ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

[burgie12]

Once again, I'm stealing this from the Hockey East thread. Todd set up the format and the amount of detail and I'm cannibalizing it for ECAC use.

--- Bye Lock - 32+
--- Home Lock - 27
Yale 22 - 38 [1-10]
UC 21 - 37 [1-10]
PU 19 - 35 [1-11]
RPI 18 - 34 [1-11]
DC 18 - 34 [1-11]
Cornell 16 - 32 [1-12]
QU 15 - 29 [1-12]
CCT 13 - 31 [1-12]
Brown 11 - 27 [1-12]
SLU 7 - 25 [1-12]
Harvard 6 - 20 [4-12]
--- Bye Eligible - 20
Colgate 2 - 18 [6-12]
--- Home Eligible - 15

Remaining League Schedules:
Yale - Harvard, DC, @SLU, @CCT, @QU, @PU, Colgate, Cornell
UC - @PU, @QU, Cornell, Colgate, @CCT, @SLU, QU, PU
PU - UC, RPI, @Harvard, @DC, Brown, Yale, @RPI, @UC
RPI - @QU, @PU, Colgate, Cornell, @SLU, @CCT, PU, QU
DC - @Brown, @Yale, QU, PU, @Colgate, @Cornell, SLU, CCT
Cornell - CCT, SLU, @UC, @RPI, Harvard, DC, @Brown, @Yale
QU - RPI, UC, @DC, Yale, Brown, @UC, @RPI
CCT - @Cornell, @Colgate, Brown, Yale, @SLU, UC, RPI, @Harvard, @DC
Brown - Harvard, DC, @CCT, @SLU, @PU, @QU, Cornell, Colgate
SLU - @Colgate, @Cornell, Yale, Brown, CCT, RPI, UC, @DC, @Harvard
Harvard - @Brown, @Yale, PU, @Cornell, @Colgate, CCT, SLU
Colgate - SLU, CCT, @RPI, @UC, DC, Harvard, @Yale, @Brown

We're down to the last 4 weekends of ECAC play and there's still a lot to be hashed out before the playoffs roll around in March. Week by week, I hope to take a mathematical approach to the possibilities that abound as each team tries to solidify their standing.

A lot of my number crunching comes from the Sioux Sports what-if calculator. I'm using the ECAC Hockey's tie-breaking guidelines to split ties that I come across. I really, really hope that slack.net puts up their ECAC Playoff Possibilities Script again this year (link goes to last year's version).

Let's start with some certainties...

Yale and Union have already racked up enough points that they cannot be caught by either Harvard or Colgate, even if they both won out all of their games (which isn't even possible). Princeton has also accumulated enough points that they cannot be caught by the Raiders.

RPI cannot finish in 12th. If the Engineers were to lose out their remaining 8 games, they would finish the season with 18 points. Colgate and Harvard would also be able to reach 18 points by winning out the rest of the season (with Colgate winning the head-to-head match-up). The 3-way tiebreaker would see all of the teams taking 4 points from the other 2 and Colgate would lose the second tiebreaker (wins because their record would be 8-12-2 while both Harvard and RPI would have 9-13-0 records), meaning that Rensselaer cannot finish 12th.

Dartmouth is in a similar predicament as RPI. They've already swept the season series against both Colgate and Harvard, so a 3-way Raider-Crimson-Green tie would put Dartmouth into 10th place. If Harvard wins the Harvard-Colgate game, then Colgate finishes in 12th place by themselves and Dartmouth / Rensselaer could slip down to 11th place.

I've tried a number of different scenarios to try and bump up Harvard and Colgate. The best I've been able to do is putting Harvard in a tie for 4th with RPI, behind Yale, Union, and Princeton. If RPI splits with Quinnipiac by tying both games, then the Crimson win the tiebreaker on the second criteria (wins). For Colgate, the best I've been able to do is 6th, either by themselves or in a tie with Clarkson, either way gives them the 6 seed come March (they would win the tiebreaker against Clarkson by taking 3 points on the season).

Next, let's look at the "thresholds" that are being employed. Bye Lock refers to the number of points that a team would have to have at the end of the season assuming that 5th place has the most points possible. Bye Eligible refers to the least possible number of points that a team can get and still finish in 4th place. Home Lock and Home Eligible are similar but refer to the 8th / 9th place race, instead of the 4th / 5th place race. Once the 4 teams that have won byes are determined, the "Bye Lock" and "Bye Eligible" thresholds will merge.

The "Bye Lock" threshold is currently set at 32+. I can get the Top 5 teams to all have at least 32 points (Dartmouth, RPI tie for 4th at 32), so to guarantee yourself a week off in the beginning of March, you need at least 32 points and the proper tiebreakers (at this time... once teams start losing, this number drops).

The "Bye Eligible" threshold is put at 20 points, for now. The six-team group of RPI, Dartmouth, Cornell, Quinnipiac, Clarkson, and Brown gets grouped up from 4th to 9th, with one team having 20 points and the other 5 having 19.

The "Home Lock" threshold is currently set at 27. I got it by getting Yale to 28 points, having a 7-way tie for 2nd place at 27, and then Union is the odd team out in 9th place with 26 points. Of course, the actual teams don't matter, and it doesn't have to be Union finishing in 9th (I just wanted to make it that way ).

The "Home Eligible" threshold lays at 15. Quinnipiac can still get home ice without getting another point on the season, as long as Brown, St. Lawrence, Harvard, and Colgate cooperate.

The travel partners of RPI / Union and Quinnipiac / Princeton are the only ones that have not played each other yet this season. Since there are so many different match-ups and the standings are so jumbled in the middle, there are lots of possibilities here. Thankfully, there's only two more weeks (give or take) where we have to deal with games in hand. After the St. Lawrence - Clarkson game on Feb 15th, all 12 teams will have 4 games remaining.

For those of you looking for a "probability"-based look at the standings and playoff possibilities, I'm going to direct you to this site. My issue is that they don't look at the possibility of ties (which is why they have RPI possibly finishing 12th) and their "probabilities" are not explained and seem like they are derived at random.

Thanks for reading. I hope that this was useful and that it helps shed some light on the playoff race as we head down the road towards Atlantic City.

[goblue78]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Most of what you're looking for is here: http://www.playoffstatus.com/ecachoc...easonprob.html

[UnionHockeyManiac]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Thanks for posting!

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Most of what you're looking for is here: http://www.playoffstatus.com/ecachoc...easonprob.html

For those of you looking for a "probability"-based look at the standings and playoff possibilities, I'm going to direct you to this site. My issue is that they don't look at the possibility of ties (which is why they have RPI possibly finishing 12th) and their "probabilities" are not explained and seem like they are derived at random.

.

[goblue78]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Apologies... I didn't read carefully down to the end. I'm not sure, but I think their probabilities are odds-based from winning percentages, and I think Krach would have been better (though still not perfect).

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Apologies... I didn't read carefully down to the end. I'm not sure, but I think their probabilities are odds-based from winning percentages, and I think Krach would have been better (though still not perfect).

I agree. That is likely from where the odds are derived, but they don't detail it anywhere. A single sentence would suffice.

My main reason for doing this was to make sure that I do this leading up to the last two weekends. Once more games get played, it's fun to see teams drop out of bye / home-ice contention and to see the number of points necessary for a bye or home-ice slowly converge.

[Ralph Baer]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

I agree. That is likely from where the odds are derived, but they don't detail it anywhere. A single sentence would suffice.

My main reason for doing this was to make sure that I do this leading up to the last two weekends. Once more games get played, it's fun to see teams drop out of bye / home-ice contention and to see the number of points necessary for a bye or home-ice slowly converge.

I read on some thread a couple of years ago that that site uses a Monte Carlo approach. They run a lot of random scenarios and get possiibilities and probabilities that way. Clearly if they don't run enough cases, they can miss something. I did not find where it said that on the site.

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

An update after last night's games. Yale can be the first team to clinch home-ice (without having to go into tiebreakers) today with any combination of 2 points between themselves (vs Dartmouth) and Cornell (vs St. Lawrence) today. A Clarkson win tonight would clinch something at the other end of the standings. The Raiders would be guaranteed to go on the road in March.

--- Bye Lock - 31+
--- Home Lock - 25+
Yale 24 - 38 [1-9]
UC 23 - 37 [1-10]
DC 20 - 34 [1-10]
RPI 19 - 33 [1-10]
PU 19 - 33 [1-10]
Cornell 18 - 32 [1-11]
QU 16 - 28 [1-11]
CCT 13 - 29 [1-12]
Brown 11 - 25 [1-12]
SLU 9 - 25 [1-12]
--- Bye Eligible - 21+
Harvard 6 - 18 [6-12]
Colgate 2 - 16 [8-12]
--- Home Eligible - 13+

Remaining League Schedules:
Yale - DC, @SLU, @CCT, @QU, @PU, Colgate, Cornell
UC - @QU, Cornell, Colgate, @CCT, @SLU, QU, PU
DC - @Yale, QU, PU, @Colgate, @Cornell, SLU, CCT
RPI - @PU, Colgate, Cornell, @SLU, @CCT, PU, QU
PU - RPI, @Harvard, @DC, Brown, Yale, @RPI, @UC
Cornell - SLU, @UC, @RPI, Harvard, DC, @Brown, @Yale
QU - UC, @DC, Yale, Brown, @UC, @RPI
CCT - @Colgate, Brown, Yale, @SLU, UC, RPI, @Harvard, @DC
Brown - @CCT, @SLU, @PU, @QU, Harvard, Cornell, Colgate
SLU - @Cornell, Yale, Brown, CCT, RPI, UC, @DC, @Harvard
Harvard - PU, @Cornell, @Colgate, @Brown, CCT, SLU
Colgate - CCT, @RPI, @UC, DC, Harvard, @Yale, @Brown

Here's a quick update after Friday's games.

A lot of my number crunching comes from the Sioux Sports what-if calculator (be careful to not specify the result for the Feb 2nd Harvard-Brown game). I'm using the ECAC Hockey's tie-breaking guidelines to split ties that I come across. I really, really hope that slack.net puts up their ECAC Playoff Possibilities Script again this year (link goes to last year's version).

RPI currently holds 4th place over Princeton (before today's game between the two) based on the third tiebreaker (points against Top-4 teams (RPI wins 8-0)).

Let's start with some certainties...

Yale's possible finishes narrows to 1st-9th place. Either Brown or SLU can catch Yale, but not both since they still have a game against each other.

Cornell has enough points that they can't finish in 12th. But, a tie with Harvard would go to the Crimson based on wins (9 vs 8) since the season series would be split.

Quinnipiac can be put into a three-way tie with Harvard and Colgate (if the Raiders beat the Crimson) but wins the head-to-head comparison (8 v 2 v 2). So, they can finish 11th if Harvard sweeps the rest of the season, including the head-to-head against Colgate, but they can't finish 12th.

Brown can still finish in 1st place (very narrowly) with 25 points. They could end up tied with Quinnipiac and would win the tiebreaker based on taking 3 points in the season series.

St. Lawrence can also still finish in 1st place. They can tie with RPI for first place with 25 points, which means that they would split the season series and could win based on wins (12 v 11).

Harvard can still take 6th place if they win out, putting them in a tie with Cornell (which they win, as detailed above).

Colgate can get into a tie for 7th with Quinnipiac, but got swept in the season series against the Bobcats and therefore cannot finish in 7th place.

Next, let's look at the "thresholds" that are being employed...

The "Bye Lock" threshold is currently set at 31+. I can get the Top 5 teams to all have at least 31 points (Princeton, RPI tie for 4th at 31), so to guarantee yourself a week off in the beginning of March, you need at least 31 points and the proper tiebreakers (at this time... once teams start losing, this number drops).

The "Bye Eligible" threshold is put at 21+ points, for now. With Princeton and RPI tied for 4th with 19 points and having not played each other yet, if they split the series, then they can tie for the bye with 21 points. (Rensselaer would win the bye based on points against Top 4 teams.)

The "Home Lock" threshold is currently set at 25+. I got it by having Brown and RPI tie for 8th place with 25 points. The Engineers would get to host the Bears because they swept the season series (but there are other teams that can tie Brown and could potentially lose the tiebreaker).

The "Home Eligible" threshold lays at 13+. Clarkson can potentially lose out and end the season in a 3-way tie for 8th place with Brown and St. Lawrence. These three teams would have split the season series with each of the other two teams and would also end the season with 6 wins each. So, the tiebreaker would go down to points against Top 4 teams (and there's no certainties as to which teams would occupy those spots.

The postponement of the Harvard-Brown game means that there will be an unbalanced number of games remaining for the 12 teams up until the last weekend.

Once again, for those of you looking for a "probability"-based look at the standings and playoff possibilities, I'm going to direct you to this site. My issue is that they don't look at the possibility of ties and their "probabilities" are not explained and seem like they are derived at random.

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

And with the conclusion of this weekend's games, the only certainty is that both Yale and Union will both be playing at home in March. They cannot finish at or below 9th place.

--- Bye Lock - 31+
Yale 26 - 38 [1-7]
UC 25 - 37 [1-8]
--- Home Lock - 25
RPI 21 - 33 [1-10]
DC 20 - 32 [1-10]
Cornell 20 - 32 [1-10]
PU 19 - 31 [1-10]
QU 16 - 26 [1-11]
CCT 13 - 27 [1-12]
Brown 11 - 25 [3-12]
SLU 9 - 23 [3-12]
--- Bye Eligible - 21+
Harvard 6 - 18 [7-12]
Colgate 4 - 16 [8-12]
--- Home Eligible - 13+

Remaining League Schedules:
Yale - @SLU, @CCT, @QU, @PU, Colgate, Cornell
UC - Cornell, Colgate, @CCT, @SLU, QU, PU
RPI - Colgate, Cornell, @SLU, @CCT, PU, QU
DC - QU, PU, @Colgate, @Cornell, SLU, CCT
Cornell - @UC, @RPI, Harvard, DC, @Brown, @Yale
PU - @Harvard, @DC, Brown, Yale, @RPI, @UC
QU - @DC, Yale, Brown, @UC, @RPI
CCT - Brown, Yale, @SLU, UC, RPI, @Harvard, @DC
Brown - @CCT, @SLU, @PU, @QU, Harvard, Cornell, Colgate
SLU - Yale, Brown, CCT, RPI, UC, @DC, @Harvard
Harvard - PU, @Cornell, @Colgate, @Brown, CCT, SLU
Colgate - @RPI, @UC, DC, Harvard, @Yale, @Brown

A lot of my number crunching comes from the Sioux Sports what-if calculator (be careful to not specify the result for the Feb 2nd Harvard-Brown game). I'm using the ECAC Hockey's tie-breaking guidelines to split ties that I come across. This season's slack.net ECAC Playoff Possibilities Script is up again and should make future looks into tiebreakers that much easier.

Dartmouth holds 4th place over Cornell based on the 3rd tiebreaker criteria (points vs Top 4 teams, 3 v 2).

Let's start with some certainties...

Yale's possible finishes narrows to 1st-7th place. They can finish in a tie that leaves them near 8th place, but they don't and can't lose any individual tiebreaker against any team in the ECAC (and finish with 26 points... if they tie some games, they'll start losing tiebreakers, but then they wouldn't be able to finish with few enough points to fall to 8th place) because no team can take more than 2 points from them and they have not tied a game yet (so they would win the wins comparison against anybody except for Harvard, but the Crimson can't catch the Elis).

Union narrowed their possible finishes to anywhere from 1st to 8th place. The Brown Bears can catch the Dutchmen, but Leaman's squires swept the season series and cannot finish in 9th. And, even that would not be enough. If Brown were to catch Union, then Quinnipiac would not have enough points to pass Union. So, Union definitely cannot finish in 9th place.

The Qpac Cats are still assured of not finishing in 12th place, but their loss to Union tonight did not let them distance themselves enough from Harvard. Quinnipiac can still finish in 1st, with some help in the tiebreaker department. Even though they would split the season series with Yale, they can take 3 points from RPI, while Yale split with the Engineers. So, a 3-way tie for first place between Quinnipiac, Yale, and RPI would give the Bobcats the #1 seed (head-to-head points, 5 v 4 v 3).

Clarkson still has the slimmest of hopes of taking home the Cleary Cup. They can rack up 27 points by winning out and if the other conference games break the right way, they can still finish in first place.

Brown can finish in a tie for 2nd, but any tie at that point would include Union. Brown was swept by Union and Union cannot be swept by any team in the ECAC, so even a 3-way tie would not split the Bears way. I'm not going to delve into a 4 (plus)-way tie, so I'm just calling Brown's ceiling 3rd place.

Harvard's ceiling keeps falling. It's now down to 7th place following Cornell's win against St. Lawrence.

With Colgate's win over Clarkson tonight, their drive for home-ice is still alive. But, the margin for error is still very thin.

Next, let's look at the "thresholds" that are being employed...

I still see the "Bye Lock" threshold at 31+ points. I can get the Top 5 teams to all have at least 31 points (Cornell, Dartmouth, RPI 3-way tie for 3rd at 31), so to guarantee yourself a week off in the beginning of March, you need at least 31 points and the proper tiebreakers. Based on the way I get to this tie, it would be broken with Cornell in 3rd, Rensselaer in 4th, and the Big Green in 5th (split by head-to-head points, 6 v 4 v 2).

The "Bye Eligible" threshold also stays stationary at 21+ points. I got there with a 3-way tie between Cornell, Princeton, and Dartmouth for 4th place. Based on the game results that I used to get there, they would each split the season series with the other two teams and Princeton would get the bye based on wins (10 v 9 v 9).

The "Home Lock" threshold drops from 25+ to 25. With Quinnipiac and Brown still having to face each other later this season, you can't get both teams to have more than 24 points.

The "Home Eligible" threshold still lays at 13+. Clarkson can potentially lose out and end the season in a 3-way tie for 8th place with Brown and St. Lawrence. These three teams would have split the season series with each of the other two teams and would also end the season with 6 wins each. So, the tiebreaker would go down to points against Top 4 teams (and there's no certainties as to which teams would occupy those spots).

[LynahFan]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Ask and ye shall receive, courtesy of Joe Schlobotnik himself.

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Ask and ye shall receive, courtesy of Joe Schlobotnik himself.

Great success!

PS Don't forget to include the Feb 22 game between Brown and Harvard.

[licwinko]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Are we sure that Yale and Union could actually finish 8th? I understand that the 8th place team could catch them in the standings, but could every team 3-8th catch them? It doesn't seem like there's enough points available for everyone to be able to catch them.

I ask because I'm too lazy to figure it out myself--also I don't want to steal your thunder. You've done some amazing work, Burgie!

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Are we sure that Yale and Union could actually finish 8th? I understand that the 8th place team could catch them in the standings, but could every team 3-8th catch them? It doesn't seem like there's enough points available for everyone to be able to catch them.

I ask because I'm too lazy to figure it out myself--also I don't want to steal your thunder. You've done some amazing work, Burgie!

Well, you caught me on one thing... Yale cannot finish in 8th. Quinnipiac can catch them, but they can't pass them, and Yale would win the tiebreaker on wins (13 v 11). So, Yale's actual basement is 7th place.

As for Union finishing in 8th, I got it with the following (winning team listed first):

Feb 11: SLU-Yale;  Cornell-UC;  RPI-Colgate;  QU-DC;  PU-Harvard;  CCT-Brown
Feb 12: CCT-Yale;  Colgate-UC;  RPI-Cornell;  DC-PU;  SLU-Brown
Feb 15: CCT-SLU
Feb 18: QU-Yale;  CCT-UC;  RPI-SLU;  Cornell-Harvard;  DC-Colgate;  PU-Brown
Feb 19: SLU-UC;  CCT-RPI;  DC-Cornell;  QU-Brown;  Colgate-Harvard
Feb 20: PU-Yale
Feb 22: Harvard-Brown
Feb 25: Colgate-Yale;  QU-UC;  PU-RPI;  Cornell-Brown;  DC-SLU;  CCT-Harvard
Feb 25: Cornell-Yale;  PU-UC;  QU-RPI;  CCT-DC;  Colgate-Brown;  Harvard-SLU

Final standings (breaking ties with slack.net):

1  Princeton    29
2  Dartmouth    28
3  Cornell      28
4  Clarkson     27
5  Rensselaer   27
6  Yale         26
7  Quinnipiac   26
8  Union        25
9  St. Lawrence 15
10 Colgate      12
11 Brown        11
12 Harvard      10

Likely? No. Possible? Yes.

[licwinko]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

I'm still amazed that that many teams can catch Yale and Union. Thanks for investigating that!

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

I'm still amazed that that many teams can catch Yale and Union. Thanks for investigating that!

The main reason that so many teams can play catch-up is that Yale, Union, and RPI have all finished their series against each other. Add in the fact that the ECAC uses a travel partner schedule instead of the series style employed by the WCHA / CCHA / Atlantic means that no one has 2 games against any single team remaining, cutting down on the number of splits that have to be put in place to bump up everyone's point totals.

ETA: If anyone wants to see some more bizarre scenarios (such as Union finishing in 8th or Clarkson in 1st or Colgate in 8th or home-ice only needing 13 points), go ahead and ask and I'll bang it out when I get the chance.