Bracketology: D-I Women

How hard can it to be to pick the four teams for NCAA Women’s Hockey tournament? Only four teams, no conference automatic bids, and there’s only one site in Providence to place them. Easy, right?

Judging by the short history of national championship women’s hockey, the answer is a resounding no. With only four teams to pick out of 30, in four conferences with a tiny number of interconference results available, all that comes easily to the selection process is controversy.

Consider the first NCAA Frozen Four in 2001, when Minnesota was the defending national champion, the WCHA regular-season champion and the inaugural Frozen Four host. Seeing as the sport only had two conferences back then and Minnesota was the regular-season champion of one of them, conventional wisdom suggested the Gophers would make the tournament, even though they placed a dismal fourth in their conference tournament.

But they didn’t, and instead the berth went to St. Lawrence, a team that placed third in the ECAC regular season and lost its conference semifinal game by a 7-1 margin. The move probably meant smaller crowds for the Frozen Four, but the committee was vindicated when the Saints stunned season-long No. 1 Dartmouth 3-1 in the first NCAA women’s hockey tournament game ever played.

While Minnesota’s demise shocked conventional wisdom, it wasn’t unforeseen by those in the know. The D-I Women’s PairWise Rankings (PWR) predicted the Gophers’ impending disaster, as well as the entire four-team field that made the Women’s Frozen Four, and its predictive success has continued each of the last three years.

That, combined with the success of PWR on the men’s side, has made the PWR so revered that various media outlets have inadvertently implied that they perfectly predict the Frozen Four selection process. While the PWR can’t perfectly match the NCAA process, it does use the same criteria as the NCAA, so it always come close.

Although the D-I Women’s PWR has had a successful history, this year’s rankings might be deceptive for a couple reasons:

  • The NCAA women’s selection criteria are written in language that is less rigid than the men’s criteria. This flexibility hasn’t resulted in Frozen Four picks distinct from the PWR yet, but that is no guarantee for the future.
  • The NCAA Women’s Ice Hockey Committee implemented changes in one of its selection criteria, the Ratings Percentage Index (RPI). has not yet implemented these changes into its RPI and PWR calculations that are updated after each D-I game result.

    Both these complicated observations require further explanation. But first let’s get to the point — what are the implications for this season?

    The former observation is favorable for teams like No. 5 Wisconsin and No. 6 Minnesota-Duluth, who are not having much luck with the rigid numbers of the current PWR. But the latter observation is dreadful news for those same teams, if those schools have been abiding by the PWR as an accurate indicator of their selection prospects.

    The direct implication of the NCAA’s new RPI adjustment is that three teams (Minnesota, Harvard, and Dartmouth) have built a nearly insurmountable lead in RPI over the rest of the country. St. Lawrence, Wisconsin, and UMD all appear to be close in the old RPI, but in the corrected RPI, St. Lawrence has a sizeable advantage.

    St. Lawrence’s current edge is so large, in fact, that even if the Saints advance to the ECAC semifinals and lose there, Wisconsin will have to win the WCHA to surmount St. Lawrence’s RPI, and UMD cannot surmount it.

    In the PWR resulting from the new RPI, Minnesota has already clinched a top-four spot, as will Harvard if it sweeps its ECAC quarterfinal series. Dartmouth will also clinch a top-four spot with an ECAC quarterfinal sweep, but by a slim margin.

    If St. Lawrence sweeps its ECAC quarterfinal series, it will be in the top four as long as Wisconsin doesn’t win the WCHA tournament. And if St. Lawrence wins its ECAC semifinal, it will be ahead of Wisconsin if the Badgers win the WCHA. UMD cannot earn a top four spot if the top three ECAC teams all sweep their quarterfinal series.

    Does this mean Wisconsin has to win the WCHA tournament to make the Frozen Four? If the Frozen Four gets picked solely based on the PWR numbers, then the answer is yes. But that’s where that first observation above comes back into play. If Wisconsin falls in the WCHA final or earlier, then the desire to have a Frozen Four field of two from the East and two from the West is going to come into conflict with any interpretation of the PWR numbers.

    The rest of this column is divided into several sections — one explaining the new RPI adjustments, one discussing the looser language of the women’s criteria, and the rest going over adjusted PWRs based on a variety of conference tournament outcomes. Those less concerned with details and more concerned with applications should skip the next two sections.

    Explaining the NCAA’s RPI Adjustment

    Here’s the new adjustment, which is indicated by an asterisk next to the definition of RPI in the NCAA women’s ice hockey tournament handbook:

    “If points awarded for up to four regular-season game wins lower a team’s average RPI, those points will not count toward the RPI. Points awarded for postseason tournament wins that lower a team’s average regular-season RPI shall not count toward a team’s RPI.”

    Note that in women’s hockey, RPI is a weighted average of won-lost record, opponents’ winning percentage and opponents’ opponents’ winning percentage, where the weights are 35 percent, 50 percent and 15 percent, respectively.

    To understand what that rule is saying, first observe that a single-game RPI can be calculated for each game a team plays in the context of the opponents’ results, and the season RPI can be written as the average of all game RPIs. For instance the game RPI of a win over Minnesota this season is about .86. The game RPI of a loss to Minnesota-Duluth is about .40. The season RPI of a hypothetical team that beats Minnesota in 15 games and loses to UMD in 15 games is about .63, which is the average of the above two numbers. (Note: Two different teams might get slightly different game RPIs for the same opponent depending on their head-to-head histories, but this is a technicality beyond the scope of this column.)

    Next, understand that some opponents have records so poor that a win against them actually lowers a team’s season RPI. For example, the game RPIs this season for wins over Union, Vermont and Bemidji State were about .44, .51, and .52 respectively. Note that a win over Vermont is worth about as much as a loss to Minnesota in RPI terms. A win over Union is worth about as much as a loss to UNH.

    Also, observe that teams like Harvard, Dartmouth, and St. Lawrence — which have RPIs greater then .60 — would all have higher RPIs had their conference allowed them to avoid Union and Vermont entirely. What the new rule does, roughly speaking, is to calculate what RPIs these teams would have had they not played games that lowered their season RPI

    Here are the results for the top nine teams in the PWR. Listed are each team’s Old RPI, New RPI, and the four wins dropped from each team’s New RPI calculation.

    Team Old RPI New RPI Wins Dropped
    Minnesota .6618 .6803 Bemidji State (4)
    Harvard .6401 .6660 Union (2), Vermont (2)
    Dartmouth .6362 .6615 Union (2), Vermont (2)
    St. Lawrence .6099 .6287 Union (2), Vermont (2)
    Wisconsin .6050 .6167 Vermont (2), Bemidji State (2)
    Minnesota-Duluth .5971 .6065 Bemidji State (4)
    Mercyhurst .5921 .5999 Bemidji State (2), Quinnipiac (2)
    New Hampshire .5906 .5961 Vermont (1), Boston College (3)
    Princeton .5757 .5913 Union (2), Vermont (2)

    (Note that the wins dropped for each team do not necessarily coincide with the teams’ opponents who have the lowest RPIs. They coincide more with lowest win percentages, but not exactly. The explanation for this is beyond the scope of this column.)

    As the numbers show, the ECAC teams — in particular the Ivy teams — receive a greater boost from the new RPI than other teams. To see why, recall that the game RPI for Union was about .44 and the game RPIs for Vermont and Bemidji State were .51 and .52, respectively, so removing the Union games from the ECAC teams’ season RPI calculation provides a larger boost than removing the Bemidji State games. The Ivy teams get the largest boost because they played fewer regular season games, so the Union games had been dragging them down more than their ECAC peers.

    For a practical interpretation of RPI numbers, note that if a team plays 35 games, its RPI would increase by .01 (.35/35) if the team could turn one loss into a win. This heuristic can be used to compare two teams, effectively controlling for their strength of schedules. The gap between Dartmouth is Wisconsin can then be interpreted as more than four wins, while the gap between St. Lawrence and Wisconsin is about one win.

    The second part of RPI adjustment is the exclusion of postseason wins that bring down RPI. It turns out that the only team affected by this is Harvard, whose ECAC quarterfinal opponent Cornell is the only postseason team weak enough for this to be an issue (a win over Cornell gets a game RPI of about .54). So playing Cornell will lower Harvard’s RPI that gets calculated on-the-fly by and used in the current PWR, but it will not affect the RPI used by the NCAA.

    Just How Rigid Are The Women’s Criteria?

    First, read the exact wording of the women’s criteria as it appears in the handbook:

    “The committee will evaluate won-lost record and strength of schedule using the following categories: (not in preferential order) Rating Percentage Index (RPI); Head-to-head competition; Results versus common opponents; Results during the last 16 games; and Results against teams under consideration.”

    (“Teams under consideration” means those with records greater than .500 here.)

    The men’s criteria are written more rigidly, stating specifically that team comparisons are made in each category with a point awarded for each category victory, except for head-to-head where a point is awarded for each head-to-head victory, and that RPI is used as a tiebreaker. This is also the methodology applied in the men’s and women’s PWR. But that specific language is absent from the women’s handbook.

    Note that last year, Harvard was ahead of UMD in the PWR immediately prior to NCAA selections, but UMD earned the top seed and played Dartmouth, while Harvard earned the No. 2 seed and played Minnesota. This is the only NCAA tournament seeding that has ever differed from the women’s PWR in its history.

    Looking at the comparison, Harvard had a head-to-head win over UMD, a slight edge in results during the last 16 games, and a slight edge in results against teams under consideration. But UMD had a sizeable advantage in both RPI and results versus common opponents. It remains unknown whether this discrepancy from the PWR was a result of Harvard’s smaller edge in various categories or the committee’s desire to avoid semifinal intraconference matchups. Perhaps it was a combination of the two.

    While the committee has made one decision that differed slightly from the PWR, there’s no precedent for the committee making decisions that would turn the PWR entirely on its head. It’s conceivable the committee might give weight to a category victory that’s decided by about a point or an RPI differential below .005, but it’s unlikely a team will get preferential treatment for the sake of regional parity or appeasing a conference. The selection of St. Lawrence over Minnesota in 2001 went in favor of the PWR numbers and against just about every intangible consideration.

    Another observation about selection decisions is that even though the women’s criteria does not say RPI will be tiebreaker, it tends to carry the most weight because it is the only criterion that evaluates a team based on the entire season’s results.

    Tournament Projections

    Now it’s time to project the implications of various conference tournament results on NCAA selection decisions. These will be addressed in a Frequently Asked Questions style.

    Before browsing these results, note that all these responses take for granted (unless otherwise stated) that the top three ECAC seeds — Harvard, Dartmouth, and St. Lawrence — sweep their quarterfinal series. At this point their three opponents — Cornell, Yale, and Colgate — haven’t proven themselves capable of beating the top three ECAC teams, only hanging with them.

    One implication of this is that Colgate will cease to be a team above .500. If these teams can prove this assumption wrong this weekend, then the implications will be discussed in next week’s bracketology column.

    Also, projected RPIs will be given rounded to three decimal places, indicating their lower precision relative to current RPIs calculated in the first section. Consider the first two digits to be precise and the third digit to be slightly fuzzy. Details regarding the error of these projections are beyond the scope of this column.

    Finally, note that the top teams in the PWR right now are No. 1 Minnesota, No. 2 Harvard, No. 3 Dartmouth and No. 4 St. Lawrence. The teams just outside the bubble appear to be No. 5 Wisconsin and No. 6 UMD.

    What does Wisconsin have to do to make the NCAA Frozen Four?

    This is the hot-button issue of the day, especially now that Wisconsin coach Mark Johnson has said at his Monday press conference that if his team beats UMD in Saturday’s WCHA semifinal, he feels comfortable with his team’s position. But going by the numbers, Wisconsin shouldn’t feel too comfortable even with a win over UMD, and Wisconsin definitely does not control its own destiny.

    To make the first point, consider a Wisconsin team that loses to Minnesota in the WCHA final. Wisconsin is compared to a St. Lawrence team that loses to Dartmouth in the ECAC semifinals, and a Dartmouth team that loses to St. Lawrence in the ECAC semifinals (two results that cannot happen simultaneously, but these comparisons are used because Wisconsin could beat out either team to make the PWR top four).

    St. Lawrence vs Wisconsin
    RPI 0.629 1 0.618 0
    L16 13- 3- 0 0 13- 2- 1 1
    TUC 11- 7- 1 0 11- 6- 3 1
    H2H 0 0
    COP 6- 1- 0 1 7- 1- 3 0
    PTS 2 2
    Dartmouth vs Wisconsin
    RPI 0.655 1 0.618 0
    L16 11- 5- 0 0 13- 2- 1 1
    TUC 10- 6- 2 0 11- 6- 3 1
    H2H 0 0
    COP 4- 2- 0 1 6- 5- 1 0
    PTS 2 2

    Under conventional PWR rules, St. Lawrence wins the former comparison based on an RPI advantage of .011, which is roughly the equivalent of one win. The common opponent comparison is fair because St. Lawrence’s performance edge over Wisconsin against Northeastern (1-0-0 vs. 0-0-2) was better than Wisconsin’s over St. Lawrence against UMD (3-1-1 vs. 1-1-0). It’s a close comparison, but not one Wisconsin should feel comfortable about winning. The Dartmouth comparison isn’t nearly as close, particularly because of Dartmouth’s huge RPI advantage.

    Now look at the same comparisons, except assume Wisconsin defeats Minnesota in the WCHA final:

    St. Lawrence vs Wisconsin
    RPI 0.629 0 0.630 1
    L16 13- 3- 0 0 14- 1- 1 1
    TUC 11- 7- 1 0 12- 5- 3 1
    H2H 0 0
    COP 6- 1- 0 1 7- 1- 3 0
    PTS 1 3
    Dartmouth vs Wisconsin
    RPI 0.655 1 0.630 0
    L16 11- 5- 0 0 14- 1- 1 1
    TUC 10- 6- 2 0 12- 5- 3 1
    H2H 0 0
    COP 4- 2- 0 1 7- 4- 1 0
    PTS 2 2

    Wisconsin wins the comparison with St. Lawrence under standard PWR rules but only by the tiniest of margins. Dartmouth wins the latter comparison by conventional PWR rules, but look more closely at the numbers there. Subtract off the two wins over Vermont from each team’s common opponent total, and it reveals common opponent records that are fairer indicators of relative performance (2-2-0 vs. 5-4-1). This category should be a push, because both teams performed the same against Vermont, Dartmouth had a slightly better performance against Minnesota, and Wisconsin had a slightly better performance against UMD.

    Yet Dartmouth does have the huge edge in RPI, by a margin of .025 — roughly 2.5 wins, and it’s questionable whether the committee would analyze the common opponent category as closely as above. It would be interesting to see what the committee would do in evaluating the above Dartmouth-Wisconsin comparison.

    Conclusion: Going straight by conventional PWR rules, Wisconsin won’t make the tournament if it doesn’t win the WCHA and the top ECAC teams win their quarterfinals. If Wisconsin wins the WCHA over Minnesota in the final, the Badgers are in good shape, but they will be much safer if St. Lawrence loses its ECAC semifinal. Also, note that it’s important Wisconsin beats Minnesota in the final — without that additional resume-building win, Wisconsin will be in trouble. The Badgers are definitely not in control of their own destiny.

    Are Minnesota and Harvard Frozen Four locks?

    Consider a Minnesota team that has a 2001-like collapse to fourth place in the WCHA tournament compared to a Dartmouth team that loses in the ECAC semifinals (this is a worst-case scenario for the Gophers):

    Dartmouth vs Minnesota
    RPI 0.655 0 0.661 1
    L16 11- 5- 0 1 10- 5- 1 0
    TUC 9- 5- 2 0 17- 5- 2 1
    H2H 1 1
    COP 2- 1- 2 0 7- 1- 0 1
    PTS 2 4

    This is an unambiguous win for the Gophers. Minnesota also wins comfortably over the Badgers and UMD on basis of RPI and head-to-head victories. Minnesota also wins comparisons comfortably over a St. Lawrence team losing in the ECAC semifinals. Any way you cut the data in the worst-case scenario, the Gophers are still in.

    Consider a Harvard team that loses in the ECAC semifinals compared with a WCHA champion Wisconsin team, or ECAC champion Princeton and St. Lawrence teams. (Note: The Princeton and St. Lawrence results cannot happen simultaneously)

    Harvard vs Wisconsin
    RPI 0.656 1 0.630 0
    L16 14- 2- 0 0 14- 1- 1 1
    TUC 11- 4- 1 1 12- 5- 3 0
    H2H 0 0
    COP 7- 0- 1 1 8- 1- 3 0
    PTS 3 1
    Harvard vs Princeton
    RPI 0.656 1 0.620 0
    L16 14- 2- 0 1 12- 4- 0 0
    TUC 10- 3- 1 1 10- 7- 0 0
    H2H 1 2
    COP 23- 2- 0 1 17- 7- 0 0
    PTS 5 2
    Harvard vs St. Lawrence
    RPI 0.656 1 0.647 0
    L16 14- 2- 0 0 14- 2- 0 0
    TUC 9- 4- 1 0 13- 4- 1 1
    H2H 2 0
    COP 23- 4- 1 0 24- 3- 1 1
    PTS 3 2

    Each comparison is a clear win for Harvard. So does that mean Harvard’s a lock if it sweeps its ECAC quarterfinal? The numbers support that view, but there could still be trouble ahead if Harvard slips in the semifinals. Consider the following scenario: Wisconsin wins the WCHA, St. Lawrence wins the ECAC, and Dartmouth and Harvard each lose in the ECAC semifinals. In that situation, conventional wisdom says, Minnesota’s already in, there’s pressure to take the two league champions, and if it comes down to Harvard-Dartmouth, guess who has the head-to-head edge?

    It’s a situation that sounds reminiscent of the 2000 AWCHA national tournament, when Dartmouth was taken over Harvard based only on head-to-head results. But a difference between then and the above hypothetical is that Harvard has comparisons locked up over St. Lawrence and Wisconsin, even if those teams win their conference titles. Also, Harvard would still have a slight comparison edge over Dartmouth if both teams lost in the ECAC semifinals, though the RPI is too close to call.

    Dartmouth vs Harvard
    RPI 0.655 0 0.656 1
    L16 11- 5- 0 0 14- 2- 0 1
    TUC 8- 6- 2 0 11- 2- 1 1
    H2H 2 0
    COP 19- 5- 1 0 22- 2- 1 1
    PTS 2 4

    These results raise the question of why Harvard has an edge over Wisconsin that Dartmouth lacks. It’s mainly because Harvard has better results against UMD and Northeastern than Wisconsin, while Dartmouth lacks that common opponent edge over the Badgers.

    Conclusions: Minnesota seems to be a mortal lock. Harvard’s close to it given an ECAC quarterfinal sweep of Cornell. Of course either team would prefer to have a superb showing in its conference tournament to be sure. The PWR is not infallible.

    Are UMD, Mercyhurst, UNH, and Princeton all finished in terms of Frozen Four hopes? Which team(s) might have the best shot?

    Believe it or not, UMD’s Frozen Four hopes are still alive, although they are on life support. To prove this, let’s see how a WCHA champion UMD team stacks up against a St. Lawrence team losing in the ECAC semifinals.

    St. Lawrence vs Minnesota-Duluth
    RPI 0.629 1 0.623 0
    L16 13- 3- 0 1 11- 4- 1 0
    TUC 10- 6- 1 1 12-10- 2 0
    H2H 1 1
    COP 4- 3- 0 0 3- 2- 1 1
    PTS 4 2

    St. Lawrence appears to have a decisive edge in the comparison, but just one Colgate win over St. Lawrence in the first round would be enough the sway this comparison to UMD’s win column. Note that even if the Bulldogs beat out St. Lawrence, they would have to win a close comparison with Wisconsin to make the Frozen Four cut. UMD would have the RPI edge over Wisconsin in that scenario, but a Wisconsin third-place loss might be necessary to sway the comparison. This result will be examined more closely if UMD does win the WCHA title this weekend.

    Princeton’s in a similar situation as UMD. Dartmouth, Harvard and Minnesota are too far away for Princeton to catch. St. Lawrence would be in striking distance were it not for two head-to-head losses to the Saints. Even if Princeton wins the ECAC, a St. Lawrence team losing in the ECAC semifinals would still have an RPI edge of nearly .01 over Princeton. So Princeton, like UMD, could use some help from Colgate this weekend.

    Mercyhurst and New Hampshire, because they play in weaker conferences, will not be able to gain the ground in RPI that they would need to make a run at the top four spots in these last two weeks. They’re both out of the running.

    So that’s the story for now. Please send any corrections, questions, requests or comments about the D-I Women’s PairWise Rankings or this column to [email protected]. Stay tuned to future columns for the implications of the upcoming weekend’s WCHA and ECAC tournament results, possible tournament seedings and more critical views of the NCAA selection criteria.