Comparing the Performance of Men and Women in Marathons and Ultramarathons

1. Comparing the Performance of Men and Women in Marathons and Ultramarathons Lauren McNulty, Drew Jack, Catherine Norbeck

2. INTRODUCTION There has been some speculation that female runners will someday “outrun” their male counterparts (especially in endurance running). To better understand this proposed trend we will consider male and female performance in marathons and ultramarathons.

3. BOSTON MARATHON • 26.2 miles • Beginning in 1897, the Boston Marathon is the world’s oldest annual marathon • Women were not allowed to enter the race officially until 1972 • Each year, an average of 20,000 people register to run the race

4. BADWATER ULTRAMARATHON • A 135-mile foot race from Death Valley to • Mt. Whitney in summer

5. The Boston Marathon • According to the article, the performance of male marathoners has remained fairly constant over the past few decades. Women’s times, however, have decreased by 15.6% between 1976 and 2005. • We collected data from 1972 to the present day since that was the year women were first permitted to enter the race. • We considered separately the times of the top five male and female finishers, and found the mean times for each year. • Using the mean for both female and male runners, we first conducted a 2-sample t-test to check if there was a statistical significance between the performance of the two groups.

6. The Boston Marathon: 2-sample t-test Two-Sample T-Test and CI: Male Mean, Female Mean Two-sample T for Male Mean vs Female Mean N Mean StDev SE Mean Male Mean 38 131.41 2.79 0.45 Female Mean 38 152.9 11.5 1.9 Difference = mu (Male Mean) - mu (Female Mean) Estimate for difference: -21.48 95% CI for difference: (-25.36, -17.61) T-Test of difference = 0 (vs not =): T-Value = -11.20 P-Value = 0.000 DF = 41

7. The Boston Marathon

8. The Boston Marathon

9. The Boston Marathon

10. The Boston Marathon Analysis of Variance of Difference between Female and Male Performance Source DF SS MS F P Regression 1 1614.2 1614.2 31.11 0.000 Residual Error 36 1867.7 51.9 Total 37 3481.9 Conclusions: As the article suggested, men’s performance has remained fairly constant over the past few decades, and women’s performance has improved. According to the regression equation from the graph of the difference between male and female times, in 2194, women will outrun men.

11. The Badwater Ultramarathon • The article referred to women’s performance in marathons, and since Badwater is an ULTRAmarathon, we thought we could more clearly see women’s dominance in endurance races. • We collected data from 1987 to the present day since that was the year when data became available. • In 1987, a woman won the race, and then a woman won again in 2002 & 2003. • We considered separately the times of the top five male and female finishers (given that there were five), and found the mean times for each year. • Using the mean for both female and male runners, we first conducted a 2-sample t-test to check if there was a statistical significance between the performance of the two groups.

12. The Badwater Ultramarathon: 2-sample t-test Two-sample T for MALE AVG vs FEMALE AVG N Mean StDev SE Mean MALE AVG 20 2308 1055 236 FEMALE AVG 20 2561 478 107 Difference = mu (MALE AVG) - mu (FEMALE AVG) Estimate for difference: -253 95% CI for difference: (-785, 279) T-Test of difference = 0 (vs not =): T-Value = -0.98 P-Value = 0.338

13. The Badwater Ultramarathon

14. The Badwater Ultramarathon

15. The Badwater Ultramarathon Class activity, follow along!

16. The Badwater Ultramarathon Discussion: given that female performance and male performance is improving, why would the difference between their performance look like this?

17. The Badwater Ultramarathon Analysis of Variance of difference of Male and Female Performance Source DF SS MS F P Regression 1 835 835 0.01 0.935 Residual Error 17 2086754 122750 Total 18 2087589 Conclusions: As seen in the first graph, male performance in the Badwater Ultramarathon has leveled off over the past 10 years. Female times, however, continue to decrease, indicating that women will soon consistently perform better in the Badwater Ultramarathon.

18. Conclusions • Based on the presentations of some of our classmates, men seem to perform better than women in 100 meter races • Women are improving at a rate (according to the article) of 15.6% in marathon performance over 30 years, meaning that soon women will outrun men in 26.2 mile races. • Based on our model, even though decreases in male and female times are less and less pronounced, women will outrun men in marathons in the late 22nd century. • In ultramarathons, women have already outrun men, which supports our original hypothesis that women are better endurance runners.

19. References • http://www.badwater.com • http://www.bostonmarathon.org • Pate, Russell R. and Jennifer R. O’Neill. “American Women in the Marathon.” Sports Medicine 2007, Vol. 37 Issue 4/5, p294-298 Look for the homework on the website!