I’ve been poking around with trying to quantify just how much rest affects the way NHL games are played.
In what follows, “0 days of rest” means “played the previous night”, “1 day of rest” means “played the night before that” and “2 days of rest” means the most recent game was at least two nights ago. Red is more shots than average, blue is less.
This is the shots the home team gets, relative to what you would expect given the team shot rates of the teams playing in each game in the last five NHL regular seasons. Mostly you see red here - home teams get more of the shots. Unsurprisingly, well rested home teams generate a pile of offence (lower-left) against tired road teams. More surprisingly, it seems as though a two-day differential (at least) of rest is required to make this kind of difference.
Similarly, at least a two day differential in rest is needed to make a serious dent in the offence the home team generates, and it doesn’t seem to hurt them as much as it benefits them when the shoe is on the other foot.
The road team’s offence hardly seems affected by rest at all - when they have a hefty rest advantage on the home team, they do well, but other than that are almost completely uniform.