TITLE:
Ultimate Olympics Records in Athletics Using Extreme Value Theory
AUTHORS:
Fumio Maruyama
KEYWORDS:
Athletics, 100 m, 200 m, 400 m, 4 × 100 m Relay, Long Jump, Extreme Value Theory, GEV Model
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.12 No.4,
April
29,
2022
ABSTRACT: Extreme value theory provides methods to analyze the most extreme parts
of data. We used the generalized extreme value (GEV) distribution to predict
the ultimate 100 m, 200 m, 400 m, 4 × 100 m relay, and long jump records of
male gold medalists at the Olympics. The diagnostic plots, which assessed the
accuracy of the GEV model, were fitted to all event records, validating the
model. The 100 m, 200 m, 400 m, 4 × 100 m, and long jump records had negative
shape parameters and calculated upper limits of 9.58 s, 19.18 s, 42.97 s, 36.71
s, and 9.03 m, respectively. The calculated upper limit in the 100 m (9.58 s)
was equal to the record of Usain Bolt (August 16, 2009). The 100 m and 200 m
world records were close to the calculated upper limits, and achieving the
calculated limit was difficult. The 400 m and 4 × 100 m relay world records
were almost equal to the calculated upper limits and the 500-year return level
estimate, and slight improvement was possible in both. At the Tokyo Olympics in
August 2021, in the 100 m, 200 m, and 4 × 100 m, in one year the probability of
occurrence for a record was about 1/30. In the 400 m and long jump, it was
about 1/20. In the 100 m, 200 m, and 4 × 100 m relay, more difficult records
show that a fierce battle has taken place.