Using Opta data from FotMob we can compare the quality of shots for and against, and the extent to which teams are making the goalkeepers work.
Shots For
The following plots the average expected goals (xG) of each shot generated and the number of saves per 90m each team is forcing the opposition goalkeeper to make.

Each team is segmented depending on the league averages for each metric.
The top right quadrant is virtuous in that you are generating well above average xG per shot and forcing the opposition goalkeepers to be busy relative to the rest of the league.
Celtic’s attack is functioning well on a comparative basis – last season the same data point averages were 0.13 xG / Shot but only 3.84 average opposition ‘keeper saves.
St Johnstone, Kilmarnock, and Ross County are all generating below-average shots and failing to keep the opposition custodian busy.
Livingston, St Mirren, Hibernian, Motherwell, and Aberdeen are generating good quality chances, but simply not enough of them on target to exercise the ‘keepers.
Heart of Midlothian is the only side in the category of generating above-average shots on target but of generally low quality.
Let’s look at defences.
Shots Against
The following plots the same data points but against each team.

The Rangers are very strong on defence with a very low average xG per shot against of 0.08. Last season this was 0.09. It may be their standard formation of two holding midfielders screening the centre-backs restricts good central chances.
Celtic’s ‘keeper makes fewer saves (1.55 to 1.9). Allan McGregor had fewer saves to make last season but was rapidly declining.
Celtic’s average shot quality against of 0.11 is up on last season's 0.1.
Motherwell and Heart of Midlothian are similar in that they are allowing above-average quality shots but their ‘keepers are relatively underworked.
Ross County and Kilmarnock allow many shots at goal, but they manage to keep them to below-average shot quality.
Half the league – Aberdeen, St Mirren, Dundee, St Johnstone, Hibernian, and Livingston all allow more than average shots on quality and of above-average quality. Sad face.
For Celtic, the attacking metrics are an improvement on last season, but they need to, on a relative basis, better restrict the quality of the chances they are presenting. A settled defence will help.