its more general applicability and true structural similarity to his Pythagorean formula. Use in basketball American sports executive Daryl Morey was the first to adapt James' Pythagorean expectation to professional basketball while a researcher at STATS, Inc. He found that using 13.91 for the exponents provided an acceptable model for predicting won-lost percentages: Daryl's "Modified Pythagorean Theorem" was first published in STATS Basketball Scoreboard, 1993–94. Noted basketball analyst Dean Oliver also applied James' Pythagorean theory to professional basketball. The result was similar. Another noted basketball statistician, John Hollinger, uses a similar Pythagorean formula, except with 16.5 as the exponent. Use in the National Football League The formula has also been used in the National Football League by football stat website and publisher Football Outsiders, where it is known as Pythagorean projection. The formula is used with an exponent of 2.37 and gives a projected winning percentage. That winning percentage is then multiplied by 17 (for the number of games played in an NFL season from 2021), to give a projected number of wins. This projected number given by the equation is referred to as Pythagorean wins. The 2011 edition of Football Outsiders Almanac states, "From 1988 through 2004, 11 of 16 Super Bowls were won by the team that led the NFL in Pythagorean wins, while only seven were won by the team with the most actual victories. Super Bowl champions that led the league in Pythagorean wins but not actual wins include the 2004 Patriots, 2000 Ravens, 1999 Rams and 1997 Broncos." Although Football Outsiders Almanac acknowledges that the formula had been less-successful in picking Super Bowl participants from 2005–2008, it reasserted itself in 2009 and 2010. Furthermore, "[t]he Pythagorean projection is also still a valuable predictor of year-to-year improvement. Teams that win a minimum of one full game more than their Pythagorean projection tend to regress the following year; teams that win a minimum of one full game less than their Pythagoerean projection tend to improve the following year, particularly if they were at or above .500 despite their underachieving. For example, the 2008 New Orleans Saints went 8–8 despite 9.5 Pythagorean wins, hinting at the improvement that came with the following year's championship season." Use in ice hockey In 2013, statistician Kevin Dayaratna and mathematician Steven J. Miller provided theoretical justification for applying the Pythagorean Expectation to ice hockey. In particular, they found that by making the