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.