What is the spiritual race for according to Paul?
Paul teaches that believers run the spiritual race to obtain a reward, not salvation. The Corinthians were already brethren and believers, so their running was not to gain eternal life but to win the prize, to be number one, exercising temperance and balance in all things.
Les explains that Paul frequently refers to the Olympic Games, and here especially the Isthmian Games at Corinth, the second greatest games in the Roman world after the Athenian Olympics. The runners did not race just for fun; they ran to win, to be number one. Paul tells the Corinthians to do the same with their spiritual race, but he is not talking about running to gain salvation. Since chapter 1 he has addressed these carnal Corinthians as believers and brethren, so the race is for reward, not salvation. Les also notes that those striving for mastery trained and practiced temperance. They did not go overboard eating everything, nor did they starve themselves; they maintained balance. Temperance means maintaining balance in any area of life, not only in relation to alcohol.