Paul, and whoever wrote Hebrews, used athletic metaphors to explain spiritual truths. Paul described his efforts as fighting a good fight and finishing a race. The main use of the athletic metaphors was to show that winning the prize requires self discipline, intentional practice, and effort. It does not just happen by itself.
An interesting fact is that Corinth (modern Korinthos, Greece) had a historical connection to athletics. It was the site of the Isthmian games which began in either 582 or 581 BC/BCE. Just as with the Olympics, the athletes competed in the nude in the sports of chariot races, wresting, boxing, and pankration, similar to modern mixed martial arts. The prizes for winning were garlands or wreaths.
When Corinth was destroyed by Rome in 146 BC/BCE, the games shifted to the city of Sicyon (modern Sikyona, Greece). In 44 BC/BCE, Corinth was rebuilt by Caesar and the games returned to the city 42 or 43 AD. They continued being observed until the 4th century AD/CE.
Hebrews 12:1; Philippians 2:16; Galatians 2:2, 2:7; 2 Timothy 4:7; 1 Corinthians 9:24-26.