Demystifying the PairWise

If you're curious about how the PairWise Rankings (PWR) or the Ratings Percentage Index (RPI) are determined, you've probably researched some of the explanations available online (such as from USCHO or Sioux Sports). Though these are helpful for gaining a basic understanding, the magic behind the PWR and RPI still often seems quite convoluted, and perhaps even a bit arbitrary or unfair.  

For teams like Michigan Tech, despite having a fairly decent win percentage this season, they are not anywhere close to receiving an at-large bid into the NCAA tournament. Why is that? It's in large part, it's due to how the RPI is calculated: 25% Team Win Percentage + 21% Opponent's Win Percentage + 54% Opponent's Opponent's Win Percentage. That's right: 54% of a team's RPI is determined by how their opponents' opponents do. Since a majority of Tech's opponents are in the WCHA and a majority of their opponents are also in the WCHA (along with their lackluster out-of-conference performance), you can begin to see why the RPI for teams in the WCHA are depressed when compared to teams in other conferences with similar win percentages.

Though the PairWise and RPI are often closely correlated, the PairWise is more than simply a comparison of RPI. To determine the PairWise Ranking, each team is compared against every other NCAA team (regardless of if they've played head-to-head). To decide who wins each comparison, there are 3 factors: number of wins/losses head-to-head, comparison of win percentage against common opponents, and comparison of RPI.

Consider this scenario: If Team A played Team B 3 times, with Team A winning twice, and the teams tying once, Team A would receive 2 "points" (1 for each win), while Team B would receive 0 (ties don't count). Further, if Team B's common opponent win percentage is greater than Team A's, Team B receives 1 point. Finally, if Team B's RPI is also greater than Team A's RPI, Team B receives another point. Since Team A and Team B both have 2 comparison "points", the winner of this comparison goes to the team with the higher RPI (Team B).

Therefore, even if a team has 2 more head-to-head wins than losses against another team, it's still quite possible for them to lose that PairWise comparison.  For example, if Michigan Tech had swept Minnesota Duluth in week 1, Tech still would have lost that PairWise comparison, because UMD had a superior RPI and record against common opponents (MTU would have needed a 3-0 record head-to-head against UMD this season to overcome this and win the comparison). That being said, though Tech could do little to win that particular PWR comparison, but even a series split would have delivered a handful of other comparisons due to a fairly significant RPI bump (demonstrating the impact of just one additional win - especially out-of-conference).

Despite these explanations and examples, it is quite tedious and confusing to actually calculate these numbers (to match those listed at USCHO), because the intermediate steps are often non-intuitive (and also not spelled out precisely anywhere online). But behold! You can finally look under the covers, and see exactly how these RPI and PWR rankings are calculated. Each school's name in the PairWise Standings is now a hyperlink which opens a new window detailing each calculation, and you can hover over the column headings to view how the calculations are derived. These pages will always reflect the latest live scores, as well as any predictions currently active in your session of the PairWise Predictor, unless you are viewing a specific static scenario from the "Share scenario" button in the PairWise Predictor. You can also use this link to always view the live data (ignoring any active predictions).  

Action buttons available in the PairWise Predictor

Action buttons available in the PairWise Predictor

Note: In the PairWise Predictor, you can click the "Reset" button above the Pairwise Standings to clear your predictions (though you may first wish to use the "Export file" button to save off your predictions to a file on your computer, which you may later import using the "Import file" button).

Acknowledgement: while we were developing our PairWise Predictor last year, we received significant help from early test versions of the PWR and RPI pages at Sioux Sports and Jim Dahl's College Hockey Ranked. Because of them, we were able to reverse-engineer the RPI much more quickly than we could have on our own. Thanks Jim!

Still confused? Disagree with our methods? We'd love to hear from you! (send us an email)

Cover image courtesy Michigan Tech Archives.