To be more specific, outfits who have invested much in not only in their own championship, but in progressing in the Champions League.
There can be a multitude of reasons peculiar to each team for this phenomenon. But, in the case of Celtic, Ajax and even AC Milan, the spectre of matchday four in Group H is exerting an overshadowing pressure on all they do.
As Neil Lennon's side had to dig to the very bottom of their barrel of reserves to claw a point from what looked to be defeat against Dundee United, Wednesday's opponents, Ajax, were losing 1-0 at home to Vitesse.
Meanwhile, Milan - who travel to play Barcelona in the Nou Camp on the same night - were crashing 2-0 to Fiorentina in the San Siro.
It is understandable if all the managers and players involved struggled to retain full focus on domestic matters with such important Champions League matches looming large.
But, for Celtic, there is perhaps a deeper-seated issue emerging, the potentially damaging effects of which Lennon is already working hard to minimise.
Twenty one games into their season, his side is starting to show the first signs of feeling the strain, physically and mentally, which is taking the edge off their performances.
Refusing to throw in the towel or accept it is a lost cause when trailing to Dundee United as the three minutes of stoppage time ticked down was laudable and said much for the resolve not to concede an unbeaten league record.
However, it was not the particular quality Lennon was looking for ahead of this pivotal Champions League tie against Ajax.
A repeat of the lack of creativity and clinical finishing, which was so debilitating against United, would be fatal in the Amsterdam ArenA, to Celtic's hopes of competing for a spot in the last 16, at any rate.
These are the two elements which always show the first signs of a team becoming jaded.
Given the fact this group has been competing in highly-charged and important games since July 17 - that's coming up for four months with their shoulder to the wheel - while most have also been engaged in international action up to half a dozen times, it should come as no surprise that quantity is beginning to overwhelm quality.
Lennon is doing what he can to ease the strain.
But, while numerically the pool of players at his disposal looks impressive - he has so far used 24 - on a number of occasions now it has been shown that the depth of quality has not matched the quantity.
Of course, this is the same at every club. But, not all are trying to defend a championship and make it back-to-back qualifications for the last 16 of the Champions League.
Lennon made a handful of changes to his first-choice starting XI for the game against Dundee United, not out of any disrespect for the challenge Jackie McNamara's easy-on-the-eye-side represented, but because he was so mindful of having the strongest hand possible available for Wednesday.
The Hoops boss was entitled to believe the team he selected was good enough to do the job and maintain their six-point lead at the top of the Premiership and send them to Holland with a spring in their step.
However, while Charlie Mulgrew's late header - cancelling out Stuart Armstrong's first-half goal - ensured they avoided a psychologically-damaging defeat, it did not camouflage the fact this was a less-than- satisfactory send-off.
Lennon himself recalled the last time he made such a tactical team selection was for the home game against Inverness Caley Thistle in August, and that match also ended in a late scramble for a point.
"They shouldn't have been like that on Saturday because they had a free week running up to the game," reflected the manager, who was not prepared to simply write it off as a bad day at the office.
"I don't know if it was the break in momentum that made a difference, or it may have been the changes we made.
"I made a lot of changes when we played Inverness at home between the Shakhter Karagandy ties, and we drew that match, too."
Lennon admits he "took a gamble" by making so any personnel changes at the weekend, not so much with who he brought in, but who he left out.
However, he insisted: "I have got to use the squad. I can't keep asking the same players to keep going because I need a freshness about us for Wednesday. That's going to be a very difficult game.
"The fact we have players ready to come back in gives us that freshness, but also quality from the likes of Georgios Samaras - who had stitches in a knee removed on Saturday - Kris Commons,Beram Kayal and Mikael Lustig. They are quality players and they will make us better."
It is essential they do because Ajax must win this game, and will go for it from the off, but are themselves struggling for form and, in particular, a cutting edge.
"We have to be better in the final third," conceded Lennon, more concerned with getting his own side back to their very best. "There was a lack of creativity on Saturday, with people just hoping someone else will do it and not taking enough responsibility.
"We need to improve because we are not clinical enough. We were poor with the final ball at times. I need people to get across defenders and get on the end of things. That's proving to be difficult for us at the minute, and I don't know why."
By the time he boards the flight tomorrow for Amsterdam, Lennon will undoubtedly have got this weekend out of his system and, hopefully, will have come up with the answers.
His side must ask serious questions of Ajax in what will be a pivotal game for their entire season.