Thanks Wikipedia. The numerator of that fraction is sometimes shortened to times on base (TOB). There's other ways to reach base (errors, fielder's choice, etc.), but the three used in calculating OBP are the most common. So in order to compare strikeouts to on base percentage, I think it would be simplest to compare strikeouts to times on base. Thus in this post strikeout percentage is that same fraction but with only strikeouts in the numerator.
Tossing out pitchers, twenty-one players had 20 or more strikeouts than times on base in their careers. Most of them had a single season's worth or fewer plate appearances. Obviously, they all struggled to get on base: the highest OBP on the list is .328. Only five hitters were over .300.
My favorite player listed above is Ed Gastfield. The youngest player in the 1884 National League, Gastfield backed up Detroit catcher Charlie Bennett. While Bennett was a hitting star (OPS+ of 129 or higher in 7 of 8 seasons in Detroit), Gastfield was hapless at the plate. It's possible he was overmatched because of how young he was, but his awful .073/.095/.085 (6-82, 1 2B, 2 BB, 34 K in 84 PA) batting line in 23 games didn't make it likely he'd get a chance when he was older. Neither did his 20 passed balls and 35 errors in 19 games. Gastfield did suit up one time for Detroit in 1885, going 0-3 with 2 strikeouts. Somehow he made his way to Chicago, appearing in one game and going 0-3 with 1 strikeout and 3 passed balls. That game ended his major league career.
Gastfield's career batting line works out to .068/.089/.080, good for a .169 OPS. I know it's comparing dissimilar things but I think it's interesting his SO% was more than double his OPS. He's one of only four players in all of major league history to have a higher SO% than OPS in 50 or more plate appearances:
- Ed Gastfield, .411 SO%, .168 OPS in 90 PA
- Enrique Cruz, .390 SO%, .240 OPS in 77 PA
- John Roskos, .358 SO%, .294 OPS in 53 PA
- Frank Cox, .346 SO%, .321 OPS in 104 PA
What of Cruz and Roskos? Well, Cruz was a rule 5 draft pick who spent all of 2003 in the majors with Milwaukee and resurfaced for one at bat with Cincinnati in 2007. Roskos was a C/1B/OF type who was drafted in the second round by Florida in 1993 and worked his way up the Marlins' minor league system but never really got a shot in the majors.