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A couple of days ago, I reviewed some well-known PairWise Rankings weirdness, and promised a new entry for the list. Here it is.

Coming into last weekend, Vermont was second in the PWR and Northeastern fourth. The teams were scheduled to play a Friday-Saturday series at Northeastern, which ended up a split with Northeastern winning Friday by a 3-1 score and Vermont returning the favor Saturday, 4-2.

Now, when two well-regarded teams play a series to a dead heat, one would expect little change in their relative rankings — if you thought one of the two teams was better to begin with, maybe a split narrows the gap in your mind, but that’s about it.

But that’s not what happened in the PairWise. Instead, the split raised Northeastern’s Ratings Percentage Index a touch, from .5895 to .5900, while Vermont’s RPI fell from .5918 to .5859. That change reversed the comparison between UVM and NU (which Vermont had been winning on the RPI tiebreaker), giving it to NU instead and leaving the Huskies in a tie for fourth in the PWR while dropping Vermont to sixth.

(Note: Sunday’s Maine-Providence subsequently pushed NU’s RPI down a bit, because the Huskies have played Maine three times this season already, so the Maine tie hurt Northeastern’s RPI. The PairWise Rankings now show Northeastern tied with Vermont, but to break that tie for NCAA tournament purposes, we look at the direct comparison between NU and UVM, which the Huskies now win. Thus Northeastern is really fifth and Vermont sixth for seeding purposes.)

What gives? How did splitting help Northeastern while hurting Vermont? The answer lies in the RPI’s calculation mechanics. RPI is a weighted average of three things: a team’s own winning percentage (WP), its opponents’ aggregate winning percentage (OWP), and (keep following along here) its opponents’ opponents’ aggregate winning percentage (OOWP).

The weights that make up the RPI are as follows: 25% WP, 21% OWP and 54% OOWP. Now, for any two teams, their OOWPs don’t usually differ all that much because OOWP is a giant amalgamation of hundreds of games played by their opponents’ opponents, one which usually includes almost every team in Division I by the end of the season. But OWPs can differ by more significant amounts, and this is what happened here.

Although the biggest disparities in OWPs are seen between teams in different leagues, going into last weekend Vermont and Northeastern had accumulated enough differences in their Hockey East schedules and in their nonconference games that Vermont’s OWP was substantially higher than Northeastern’s. (That’s mostly due to Vermont playing Boston University three times already to Northeastern’s once, and UVM having a pair of nonconference games against Miami.)

Summed up mathematically, Vermont’s OWP was .5707 while Northeastern’s was .5371, a difference of .0336. If that doesn’t sound like a lot, consider that the difference in RPI between Miami, which is currently projected into the NCAA tournament, and Yale, which is 28th nationally in RPI and therefore not even ranked in the PairWise, is less than that.

Now (finally!), here’s the point. When Vermont played Northeastern last weekend for the second and third times this season, it meant that Vermont’s opponents’ records were added twice more to Northeastern’s opponents’ opponents, and vice versa.

That means that by playing Vermont, Northeastern reaped the benefits of Vermont’s healthy OWP by getting it added two more times to its own OOWP, while Vermont had Northeastern’s lower (though still decent) OWP added twice more to its OOWP. That difference is all it took to reverse the RPI comparison between the two teams, even though both squads were top-five in the PairWise and the RPI at the time.

And there it is — the anatomy of how two similar teams, playing each other to a split, caused the PairWise to change its mind.