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ABOUT THE CPI
The CPI (Comparative Performance Index) reflects the strength of team performance during a season by balancing a team's record with those of its opponents independent of the team. The formula is simple, clear, and intuitive, with accurate, sensible results.
Similar to the NCAA's RPI, teams are rated using only the win percentages of themselves and their opponents. Each team is rated by:
[ CPI Rating = W%3 × Ow%2 × Oow%1 ]
where W% is the team's win percentage,
Ow% is the team's opponents' win percentage independent of the team, and
Oow% is the team's opponents' opponents' win percentage independent of the team's opponents.
All percentages are taken as the sum of wins over the sum of wins and losses. The design gives greater importance to games closer to a team's circle of competition, balances a team's record equally with its schedule, is unbiased, and makes no arbitrary adjustments.
For the College Football Playoff, the CPI top four has matched the Selection Committee's final four for 32 of 36 selections (89%). (For the Committee's in-season weekly top four, the CPI top 4 has matched 80%, better than 3 of 4.)
In the BCS era, the CPI matched the selection of 28 of the 32 teams (88%) chosen for the BCS title game, more accurate than the computers and on par with polls in aligning with the BCS standings for the title matchup. The CPI also aligned well with the 25-team BCS Standings throughout a given season.
The results strongly align with polls of college football experts and more complex computer algorithms. Ratings and percentages from past years can be compared in a consistent way with today's teams, for insight into the shape of the college football landscape and the quality of title contenders. These results help shed light on current Playoff Selection debates, and may make a case for some overlooked championship-caliber teams down the years.
Importantly, the results are transparent and easy to understand. Ratings are listed with wins and losses, win percentages, and the team's strength of schedule ranking. Readers can see exactly how each team is ranked on the basis of its record, and can judge the legitimacy of each ranking. The ratings are also verifiable thanks to an open formula. By compounding the win percentages through multiplication, the CPI creates a more accurate rating while maintaining the common sense intuition of a formula like the RPI. The CPI is the only such ratings system that is easily understood and completely unbiased.
On the quality of wins and losses the ratings are unbiased. A team may get up for a big game only to have a letdown the next week, may have more than one week to prepare, or may happen to have a home field advantage in a given year; the converse may also be true, as may many other circumstances. And as iron sharpens iron, a team may ultimately help its opponents become stronger or weaker after it has played them. The theory of the CPI and other unbiased systems, such as Wolfe's and Colley's, is that the total record and schedule strength will tend to balance out over a season.
In accounting for FCS competition -- they tend to be simple in-state partnerships, but FBS teams sometimes lose these matchups. Playing a strong FCS opponent may slightly help a team's strength of schedule, but playing a weak one shouldn't hurt it. Thus, two calculations are made: one which includes all games played, including FCS opponents' records, and one which ignores results of games between FCS-only competition. The final rating is the greater of the two. This eliminates negative distortion from results outside of FBS competition. All FCS ratings use only games involving FCS teams to calculate opponents' records.
The CPI does not take into account margin of victory, location, or any measure other than win percentage in its calculation.
For College Football and basketball, I use score data from Peter Wolfe's site, and I along with many others am indebted to his work in compiling.
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