I think you'll find that very few teams have even gotten into a World Series since 1955 with a starting shortstop over 35. It may be worth starting the investigation by simply asking how many teams since 1955 (or ever) have had a regular shortstop over 35. Just to pick a year at random, in 2003, only two teams had a regular shortstop over 35, and you really have to stretch the definition of regular to count either of them. Omar Vizquel played 64 games at short for the Indians (he was 36), and Barry Larkin, at 39, played 60 games at short at the other end of Ohio.
If teams just aren't using old shortstops, then it's no surprise they aren't winning World Series with them.

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