98.5 runs HD AFAIK, and that adds about 8 seconds of delay. Plus another 1-2 seconds (maybe less) of transmission delay between the rink and the studio, assuming they're using ISDN or maybe a Comrex Access or a Tieline iMix or similar. If, for some reason, they're using satellite that would add about 5 seconds of delay, IIRC. Add another 7-10 seconds of profanity delay that the station probably runs 24/7 (most non-music stations do). Probably a slight delay, 1-2 seconds max, for the STL link...although the STL may have less than 0.5 sec delay, too.
As for the remaining 10 seconds of delay I'm a little stumped. It's possible they run with a LOT of profanity delay (i.e. 15-20 seconds) and leave it on 24/7. That seems like a lot of profanity delay to me, but I'm not running their station. (shrugs)
TV feeds, of course, are another ball of wax. You can easily have 10-30 seconds of delay for a satellite video feed, plus encoding/decoding delay at the cable/satellite head-end, and additional delay from your cable/set-top box decoding the signal. That's ignoring any profanity delay the video might have (always a problem that some dumbass brings a "naughty" sign and flips it up at the last second) and the various delays throughout the video signal chain. It can add up to 1 - 3 minutes pretty easily...although I remember the Sox games on NESN via Comcast being about 20 seconds behind WEEI, which itself was close to real-time (maybe a few seconds behind, total).
BTW, there wouldn't be any delay on Sox games at Fenway Park because WRKO/WEEI don't run HD Radio; their only delay is the ISDN link between the booth and the station, which is about a half-second at most. Actually I think the booth at Fenway has a fiber link back to the studio, and that'd have even less delay...but road games are probably ISDN. I remember asking them about this once and I think that WEEI doesn't run profanity delays on the Sox games. I could be wrong, or it could've changed (the last time I would've asked would've been at least three years ago), but I don't think they do; the booth is far enough away from the fans that it's not a problem. If they did run a profanity delay, I imagine it'd be in the 7-10 second range.
Some arenas will set up Part 15 transmitters so if you bring a radio to the game, you can hear things in real-time with no delay at all. Most don't bother, though...it's not cheap to set up a good Part 15 system and it's got limited ROI given how few people bring radios these days.