That's because the formerly unheralded hurler found himself not only drafted, but taken 36th overall by the Athletics.
"To go from somebody being a walk-on, somebody not recruited, to 36th pick is hard to believe," Shaw told The Lawrence Journal-World after his selection in June 1990. "I owe a lot to coach (Dave) Bingham. He saw something in me. He gave me a chance to pitch."
From that chance to pitch, Shaw went on to a professional career that spanned nine seasons. He made AAA in four of those seasons, but he never made the bigs.
At Kansas, Shaw matured with time. By May 1990, nearing the end of Shaw's junior year, it was apparent that scouts were noticing, according to The Journal-World. By mid-May, Shaw had a conference-leading 10 wins and an 89 mph fastball.
"It's a fairly tale story," Bingham told The Journal-World in May. "He went from a walk-on to somebody who is going to be a very high draft choice."
With the Athletics, Shaw was assigned to short-season Southern Oregon. In 17 outings, nine starts, Shaw went 4-6, with a 3.53 ERA. In a late-August start, Shaw went seven innings, giving up one earned, but took the loss.
He moved to single-A Madison for 1991, then high-A Modesto in 1992. At Modesto, Shaw went 13-4, with a 3.05 ERA.
Shaw made AA Huntsville in 1993. But his luck ran out. Overall, he went 6-16, with a 4.93 ERA. He also started the year with a grisly 0-10 record.
''I guess you could say he's been a tough-luck pitcher,'' Huntsville manager Casey Parsons told The Orlando Sentinel that June of Shaw. "When he's got his good stuff, we don't hit. If he keeps it close, we let it slip away. He's just hit a string of bad luck."
But he came back and won those six. In a late-July game, his second win of the year, he even pushed a no-hitter into the seventh inning.
Shaw made AAA Tacoma for 32 outings in 1994. He came in with a 6.91 ERA. He got 42 more outings at AAA in 1995, at Edmonton, but he did little better. He won six, saved two and had a 4.67 ERA. He also didn't see Oakland.
His 1996 season was spent largely back at Modesto, his last season with the Athletics. He signed with the Pirates for 1997, splitting the year between AA Carolina and AAA Calgary. His final season came in 1998, with five final outings, ending his career.
- Lawrence Journal-World, May 10, 1990: Shaw emerges as pro prospect
- Lawrence Journal-World, June 5, 1990: Oakland selects Kansas pitcher Shaw
- Orlando Sentinel, June 27, 1993: Stars Pitcher Doesn't Like Similarities To Mets' Young
Made the Majors: 764 - 48.8%
Never Made Majors: 801-51.2%-X
5+ Seasons in the Majors: 331
10+ Seasons in the Minors: 198