TOKYO — Itaru Kobayashi remembers what his baseball coach at the University of Tokyo used to tell the team before games, and he remembers what the coach said after the team inevitably lost.

“It was, ‘Hey, this is the day we are going to win,’ ” said Kobayashi, the team’s ace a quarter-century ago and now the general manager of the Fukuoka SoftBank Hawks. “But after the game, it was, ‘Hey, there is always tomorrow.’ ”

Tomorrow, it seems, never arrived. Todai, as it is known colloquially, is the country’s premier university, producing many of its top politicians, doctors, lawyers and even baseball team owners. Students who pass its famed entrance exam are guaranteed a status unmatched by any other college.

Yet the university is a lightweight when it comes to the nation’s most popular sport, baseball. A national institution, Todai does not scout high school players, offer scholarships or consider sports in the admissions process. Students must get in by their wits, not their bat or glove.