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College Football: Doing Less With More and More With Less
| Content Provider | Semantic Scholar |
|---|---|
| Author | Smith, Gary Hawkins, Jordan L. Storrs, Jack |
| Copyright Year | 2019 |
| Abstract | There is a substantial and highly significant correlation between the performance of widely followed college football teams and the pre-college recruiting scores received by their players. This correlation implies a regression toward the mean that should be taken into account in the identification of under-performing and over-performing teams and can also be used to improve pre-season predictions of the performance of teams with highly rated and lowly rated recruits. College Football: Doing Less With More and More With Less One of the most anticipated sporting events of the year is not an actual game, but college football’s National Signing Day, where high school seniors commit to college football programs in return for athletic scholarships. Drama builds as recruited athletes announce their decisions throughout the day, sometimes surprising fans and coaches who are disappointed by lost prospects or elated by signed prospects. The most highly coveted players hold nationally broadcast press conferences. Is the hype and hysteria warranted? How well do recruiting successes and failures predict the performance of college football teams? Background Four major scouting services, Scout, Rivals, 247 and ESPN, grade college football prospects by star values ranging from 5-star (an immediate impact player, among the top 2 to 3 dozen prospects in the country) to 2-star (potential role player). Unknown players are rated 1-star. Caro (2012) looked at how well recruiting success, as measured by a team’s average star score, predicted victories in conference games. She found that differences in average star rankings explained 80, 63, and 78 percent of the variance in conference winning percentages within the Southeastern Conference (SEC), Big 10, and Big 12 conferences, respectively. Average star rankings were less successful in predicting performance in other conferences and did not produce statistically significant results. Bergman and Logan (2013) studied the impact of top recruits on the performance of teams that are in the Division I Football Bowl Subdivision (FBS) of the National Collegiate Athletic Association (NCAA). Looking at data for the years 2002 through 2012, they found a substantial and statistically significant relationship between recruit quality and both field success and the !2 chances of appearing in a post-season bowl game. They estimated that a 5-star recruit is worth more than $150,000 in expected bowl revenue. Hummer (2013) identified several players who had been underrated when they were recruited. For example, Johnny Manziel was only a 3-star recruit but won the Heisman trophy as a college freshman and was a first-round pick in the National Football League (NFL) draft. Overall, however, Hummer found that Rival’s recruiting rankings were useful in predicting team performance. Meers (2013) addressed the perception that college football recruiting has a lagged effect on a team’s success. He examined the 2002 through 2011 Rivals recruiting rankings and the 2006 through 2012 college football F/+ rankings. F/+ is a statistical measure of a team’s success rate and efficiency invented by Bill Connelly and Brian Fremeau that takes into account the strength of the opponent. The offset time periods were used to account for the recruiting class of 2002 becoming seniors in the 2006 season and so on. Meers found that the sophomore and junior class recruiting rankings had a mild, and not quite statistically significant, effect on a team’s performance. Regression Toward the Mean In educational testing (Lord and Novick 1968, Smith and Smith 2005), a student’s ability μ is the statistical expected value of his or her test score, and a student’s actual score X on any particular test differs from ability by an independent and identically distributed error term ε: X = μ + ε (1) If the error scores are independent of abilities, then the variance of the observed scores across students is equal to the variance of abilities plus the variance of the error scores: !3 ! Because the variance of scores is larger than the variance of abilities, observed differences in scores typically overstate the differences in abilities. If we knew the students’ abilities, Equation 1 could be used to make unbiased predictions of each student’s score. However, teachers are interested in the reverse question, using observed scores to estimate unobserved abilities. Kelley’s equation (Kelley, 1947) says that a student’s ability can be estimated from a weighted average of the student’s score and the mean score, ! (2) where the weight ! (the test’s reliability) is the squared correlation between scores and abilities, which equals the ratio of the variance of abilities to the variance of scores: ! If a test’s reliability were 1, so that scores and ability are perfectly correlated, each student’s estimated ability would be equal to the student’s test score. If a test’s reliability were zero, so that scores are unrelated to ability, every student’s estimated ability would equal the average test score because there is no way to distinguish between above-average and below-average students. For cases between these extremes, a student’s estimated ability regresses toward the average test score, and there is more regression for less reliable tests. In college football, those athletes with the highest and lowest recruiting scores are, on average, closer to the mean ability than their scores indicate. How much closer depends on the σ X 2 =σ μ 2 +σε 2 μ̂ = ρ2X + 1− ρ2 ( )X ρ2 |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://economics-files.pomona.edu/GarySmith/Econ190/Econ190%202019/NCAArecruiting.pdf |
| Alternate Webpage(s) | https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1008&context=pomona_fac_econ |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
