The practice went on for years, picking up a lot of steam when he signed with the A's in 2012. He was a feel-good story at the All-Star Game this year in Minneapolis, where the story re-emerged, and as a result the amount of fan mail also increased.
To date, Neshek estimates that he has obtained 10,000 to 20,000 cards, just by trading them with others, from the time this whole exercise started eight years ago.
This isn't just a way to engage with the fans. An avid collector, Neshek obtains as many autographs as he can from players whose cards he has. Last year he worked on the entire 1985 set, obtaining most of those cards through exchanges from fans. This year he targeted the 1970 set.
"It's been tough," Neshek said. "I've got, like, 160 to go. It's a 720-card set."
As for why he has chosen this as a hobby, Neshek laughed and said, "I'm a nerd."
Maybe so, but he does have an added advantage in that because of what he does for a living, he's more likely to run into players from the 1970 season who may be willing to sign the cards.
Such was the case on Monday in St. Louis, when Major League Baseball executive Joe Torre dropped by the Cardinals' clubhouse. In the baseball collecting world, Torre's autograph is a tough one to obtain, and, as Neshek said, "I didn't want to go on eBay."
Then it happened. Neskek was in the clubhouse dining area, and ... Who does he see out of the corner of his eye?
"I'm like, 'That's Joe Torre!" Neshek said.
After some coaxing from Randal Grichuk, Neshek sprinted after Torre.
"It's been a good day," Neshek beamed.
He has a few more targets. One, Steve Carlton, is a rare presence around the Cardinals. Joe Morgan is another.
Two more targets might become realities.
"I need a Juan Marichal really bad, so maybe we'll play the Giants," Neshek said before the Giants clinched their Division Series over the Nationals. "That would be nice. I need [Bruce] Bochy, too. ... I could finish a lot of this."