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wesleyW502s are closely related to several ice cream and caramel sets (York Caramel, Tharps, Harrington, Sweetman, Yuengling) Each one of those sets have the same checklist of sixty players (and for the most part use the same photographs). Aside from the E210 York Caramel, which is from 1927, each of those sets are listed as 1928 issues.
The W502 in particular was meant for some kind of baseball game. There are actually different backs (one bagger representing a single, two bagger representing a double, etc). My guess is when someone collects four baggers or a run, they can be redeemed for a prize. W502s have been designated as W cards, but they are not really cut from strips. The blank back variation of the W502s are from the same series only missing the final part of the printing process.