Understanding RPI (Ratings Percentage Index)
The RPI is a ranking system used in various sports to help compare teams' strength of schedule and overall performance. Let's break down how it works using a few examples.
Basic Components of RPI
RPI consists of three main components:
- Winning Percentage (WP) - 25% of RPI
- Opponents' Winning Percentage (OWP) - 50% of RPI
- Opponents' Opponents' Winning Percentage (OOWP) - 25% of RPI
1. Winning Percentage (WP)
This is the simplest component - it's just wins divided by total games.
Team A has 8 wins and 2 losses
WP = 8 ÷ 10 = 0.800 (or 80%)
2. Opponents' Winning Percentage (OWP)
This is where things get interesting. Let's walk through a detailed example:
Suppose we're calculating the RPI for "Team A". Here are Team A's opponents:
Team B: 7-3
Team C: 5-5
Team D: 3-7
Important Caveat
When calculating OWP, we remove all games against Team A from each opponent's record. This prevents circular influence. Here's why:
Let's say Team A played Team B twice and won both games. Team B's original record is 7-3, but two of those losses were against Team A. So for OWP purposes, we remove those games:
Team B's Original Record: 7-3
Remove games vs Team A: -0 wins, -2 losses
Team B's Adjusted Record: 7-1 (87.5%)
Why Remove Games Against Team A?
Let's illustrate why this is important with an example:
Scenario 1 (WITHOUT removing games):
Team A is 10-0
Their opponents' combined record is 30-70
Raw OWP would be 30%
Scenario 2 (WITH removing games against Team A):
Team A is 10-0
Their opponents' combined record was 30-70
After removing the 10 losses against Team A:
New opponent record: 30-60
Adjusted OWP is 33.3%
3. Opponents' Opponents' Winning Percentage (OOWP)
This follows the same principle but goes one level deeper. For each of Team A's opponents, we:
- Identify all of their opponents
- Calculate their winning percentages
- Average them together
Final RPI Calculation
Once we have all components, we apply the weights:
RPI = (0.25 × WP) + (0.50 × OWP) + (0.25 × OOWP)
Example:
WP = 80%
OWP = 56.9%
OOWP = 55%
RPI = (0.25 × 0.800) + (0.50 × 0.569) + (0.25 × 0.550)
= 0.200 + 0.2845 + 0.1375
= 0.622 or 62.2%
Counter-Intuitive Results
Sometimes, removing games against a winning team can actually lower the OWP. This happens when:
- The team has beaten several strong opponents
- Lost to several weak opponents
- Removing these games disproportionately affects the strong teams' records
Team X (8-2) has beaten:
- Top Team (9-1, becomes 8-1 after removal)
- Good Team (7-3, becomes 6-3 after removal)
- Average Team (5-5, becomes 4-5 after removal)
Original average: (9-1, 7-3, 5-5) = 70% win rate
Adjusted average: (8-1, 6-3, 4-5) = 67% win rate
This shows how the adjustment process, while more accurate, can sometimes lead to seemingly counter-intuitive results while still reflecting the true strength of schedule.