Since Draper's last appearance at Wimbledon, he has reached a Grand Slam semi-final at the US Open, won one of the biggest titles on the ATP Tour in Indian Wells and become only the fourth British man to crack the world's top five.
That means he is widely regarded as the fourth favourite - behind Jannik Sinner, Carlos Alcaraz and Novak Djokovic - at this year's grass-court major.
A big reason why left-handed Draper can thrive on the slicker surface is his serve.
The power and variety of his opening shot enables him to start points strongly.
When he lands his first serve, it is effective. His first-serve percentage is only the 43rd best on the ATP Tour this year, but he is 14th in terms of points won after it.
Against 38th-ranked Baez, Draper broke in the first game of the match and the strength of his first serve meant the Argentine had little chance of responding.
He landed 78% of his first serves in the first set, winning 86% of those points with the help of four aces.
By the time Baez decided he could not continue, Draper had won 23 of his 25 first-serve points (93%).
"I served well, although I could have been a bit cleaner off the ground," said Draper.