Peer Effects

Some of the benefits from attending a more selective school are due to learning from smarter and more dedicated classmates whose parents encourage success in school.  Similarly, student athletes who attend schools with better athletic programs benefit from not only better coaches and facilities, but also by being pushed harder and learning from superior teammates in practice.  In principle the magnitude of these peer effects can be determined in a sport such as track and field where objective measures of an athlete’s performance are readily available.

Most high school state championship tournaments segregate schools by enrollment size to provide greater parity among competing teams.  In team sports, it is obvious that larger schools have an advantage.  A football, baseball or soccer team will be more successful if they have more good players, which is more likely to occur at a larger school.  In individual track and field events it is less obvious why a student from a larger school should be faster than a student from a smaller school.  Larger schools may have better coaches and facilities, but some of the benefit from attending a larger school is the chance to practice and train with superior teammates. 

The magnitude of peer effects became clear as I watched my daughter compete this weekend in the San Diego Section prelims for high school track and field.  In the prelim heats athletes in all events are grouped into two divisions based on the enrollment size of their school.  In the finals for the 1600m (which will be held next weekend) the 12 runners with the fastest times, regardless of school size, compete for positions in the California State High School Championship meet.  This year two of the top twelve runners in the 1600m race were from a smaller (Division II) school.  Over the past six years 25% of the top 12 runners each year were enrolled in a Division II school.

In San Diego about 36.4% of students are enrolled in Division II schools.  If track and field ability was identically and independently distributed across student athletes, 36.4% of the top twelve runners each year, on average, would come from a smaller school.  In fact only 25% of the top twelve runners over the past 6 years have been from a smaller school.  The likelihood of observing so few runners advancing from small schools, due to random chance, is just 2.7%.  In other words there is reasonably strong evidence that female high school runners from larger high schools in San Diego are faster than their competitors from smaller schools.

Larger schools may have better coaches and facilities than smaller schools, but students at larger schools also benefit from training and practicing with stronger and faster teammates.  Peer effects are important for human capital accumulation as well as athletic training.  Students relegated to weaker schools, where many of their classmates are disinterested and unmotivated, are disadvantaged.

In Majors Tiger Doesn’t Compare to Jack

Comparing great athletes across generations is often an entertaining conversation.  No such discussion has garnered more attention than comparisons of Tiger Woods and Jack Nicklaus.  Comparing the two greatest golfers in the past 50 years is like asking a Chicago Bears fan whether Walter Payton or Gale Sayers was the better running back.  Comparisons are complicated by improvements in equipment, changes in training techniques, and differences in the strength of each golfer’s competition.  My comparison uses the World Golf Rankings methodology and leaves no doubt that Jack Nicklaus’ record in major championships is superior to Tiger’s, at the same point in their careers.

The World Golf Rankings award 100 points to a golfer who wins a major tournament, 60 points for second place, 40 for third, 30 for fourth and 24 and 20 points for fifth and sixth place finishes.  The points drop steeply with rank order finish with 1.5 points awarded to any golfer who made the cut and finished 60th or lower in the tournament.  This system rewards winning and competing for a championship more than consistent top ten finishes.  For example a golfer who wins one of the major championships but misses the cut at the other three earns more points for the year than a golfer who finished fifth in all four majors.

Jack Nicklaus won his first major at the 1962 U.S. Open and Tiger Woods won his first at the 1997 Masters, 35 years later.  Since then Tiger has played in 57 major championships (and missed four due to injuries).  Over that span Woods earned 33.8 points per major played, a remarkable record but far less than Nicklaus’ 45.3 points per major over a comparable span of 57 tournaments.  In other words Nicklaus averaged better than a third place finish in majors over nearly 15 years, using a scoring system that penalizes performances that are less than spectacular.

The World Golf Rankings takes a weighted average of the past eight major championships (over two years).  The following chart illustrates the difference in the rankings of Nicklaus and Woods in major championships over the fifteen years after they each won their first major.  The difference in rankings is presented as the percentage of the highest possible ranking (eight straight major championships).  Nicklaus had a higher ranking in majors over 82% of their overlapping careers.  The exceptions are that Woods’ performance in 2000-2003 was better than Nicklaus’ record in 1965-1968, and again in 2008-2009 compared to Nicklaus in 1973-1974.

In the years following this chart, Nicklaus would go on win four of the next 40 majors he played culminating in the 1986 Masters.  Even in this second half of his career Nicklaus averaged 27.6 points per major championship played.   Tiger’s disappointing performance at the Masters this weekend makes it seem doubtful that he will tie or break Nicklaus’ record of 18 Major championships (Tiger has 14).  Woods has earned 18.6 points, on average, in the eleven major tournaments he has played since 2009.

Woods is one of the greatest golfers of all time and may again become the best player in the world.  When evaluating performances on the biggest stages against the best competition, Jack Nicklaus from 1962 to 1977 was better than Tiger Woods from 1997 to 2012, with few exceptions.



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