alter a team's record in a way that is easily understandable. Sportswriter Gregg Easterbrook created a measure of Authentic Games, which only considers games played against opponents deemed to be of sufficiently high quality. The consensus is that all wins are not created equal. Pythagorean Pythagorean expectation, or Pythagorean projection, calculates a percentage based on the number of points a team has scored and allowed. Typically the formula involves the number of points scored, raised to some exponent, placed in the numerator. Then the number of points the team allowed, raised to the same exponent, is placed in the denominator and added to the value in the numerator. Football Outsiders has used The resulting percentage is often compared to a team's true winning percentage, and a team is said to have "overachieved" or "underachieved" compared to the Pythagorean expectation. For example, Bill Barnwell calculated that before week 9 of the 2014 NFL season, the Arizona Cardinals had a Pythagorean record two wins lower than their real record. Bill Simmons cites Barnwell's work before week 10 of that season and adds that "any numbers nerd is waving a “REGRESSION!!!!!” flag right now." In this example, the Arizona Cardinals' regular season record was 8-1 going into the 10th week of the 2014 season. The Pythagorean win formula implied a winning percentage of 57.5%, based on 208 points scored and 183 points allowed. Multiplied by 9 games played, the Cardinals' Pythagorean expectation was 5.2 wins and 3.8 losses. The team had "overachieved" at that time by 2.8 wins, derived from their actual 8 wins less the expected 5.2 wins, an increase of 0.8 overachieved wins from just a week prior. Trading "skill points" Originally designed by Arpad Elo as a method for ranking chess players, several people have adapted the Elo rating system for team sports such as basketball, soccer and American football. For instance, Jeff Sagarin and FiveThirtyEight publish NFL football rankings using Elo methods. Elo ratings initially assign strength values to each team, and teams trade points based on the outcome of each game. Solving equations Researchers like Matt Mills use Markov chains to model college football games, with team strength scores as outcomes. Algorithms like Google's PageRank have also been adapted to rank football teams. List of sports rating systems Advanced NFL Stats, United States of America National Football League ARGH Power Ratings ATP rankings, international tennis Colley Matrix Dickinson