Stephen Robinson’s post-match comments in the wake of St Mirren’s 5-2 defeat at Ibrox contained an increasingly familiar refrain heard around these parts in recent years. The Buddies had fought valiantly in Govan, twice dragging themselves level before their hosts blew them away in the final 10 minutes or so as Rangers racked up a commanding lead that put the result beyond doubt.

Robinson admitted that his side weren’t at their best on the day; that Michael Beale’s men were worthy winners. And as he analysed the defeat in its immediate aftermath, one particular observation was made.

“I don’t think we played as well as we can,” he said. “It wasn’t good enough but when you look at what they brought on to win the game – as opposed to our two 18-year-olds – there is a huge gulf in resources.”

Robinson was referring to the players that clambered off the bench a week ago. The home side brought on four players with international experience, while St Mirren turned to relatively untested teenagers to swing the game in their favour. The outcome was almost inevitable.

The Herald:

The notion that both halves of the Old Firm possess benches comprised of players who would be star men elsewhere, but struggle to get into their starting XI in Glasgow, is hardly a new phenomenon but it is one that is becoming far more pronounced. The gap between the big two and the rest appears to be widening and Premiership clubs only have themselves to blame.

When the five-substitute rule was introduced at the start of the 2020/21 campaign, there was a reasonable amount of justification for it. Players were unfit as they returned to duty after the initial outbreak of the pandemic and there were worries that they could struggle to adjust to the physical demands of full-time football.

There were extenuating circumstances when it was first introduced, then, and it fell by the wayside when the following season kicked off. But managers could now see the benefits of the five-sub rule – it gave them greater options when trying to change a game’s outcome from the sidelines, and it allowed them to give more game-time to more members of their squad.

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It’s for these reasons, presumably, that the rule was reintroduced midway through the 2021/22 season. Premiership clubs held a vote and decided that increasing the number of subs permitted per game sounded like just the ticket and so it was waved through. One wonders how many of those that cast their ballots regret that decision now.

The rule has its advantages for everyone but there is no getting around the fact that two clubs in particular reap the rewards more than anyone else: the two that are already blessed with far greater resources than the rest of Scottish football combined.

The sheer strength of Celtic and Rangers’ squad depth means they were always going to be the five-subs rule’s biggest beneficiaries – and the numbers are bearing that out.

Let’s start with the basics: points. Between the current campaign, the second half of the previous one and the 2020/21 season, we have a touch over two years of data to go on where the five-substitute rule has been in place. For the purposes of this analysis, we’ll be comparing how Celtic and Rangers fared during the aforementioned seasons to the few campaigns previous.

From 2017/18 onwards, any time Celtic played with the three-subs rule in place, they would pick up an average of 2.33 points per league outing. That includes the end of Brendan Rodgers’ reign at Parkhead, he first two years of Neil Lennon’s stint in charge and the first half of last season. Since the five-subs rule was introduced, Celtic pick up 2.51 points per game (including that season under Lennon that supporters would prefer to forget all about). That works out at an additional six or seven points a year.

It’s a similar story with Rangers. Over the same period, the men from Ibrox accrued 2.19 points per game with three substitutes but this has risen to 2.39 when an extra couple of players are able to enter the fray – that’s worth between seven and eight points a season.

We must be wary of correlation without causation, though. The change in rule is just one of dozens of factors at play that could be behind the improvement in the Old Firm’s points haul, so we are going to need to dig a little deeper.

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We need to examine the impact of substitutes once they come on the park. In order to do this, we can look at the distribution of goals scored and conceded over the course of 90 minutes. We need to split a match into two sections: the first 75 minutes and the final 15. It’s not a perfect dividing line but given most changes are made between 60 minutes and 75, we can say that the final 15 minutes or so are where substitutes make their impact felt. It is a somewhat arbitrary line but it has to be drawn somewhere.

Within our sample period, when the three-subs rule was in play, around a fifth (20.6 per cent) of Celtic’s goals scored would arrive from 75 minutes onwards. Since the number of substitutes was bumped up to five per game, that figure has risen to 22.9. The effect is even more pronounced in defence: where Celtic were previously shipping 17.5 per cent of their goals after the 75-minute mark, that time period now only accounts for 10.7 per cent of goals conceded.

Rangers, too, have improved at the back late on in matches with the five-subs rule in place. Almost a quarter of goals conceded (24.5 per cent) were let in from 75 minutes onwards under the old rules; in the new regime, it’s dropped to 17 per cent. Curiously, though, the team’s attacking output towards the end of matches has dipped slightly, with goals from the final 15 minutes (plus stoppage time) accounting for 21.6 per cent of goals scored rather than 22.2.

The broad trend here is that both Celtic and Rangers are finishing matches in stronger fashion than they were previously and it is hard to overlook the five-subs rule as the primary cause. Before we can say that with certainty, though, we can dig a little deeper still.

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Under the old rules, Celtic’s substitutes would provide 12.5 goal involvements (either a goal or an assist) per season on average. Rangers’ replacements lagged behind a little, providing 11 goal involvements per season. With the new rules in place, Celtic’s subs’ goal involvements shoot up to 21 per season (a mammoth 60-per-cent increase) and it’s a similar story with Rangers, whose players coming off the bench now chip in with 16 goal involvements each year.

This should be a matter of great concern to the other 10 sides that comprise the top flight in Scotland. The Old Firm’s substitutes are making their presence felt more than ever and are receiving more minutes than was previously possible. More goals and assists are coming from those who don’t start the game and at the other end, teams are scoring fewer and fewer goals against Glasgow’s big two as the game enters it’s closing stages. Both teams are collecting more points than they were previously and the gap between Scottish footballs haves and have-nots is growing under the new rules.

It makes the other clubs’ decision to vote through the increase in substitutes mystifying. There are benefits, such as the ability to give minutes to more players, that help teams on an individual basis. But the big picture is that matches against Celtic and Rangers have never been as difficult to navigate as they are now, and it is their divisional rivals that have allowed the gap between the Glasgow duopoly and the rest to grow. The turkeys have voted for Christmas – and they will continue to count the cost.