Typically a team sees about 12 back to back games and plays against 12 teams who played the day before. Nashville lucked out this season. They are scheduled to play 24 games (30% of the season) against tired teams [listed to the left] and play only 10 back to back games themselves.
Generally I argue that these games have a cost of about 5% in terms of winning percentage or 0.05 wins. So Nashville loses 0.50 games in the 10 games they play back to back and gains 1.2 wins in the 24 games they play against a back to back team. In essence the NHL has given Nashville 1.5 extra points. (this is worth approximately $700,000). Of course this isn't huge, but essentially Nashville has a 1.5 point advantage before the season starts.
It's interesting, but the majority of these games are in the first half of the season, possibly to get the team an early lead and to attract attention to the team. For example, Nashville plays tired teams for a whole week: Dec 6 to Dec 13.
Last season the NHL was very good at making sure back to back games were scheduled fairly and the largest difference was 5 (Col, S.J, NYI)