The Owls were beaten by Sunderland in the League One play-offs last term while the Tykes were relegated from the Championship.
The Reds are closing in on the appointment of Michael Duff as their new head coach, with Cheltenham Town confirming the former Northern Ireland international's departure as their manager on Monday.
Derby County and Peterborough United were relegated from the second tier alongside Barnsley last season and are both tipped to be challenging at the top end of League One next campaign.
However, the Rams' odds of being relegated are much higher than the other clubs expected to challenge for promotion, largely due to the ongoing uncertainty over their ownership after it was confirmed on Monday that American businessman Chris Kirchner has pulled out of his deal to buy the club.
Wednesday are set to stick with Darren Moore as he looks to guide the Hillsborough outfit back into the second tier. The Owls are also are closing in on the signing of central defender Ben Heneghan, with the 28-year-old having agreed personal terms.
Based on every team's odds of winning the title and their chances of relegation, we have worked out how the bookmakers see the League One table shaping up next season...