win in their game against the Raiders leaves 8th place at 11 points. It's not likely to be that low, but if you can get to 11 points, you can get into the playoffs.
For the simulation, I used Rutter's adaptation of the Mease Rankings that allows for ties. Since I don't want to deal with Minnesota's perfect season, I'm not going to calculate theta values myself. That means that I also didn't calculate phi myself. All of the values used in the simulation can be found on
his webpage. He calculates ratings at the end of each weekend of play. That means that Tuesday games (such as the Women's Beanpot) don't get factored in until the next Sunday.
There are a lot of flaws in this system. 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!
There were only 32,000 trials and there are over 150 x 10^15 possibilities remaining. There's nothing in the code to stop all 32,000 trials from being the exact same game results as one another than pure chance. So, there's not even the guarantee of uniqueness between trials.
Mease Rankings (THETA) as of 02/03/13:
Code:
-------------------------
| Team | Theta |
-------------------------
| Harvard | 1.243 |
| Cornell | 1.525 |
| Clarkson | 0.997 |
| St. Lawrence | 0.392 |
| Quinnipiac | 0.220 |
| Dartmouth | 0.296 |
| Rensselaer | -0.614 |
| Princeton | -0.439 |
| Colgate | -0.622 |
| Yale | -1.120 |
| Brown | -1.175 |
| Union | -0.939 |
-------------------------
PHI = 0.195
