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lugnut92
02-03-2013, 10:53 AM
After this weekend, RPI cannot take last place! The best Union can do is match our 15 league points, and we have the tiebreaker. Now let's see if we can clinch a playoff spot. Any combination of RPI winning and Colgate losing 7 points puts us out of their reach, and assuming the teams below them don't make a run, that would guarantee us 8th or better.

Stat Man
02-04-2013, 03:08 PM
RPI would have to get no points in its games against Brown, Yale and Colgate to not finish in 7th. Any points against SLU,Clarkson or Cornell and they might have a chance to catch Dartmouth (But that is highly unlikely)

hab
02-04-2013, 05:22 PM
RPI would have to get no points in its games against Brown, Yale and Colgate to not finish in 7th. Any points against SLU,Clarkson or Cornell and they might have a chance to catch Dartmouth (But that is highly unlikely)

I hesitate to question the math skills of someone named "Stat Man"...but I will anyway. Everybody has six games left (12 possible points) and only Union is more than 12 points behind RPI. Or are you making the assumption that none of the other playoff contenders can pick up a point against any of the top-half teams? In that case, I think the numbers would work.

We all seem to be in agreement that, barring an incredibly strong finish or a complete collapse the Engineers are highly likely to finish seventh, and face Harvard, Clarkson or Cornell on the road. Probably the real significance of the next 6 games is a test of whether the team has another gear that will make it possible for them to pull off a playoff upset. And that test comes this weekend (Clarkson, SLU) and the last weekend (Cornell), all home games. I expect that all of these will be great games to watch.

Stat Man
02-05-2013, 09:14 AM
I hesitate to question the math skills of someone named "Stat Man"...but I will anyway. Everybody has six games left (12 possible points) and only Union is more than 12 points behind RPI. Or are you making the assumption that none of the other playoff contenders can pick up a point against any of the top-half teams? In that case, I think the numbers would work.

We all seem to be in agreement that, barring an incredibly strong finish or a complete collapse the Engineers are highly likely to finish seventh, and face Harvard, Clarkson or Cornell on the road. Probably the real significance of the next 6 games is a test of whether the team has another gear that will make it possible for them to pull off a playoff upset. And that test comes this weekend (Clarkson, SLU) and the last weekend (Cornell), all home games. I expect that all of these will be great games to watch.

If you approach it solely looking at the math then RPI could still get 6 wins and finish in fourth if the three teams in front of them forget how to play hockey. Not that likely to happen though.

Each of the teams 7th through 12th has three winnable games on the schedule in the remaining 6, with a lot of head to head going on. If any one of these teams can pull of an upset it will most likely be only 1 upset. (ie the chance of one of these teams running the table and finishing with 6 wins is really low). That taken into account RPI would have to lose all 6 remaiing games to not finish in the playoffs and even then they might sneak in based upon tiebreakers and head to head matchups.

hab
02-05-2013, 05:58 PM
Statman, I agree with everything you say in your last post, which makes some significant qualifications and amendments to your earlier post.

Ralph Baer
02-05-2013, 09:52 PM
burgie12 could run the simulations that he ran on the men's side http://board.uscho.com/showthread.php?103178-ECAC-Byes-and-Home-Ice-A-Mathematical-Journey-2012-13.

burgie12
02-06-2013, 02:10 PM
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:

----------------------------------------------------------
| | ||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 (http://math.bd.psu.edu/faculty/rutter/WomensRankings.html). 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:

-------------------------
| 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

burgie12
02-06-2013, 02:11 PM
The probability that the away team wins is equal to the probability that a standard normal distribution (NORMSDIST in Excel) will have a value less than [(their theta) - (home team's theta) - (phi)]. The probability that the home team wins is equal to 1 - {the probability that a standard normal distribution will have a value less than [(their theta) - (away team's theta) - (phi)]}. The probability of a tie is the leftover remainder. So, have Excel generate a random number between 0 and 1 and see where it falls on this distribution scale. Repeat it for each of the remaining 36 games, find the standings after said 36 games have been completed, and voila, that is one trial.

And, here are the results, organized by expected final standings...
Mease Simulation (32,000 trials):

------------------------------------------------------------------------------------------------------------
| | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | 9th | 10th | 11th | 12th | ExpPl |
------------------------------------------------------------------------------------------------------------
| Cornell | 52.2 | 40.2 | 7.6 | XXXX | XXXX | XXXX | ---- | ---- | ---- | ---- | ---- | ---- | 1.55 |
| Harvard | 44.6 | 39.3 | 16.2 | XXXX | XXXX | ---- | ---- | ---- | ---- | ---- | ---- | ---- | 1.72 |
| Clarkson | 3.2 | 20.6 | 76.1 | 0.1 | 0.0 | XXXX | XXXX | ---- | ---- | ---- | ---- | ---- | 2.73 |
| St. Lawrence | XXXX | XXXX | 0.1 | 70.6 | 26.5 | 2.8 | 0.0 | XXXX | ---- | ---- | ---- | ---- | 4.32 |
| Quinnipiac | XXXX | XXXX | 0.0 | 28.2 | 61.8 | 9.9 | 0.0 | XXXX | XXXX | ---- | ---- | ---- | 4.82 |
| Dartmouth | ---- | XXXX | XXXX | 1.1 | 11.6 | 83.2 | 4.1 | XXXX | XXXX | XXXX | XXXX | ---- | 5.90 |
| Rensselaer | ---- | ---- | XXXX | XXXX | 0.0 | 4.1 | 92.5 | 3.3 | 0.1 | XXXX | XXXX | ---- | 6.99 |
| Princeton | ---- | ---- | ---- | XXXX | XXXX | XXXX | 2.7 | 67.7 | 24.7 | 4.4 | 0.5 | XXXX | 8.32 |
| Colgate | ---- | ---- | ---- | ---- | XXXX | 0.0 | 0.7 | 25.5 | 53.4 | 17.3 | 3.0 | 0.1 | 8.97 |
| Yale | ---- | ---- | ---- | ---- | XXXX | XXXX | 0.0 | 3.2 | 18.3 | 51.3 | 23.7 | 3.4 | 10.06 |
| Brown | ---- | ---- | ---- | ---- | ---- | XXXX | XXXX | 0.3 | 3.1 | 20.6 | 55.9 | 20.2 | 10.93 |
| Union | ---- | ---- | ---- | ---- | ---- | ---- | ---- | XXXX | 0.5 | 6.4 | 16.8 | 76.3 | 11.69 |
------------------------------------------------------------------------------------------------------------
"XXXX" indicates that the finish is mathematically possible, but did not occur in any of the 32,000 trails. "----" indicates that it is not possible. "0.0" means that it occurred 15 times or less.

Here are the resulting quarterfinal match-ups. The hosting team is listed on the left and the away team is listed on top. These matchups adds up the number of occurrences of the 1v8, 2v7, 3v6, and 4v5 matchups and lists it all in one block.

HOST (the far right column) indicates how often a team finished in Spots 1-4. ROAD (bottom row) indicates how often a team finished in Spots 5-8. The difference of 100% and the sum of HOST and ROAD indicates how often a team missed the playoffs (Spots 9-12).

Potential Quarterfinal Match-ups:

-------------------------------------------------------------------------------------------------
|TEAM| CR | HA | CK | SL | QN | DA | RP | PN | CG | YA | BN | UC | HOST |
-------------------------------------------------------------------------------------------------
| CR | XX | 0.0 | 0.0 | 0.2 | 0.7 | 8.0 | 39.1 | 36.0 | 14.2 | 1.7 | 0.1 | 0.0 |100.0 |
| HA | 0.0 | XX | 0.0 | 0.3 | 1.3 | 15.5 | 38.5 | 31.7 | 11.2 | 1.4 | 0.1 | 0.0 |100.0 |
| CK | 0.0 | 0.0 | XX | 2.4 | 8.0 | 63.7 | 22.3 | 2.7 | 0.9 | 0.1 | 0.0 | 0.0 |100.0 |
| SL | 0.0 | 0.0 | 0.0 | XX | 61.0 | 9.6 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 70.7 |
| QN | 0.0 | 0.0 | 0.0 | 26.1 | XX | 2.1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 28.3 |
| DA | 0.0 | 0.0 | 0.0 | 0.4 | 0.7 | XX | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 1.1 |
| RP | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | XX | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| PN | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | XX | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
-------------------------------------------------------------------------------------------------
|ROAD| 0.0 | 0.0 | 0.0 | 29.3 | 71.7 | 98.9 | 99.9 | 70.4 | 26.2 | 3.2 | 0.3 | 0.0 | |
-------------------------------------------------------------------------------------------------

The bottom line is that RPI finished in 9th place in 28 trials of 32,000. 20 of them came when RPI failed to get any more points and Colgate and Princeton were both able to pass the Engineers with at least 16 points each. Five times they got a tie, but still got passed (or tied) by both the Lady Raiders and Tigers. Twice it was a three-way tie for 7th with 17 points and once Colgate got 19 points and RPI and Princeton each had 18 and RPI lost the tiebreaker. On the other hand they finished in 8th place with 15 points 184 times without being tied and another 67 times with 9th place also having 15 points. And that's just in 8th place. They also finished in 7th place without earning another point in a total of 252 trials.

Here, this might be a better way of explaining it...

--------------------------------------------------------------------------------------------
|Pl\Pts| 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | |
--------------------------------------------------------------------------------------------
| 3rd | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0|
| 4th | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0|
| 5th | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 5 | 4 | 0 | 0 | 13|
| 6th | 0 | 0 | 0 | 3 | 44 | 88 | 484 | 245 | 375 | 60 | 18 | 0 | 0 | 1317|
| 7th | 252 | 692 |3621 |4043 |8672 |5017 |5438 |1245 | 555 | 44 | 5 | 0 | 0 |29584|
| 8th | 251 | 213 | 359 | 181 | 37 | 17 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1058|
| 9th | 20 | 5 | 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 28|
| 10th | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0|
| 11th | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0|
--------------------------------------------------------------------------------------------
| | 523 | 910 |3982 |4228 |8753 |5122 |5922 |1490 | 934 | 109 | 27 | 0 | 0 | |
--------------------------------------------------------------------------------------------

Ralph Baer
02-06-2013, 02:18 PM
Thanks, burgie.

OnMAA
02-06-2013, 04:25 PM
Thanks, burgie.

I second that. Burgie is the man of the hour.

hab
02-06-2013, 04:36 PM
Burgie's very detailed simulations strengthen my conviction that we are now at the point where the importance of RPI's remaining games is in preparing for the playoffs, and in particular, testing themselves against teams like Clarkson and Cornell, rather than in determining what position they will finish. While (almost) anything is possible, Burgie's analysis indicates that the highest probability that any team in the ECAC has of finishing in any particular spot is RPI's probability (92.5%) of finishing seventh.

hab
02-07-2013, 06:14 PM
I'm a little surprised we haven't heard anything on the recruiting front for awhile...does anyone know if we have more announcements coming (I would even settle for a good rumor) ? At this point we have two forwards (Rooney and Horwood) and one defence (Behounek). We have five seniors leaving, although two of them have seen limited action over the last 2 years (Padmore and Jakubowski) so its conceivable that we are only bringing in three. However, we have two starting defence leaving (LeDonne and Daniels) so I have been expecting to see another D coming in.

FlagDUDE08
02-07-2013, 09:18 PM
Forget green mushroom, that's a Super Mario World zone filled with nothing but moons! :eek:

Ralph Baer
02-08-2013, 01:19 AM
I'm a little surprised we haven't heard anything on the recruiting front for awhile...does anyone know if we have more announcements coming (I would even settle for a good rumor) ? At this point we have two forwards (Rooney and Horwood) and one defence (Behounek). We have five seniors leaving, although two of them have seen limited action over the last 2 years (Padmore and Jakubowski) so its conceivable that we are only bringing in three. However, we have two starting defence leaving (LeDonne and Daniels) so I have been expecting to see another D coming in. I would think that there will be others, perhaps even already in the directory. Info on women's recruits does not seem to be as widespread as that for the men. I think last year, however, the only recruit whom we did not know about prior to the formal announcement was Sara Till. Also, Padmore has another year of eligibility since she received a medical redshirt for 2011-12. I don't know if she plans to use it.

Stat Man
02-08-2013, 09:11 AM
I would think that there will be others, perhaps even already in the directory. Info on women's recruits does not seem to be as widespread as that for the men. I think last year, however, the only recruit whom we did not know about prior to the formal announcement was Sara Till. Also, Padmore has another year of eligibility since she received a medical redshirt for 2011-12. I don't know if she plans to use it.


I believe Padmore's hockey career is over.

Hockeydad4two
02-08-2013, 12:10 PM
Remember that the sports infomation department is short one person. That leaves them to divy up the duties and it appears, to me at least, that the women's team is getting little support.

hab
02-08-2013, 12:54 PM
For those interested, today's game (Clarkson at RPI 7 pm ET) will have live video from RPITV (high quality broadcasts, and free). Check www.rpitv.org

jericho
02-08-2013, 05:14 PM
Remember that the sports infomation department is short one person. That leaves them to divy up the duties and it appears, to me at least, that the women's team is getting little support.

?

Hockeydad4two
02-08-2013, 06:31 PM
Remember that the sports infomation department is short one person. That leaves them to divy up the duties and it appears, to me at least, that the women's team is getting little support.

This is what I was responding to from Ralph:

I would think that there will be others, perhaps even already in the directory. Info on women's recruits does not seem to be as widespread as that for the men. I think last year, however, the only recruit whom we did not know about prior to the formal announcement was Sara Till. Also, Padmore has another year of eligibility since she received a medical redshirt for 2011-12. I don't know if she plans to use it.

whoop87
02-08-2013, 07:26 PM
Hab - Thanks for the link and the heads up that the game would be webcast free for all tonight. I'm looking forward to a lively 3rd period. It's a real nice feed and the first I've seen of both RPI and Clarkson this year.