CELTIC'S last four matches have displayed a certain symmetry.

A two-goal lead was established before half-time in each game, then came a less dominant second half. All of St Johnstone, Hibernian and Alloa Athletic pegged Celtic back a goal and a nervy moment ensued.

In all four matches, victory was sealed but is this a habit to tail off in games? Was Christophe Berra correct to state, in Sky commentary during the midweek game against Hearts, that Celtic are known to tire in the second half?

Firstly, let’s see if the perception is reality...

Goals for and against by 'game segment'

I’ve divided the match time up into 10-minute segments other than the five minutes before and after half-time.

Here are the actual goals scored and conceded by Celtic in those segments:

Celtic Way:

There are the expected lulls as the game starts, and near and after half-time. Also, the peak in the last 10 minutes is exacerbated by the fact this accounts for all goals scored in injury time.

The important areas to focus on are the two trend lines (dotted). The black line shows Celtic’s scoring tailing off the longer the game goes on. Meanwhile, the opposite trend (red line) is true for the opposition.

Very simply, Celtic score 55 per cent of their goals in the first half and 45 per centin the second half.

Their opponents score 38 per cent in the first half and 62 per cent in the second.

Conclusive then? Well, first let’s look at expected goals (xG) as this is reflective of all the chances created and is more predictive of longer-term trends than actual goals.

xG per 'game segment'

Celtic Way:

This is a far more nuanced picture.

If we focus again on the trends then Celtic (black dotted line) are showing a very slight decrease of xG created over game time. Again, the opposition trend slightly upwards over game-time (red dotted line).

Oddly, Celtic have not conceded any chances in the 14th or 15th minutes of games.

But you can see that the two lines are far closer for much of the second half before Celtic spring back into life in the last 10 minutes creating much more xG than the opposition.

Pack score by 'game minute'

Packing measures forward passes that take opponents 'out' of the game. It is a measure of creativity and the ability to play through opponents.

Packing is a very useful proxy for a number of on-field actions: vision, creative passing, movement off the ball, control under pressure. All these things you would expect to be stressed when tired.

Here are the packing scores (opponents taken out of the game) by 'game minute':

Celtic Way:

I have removed the 45th and 90th minutes from this graph as those time segments include injury time and therefore are distorting for both Celtic and the opponent.

Again, focussing on the trend lines, there are clear indications that Celtic’s ability to play through their opponents decreases over time while they appear to be easier to play through over time too.

Again, there is an uptick from Celtic in the last 10 minutes of games.

So why are Celtic flagging?

The most compelling but least predictive data (actual goals) shows Celtic are less dominant in the second half of games.

More predictive performance data backs this up but not as starkly. Also, there are nuances. The Hoops seem to spring back into life in the last 10 minutes of matches.

Celtic are seven months into a new manager, a whole new squad of players and a very demanding playing style.

We can add in, too, that the raft of new players are all at different stages of fitness (e.g. James McCarthy and Giorgos Giakoumakis had no pre-season while Reo Hatate, Daizen Maeda and Yosuke Ideguchi have been off for their post-season break after the end of the J1 League).

READ MORE: Predicted Celtic line-ups for Dundee United - Ange Postecoglou faces James Forrest or Liel Abada conundrum

The injury roster has been extraordinary. On average, there are more than six Celtic players out for every game. Each of them has been (or currently are) out for different periods and each individual requires different time periods for recovery, reconditioning and match fitness.

As regards player availability and conditioning, this season has been nothing short of a disaster. Therefore, odd variances in performance data are perhaps to be expected.

Then you have the demands of the system. Celtic press often. Pressing is a skill, an art really. Learning the triggers, responding collectively and implementing at the right moments takes practice, organisation and time. Implemented sub-optimally, it is likely to result in wasted energy and effort. Unless you are Maeda and literally chase every ball like a puppy with a paper bag in the wind.

What can be done?

Celtic have had 45 players make appearances or at least make the bench. Many of the B team have been drafted in. Sixteen-year-old Ben Doak was on the bench versus Hearts in midweek.

Although he has a large squad compared to most of the SPFL, the Celtic manager has over the months been filtering and sorting in his mind who are the players he likes and vice-versa. It is not difficult to see that the likes of Vasilis Barkas, Boli Bolingoli, Ismaila Soro and Albian Ajeti are surplus to requirements.

The point is the manager has worked out who he can 'trust'. He will be reluctant to throw people on who have not earned that trust.

Against Hibernian, Celtic did not even use their allocation of five substitutes despite some obvious flagging in their ranks. Matt O’Riley went down with severe cramp against Hearts but had been struggling for at least 10 minutes before that. Hatate too. Both were eventually replaced well into the last 10 minutes.

READ MORE: Celtic's resilience is to be applauded... but they must find a way to finish teams off earlier - Alison McConnell

There is little to criticise Postecoglou about but one is that he does not make substitutions early enough. Players get tired and injured. Celtic need to exploit the five-sub rule and get fresh energy into the games earlier.

Chris Davies was a master of detecting nuanced momentum shifts in games. Brendan Rodgers made substitutions any time from the 55th minute onwards in response to guidance from his assistant.

Postecoglou tends to make substitutions from the 75th minute on. Given the variable state of fitness and recovery within the current squad, he needs to be more flexible and prioritise energy and freshness to avoid the mid-second half declines we are seeing.

Celtic seem to revitalise and dominate the last 10 minutes of games which further supports this. That is to say, when the subs eventually do get on, the Hoops recover their control and dominance of games.

Ange, please use the bench a bit earlier...