Quiz: Elo and Power Ratings

Question 1

The Elo system was originally developed for ranking:

A) NFL teams B) Chess players C) Tennis players D) Video game competitors

Question 2

If Team A has an Elo rating of 1600 and Team B has 1400, Team A's expected score is approximately:

A) 60% B) 76% C) 85% D) 90%

Question 3

A higher K-factor in Elo ratings causes:

A) More stable ratings that change slowly B) More volatile ratings that respond quickly to results C) Higher average ratings across the league D) Lower home field advantage

Question 4

The typical K-factor range for NFL Elo systems is:

A) 5-15 B) 20-35 C) 50-75 D) 100-150

Question 5

Home field advantage in Elo terms is typically around:

A) 10 Elo points B) 25 Elo points C) 48 Elo points D) 100 Elo points

Question 6

In a pure Elo system, total rating points across all teams:

A) Always increase over time B) Always decrease over time C) Remain constant (conservation) D) Vary randomly

Question 7

Margin-of-victory adjustments help Elo by:

A) Making ratings change more slowly B) Distinguishing blowout wins from close wins C) Removing home field advantage D) Increasing league parity

Question 8

The autocorrelation adjustment in margin-based Elo:

A) Amplifies rating changes when favorites win big B) Dampens rating changes when favorites win big C) Has no effect on rating changes D) Only affects underdog wins

Question 9

Between NFL seasons, ratings should be:

A) Reset to the initial value for all teams B) Kept exactly as they were C) Regressed toward the mean D) Randomly shuffled

Question 10

A typical regression factor between NFL seasons is:

A) 10% B) 33% C) 67% D) 90%

Question 11

The Simple Rating System (SRS) formula is:

A) Rating = Wins / Games B) Rating = Average Margin + Average Opponent Rating C) Rating = Points For - Points Against D) Rating = (Wins × 2) + Ties

Question 12

SRS differs from Elo in that SRS:

A) Updates game-by-game B) Solves for all ratings simultaneously C) Ignores margin of victory D) Uses probability-based expectations

Question 13

Approximately how many Elo points equal 1 point spread?

A) 5 points B) 15 points C) 25 points D) 50 points

Question 14

An efficiency rating system typically uses:

A) Only game outcomes B) Play-by-play data C) Only win-loss records D) Point differential only

Question 15

For converting spread to win probability, NFL's standard deviation is approximately:

A) 5 points B) 8 points C) 13.5 points D) 20 points

Question 16

A team rated 1550 in a league where average is 1500 is:

A) Below average B) Exactly average C) 50 Elo points above average D) In the top 10%

Question 17

The main advantage of SRS over Elo is:

A) Better for cross-season comparisons B) Built-in strength of schedule adjustment C) More volatile ratings D) Easier to implement

Question 18

When evaluating rating systems, a Brier score of 0.210 indicates:

A) Poor performance B) Average performance C) Excellent performance (close to market efficiency) D) Perfect predictions

Question 19

Why cap margin of victory in ratings?

A) To speed up calculations B) To prevent blowouts from distorting ratings C) To increase home field advantage D) To reduce K-factor

Question 20

An ensemble of rating systems typically works because:

A) All systems make the same errors B) Different systems capture different information C) More systems means more data D) Ensembles are always better

Answer Key

  1. B - Arpad Elo developed the system for ranking chess players in the 1960s, later adopted by FIDE.

  2. B - Using E = 1/(1 + 10^((1400-1600)/400)) = 1/(1 + 10^(-0.5)) ≈ 0.76 or 76%.

  3. B - Higher K-factors make ratings more responsive to recent results, increasing volatility.

  4. B - Most NFL Elo implementations use K-factors between 20 and 35, with 28 being common.

  5. C - Home field advantage is typically around 48 Elo points, equivalent to approximately 2.5 points.

  6. C - In pure Elo, when one team gains points, the opponent loses the same amount (conservation).

  7. B - Margin adjustments distinguish between barely winning and winning convincingly.

  8. B - Autocorrelation dampens rating changes when favorites win big, as this is expected.

  9. C - Regression to mean acknowledges roster changes and that extreme ratings partly reflect luck.

  10. B - Most implementations regress about 1/3 (33%) toward the mean between seasons.

  11. B - SRS defines rating as average margin plus average opponent rating, solved iteratively.

  12. B - SRS solves for all ratings simultaneously rather than updating game-by-game like Elo.

  13. C - Approximately 25 Elo points translates to 1 point on the spread.

  14. B - Efficiency ratings like DVOA analyze play-by-play data for more granular insights.

  15. C - NFL point differentials have approximately 13.5 point standard deviation.

  16. C - With league average at 1500, a rating of 1550 is exactly 50 points above average.

  17. B - SRS automatically adjusts for strength of schedule through its iterative solution.

  18. C - Brier score around 0.210 is close to market efficiency (~0.208-0.212).

  19. B - Capping margins prevents garbage time and one-off blowouts from distorting ratings.

  20. B - Ensembles work when systems capture different information and make uncorrelated errors.

Scoring Guide

  • 18-20: Excellent - Ready to build and optimize rating systems
  • 15-17: Good - Solid understanding of rating fundamentals
  • 12-14: Satisfactory - Review Elo mechanics and calibration
  • Below 12: Needs Review - Revisit chapter material on Elo basics