35 – Statistics in Sports, Competitions, and the Arts
Senior Swim Competition Times
David P. Doane
Oakland University
Lori E. Seward
University of Colorado
Kevin Murphy
Oakland University
We present a multivariate data set of 878 observations (395 men, 483 women) on 500-yard freestyle swim times in the biennial U.S. National Senior Games (ages 50 and up) in five successive NSGA competitions (2009, 2011, 2013, 2015, 2017). We focus on these questions: (1) What is the relationship between age and swim time, and how should it be modeled? (2) Do men and women exhibit the same patterns of change by age? (3) How well do seed times predict actual times? (4) Do competition years differ? (5) What is the pattern of split times (i.e., in each of the 10 laps)? We examine the time-age relationship using age category binaries as well as quadratic and semi-log models of age. We report parameter estimates using both OLS and quantile regression (25%, 50%, 75%) with bootstrap standard errors. To predict time for a "typical" swimmer, quantile regression seems most appropriate. Time increase is nonlinear after age 50, and women's average times increase earlier than men's. Competition year plays no consistent role. Seed times slightly overestimate actual time. Split times are faster in the first and last laps of the race and fairly level in between.