i imagine sisko had been planning a baseball game well in advance of this episode, probably as soon as he knew he had nine or so capable players on the station. i would even hazard to guess that as early as season 3 he was already building his dream team and replicating the fitted hats. past that it was just a waiting game til nog n jake had aged to their prime baseball playing years. soloks arrival on ds9 just as the DT (dream team) had begun to burgeon was entirely coincidental 

jackie

what I love most about this 100% accurate post is that it is proven true by this screencap, because this is not the baseball episode, this is Starship Down, s4, the one in which Kira is like ‘I DON’T KNOW WE NEVER HANG OUT OUTSIDE OF WORK IS IT BECAUSE IT FREAKS YOU OUT THAT I SECRETLY WORSHIP YOU OR WHAT’ and Sisko is like, ‘I know what would solve this problem: a baseball game,’ because that’s how he solves literally all problems. Anyway at that point he clearly had already begun to plan, sooooo…