The Pairwise Rankings Explained

If you're a college hockey fan of any sort you've likely heard some mention of the Pairwise Rankings. Now that we're into the final weeks of the season, they're becoming more and more important. So it's time to stop nodding politely any time someone brings them up and learn about how they work.

With inspiration from our colleagues at Vox.com, here are the Pairwise Rankings, explained:

How important is this thing?

Extremely! The NCAA Selection Committee looks at the Pairwise Rankings, and only the Pairwise Rankings when determining the at-large bids for the NCAA tournament with zero exceptions. Though the field won't officially be announced until Sunday March, 22nd, we will know what teams are in the NCAA tournament, and what they will be seeded, by that Saturday evening when the final game has been played.

So how does it work?

Every team is compared head-to-head against every other team based on three categories: RPI(Ratings Percentage Index), Record vs. Common Opponents, and Head-to-Head record. The team that wins more of those categories wins the comparison. The team with the most total comparison wins is ranked first, followed by the team with second most comparison wins, and so on.

If two teams are tied at one category apiece, the comparison goes to the team with the higher RPI. If two teams have the same number of comparison wins, the team with the higher RPI is ranked higher.

That sounds like the whole thing is basically just RPI.

It's basically just RPI. A comparison is decided by RPI unless the two teams have played head-to-head, and with relatively few out-of-conference games, it doesn't come up that often. Out of the 59 teams in Division I, there are only five instances where the final Pairwise differs from RPI, and never by more than a single spot.

How does RPI work?

There are four things you need to know about how RPI is calculated:

1. RPI is expressed as a winning percentage calculated by three weighted factors: 25% is a team's overall record, 21% is the record of a team's opponents, and 54% is the record of an opponent's opponents.

2. Games are weighted based on where they are played. Winning a road game counts as 1.2 wins, winning at home counts as .8 wins. Conversely, losing at home counts as 1.2 losses, and losing on the road only counts as .8 losses.

3. There is a 'Quality Win Bonus' added to a team's RPI for beating a team ranked in the top-20 of the country. A win against the top-ranked team earns a .050 bonus in RPI, with the bonus decreasing in incremental amounts down to a .0025 bonus for beating the 20th-ranked team.

4. If a team with a very high RPI ranking beats a team with a very low ranking RPI ranking, it is possible for the result of the win to lower the winning team's RPI. In these instances, that game is removed from the RPI count so that a "bad win" doesn't hurt them.

That seems like a lot of math. I was told there would be none.

It is. Other than the roughest of estimates, you're basically relying on a computer program to do all of your calculations for you. All you really need to know is that winning helps, playing good teams helps, and playing on the road helps. Any combination of those three things helps even more. Strength of schedule(how your opponents and opponents' opponents do) is also a huge factor. So having members of your conference do well in out-of-conference games, and then subsequently, teams you played out-of-conference doing well in their own conference helps as well.

My team won a game. Why didn't they move up in the rankings?

Most casual fans are used to the logic of human polls, where if a team wins, they move up a few spots in the rankings and if they lose, they drop a few spots. The Pairwise takes into account *every* game though. Your team's record may have become slightly better, but at the same time, there's also a slight adjustment to the record of every team they've played this season, and every team your opponent's opponents have played this season, and every team near them in the rankings, and so on. There are a million different factors outside of just a single game result that go into figuring out the final numbers, and sometimes, a lot of little, near invisible things can add up to outweigh the big, visible things.

It's also worth remembering that the space between rankings isn't necessarily equal. For example, in last Monday's Beanpot consolation, Boston College stayed in 9th place with a win over Harvard, but would have dropped to 16th with a loss. That seems illogical, but Boston College's RPI ranking was closer to 15th place than it was to 8th place, which meant a little drop in RPI would have added up to a big drop in the final PWR rankings.

Bottom line, what does my team need to do to get into the tournament?

It's very difficult to answer a question like that because everything is so dependent on other results around the country. There are some resources to help you out there. Jim Dahl's College Hockey Ranked makes a lot of pretty charts and graphs showing the range a team can finish with a certain set of results. If you're a bit more independent, College Hockey News allows you to customize game results and see how that would affect the final Pairwise Rankings.

Any other questions? Feel free to ask them in the comments and we're happy to help you out.