According to the pilot of the tricycle landing gear-equipped airplane, during the landing roll in calm wind, the airplane touched down on the main landing gear first and he held the nose landing gear up as long as possible. He reported that while holding the nose landing gear up, the airplane began to drift to the left, and he slowly applied the brakes. He recalled that when the nose gear came down the airplane was too far to the left side of the runway, he continued to apply the brakes and the airplane exited the runway to the left. He reported that the more brake pressure that he applied, the further to the left the airplane drifted. He recalled that he then "removed the throttle" and when he attempted to shut off the fuel, the airplane struck a drainage culvert and sustained substantial damage to the firewall. The pilot reported that he was unsure whether a mechanical anomaly occurred during the landing. Per the Federal Aviation Administration Aviation Safety Inspector that examined the airplane, there were no mechanical malfunctions or anomalies with the airplane's brake system.